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Pascal, Devout Savant

Permanent Link: http://ufdc.ufl.edu/UFE0022860/00001

Material Information

Title: Pascal, Devout Savant Science, Religion, and the Learned Community in Seventeenth-Century Paris
Physical Description: 1 online resource (377 p.)
Language: english
Creator: Julich, Daniel
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: academies, artisans, childhood, childlikeness, discipline, france, geometry, jansenism, mathematics, mersenne, play, religion, science, virtue
History -- Dissertations, Academic -- UF
Genre: History thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Blaise Pascal (1623-1662) ranks among the best known intellectual icons in Western culture. Recognized as a child prodigy since his youth, Pascal was celebrated throughout his adult life for his contributions to science, mathematics, philosophy, religion, and literature. But unlike Mozart, whose musical genius was singular, Pascal remains a puzzle. The complexity of his thought (much like his Pens?es) underscores deep ambiguities in his thought and identity. This study aims to draw Pascal's life and career into a more coherent whole, particularly the relationship between science and religion. The central perspective that shapes this study is the tension between two sets of human virtues: the virtues of childhood and the virtues of maturity. Each group of virtues provides insight into Pascal, his social, cultural, intellectual, and religious milieu. Given these issues, it is clear that Pascal's life and thought cannot be treated as mere abstractions; a coherent and satisfying interpretation must combine critical conceptual analysis with a nuanced reading of his personal development. Drawing on the earliest studies about Pascal's childhood, as well as his own statements, the present study tests the tension between childlikeness and maturity as a means of making sense of Pascal's 'scientific' and 'religious' worlds. A key objective is to trace these interconnections throughout his life and work: his earliest development as child prodigy, his youthful acclaim in the learned circles of Paris, and the later struggles that marked his 'maturity' as one of Europe's most celebrated savants. The pattern of Pascal's life and career was not linear or oppositional. The unfolding of the child into the mature and disciplined scholar had unexpected turns. To provide detail and nuance, I aim to explore the role of mathematics within learned culture through the example of Pascal, showing that his life, like his thought, was not free from reversals and contradictions. This study also aims to understand how religious devotion and the learned community were related in the seventeenth century. Biographically, I argue that Pascal's career was launched by a group of scholars who recognized a significant talent that could accomplish, if cultivated, the 'perfection' of geometry. The early association of Pascal's talent with his youth was tempered by Pascal's expressions in his scientific work that suggested his distance from childhood. This distance, however, was tested by Pascal's association with the Jansenists and the biblical tension between childlike and spiritual maturity. In the end, Pascal's last mathematical work drew from the same source of virtues, both childlike and mature qualities, but this dual identification was rejected by the learned community, given the aura of secrecy and incommunicability of Pascal's geometrical connections. Although Pascal sought to balance the devout and the mathematical life, the ambiguities between precocious child and disciplined scholar remained unresolved.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Daniel Julich.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Hatch, Robert A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0022860:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022860/00001

Material Information

Title: Pascal, Devout Savant Science, Religion, and the Learned Community in Seventeenth-Century Paris
Physical Description: 1 online resource (377 p.)
Language: english
Creator: Julich, Daniel
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: academies, artisans, childhood, childlikeness, discipline, france, geometry, jansenism, mathematics, mersenne, play, religion, science, virtue
History -- Dissertations, Academic -- UF
Genre: History thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Blaise Pascal (1623-1662) ranks among the best known intellectual icons in Western culture. Recognized as a child prodigy since his youth, Pascal was celebrated throughout his adult life for his contributions to science, mathematics, philosophy, religion, and literature. But unlike Mozart, whose musical genius was singular, Pascal remains a puzzle. The complexity of his thought (much like his Pens?es) underscores deep ambiguities in his thought and identity. This study aims to draw Pascal's life and career into a more coherent whole, particularly the relationship between science and religion. The central perspective that shapes this study is the tension between two sets of human virtues: the virtues of childhood and the virtues of maturity. Each group of virtues provides insight into Pascal, his social, cultural, intellectual, and religious milieu. Given these issues, it is clear that Pascal's life and thought cannot be treated as mere abstractions; a coherent and satisfying interpretation must combine critical conceptual analysis with a nuanced reading of his personal development. Drawing on the earliest studies about Pascal's childhood, as well as his own statements, the present study tests the tension between childlikeness and maturity as a means of making sense of Pascal's 'scientific' and 'religious' worlds. A key objective is to trace these interconnections throughout his life and work: his earliest development as child prodigy, his youthful acclaim in the learned circles of Paris, and the later struggles that marked his 'maturity' as one of Europe's most celebrated savants. The pattern of Pascal's life and career was not linear or oppositional. The unfolding of the child into the mature and disciplined scholar had unexpected turns. To provide detail and nuance, I aim to explore the role of mathematics within learned culture through the example of Pascal, showing that his life, like his thought, was not free from reversals and contradictions. This study also aims to understand how religious devotion and the learned community were related in the seventeenth century. Biographically, I argue that Pascal's career was launched by a group of scholars who recognized a significant talent that could accomplish, if cultivated, the 'perfection' of geometry. The early association of Pascal's talent with his youth was tempered by Pascal's expressions in his scientific work that suggested his distance from childhood. This distance, however, was tested by Pascal's association with the Jansenists and the biblical tension between childlike and spiritual maturity. In the end, Pascal's last mathematical work drew from the same source of virtues, both childlike and mature qualities, but this dual identification was rejected by the learned community, given the aura of secrecy and incommunicability of Pascal's geometrical connections. Although Pascal sought to balance the devout and the mathematical life, the ambiguities between precocious child and disciplined scholar remained unresolved.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Daniel Julich.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Hatch, Robert A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0022860:00001


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PASCAL, DEVOUT SAVANT: SCIENCE, RELIGION, AND THE LEARNED COMMUNITY IN SEVENTEENTH-CENTURY PARIS By DANIEL T. JULICH A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009 1

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2009 Daniel T. Julich 2

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To Sarah, Olivia, and Cecily 3

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ACKNOWLEDGMENTS I gratefully acknowledge my debts to my adviser, Dr. Robert A. Hatch, whose encouragement and input are evident on each page of this dissertation. His in sights into the craft of writing history and into the psychological challenge of such a large project have sustained me throughout my doctoral studies. I also wish to acknowledge the other members of my committee: Drs. John Biro, Frederick Gregor y, Howard Louthan, and Maria Portuondo. Dr. Susan Read Baker provided insight, resources, and sympathy for the project during its early stages. I also thank Dr. Richar d Horner, Director of the Chris tian Study Center of Gainesville, for offering timely advice and for the opportunity to share my interest in Pascal with a wider audience. I am grateful to Todd Bohlander, who willingly and ably assisted me in the verification and improvement of th e Latin translations and to Betty June Moninger, who read and corrected the penultimate draft. I cannot omit mention of the enormous debt that I owe my parents for many years of support and for sympathy for my academic goals. Finally, I thank Sarah, whose sacrifices in the completion of this study have been numerous and onerous. I would not have finished w ithout her unfailing support. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF FIGURES .........................................................................................................................9ABSTRACT ...................................................................................................................... .............101 INTRODUCTION ................................................................................................................ ..12Pascal: Contested Identities ....................................................................................................12Fragmented Pascal ..................................................................................................................15First Source: Pascals Life ...............................................................................................15Posthumous Biographical Accounts and the Penses .....................................................16Childlikeness and Maturity in th e Historiography of Pascal ..................................................18Pascals Character and the Essai Pour Les Coniques .....................................................22Religion and Childlikeness ..............................................................................................23Influences of Childhood: The Mersenne Group ..............................................................29Mature Virtues in Pascal Historiography ...............................................................................31Childhood and Childlikeness in th e Early Modern Period .....................................................33Childlikeness and the Historic ity of Childhood and Youth .............................................35The Virtues and Vices of Childhood ...............................................................................38Overview & Summary ............................................................................................................ 452 PASCAL IN THE TEMPLE: A NEW ARCH IMEDES AND HIS EARLY TRAINING .....48Mersenne and His Circle ....................................................................................................... .48The Mersenne Circle: Its Organi zer, Members, and Purpose .........................................50Mersennes Educational Goals and the Order of the Minims .........................................51The Beatific Completion of Mathematics: Mersennes Vision ..............................................53Mathematics as Epistemological Foundation ..................................................................53Mathematics as Divine Science .......................................................................................55God and mathematical objects .................................................................................55God the transcendent geometer ................................................................................56Mathematics as Imitation of God ....................................................................................58Apprenticeship to a divine artisan ............................................................................58Actualizing the infinite pote ntialities of mathematics ..............................................60Approximating the heavenly state ............................................................................60Finding Talent in Unexpected Places .....................................................................................62Recruiting the Best Minds to Perfect Mathematical Disciplines .................................62Recovering Ancient Analysis: Sear ching for New Archimedeses ..............................66Promoting Provincial Talent ............................................................................................68Mersennes Investment in Youthful Talent .....................................................................71Two New Archimedeses: Pasc al and Christiaan Huygens ..........................................73Mersenne and the youthful Pascal ............................................................................73 5

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Pascals counterpart: Christiaan Huygens ................................................................77The Mersenne Circle and Pascals Mathematical Apprenticeship .........................................82Pedagogical Interests and Activities of the Participants ..................................................82Desargues: self-taught master ..................................................................................83Roberval: university connection ...............................................................................87Le Pailleur: fatherly poet ..........................................................................................90tienne Pascal ..........................................................................................................91The Acadmie as an Educational Alternative ..................................................................92Pascals Model of Mathematical Success ...............................................................................983 PAINFUL LEGITIMATION: NATUR E, DISCIPLINE, EXERCISE ................................101Inclinations and Intellectua l Pursuits in Context ..................................................................102Classification of Inclinations .........................................................................................102Intellectual Inclinations and the Choice of Career ........................................................103Huartes Examen and types of esprit ......................................................................103Bartoli and the relationship betw een inclination and effort ...................................105The Ratio studiorum and selection th rough inclination .........................................107Mersenne and the Limits of Intellectual Inclinations ...........................................................107Mersennes Rejection of Determinis m for Intellectual Inclinations .............................108Astrological determinism .......................................................................................108Temperament and inclination .................................................................................110Nature, Discipline, Exercise: N ecessary Components for Learning ..........................111Becoming Archimedes: Wo rking for Legitimacy ................................................................117Imitating the Creator: Pascals Calculating Machine ....................................................118Narrative summary .................................................................................................118Trouble with clockmakers ......................................................................................122Technicians and theorists in the work of Desargues ..............................................124Pascals defense .............................................................................................................128Novelty, rashness, and daring ................................................................................129Imitating God in the act of creation .......................................................................131Monstrosities: Trial and error .................................................................................132Endorsements compared ........................................................................................138The machine as transcendent ..................................................................................142Childlikeness and the Arithmetic Machine ...................................................................146The Controversy of the Void: Neither Beast nor Child .................................................148Empty argum ents ....................................................................................................149New roles, old roles: childlikeness and maturity in the que stion of the void.........156Pascals Preface: mature thinking .......................................................................1684 A MAN BETWEEN : THE STRU GGLE FOR A YOUNG TALENT (1647-1654) .181Encountering the Limits of Savant Pursuits .........................................................................182Experiments on the Void ...............................................................................................182Jansenism and the Evaluation of Mathematics ..............................................................183Jansenism: the first conversion ..............................................................................184Jansenism and the question of priorities ................................................................185 6

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The Boundaries of Orthodoxy: The Saint-Ange Affair ........................................................188Background to the Conferences .....................................................................................189Saint-Anges Religious Reasoning ................................................................................190Failure of Saint-Anges Appeal for Legitimacy ............................................................191Knowledge without Effort .............................................................................................193Forging a New Identity: Une Personne Qui Nest Plus Mathmaticien ...........................197Awareness of Limitations ..............................................................................................197Discovering Restricted Perfec tion: Port-Royal Spirituality .......................................199The Coexistence of Childlikeness and Maturity ...........................................................200Pascals Continuing Role as Protg Mathematician ...........................................................205Influence of the Mersenne Circle ..................................................................................206Pitching the Pascaline and Himself: The Letter to Queen Christina .............................208Defending Work on the Void ........................................................................................211Pascal versus the ignorant: correspondence with Ribeyre ..................................212Geometry overcoming limits ..................................................................................215Pascals Role in Continuing the Mersenne Circle .........................................................217Treatise on the Arithmetic Triangle: Continuing Mersennes Project ..........................219Multiplication of connections .................................................................................221Relationship to Mersennien view of mathematics .................................................224Worldly Values and the Limits of Specialized Learning ......................................................228Mrs De lesprit and the Limitations of Mathematics ...............................................231Mr, Mersenne, and Pascal on Inclination and Exercise .............................................234Mr and Mersenne ................................................................................................234Mr and Pascal .....................................................................................................235Mr and Port-Royal on the lim itations of mathematics ........................................237Redirected Efforts: New Goal s and Pascals Memorial ....................................................2395 PASCAL, PEDAGOGUE .....................................................................................................243Children, Moral Inclinations, and Education ........................................................................244Resisting the science of sins: Ch ildlikeness and Maturity in the Provincial Letters ........249Merits and Demerits of Children: Pascals Comparaison des chrtiens ..............................260Two Childhoods of Christianity and the Necessity of Christian Instruction .................260Pascals Comparaison and His Baptism as a Savant .................................................264Positive and Negative Views of Childhood in the Intellectual Realm ..........................264Pascals Comparaison and the Spiritual Duality of Childhood .....................................267Childhood Innocence and the Correction of Inclinations: Jacquelines Rglement pour les enfants ..........................................................................................................................268Dual Nature of Childhood in the Reglement .................................................................268Natural Inclinations and Discipline in the Reglement ...................................................270From Pupil to Pedagogue: Pascals Educational Contributions and the Petites coles of Port-Royal .................................................................................................................... .....274Spiritual Work at the Petites coles ..............................................................................275Intellectual Training at the Petite coles .......................................................................276Pascals Work with the Petites coles ..........................................................................278A pedagogical turning point ...................................................................................278Pascal, contributor to textbooks .............................................................................280 7

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Final Contribution to Pedagogy: Pascals Discourses on the Condition of the Great .........................................................................................................................2826 PASCAL AS AMOS DETTONVILLE: A RETURN TO CHILDHOOD ...........................287A Mathematical Remedy ......................................................................................................289Playful Problem-Solving ...............................................................................................290Discovery in isolation .............................................................................................290Effortlessness of solution .......................................................................................291Overcoming restrictions .........................................................................................292Lingering Childhood Influences ....................................................................................294Backdrop to Diversion: The Sluse-Pascal Correspondence ..........................................297Paradox of Mathematical Ease and Difficulty ......................................................................301Contemporary Background ...........................................................................................301Sluses Language of Ease and Difficulty ......................................................................307Pascals Language of Ease a nd Difficulty and the Roulette .................................................314A Game for the Learned .......................................................................................................3 24Limitations of a Math ematical Mtier ..................................................................................327Criticisms of the Contest: Between Childhood and Sociability ...........................................333Objections to the Characterizat ion of the Problems as Easy .........................................334Rejection of Detonvilles Anti-Social Be havior with Roberv als Rusticity ..............339Two Archimedeses: Pascal and Huyge ns in the Roulette Contest .......................................3417 CONCLUSION .................................................................................................................. ...348CHRONOLOGY..........................................................................................................................352LIST OF REFERENCES .............................................................................................................357Primary Sources ............................................................................................................... .....357Secondary Sources ................................................................................................................362BIOGRAPHICAL SKETCH .......................................................................................................377 8

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LIST OF FIGURES Figure page Figure 1: Arithmetic Triangle ................................................................................................. .....221 9

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Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PASCAL, DEVOUT SAVANT: SCIENCE, RELIGION, AND THE LEARNED COMMUNITY IN SEVENTEENTH-CENTURY PARIS By Daniel T. Julich May 2009 Chair: Name Robert A. Hatch Major: History Blaise Pascal (1623-1662) ranks among the best known intellectual icons in Western culture. Recognized as a child prodigy since his youth, Pascal was cel ebrated throughout his adult life for his contributions to science, mathematics, philosophy, religion, and literature. But unlike Mozart, whose musical genius was singular, Pascal remains a puzzle. The complexity of his thought (much like his Penses ) underscores deep ambiguities in his thought and identity. This study aims to draw Pascals life and career into a more coherent whole, particularly the relationship between science and religion. The cent ral perspective that sh apes this study is the tension between two sets of human virtues: the virtues of childhood and the virtues of maturity. Each group of virtues provides insight into Pascal, his social, cultural, inte llectual, and religious milieu. Given these issues, it is clear that Pas cals life and thought cannot be treated as mere abstractions; a coherent and satisfying interpretation must combine critical conceptual analysis with a nuanced reading of his personal developm ent. Drawing on the earliest studies about Pascals childhood, as well as his own statements the present study tests the tension between childlikeness and maturity as a means of making sense of Pascals scientific and religious worlds. A key objective is to trace these in terconnections throughout his life and work: his 10

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11 earliest development as child prodigy, his youthful acclaim in the learned ci rcles of Paris, and the later struggles that marked his maturity as one of Europes most celebrated savants. The pattern of Pascals life and career was not linear or oppositional. The unfolding of the child into the mature and disciplined scholar had unexpected turns. To provide detail and nuance, I aim to explore the role of mathematic s within learned culture through the example of Pascal, showing that his life, like his thought, was not free from reversal s and contradictions. This study also aims to understand how religious devotion and the le arned community were related in the seventeenth centu ry. Biographically, I argue that Pascals career was launched by a group of scholars who recognized a significant ta lent that could accomplish, if cultivated, the perfection of geometry. The early association of Pascals ta lent with his youth was tempered by Pascals expressions in his sc ientific work that suggested his distance from childhood. This distance, however, was tested by Pa scals association with the Jansenists and the biblical tension between childlike and spiritual maturity. In the en d, Pascals last mathematical work drew from the same source of virtues, both childlike and matu re qualities, but this dual identification was rejected by the learned communit y, given the aura of secrecy a nd incommunicability of Pascals geometrical connections. Alt hough Pascal sought to balance the devout and the mathematical life, the ambiguities between precocious child and disciplined scholar remained unresolved.

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CHAPTER 1 INTRODUCTION Knowledge has two extremes which meet; one is th e pure natural ignorance of everyone at birth, the other is the extreme reached by great minds who run through the whole range of human knowledge, only to find that th ey know nothing and come back to the same ignorance from which they set out, but it is a wi se ignorance that knows itself Blaise Pascal, Penses (Brunschvicg 327) Translated by A. Krailsheimer Pascal: Contested Identities Blaise Pascal (1623-1662) ranks among the best known intellectual icons in Western culture. Recognized as a child prodigy from his youth, Pascal was cel ebrated throughout his adult life for his contributions to science, mathematics, philo sophy, religion, and literature. Subject to serious scholarly cons ideration for over three hundred years, Pascal continues to defy traditional labels, whether as mathematician, th eologian, philosopher, physicist, or literary scholar. The complexity of Pascals career (much like the fragmentary Penses ) underscores deep ambiguities in his thought and identity. The present study does not aim to resolve these longstanding difficulties. Instead, the central pe rspective that shapes this study is a tension between two sets of human virtue s: the virtues of childhood and th e virtues of ma turity. This tension provides insight into Pa scals life, his work, and his so cial, cultural, intellectual, and religious milieu. A key objective of this study is to draw Pascals life and career into a more coherent whole, particularly the relationshi p between science and religion. Employing the tension between childhood and adult virtues, th is study aims to avoid anachronism by testing distinctions used by Pascal and his contemporaries. Pascals resistance to labels reflects his historical status as a ch ild prodigy and mature polymath. For nearly four centuries scholars have attempted to categorize his achievements. As a mathematical and scientific icon, his name is at tached to a numerical pa ttern (Pascals triangle), a unit measure of pressure (the pascal = 1 Nm-2), and a computer programming language 12

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(Pascal). As a French literary icon, Pascal c ontinues to be celebrated for his classic work Les lettres provinciales As a religious icon, he is touted as a mystic and critical thinker for his response to skepticism, which balan ces intuitive and reasoned belief. Pascals iconic status is especially striking because of the scope of hi s achievements. Unlike Mozart, whose musical genius was singular, Pascals breadth of talent and accomplishment has shaped his image as an enduring puzzle. Pascals image as a child, eas ily dismissed as simple genius, was quickly outgrown, as it no longer befitted the complexity of his mature work as a mathematician, natural philosopher, and religious devout. Since the ap pearance of Pascals first biography, written by his sister, the image of Pascal has grow n more complex but somehow less telling. Pascals complexities were evident during hi s lifetime and spread with the publication of the first biography and his fragmentary thoughts ( Les Penses ) immediately following his death. Like his unpolished religious reflections, scribble d in multiple directions and gathered loosely into thematic categories, Pascals life could not be readily be reduced to a formula by his friends or foes. Having died at the age of 39, Pascal s life, like his planned apology for the Christian religion, remained brilliantly piecemeal and finally unfinished. In the centuries following his death, ambi valence toward Pascals life increased. Celebrated and derided by those who encounter ed his life and writings, one writer concluded one loves him or one detests him.1 Some authors have done both. For Voltaire and Nietzsche, Pascal, by turns, inspired admiration and provoked disgust.2 1 Maurice Anatole Souriau, Pascal (Paris, 1898), 236. 2 Voltaire wrote of him: I respect the genius and eloquence of Pascal, Voltaire, Letters on England, trans. Leonard W. Tancock (New York, 1980), 120. He goes on to critic ize him, however, since he believed it was Pascals goal to portray man in a hateful light, using false and dangerous reasoning, ibid. 121, 120. For Nietzsche, Pascal was an example of an admirable human intellect corrupted by Christianity: We must not deck out and adorn Christianity: it has waged a deadly war upon this higher type of man, it has set a ban upon all the fundamental instincts of this type, and has distilled evil and the devil himself out of these instincts: the strong man as the typical pariah, the villain. Christianity has sided with everything weak, low, and botched it has corrupted even the 13

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The present study takes cues from a long tradition that has puzzled over Pascal. It aims to bring together, rather than separate, his religi ous and scientific work. Specifically, it draws on Pascals identification as child prodigy and childlike mystic to analyze his life and work as a tension between the virtues of childlike-genius and the disciplined scho lar. Working against earlier interpretations, this interpretive strategy is sustained by contradictions in Pascals life as well as contradictions in earli er biographical treatments. Th e present study aims to draw together Pascals life and work into a more sa tisfying whole: his early development as a child prodigy, his youthful acclaim in the learned circle s of Paris, and his final struggle as one of Europes most celebrated savants. The purpose of this Introduction is to addr ess one of the defining issues in Pascal scholarship, the reduction of Pascals legacy to a basic opposi tion between religion and science. Thereafter, the present chapter explores the c ontours of Pascal historiography, identifying suggestions by earlier scholars about the importance of child hood and childlikeness and the implications for understanding Pascal s identity. To supply further context, I then provide a brief overview of the notions of chil dhood, childlikeness, and maturity that govern this study, and in turn, I argue that these ideas are not anachronistic but deeply rooted in early modern culture. The last section of this Introduction identifies key questions and summarizes the central argument that shapes the present study. reason of the strongest intellects, by teaching that the highest values of inte llectuality are sinful, misleading, and full of temptations. The most lamentable example of this was the corruption of Pascal, who believed in the perversion of his reason through original sin, whereas it had only been perverted by his Christianity, Friedrich Nietzsche, The Complete Works of Friedrich Nietzsche, vol. 16, ed. Oscar Levy (New York, 1911), 130. 14

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Fragmented Pascal First Source: Pascals Life Pascals identity is not so much a puzzle as a series of historical and biographical puzzles. Any exploration of his fragmented identity mu st begin by addressing the work of earlier scholars. Through a unique set of circumstances, Pa scal earned a reputation for his mathematical and scientific works and his religious writings.3 Pascal was born 19 June 1623 in Clermont, France and died 19 August 1662 in Paris. As a t eenager, he composed a work on conic sections that was announced to some of Europes le ading mathematicians by Marin Mersenne, the secretary of Learned Europe. Pascals subsequent inventi on of a machine for arithmetic calculations, begun at age ninetee n, and a set of writings about the artificial creation of void spaces in glass tubes, earned him recognition and respect in the learned world by his late twenties. Pascal, in the meantime, became acquainted wi th the spirituality of a relatively new Catholic movement, Jansenism. After his younger sisters entry into the convent of Port-Royal, the epicenter of French Jansenism, Pascal became even more involved with the group. A mystical experience in 1654 (often called his Night of Fire) led hi m to seek a spiritual director at Port-Royal and, according to some, resulted in his decisive renunciation of mathematics and natural philosophy. Pascal then wrote the Provincial Letters (1656-1657) a defense of Jansenism and an ironic attack on the spir itual principles expressed by Jesu it writers. Though this work was written pseudonymously, Pascals authorial id entity was widely known prior to his death. 3 The terms science and scientific are not entirely proper to the ea rly modern period. There are fine distinctions, however, between the several disciplines of pure and mixed mathematics (geometry, arithmetic, music, and astronomy) and natural philosophy during the seventeenth century. In order to refer to Pascals diverse work collectively and conveniently I will employ the word scientific in va rious places throug hout this study. 15

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In 1657-1658, between intermittent bouts with the illness that would eventually kill him (an undiagnosed malady that caused damage to both brain and stomach) Pascal found longsought solutions to a set of mathematical pr oblems related to a curve called the roulette.4 The solution was perhaps less important than the presentation. Pascal st irred up the learned community by anonymously proposing a contest to solve these probl ems. He then published his own results under the name Amos Dettonville. Even more thinly veiled than the Provincial Letters, this work secured Pascals reputation as a talented mathematician. Yet Pascals generally positive reception was tempered by knowle dge of his religious connections with PortRoyal. Posthumous Biographical Accounts and the Penses Pascal was known for his mathematical, scient ific, and religious work long before his death, but the connections between these aspects of his life were te nuous at best. The preface to the posthumous publication of a pa ir of scientific treatises ( Traitez de lequilibre des liqueurs et de la pesanteur de la masse de lair 1663) supplied a short biogra phy of Pascal. The account proposed a link between Pascals scientific and religious work that that placed them in opposition. The narrative highlighted Pascals preter natural talent for mathematics and its early onset, but it went on to claim that more serious studies (i.e., re ligious projects) prompted him to leave his mathematical and physical interests.5 The short account did not specifically mention 4 Pascals illness has been the subject of many hypotheses. A brief summary of the different diseases suggested by three centuries of scholars who have studied the descriptions of his autopsy is in Georges Deboucher, La maladie de Pascal: une mise jour, Courrier du Centre International Blaise Pascal 14 (1992), 8-9. Debouchers diagnosis is that Pascal was afflicted by a combination of an intracra nial aneurysm and polycystique kidney disease, ibid., 10. 5 Ce fut incontient apres ce temps l que des estudes plus serieuses ausquelles Monsieur Pascal se donna tout entier, le dgousterent tellement des Mathematiques & de la Physique quil les abandonna absolument, Blaise Pascal, Traitez de lequlibre des liqueurs et de la pesanteur de la masse de lair (Paris, 1663), all translations mine unless otherwise noted. 16

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the Provincial Letters, but referred instead to fragmentary penses [thoughts] that Pascal had penned before his death. Pascals Penses were published for the first time in 1670 by his family. The work was ostensibly an apology for the Christian religi on that Pascal had planned but was unable to complete. The Penses cover a wide range of topics: human nature, skepticism, justification for belief, and the relationship between knowledge of nature and knowledge of God. Pascals religious reflections tended to downplay the usefulness of scie ntific knowledge, reiterating the split between Pascal devout and Pascal savant. The lack of organization of the fragments also encouraged two basic responses fr om scholars. On one hand, the ga ps in Pascals organizational plan for his work meant that the puzzle of hi s thought could be assembled in multiple ways, creating significantly different Pascals. On the other hand, isolated fragments of the Penses developed a life of their own, separate from the apparent concerns of the author. The most famous example of the second trend is the fragment entitled Infini rien popularly known as Pascals Wager. Pascals reasoning that it is expedient to bet on th e existence of God has inspired philosophical debate while ignoring it s significance for understa nding Pascals thought in historical context.6 The publication of the Penses firmly established the proble m of Pascals unification. Writings about Pascal since his death have multiplied steadily. For obvious reasons, the figure of Pascal looms large in his native country, where French monographs regarding Pascals faith, philosophy, science, literature, and mathematics regularly appear. A cademic specialization has further fragmented Pascals identity by enge ndering studies that focus on a single dimension of his life or thought. The search for a holistic view of Pascal is daunting but alluring. Previous 6 One collection of essays on the philosophical and religious issues surrounding the Wager is Gambling on God: Essays on Pascals Wager ed. Jeff Jordan (Lanham, MD, 1994). 17

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attempts to describe Pascal and his work provide a rich set of in terpretations that inform this study and Pascals portrayal in terms of childlikeness and adult discipline. Childlikeness and Maturity in the Historiography of Pascal One strategy for integrating Pascals identitie s has been to emphasize his role as a child, the perspective that first suggest ed this studys focus. Previo us Pascal scholars have placed particular emphasis on his childhood or his childliken ess. Others have atte mpted to highlight his accomplishments and ambition. No previous study has considered in any detail how the interaction between childlikeness and maturity relate to Pascals life and works. This study attempts to provide that analysis while sustaining the historical dimens ion of the categories of childhood, childlikeness, and maturity. The focus on childhood as a central theme for Pa scals life begins with the first full biography. Written by Pascals sister, Gilberte Prier, La vie de M. Pascal introduces enduring examples of Pascals precocity and his emerge nce onto the French savant scene. The most telling and famous episode is his near-miracul ous discovery of mathematics on the playroom floor. The story foreshadows and seemingly foretells Pascals mathematical future and his destiny as a devout. For the first time, Pascal is presented as a special child with shockingly adult-like qualities.7 7 Gilberte Priers biography of Pascal was probably composed very soon after his death, not with the view of publication, but for those close to Pascal and his fa mily. It was first printed in Amsterdam in 1684, La vie de Monsieur Pascal (Amsterdam, 1684). The text of this biography in two slightly different versions is in Blaise Pascal, Oeuvres compltes de Blaise Pascal, 4 vols., edited by Jean Mesnard (Paris, 1964-1992), vol. 1, 571-642 (hereafter Mesnard OC [vol#]:[page#]). For a critical study of the composition and publication of the work, see Mesnard OC 1:539-570. More information of biographical interest may be found in Gilbertes biography of Jacqueline Pascal, La vie de Jacqueline Pascal, Mesnard OC 1:657-671. It was first published as a part of a collection of spiritual biographies in 1751, Mesnard OC 1:652-653. A recent edition of these two early works is Gilberte Prier, La vie de Monsieur Pascal: suivi par la vie de Jacqueline Pascal trans. and ed. Alain Couprie (Paris, 1994). A much later composition, which yet holds in terest for the family tradition it preserves, is written by Margurite Prier, Gilbertes daughte r, sometime around 1732, Mesnard OC 1:1063. The piece is entitled Mmoires concernant M. Pascal et sa famille, and a critical rend ering of it is given in Mesnard OC 1:1091-1105. This account is the source of some of the less substantiated claims about Pascals life, including the story of the spell cast on Blaise as a boy. The first posthumous writing that provides some biographical information is in Florin 18

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Gilbertes narrative of Pascals early geometrical discovery offe rs a striking parallel to the New Testament story of the appearance of Jesus in the temple. The gospel according to Luke records the surprise of Jesuss parents when they found their twelve-y ear-old conversing with elders about Scripture. Pas cal was just twelve when hi s father discovered him doodling geometrical diagrams from Euclids thirty-second pr oposition of his Elements (Bk. 1). Like Jesuss astonished parents, Blaises surpris ed father was terrified. The comparison between Jesus and Pascal became an enduring piece of the Pascal puzzle. Although the foray into adult realms of knowledge risked parental displeasure, t ienne, like Mary and Joseph, could not punish such unusually mature behavior. From the moment his father recognized his sons striking potential, Pascal took a place among his elders, the mathematicians of Paris. Gilbertes story links Pascals youthful genius to his adult accomplis hments. Her account of Blaises last days of life, in turn, reverses the direction, drawing atte ntion back to Pascals childhood. As she provides details of Pascals fina l years, Gilberte takes pains to emphasize her brothers humility and submission. Prier recounts the words that Pascals last confessor spoke about Blaise: This is a child, he is humble and submitted as a child.8 Prier brackets Pascals life by the mature discovery of Euclids thir ty-second proposition and his childlike acceptance of Priers preface to one of Pascals physical treatises. Monsieur Prier borrows some passages from his wifes biographical account to write his Prface contenant les raisons qui ont porte p ublier ces deux Traits aprs la mort de Monsieur Pascal, et lhistoire des diverses expriences qui y sont expliques. The work was published as Trait de lquilibre des liqueurs et de la pesanteur de la masse de lair (Paris, 1663). The Preface is 23 pages, nonpaginated. 8 Cest un enfant, il est humble et soumis comme un enfant, La vie de Monsieur Pascal, Mesnard OC 1:637. The literature on Pascals last illness, and his religious opinions at his death, is extensive. Mesnard provides a historiographical study of La maladie de Pascal, whic h traces Pascals symptoms, treatments, and the various medical explanations that have been given, Mesnard OC 4:1469-1503. This study concludes with a bibliography of both primary and secondary sources. Pascals relationship with Port-Royal at his death has been the subject of speculation, with some claiming that he had renounced his association with the Jansenists sometime during the last two years of his life. Mesnard consider s this question in his Note sur les derniers sentiments de Pascal, Mesnard OC 4:1511-1517. As on most issues, Mesnard hews closely to the traditional view of Pascal as obstinately faithful to Port-Royal to the last, Mesnard OC 4:1514. 19

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suffering during his last illness. Gilberte made Pascals childhood the center of gravity for his life and work. The theme of wunderkind was the central featur e of Priers biography. In addition to the story of Pascals precocity in the playroom, P rier emphasized her brothers unusual curiosity for knowledge and his talent for philosophical explan ation of natural phenomena. Famously, Prier writes that after having heard a fork and plate hit one another at random at the dinner table, young Blaise wrote a treatise on sounds. For Pas cals sister, these youthful episodes announced qualities of mind that would be de monstrated by adult discipline: an admirable clarity of mind for discerning what is false; his genius fo r geometry; his curiosit y; and this mind, which could not remain within boundaries.9 Pascals childhood display of his aptitude fo r geometry provided other writers with a similar key to Pascals identity. Talleman t des Raux (1619-1692), noted gossip, wag, and author of the Historiettes wrote that through the discovery of Euclids thirty-second proposition, Pascal testified from his childhood the inc lination that he had toward mathematics.10 Pierre Bayles entry in his Dictionnaire historique et critique, written shortly after Pascals death and drawing heavily on the Prier biography, claimed that from childhood [he] gave proofs of a mind very much above the common.11 Likewise, for the romantic Chateaubriand, the episode 9 La vie de Pascal, Mesnard OC 1:572-574. 10 Le president Paschal a laiss un filz, qui tesmoigna de z son enfance linclination qu il avoit aux Mathematiques, Tallemant des Raux, Les Historiettes ed. Antoine Adam, vol. 2 (Paris, 1961), 57. This description of Pascal is included in des Rauxs longer description of Le President Paschal, 56-58. 11 Pierre Bayle, Pascal, in Dictionnaire historique et critique (Amsterdam, 1734), 4:734. 20

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of the invention of mathematics foreto ld Pascal as this frightful genius [ cet effrayant gnie ].12 More recent scholars have followed suit in their interpretation of the young Pascal, among them the most influential Pascal scholars of the twentieth century. L on Brunschvicg, editor of the seminal Oeuvres compltes (1914-1923), recognized in Pas cals childhood discoveries the prodigious capacity that [he] mani fests for observation and reflection.13 Jean Mesnard, Pascal scholar par excellence since the 1950s, averred that the playful geometrical doodling of the twelve-year-old marked the primacy of intuition over reason, one of the themes of Pascals later religious reflections.14 Pascals earliest indication of geometrical talent has also suggested to scholars the youthful nature of his genius.15 Characteristics of the child Pascal are used to generalize to the tendencies of the later Pascal, providing unity to his life. William Russell exemplifies an early version of this perspective: In fact, every attribute of character which marked his maturity was but the continuous development of qualities which grew with him from his earliest youth, the stupendous intellect united with the humblest, simplest fa ith, the playful sparkling wit, the polished subtle sarcasm, restrained only by kindliness and generosity of mind, the ardent devotion to truth; in all things the child was emphatically the Father of the man.16 On a first reading, Russells claim that Pascals early years were important for his adulthood is no more than could be said for anyone. Bu t for Russell, Pascals boyhood was not common; more than others, only the thinne st veil separated the virtuous disp lays of the child Pascal from 12 Franois Ren de Chateaubriand, Gnie du christianisme, ou Beauts de la religion chrtienne (Paris, 1803), 3: 90. 13 Lon Brunschvicg, Blaise Pascal (Paris, 1953), 21-22. 14 Jean Mesnard, Pascal, his life and works trans. G. S. Fraser (New York, 1952), 12-13. 15 Albert Bguin, Pascal par lui-mme (Paris, 1952), 5. 16 William Russell, Extraordinary Men: Their Boyhood and Early Life (London, 1853), 66. 21

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the outstanding accomplishments of the adult. Pa scals life is offered as a unique blend of childlikeness and maturity. Pascals Character and the Essai Pour Les Coniques The first documentary evidence of Pascals early talent, his Essai pour les coniques has also been used to emphasize the centrality of youth in Pascals la ter career. When Pascal wrote this Essai a single sheet of geometri cal propositions concerning projective geometry, he was only 17. A number of biographers have used this treatise as a startingpoint for themes that shaped Pascals adult life. Some scholars ha ve identified intellectual qualities that marked Pascals Essai and have sought to show how these i nnate characteristics might sharpen and simplify Pascals varied and complex career. Se veral Pascal studies have argued that his early work on conic sections evidenced reliance on vis uality in approaching geometrical problems. Pierre Humbert, Thomas More Harrington, and Daniel C. Fouke have claimed that this disposition toward visual stra tegies extends to Pascals work in natural philosophy and his religious reflections.17 Pascals perspectivist approach is an early ma nifestation of his attention to the concrete character of geometry.18 For Humbert, Harrington, Fouke, a nd other scholars, Pascals early work in projective geometry pr esaged his later tendency to offer parallels between sensory processes and abstract thought. Jacques Chevalier, whose opinion was echoed by Michel Le Guern, distinguished Pascals realistic, intuitive, and concrete mind from Ren Descartes 17 Pierre Humbert, Cet effrayant gnie: Loeuvre scientifique de Blaise Pascal (Paris, 1947), 166-167; Thomas More Harrington, Pascal philosophe: une tude unitaire de la pense de Pascal (Paris, 1982), 12-20; Daniel C. Fouke, Pascals physics, in The Cambridge Companion to Pascal ed. Nicholas Hammond (Cambridge, 2003), 99-100. Fouke provides a full analysis of Pascals Method of Disc overy, which includes elemen ts of perspective and the visual in Fouke, Pascals Method of Religious Investigation and Its Relation to His Methodology in Mathematics and Physics (Ph.D. diss., University of Chicago, 1986). 18 mile Caillet and John C. Blankenagel, introduction to Blaise Pascal, Great Shorter Works of Pascal (Philadelphia, 1941), 20. 22

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tendency to abstraction.19 This characteristic of Pascal was also employed by Mesnard and others when describing Pascals religious works.20 Ernst Mortimer used Pascals realism as the central theme of his 1959 monograph.21 During the early modern period, the senses were considered central to childhood.22 Religion and Childlikeness Gilbertes emphasis on Pascals childlike virtues was not entirely innocent. It is important to note that her narrative stress ed the maturity Pascals childh ood as a means of emphasizing his saintliness. She also recollected the account of Pascals confesso r, Jean Beurrier, regarding the childlike piety of her brother, es pecially his un troubled trust in God. The general tone and message of La vie de M. Pascal builds on the same identification: [He] was simple as a child in what regards piety.23 Pascals simple genius went hand in hand with simple piety. A variety of scholars have commented on Pascals spiritual childlikeness.24 Ivan Gobry expanded on one dimension of childlike spirituality in his Pascal ou la simplicit. Simplicity, argues Gobry, is safeguarded by submission and humility; each virtue, he claims, characterizes Pascal, who bears a heroi c spirit of childhood.25 Dawn Ludwins more recent work 19 Jacques Chevalier, Pascal (New York, 1930), 51. Michel Le Guern highlights the importance of Pascals and Descartes educational backgrounds as the source of the change, Le Guern, Pascal et Descartes (Paris, 1971), 89-90. 20 Pascals style in the Penses writes Mesnard, is coloured by a powerf ul imagination, which transforms every idea into a concrete vision, every demonstration into an analysis of facts, Jean Mesnard, Pascal, Life and Works 178. 21 Ernst Mortimer, Blaise Pascal, the Life and Work of a Realist (London, 1959). 22 See below, p. 38. 23 La vie de Monsieur Pascal, Mesnard OC 1:636. 24 Some examples of childlikeness as a positive religious quality in the secondary literature, include: Alexandre Rodolphe Vinet, tudes sur Pascal (Paris, 1848), 111-112; A. J. Krailsheimer, Pascal (New York, 1980), 75. 25 Gobry, Pascal (Paris, 1985)., 122. In discussing these aspects of Pascal, Gobry reflects on this spirit of childlikeness: It is not that children are without defects: on the contrary, they abound in them. But it is the recognition of his powerlessness, his smallness, and his in corrigibility, which makes the spirit of childhood, ibid., 119. He also writes: The spirit of childhood is not angelicalism but the accep tance of not being an angel; it is not 23

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describes Pascals phenomenologi cal approach to religion, whic h Ludwin associates with a childlike, common sense perspective that links Pascals theological thought to mystical traditions.26 Childlikeness has also been considered crucial to Pascals Provincial Letters Widely recognized, the Provincial Letters used naivety as a strategy to highlight Pascals argument. Naivety was first pinpointed as a central charact eristic of Pascals writing style by Faugre nearly two centuries ago.27 More recently, Pasc als strategy of naivety was examined by Robin Howells who characterized it as polemical stupidity.28 Pascals Childhood: Health and Psychology Pascals simplicity, humility, and naivety have also been are linked to psychological analyses. These writers have also expanded the repertoire by adding a new childhood episode and placing it center-stage in their psychological accounts. Marguerite P rier, Pascals niece and the daughter of the author of La vie de M. Pascal wrote a Memoir on Pascal and His Family, where she provided a fascinating story.29 According to legend, someti me before he reached his innocence, but the opinion that one has lost innocence, and the confidence in those who want to make us draw profit from this opinion, ibid., 118-119. 26 The phenomenological way of seeing is the way of common sense (dans lusage commun). It is often formulated in the Penses as a childs e xperience of the world, that is to say, a simple perception that is free from preconceived notions and school jargon, Dawn Ludwin, Blaise Pascals Quest for the Ineffable (New York, 2001), 132. Ludwins analysis compares Pascals writing to that of apophatic, or negative, theology, with its origins in the treatises of a fifth-century theologian who wrote under the name Dionysius, ibid., 4-5. 27 Vinet, tudes 116. 28 Robin Howells, Polemical stupidity in the Lettres provinciales in Pascal: New Trends in Port-Royal Studies ed. David Wetsel and Frdric Canovas (Tbingen, 2002): 231-237. 29 This anecdote is based on a recollection made by Gilberte on 14 August 1661, preserved in original by the Oratory of Clermont, and first published in Gilberte P rier, Jacqueline Pascal, and Jacqueline Prier, Lettres, opuscules et mmoires de Madame Prier et de Jacqueline, soeurs de Pascal, et de Margurite Prier, sa nice ed. Armand Prosper Faugre (Paris, 1845), 471-473; Mesnard OC 1: 507-508. Marguerites more detailed version, which appeared in her Mmoire sur Pascal et sa famille, was also kept by the Oratory of Clermont. The portions of the memoir dealing with this episode were publis hed in ibid., 447-459 and in Blaise Pascal, Des Penses de Pascal: rapport lAcadmie franaise sur la nces sit dune nouvelle dition de cet ouvrage ed. Victor Cousin (Paris, 1843), 390-394. 24

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second birthday, Blaise fell ill and came close to death. The incident involved his violent reaction to the sight of his mother and father embracing and also, pecu liarly, to the sight of water. The origin of Pascals illness was eventually traced to an old woman who had placed a spell on the child to take revenge on tienne Pas cal for his neglect of a law case. After the source of mischief was discovered, following negotiations carried out be tween tienne and the unnamed witch, a cat was convenien tly substituted for the young chil d. By tradition, Pascals family applied herbs to Blaises stomach and he gradually returned to health. This Pascal legend was first published in 1843 and quickly became the bellwether of Pascals persistent ill-health. This new episode resonated with ear lier reports found in Gilbertes biography, which spoke of her brot hers sickness with sympathetic and reverent tones regarding his patience under suffering and the constant scourge of his illness.30 Her claims were in turn buttressed by a prayer composed by Pascal in wh ich he praised God that it has pleased you to reduce me to the incapacity of rejoicing in th e sweetnesss of health and the pleasures of the world.31 Pascals illness was a life-long and genuine c oncern that forced him, on several occasions, to retreat from concentrated work.32 The story of the vengeful witch became a recurring interpretation of Pascal by focusing on his ever-p resent maladies, furthe r buttressing Gilbertes view of Pascals pain and suffering, now common knowledge. Enlightenment thinkers continued expand the place of Pascals health. For his part, Voltaire criticized the Penses connecting 30 [I]l nous a dit quelquefois que depuis lge de dix-huit ans il navait pas pass un jour sans douleur, La vie de M. Pascal, Mesnard OC 1: 577. 31 Blaise Pascal, Prire pour demander a Dieu le bon usage des maladies, in Brunschvicg OC 9: 325. 32 The various periods of Pascals ill-health are summarized in Georges Duboucher, La maladie de Pascal: une mise jour, Courrier du Centre International Blaise Pascal 14 (1992), 6-7. 25

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vague suggestions of Pascals ill-health with what the philosophe deemed fanaticism, apparently in an attempt to discredit the legitimacy of Pascals religious devo tion by making it aberrant.33 During the late eighteenth and nine teenth centuries, Romanticism gl oried in the peculiarities and tragedies of its literary heroes rather than feeling repulsed. Pas cals strange illn esses became the feature attraction in interp reting his peculiar genius. Louis Francisque Llut wrote a study of Pas cals life shortly after the publication of the account of Blaises curious en counter with witchcraft. Lamulette de Pascal, pour servir lhistoire des hallucinations (1846) was sold as a case study of nervous disorders that built on family legends.34 The tale was good evidence, Llut claime d, that the constitution of Pascal so feeble, so irritable, and finally so sickly, date d from the first year and that the sad bizarrerie of the alterations which menaced [his health] were betrayed from the crib.35 Llut focused on Pascals health to explain the renunci ation of mathematics and science, his austere religious discipline, his rejection of familial a ffection, and the nearly insane melancholy of a man so full of oppositions and miseries.36 Llut catalogued and addr essed a growing list of apparent contradictions in Pascals life, especially those that appeared unattractive to thinkers like Voltaire. Llut argued that clear understanding of Pascals illness, which began with the early tale of the witch, would allow readers to see Pascals true greatness despite his weaknesses and all the pr oofs of his dependency.37 Lluts claim that Pascal skirted insanity 33 In remarks on Pascals Penses Voltaire writes: Pascal, one indeed sees that you are ill, Voltaire, Lettres philosophiques, ou Lettres anglaises, avec le text e complet des Remarques sur les Penses de Pascal (Paris, 1964), 286; True discourse of illness, ibid., 289; and Pascal speaks always en malade ibid., 291. 34 Louis Francisque Llut, Lamulette de Pascal, pour servir lhistoire des hallucinations (Paris, 1846). 35 Ibid., 128. 36 Ibid., 114. 37 Llut, Lamulette de Pascal 117. 26

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might have tainted his image for some, but it undoubtedly focused attention on Pascals psychological state. Lluts conclusions reflect contemporary studi es related to the ner vous system, disorders of the brain, and a biographical strategy to understand past great men based on medical factors.38 Lluts physiological account was written ten years before the birth of Sigmund Freud, whose psychoanalytic theories would eventually add another layer of interpretation to Pascals childhood. In 1958, Erik Erikson pioneered an approach to biography known as psychohistory that sparked a flurry of similar st udies and signifi cant criticism.39 The psychoanalytic approach of Erikson, building on Freuds pioneering work, had dr awn attention to Luthe rs relationships with his parents and his childhood experiences.40 The tradition conti nued. Charles Baudouin contributed a psychohistorical acco unt of Pascals life in 1962, ju st a few years after Eriksons work.41 Drawing on the story of the witchs spe ll, and Pascals early loss of his mother, Baudouin offered a new reading of Pascals life inspired by the work of Freud and Jung. For 38 Some years previously, Llut had written Du dmon de Socrate (1836), in which he had claimed that Socrates was the victim of hallucinations. This work, and the study of Pascal, are a part of Lluts drive to assume the position of physician-philosopher, Floren ce Vatan argues. Vatan argues that Llut is a representative of a nineteenth-century movement that aims for a holistic treatment of man, Vatan, The Poet-Philosopher and the PhysicianPhilosopher: A Reading of Baudelaires Prose Poem Assommons les pauvres!, Nineteenth-Century French Studies 33 (2004-2005), 89-93. Llut, among others, w ould help to encourage the acceptance of Pascals complexity. 39 Erik H. Erikson, Young Man Luther: A Study in Psychoanalysis and History (New York, 1958). An introduction to the issues and retrospective response s to Eriksons work may be found in Psychohistory and Religion: The Case of Young Man Luther ed. Roger A. Johnson (Philadelphia, PA, 1977). 40 In a representative passage from Eriksons work, he write s: [T]his observant and imaginative boy, inclined to rumination about the nature of things and Gods justification in having arranged them thus, may well have suffered call it neurotically, call it sensitivelyunder observations which leave (or, indeed, make) others dull. At any rate whatever happened in this boys dreams and in his half-dreams, and was sensed and heard in sleep and half-sleep, became richly associated with the sini ster dealings of demons and of th e devil himself; while some of the observations made at night may have put the fathers mo ralistic daytime armour into a strange sadistic light, Erikson, Young Man Luther 63. 41 Charles Baudouin, Blaise Pascal: ou lordre du coeur (Paris, 1962). Subsequent references are from idem, Blaise Pascal (Paris, 1969). 27

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Baudouin, Pascals early illness revealed the extreme and precocious nervous susceptibility of Pascal.42 In Freudian terms, Baudoui n drew from Pascals childhood experiences to argue for a pre-oedipal and pre-gen ital understanding of the astonishing genius, stating that it is not certain that the genital stage had ever been fully attained.43 Following Baudouins lead, a later psychologi cal account by John R. Cole focused on Pascals childhood as a key to interpreting his ca reer and religious sentiments. According to Cole, the early loss of Pascals mother resulted in profound difficulties with attachment. Latent anxieties about losing his father also provoked attempts to please hi m with scientific offerings. These responses of Pascal, Cole argued, were ac centuated by the fathers possessiveness of his sons affections. Extending his view further, Co le concludes that the de ath of Pascals father, and the loss of his sister to a cloistered life at Port-Royal, caused crises in Pascals life that eventually led to his religious conversion and to alternations between mania and depression.44 The work of Llut, Baudouin, and Cole demons trates how various approaches to Pascals life converge on the formative role of Pascals childhood. Coles work, for instance, emphasizes the infantile qualities of the adult Pascal and his dependence on his father. Each of these three writers de-historicized Pascals childhood as it related to the broad scope of his work and the 42 Baudouin, Blaise Pascal (1969), 10. 43 Ibid., 17. 44 John R. Cole, Pascal: The Man and His Two Loves (New York, 1995). Cole interprets the story of the witch from Pascals early childhood as possibly having to do with we aning, ibid., 16-25; on Coles interpretation of the arithmetic machine and the writings on th e void as offerings to his father, see ibid., 42-49; concerning the crises of separation and loss, see ibid., chapters 4-6, 51-82. Cole considers the conn ections between these early attachment issues and Pascals involvement with Port-Royal and his religious writings in ibid., chapters 7-14, 91230; evidence for Pascals depression during his later years is considered in ibid., chapter 15, 231-251; finally, psychological issues and apparatus are considered in seve ral appendices to Coles book, ibid., 261-276. Coles connection of Pascal with manic-depressive symptoms draws on an increase in interest during the late twentieth century in the relationship between cr eativity and specific mental disorders. Jablow Hershman and Julian Lieb, The Key to Genius (New York, 1988), describes Newton, Beethoven, Dickens, and Van Gogh as manic-depressive and examine the contributions and costs of such psychological disorders on these noted individuals. These sorts of works should be distinguished from earlier, more general attempts to link genius with madness. 28

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continuing course of his life. The psychoanalytic approach empl oyed in these studies failed to draw on Pascals contemporaries to understand th e context of his childhood; instead, the aim was to develop a more general scientific understanding of human deve lopment. In each of these studies, to be like a child was to be psychologi cally immature, while to be complete was to overcome the complexes of infancy by attaining the goal of maturity. While these studies offer a general picture of Pascals development, they offer little insight into the biographical complexities that went unresolved, nothing new about the historical pa rticulars that shaped Pascals life. The present study is an attempt to understand Pascal as his contemporaries might have viewed him. Importantly, this is not psyc hohistory in the manner of Baudouin and Cole. Instead, the present study draws at tention to historical notions of childhood and childlikeness. Rather than search for the hi dden secrets of Pascals psychology, this study focuses on how Pascals mentors treated him, how they unders tood his position as an apprentice savant, how Pascal presented himself and his work, and how these perspectives re flect an early-modern tension between childlikeness and maturity. Influences of Childhood: The Mersenne Group Pascals childhood was also considered influent ial in more historically-centered ways. Some scholars have examined the formative role of his education and the learned community where Pascals career began. Instead of isolati ng character traits that appear in childhood, some twentieth-century historians of science sought to uncover other in fluences (in the form of books, correspondence, and personal meetings) that shaped the thought of indivi duals such as Pascal. Positivist philosophy, since the turn of the tw entieth century, became a driving force for understanding the social underpinnings of science. For some, Pascals interest in method made him an icon of positivism. In his Positivist Calendar (a list of intellect ual saints), Auguste 29

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Comte included Pascal under the month devoted to modern philosophy, joined by Francis Bacon, Thomas Hobbes, and John Locke.45 Pascals work in physics, portrayed as perfectly distinct from his religious devotion, was also considered important. As an exemplary model of method, Pascal was virtually canonized for his cautious ap proach to hypothesis and his critically reasoned experimental designs.46 The history of science in its early decades wa s influenced by the assumption that science is essentially cumulative but punctuated by great discoveries of great men. The positivistic picture of Pascal reflected the philosophy he was made to represent. Pascals positive contributions to physics were methodically isol ated from his other, often disappointing and frightening, contributions to le arning. Ernst Mach, a quintesse ntial positivist, specifically highlighted Pascals experiments on the equilibrium of fluids and on atmospheric pressure as a key contribution to positive knowledge.47 Others looked to Pascals mathematical work and saw an anticipation of the integral calculus of Leibniz and Newton. These and similar evaluations were often accompanied by the lament that becau se of his abandonment of mathematics Pascal was perhaps the greatest might-have-been in history.48 45 Auguste Comte, Calendrier positiviste, ou systme gnral de commmoration publique (Paris, 1849), 33. 46 Pascals conservative attitude toward hypoth eses is upheld in E. J. Dijksterhuis, The Mechanization of the World Picture trans. C. Dikshoom (Oxford, 1961), 450. Reijer Hooykaas labels Pascal a positivist for his distrust of corpuscularian and Aristotelian hypotheses, Hooykaas, Fact, Faith, and Fiction in the Development of Science (Boston, 1999), 347. J.-P. Fanton d Andon denies the positivis t label to Pascal, but allows him a place as the shortest path between medieval thought and modern scienc e, since he was able to fill in gaps in a Cartesian approach, Fanton dAndon, Lhorreur du vide: exprience et ra ison dans la physique pascalienne (Paris, 1978), vi. 47 Ernst Mach, The Science of Mechanics: A Critical and Historical Account of its Development trans.Thomas J. McCormack, 6th ed.(Lasalle, IL: Open Court, 1960), 66, 111, 116, 117, 119, 137-141. Machs work was first published in 1893. Mach also mentions Pascals religious beliefs, but not to criticize them. As the foremost of scientific discoverers, Pascal, Leibniz, Newton, Euler, and others, were able, in spite of the contracted horizon of their age, to which even their own aperus were chiefly limited, to point out the path to an elevation, where our generation has attained a freer point of view, ibid., 545-546. 48 Eric Temple Bell, Men of Mathematics (New York, 1937), 73. 30

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Historians of science imbued with positivistic tendencies made efforts to create a grand narrative of progress that magnifi ed individual genius and trium phal discovery in a relentless search for precursors. This approach also fostered investigation of the educational background of individuals, and here interest in Pascals in tellectual circles took r oot. These early studies were also encouraged by fresh scholarship about early-modern intelle ctual groups. Martha Ornstein, Harcourt Brown, Frances Yates, and Re n Taton pioneered early inquiries on the formation of informal academies, especi ally those devoted to natural philosophy.49 These efforts prompted further scholarship on the relations hip between Pascal and the mathematical academy organized by Mersenne. Pierre Humbert, against tradition, argued that Pascal was not essentially a loner but the product of a social network of savants.50 The childhood dimension of Pascals biography, showing the importance of such networks, will be the s ubject of chapter 2 of this study. Pascals experience in the Mersenne group launched his career and situated him as a promising young geometer. As this study seeks to show, the groups expecta tions for intellectual productivity prompted young Pascal to develop his natural inclinati ons, which eventually transformed him into one Europes most celebrated scholars. Mature Virtues in Pascal Historiography It is clear from the precedi ng sketch that Pascals chil dhood and his characterization as childlike have been pivotal con cerns among Pascal scholars. By contrast, the complimentary 49 Martha Ornstein, The Rle of Scientific Societies in the Seventeenth Century (Chicago, 1928); Harcourt Brown, Scientific Organizations in Seventeenth-Century France (Baltimore, MD, 1934); Frances A. Yates, The French Academies of the Sixteenth Century (London, 1947; repr., 1988); Ren Taton, Les origines de lAcadmie des Sciences (Alenon, 1965). 50 Humbert, Cet effrayant gnie Alexandre Koyr reiterated the importance of influence for Pascal, primarily in order to temper heroic, hagiographic portrayals in Koyr, Pascal Savant, in Blaise Pascal: Lhomme et loeuvre ed. M. A. Bera (Paris, 1956), 262. Koyr states: Je croi s que nous pouvons voir dans Pascal un vritable lve de Desargues, Alexandre Koyr, An English translation of the essay is available: idem, Pascal Savant, in Metaphysics and Measurement: Essays in Scientific Revolution trans. R. E. W. Madison (Cambridge, MA, 1968): 131-156. 31

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aspect of this study (maturity) is marginal in the scholarly litera ture. The mature Pascal has been posited as a generally vague and always und eveloped counterpoint to the childlike image of Pascal. The traditional gloss of Pascal as the perpetual child is sometimes punctuated by suggestions of opposition, with hints that Pas cals ambition and stubborn intellectual pride showed shades of maturity, though not necessarily virtuous maturity.51 The clearest examination of Pascals attempts to establish a self-sustaining, mature identity is a study published by Robert Nelson (1981).52 Nelsons work stresses the self-assertiveness of Pascal that he perceives as coexisting with Pa scals more traditional submissiveness. By doing this, Nelson creates a picture of a man at on ce reflective and spontaneous, compassionate and combative, submissive and impetuous.53 And while from a psyc hoanalytic perspective he recognizes Pascals filial dependency, Nelson ha stens to add that it l eaves much room for self-assertion and self-distinction. 54 Pascals pedagogical efforts have also been viewed as indicators of Pascals maturity. As this introduction will later show, one of the early-modern hallmarks of reaching a mature stage of life was the transition fr om learner (student) to teache r (master). Although Pascal was never a teacher in an official capacity, he was involved in the pr oject of Port-Royals petites coles in substantial ways. Pascal invented a method for teachi ng reading that the schools of Port-Royal adopted, and his ideas on argument a nd proof found a place in textbooks composed by the movements leaders. Pascal also contribut ed to discussions on the education of princes. 51 Jean Mesnard describes Pascals spiritual struggle with ambition as an interior dr ama that takes place between pride and humility, between glory and obscurity, Mesnard, Pascal: His Life and Works (New York, 1952), 63. Elsewhere, Mesnard emphasizes Pascals assertiveness by describing him as a man of violence and a man of selfmastery, ibid., 185. 52 Robert James Nelson, Pascal, Adversary and Advocate (Cambridge, MA, 1981). 53 Ibid., 29. 54 Ibid. 50. 32

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These manifestations of pedagogica l interest are underrepresented in Pascal studies, and it is only with the recent work of Nicholas Hammond th at they have been considered in depth. In an article that focuses on Pascals Penses the Port-Royal document Recueil de choses diverses and Pascals Entretien de M. de Sacy Hammond argues that Pascals religious works should be given a pedagogical reading that includes the petite coles 55 He calls Pascal a teacher figure, drawing on his reputation fo r contributions to e ducation at Port-Royal.56 Hammond expands on this theme in a subsequent book that uses memory as a lens for viewing the approach of the schools. An examination of Pascals Penses he argues, demonstrates the pedagogical purpose of the unfinished work.57 Hammonds pedagogical Pascal provides a link to seventeenth-century notions of the virtues of a mature adult. The ages of Man concept that recurs in some early modern literature (and is described below) stress es the natural progre ssion during the life-span from student to teacher. This study sheds light on how Pascal s work reflects the value of moving from childhood to maturity, from protg of th e Mersenne group to teacher figure. Childhood and Childlikeness in the Early Modern Period The foregoing section suggests that secondary scholarship on Pascal includes significant themes of childhood/childlikeness and, clearly but less promin ently, of adult virtues and maturity. The two themes have occasionally be en linked, albeit suggestively and tenuously. 55 Nicholas Hammond, Pascals Penses and the Art of Persuasion, in The Cambridge Companion to Pascal ed. Nicholas Hammond (Cambridge, 2003): 235-252; idem, Pascal, Port-Royal, and the Recueil de choses diverses Romance Quarterly 50 (2003): 131-148. The Recueil de choses diverses is a recollection of some of the teachers and pupils of Port-Royals petite coles A recent critical edition of the text is Jean Lesaulnier, ed., Port-Royal Insolite: dition critique du Recueil de choses diverses (Paris, 1992). 56 Hammond, Pascal, Port-Royal, and the Recueil de choses diverses 144-145. 57 Nicholas Hammond, Fragmentary Voices: Memory and Education at Port-Royal (Tbingen, 2004). Indeed, it was an attempt to expand the scope of Hammonds pedagogical interpretation of Pascal that led to this dissertation. 33

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Nelsons work argues, for example, that submi ssion and self-assertion co exist in Pascal, while other scholars merely acknowledged seemingly c ontradictory qualities. mile Boutroux writes: Pascal united in himself singularly diverse qua lities; a gift for the sciences depending on observation and on reason, together with the mo st penetrating sense of the things of the heart and the soul; the cravi ng to know and the craving to love; a drawing towards the inward life, and an ardent desire to infl uence other men; childlikeness and ambition; simplicity and passion and will-power; the s pontaneity of a generous nature, and inclination for work, struggle and effort.58 Pascals identification as a child prodigy serves as another m eans to link the opposing categories. The image of a child prodigy carries the impression that the child has skill that is unusually mature for others the same age. The st ories of Jesus in the te mple and Pascal in the playroom feature the adult surprise of seeing children with learning that is typically reserved for adults. For the most part, in the case of Pascal the peculiar problems of the maturation of gifted children have not been considered by scholars. This study underscore how Pascals early exposure to Mersennes learned ci rcle, and his own claims to sava nt maturity, created a sense of expectation for Pascals future. The possibility of anachronism is a key danger of the analytical strategy proposed in this study. A historically sound approach necessitates i nvestigating Pascal not from the point of view of modern categories but from a perspective Pascals contemporaries might recognize. This study takes care to present the virt ues of childlikeness and maturity in their early-modern dress. This approach represents a unique contribution to Pascal scholars hip and brings new clarity to Pascals identification as a man living between these always dynamic categories. In return, it offers a reflection on early modern views of human nature and the acquisition of spiritual and learned virtues. 58 mile Boutroux, Pascal (Manchester, England, 1902), 195. Cf., Mesnard, Pascal, His Life and Works 185. 34

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The seventeenth-century percep tion of childhood, child likeness, and maturity provides the backdrop for the present study. In the following s ection, associations betw een age and virtue are identified and evaluated. The key ideas of child likeness and maturity will be introduced with a preliminarily sketch before developi ng them further later in the study. Childlikeness and the Historici ty of Childhood and Youth The characteristic of childlikeness is a re flection and a developmen t of the category of childhood. That said, it is cl ear that during the seventeenth century the concept and understanding of childhood was not unproblematic. Philippe Ariss hist ory of childhood during the early-modern period has been a traditional point of departur e for understanding the social and intellectual status of children.59 First published in 1960, Ariss fi eld-defining work attempted to locate a particular shift in at titudes toward childhood in early-modern Europe. According to Aris, the Middle Ages had been devoid of a distinctive attitude toward childhood. Children were introduced to adult society and treated as little adults from the age of seven years old.60 During the early-modern period, however, children were increasingly viewed as needing special attention because of their wea knesses. New ways of dealing with children emerged, including isolation from adults.61 Ariss study problematized the hi storical construct of childhood and prompted a number of studies arguing for an earlier and more differentiated view of childhood, including adolescence. 62 59 Originally published as Philippe Aris, LEnfant et la vie familiale sous lancien rgime (Paris, 1960); it was translated into English in idem, Centuries of Childhood: A Social History of Family Life trans. Robert Baldick (New York, 1962). 60 Ibid., 329. 61 Ibid, 415. 62 Shulamith Shahar, for example, made the claim that adolescence was a defina ble period by the time of the Late Middle Ages, Shahar, Childhood in the Middle Ages (New York, 1990). 35

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The emergence of a more nuanced understand ing of childhood is lin ked to the notion of ages of life. In antiquity and during the Mi ddle Ages, thinking about the life-process had evolved into a systematic way of subdividing huma n existence. Traditionally, there were seven ages: childhood, puerility, adolescen ce, youth, senility, and old age.63 Aris argues that, despite this original separation, there wa s no intelligible difference between adolescence and the rest of childhood until the eighteenth century. The origin al age of adolescence (which was sometimes considered to extend until 25) was combined wi th the previous two ages into a single long childhood.64 Despite the successive changes in attit udes posited by Aris, linguistic limitations (the lack of a word equivalent to the Latin adolescens ) meant that there was much ambiguity about different stages of childhood.65 Scholars have taken issue with Aris linguistic claim that there was no coherence to an idea of adolescence before the eighteenth century. Natalie Zemon-Davis argues, for example, that one cannot infer that a period of adolescen ce was not recognized merely from a lack of a precise vocabulary.66 What may be concluded, however, is that if there was a clear conception of adolescence during the sevent eenth century, there was at the least a common practice of collectively referring to all simply as children. One example of this generalization of ages is Juan Huartes work on judging childrens intellectual proclivities.67 Huarte divides the human life sp an into five stages: childhood, youth, 63 Aris, Centuries of Childhood 18-19. 64 Ibid., 25. 65 Ibid., 25-29. 66 Natalie Zemon-Davis, The Reasons of Misrule: Youth Groups and Charivaris in Sixteenth-Century France, Past and Present 50 (1971), 61-62 n63. 67 Huartes views are considered at some length below, pp. 103-105. 36

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manhood, middle-age, and old age.68 The divisions between ages outlined in Huartes work (originally published in 1575 and widely translated through the se venteenth century ) suggest the continuing ambiguities in the definition of childh ood. Huarte recognizes, for instance, different lengths for the various stages of life: childhood, he states, may e nd anywhere from twelve years old to eighteen. Similarly, the age of youth ma y extend to as late as forty years of age.69 Other evidence supports diverse intellectual attitudes toward th e ages. Within learned treatises, the Latin term adolescens had some currency as an ironi c, derogatory term. Jean Chapelain lobbied Guez de Balzac on beha lf of a friend to remove the term adolescens as a part of the description of him: this term is in our la nguage no longer taken up, and is said only in an ironic way of speaking.70 The seven age divisions, in some cases at least, were replaced by a generalized contrast between young and old, between childhood and maturity. The boundaries of childhood were fluid during the seventeenth century and this imprecision is reflected in contemporary perceptions of young Pascal. As this study will reveal, references to Pascals early display of mathemati cal talent are typically confined to generalized marveling at his productions, works usually associat ed with older, more experienced savants. Despite the lack of a traditional, well-defined categorization of ages, an understanding of the intellectual background for such dist inctions is important to this study. They are the clearest source of information about the virtues and vices that Pascal and his contemporaries would have 68 Juan Huarte, Tryal of Wits, Discovering the Great Difference of W its among Men, and what Sort of Learning Suits Best with Each Genius (London, 1698), 45. 69 Huarte, Tryal of Wits ibid. Huartes extended discussion of the ages of man lists the offici al years of childhood as through age fourteen and the years of youth from fourteen to twenty-five, ibid., 82. 70 Jean Chapelain to Guez de Balzac, 17 February 1636, in Lettres de Jean Chapelain, de lAcadmie franaise ed. Philippe Tamizey de Larroque, vol. 1 (Paris, 1880; repr. 1968), 108. 37

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associated with childhood and maturity. E qually clear, the connot ations of childhood and adulthood ground the related concept of childlikeness in adults. Childlikeness assumes a distinction between chil dren and people of other ages. To be childlike is to exhibit a set of traits that child somehow represents. These characteristics may be deemed positive by serving as a model of emulation for adults. They may also be deemed negative, a contrast to proper a dult behavior, as a term for those who exhibit traits deemed childish. This study attempts to show that the two concepts of positive childlikeness and negative childishness framed the impera tives that shaped Pascals career. The Virtues and Vices of Childhood Most historians of childhood r ecognize that attitudes toward children have consistently hesitated between suspicion and admiration. This is nowhere more clearl y evident than in the period from the Middle Ages through the sevent eenth century. Some scholars have argued that the view of children during this period was primaril y negative, that children were seen merely as imperfect adults.71 Most studies also acknowledge that attitudes about childhood were profoundly ambivalent. Negatively, children we re thought to lack th e capacity for reasoning because they were entirely submerged and entirely shrouded in the senses.72 The Augustinian doctrine of the depravity of huma n beings also stressed that child ren were born with evil desires and that childhood was a time of unbridled lust.73 Lack of reasoning a nd self-control made the 71 This is the view of James A. Schultz in Schultz, The Knowledge of Childhood in the German Middle Ages, 11001350 (Philadelphia, 1995), 244-256. Schultz claims that it was not until the eighteenth century that a different view of children developed that enhanced their unique positive attributes, 249. 72 [D]ans les premieres annees de len fance lame de lhomme est comme toute plonge & toute ensevelie dans les sens, & elle na que des perceptions obscures & confuses des obbjets qui font impression sur son corps, Antoine Arnauld, Nouveaux elements de gomtrie (Paris, 1667), preface, n.p. [3] 73 Shahar, Childhood in the Middle Ages 14-16. 38

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child no more than a Brute Beast.74 Notions of the depravity of childhood will be further developed in Chapter 5, where moral inclinations and discipline are considered at length. Children were not only viewed negatively. In her study of childhood in the Middle Ages, Shahar argues that Augustines view of children also stressed the innocence of baptized children in comparison with their adult counterparts.75 The importance of the virtue of the child was rooted in Jesuss words in the synoptic gospels: Let the children come to me, and do not hinder them; for to such bel ongs the kingdom of God.76 This sentiment was further reiterated by the requirement for childlikeness in adults: Truly, I say to you unless you turn and beco me like children, you will never enter the kingdom of heaven. Whoever humbles himself like this child, he is the greatest in the kingdom of heaven.77 The innocence and purity of childre n also appeared in the Middle Ages in the form of cults of the infant Jesus and in stories of the early lives of the saints.78 Saint-Cyran, one of the key figures of Jansenism, the religious movement w ith which Pascal would be associated during the last years of his life, was part icularly imbued with the virtues of childhood, including spiritual receptivity: God who says that he rejoiced with his eter nal Wisdom in making th e world, rejoices often in these little souls, and doe s in them what he would like to do in big ones [but cannot] because of the opposition and the continua l resistance that he meets in them.79 74 Juan Huarte, Tryal of Wits 59. 75 Shahar, Childhood in the Middle Ages 16-17. 76 Matthew 19.14, Revised Standard Version; cf., Mark 10.14; Luke 18.16. 77 Matthew 18.3-4, RSV. 78 Shahr, Childhood in the Middle Ages 18-20; Colin Heywood, A History of Childhood: Children and Childhood in the West from Medieval to Modern Times (Malden, MA, 2001), 32-34. 79 Jean Duvergier de Hauranne to Princesse de Gumne, n.d. [January 1642], in Jean Duvergier de Hauranne, Lettres indites de Jean Duvergier de Hauranne,labb de Saint-Cyran ed. Annie Barnes (Paris: J. Vrin, 1962), 265. 39

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The virtues of childhood did not always e nd with innocence, purity, and receptivity. Huarte extends their scope to include docil ity, tractability, gentleness, bashfulness and fearfulness (which he views as the basis of te mperance), credulity, submissiveness, frankness, humility, and lack of deception.80 For Huarte, the virtues of childhood outweighed its vices. The virtues of childhood, as many as they may be, were not understood as the final product; maturation was necessary. The goal of the child was always to become an adult. The process of growth included increasing self-control a nd the development of good manners, each virtue encouraged by innumerable manuals of eti quette that appeared from the late Middle Ages onward.81 The mature person was also called to foll ow the natural evolution from learner to teacher, which, as this study shows, is reflected in Pascals assumption of informal teaching roles.82 The clearest source of the childlike/mature dua lity for learned indi viduals in the early modern period was the New Testamen t. Carrying the authority of scripture, it employs a positive view of children worthy of im itation; but it also urges growin g up and abandoning childish ways. Neither mandate takes precedence over the other; th ey are frequently quoted in the same passage. Scriptural evidence continued to carry great weight. Jesu ss well-known articulations of childrens privileged position in the kingdom of heaven ha ve already been mentioned.83 Jesus 80 The Virtues of Infancy are very many, and the Vices but very few; Children, says Plato admire from what Principles the Sciences arise. In the next Place they are Docile, Tractab le, Gentle, and Easy to receive the Impression of all Kinds of Virtues. In the third Place, they are Bashful, and full of Fear, which, according to Plato is the Foundation of Temperance. In th e fourth place they are Credulous and Ea sy to be led; they are Charitable, Frank, Chast, Humble, Innocent, and Undesigning. To which Virtues Jesus Christ had regard, when he said to his Disciples, Except you become as little Children, you shall not Enter into the Kingdom of Heaven Huarte, Tryal of Wits 81. 81 These manuals are a central component of the important work by Norbert Elias, The Civilizing Process trans. Edmund Jephcott (New York, 1978). 82 Daniel Bartoli, for example, argues that life should be subdivided into three parts, in which an individual learns, practices, and then teaches, Bartoli, The Learned Man Defended and Reformd (London, 1660), 333. 83 See p. 38, n. 73. 40

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also cites an advantage that children (and by ex tension childlike adults) have in receiving the revelation of God: I thank thee, Father, lord of heaven and earth, that thou hast hidden these things from the wise and understand ing and revealed them to babes.84 In addition, Peter commands his readers like newborn babes, [to] long for the pure spiritual milk while the Pauline writer urges the Corint hians to be babes in evil.85 Peters imperative to crave the milk of divine revelation assumes, however, that the nourishment will then enable believers to grow up to salvation.86 Moreover, the writer of the book of Hebrews describes the milk imbibed in Christian childhood not as the source of maturity, but as a less nutritive substitute for the solid food of mo re difficult doctrines.87 And importantly, if the Christians at Corinth should maintain a childlike innoc ence, they should also have the disciplined mind of an adult: do not be children in your thinking ; be babes in evil, but in thinking be mature.88 Thus, the New Testament writers maintain the n ecessity of childlikeness, for it is as a child that the kingdom is inherited. But there is also the final goa l of a mature manhood in which believers are called to no longer be children, to ssed to and fro and carried about with every 84 Matthew 11.25, RSV; cf. Luke 10.21. 85 1 Peter 2.2, RSV; 1 Corinthians 14.20, RSV. 86 1 Peter 2.2. 87 About this we have much to say which is hard to explain, since you have become dull of hearing. For though by this time you ought to be teachers, you need someone to teach you again the first pr inciples of Gods word. You need milk, not solid food; for every one who lives on milk is unskilled in the word of righteousness, for he is a child. But solid food is for the mature, for those who have their faculties trained by practice to distinguish good from evil, Hebrews 5.11-14, RSV. 88 1 Corinthians 14:20, RSV. 41

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wind of doctrine.89 Instead, they move beyond their age of minority to their full status as heirs of Gods gracious promises.90 The biblical pairing of childlikeness and maturity, as interpreted through Augustine and other theologians, is undoubtedly the source fo r Jansenist doctrines. This tension between submissive receptivity and striving for perfectio n are evident in Pascals religious writings.91 The relationship expressed in the New Testament be tween these two types of virtues also serves as a backdrop to early-modern intellectual issues The present study aims to show the value of exploring this duality by linking early modern religious and sc ientific work. Two examples suggest further possibilities from this perspective. Francis Bacons inductive method bears the sign ature of both adult control of nature and childlike openness to it. Carolyn Merchant has famously sketched the themes of the dominance, control, and interrogation of nature during the early modern period, all of which are linked to its coding as female. The role of the violent inve stigator undoubtedly repres ents the authority and purposefulness of the adult, while the natural world ultimately submits to its patriarchal inquisitors. Merchant suggests that this attitude toward nature re presents a transformation of the perennial identification of nature as female, as an organic, productive, and nurturing mother. But even in the works of Bacon the natural philosopher was idealized at once as the receptive child 89 And his gifts were that some should be apostles, some prophets, some evangelists, some pastors and teachers, to equip the saints for the work of ministry, for building up the body of Christ, until we all attain to the unity of the faith and of the knowledge of the Son of God, to mature manhood, to the measure of the stature of the fullness of Christ; so that we may no longer be children, tossed to and fro and carried about with ever y wind of doctrine, by the cunning of men, by their craftiness in d eceitful wiles, Ephesians 4.11-14, RSV. 90 I mean that the heir, as long as he is a child, is no better than a slave, though he is the owner of all the estate; but he is under guardians and trustees until the date set by th e father. So with us; when we were children, we were slaves to the elemental spirits of the universe. But when the time had fully come, God sent forth his Son, born of woman, born under the law, to redeem those who were unde r the law, so that we might receive adoption as sons, Galatians 4.1-5, RSV. 91 See Chapter 3. 42

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and as the strategic, aggressive probing manipulator. The attit ude and difference is clear in Bacons Of the Interp retation of Nature: For as in the inquiry of divine truth, the pride of man hath ever inclined to leave the oracles of Gods word, and to vanish in the mixture of their own in ventions; so in the selfsame manner, in inquisition of nature, they have ever left the oracles of Gods works, and adored the deceiving and deformed imagery, which th e unequal mirrors of their own minds have represented unto them. Nay, it is a point fit and necessary in the front, and beginning of this work, without hesitation or reservation to be professed, that it is no less true in this human kingdom of knowledge, than in Gods ki ngdom of heaven, that no man shall enter into it, except he become first as a little child.92 Bacons advocacy of a childlike approach to na ture is drawn explicitly from the biblical passage and demonstrates, like Pascal, that the Chri stian tradition provided a justification for the submissiveness of human beings to well-ordered experience, not unlike the Adamic subduing of nature. According to John Henry, Bacons method should be understood as religiously motivated, an attempt to return mankind to the prelapsarian state.93 The original man, according to Bacon, was at once childlike and mature, and thus the fall was one from the state of innocence as well as from the kingdom over the creatures.94 Bacons project sought to create a mind totally liberated and cleansed, bu t it did so through the disc iplined application of his New Organon, which overcame elements of credulity and childishness in method.95 92 Francis Bacon, Of the Interpretation of Nature, The Works of Francis Bacon 3 vols. (Philadelphia, 1844), 1:84. There is a similar passage in the Novum Organum which especially emphasizes the need to leave aside ones preconceptions when approaching natu re: So much for the kinds of idols and their trappings; all of which must be rejected and renunced and the mind totally liberated and cl eansed of them, so that ther e will be only one entrance into the kingdom of man, which is based upon the sciences, as there is into the kingdom of heaven, into which, except as an infant, there is no way to enter, Bacon, The New Organon, ed. Lisa Jardine and Michael Silverthorne (New York, 2000), Book 1, Aph. 68, 56. 93 John Henry, Knowledge is Power: Francis Bacon and the Method of Science (Cambridge, 2002), 136. 94 Bacon, New Organon, Book 2, Aph. 52, 221. 95 Bacon equates the cleansing of the understanding to the biblical becoming like a child, ibid., Book 1, Aph. 68, 56. But he also describes unreflective wonder at learning and the arts, which is simple enough in itself and almost like the wonder of children, ibid., Book 1, Aph. 86, 71. Bacon also believes that the prior practices of induction also partook of the negative aspect of ch ildhood activity: For the in duction which proceeds by simple enumeration is a childish thing, its conclusions are precarious, and it is expo sed to the danger of the contrary instance; it normally 43

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If Bacon represents England and the empi rical tradition, Descartes represents the continental rationalist tradition. In his 1616 law thesis, Ren Des cartes portrayed the process of learning with images of the receptive infant, again embracing the metaphor of the nurtured child and the disciplined adult. [W]hen, a short time ago, with a peculiar felic ity I began learning, almost from the tender conclusion of a squalling young age until now, I a ttached my little lip s to the delicious well-springs of the liberal arts with the foster-mothers moist milky dew.96 This childlike metaphor is best understood in th e context of Descartes later philosophical project. In the course of his publications, De scartes would argue that many of the errors of adulthood were acquired in childhood, when the senses govern ones view of the world.97 As a double metaphor, his meditations by the fireside were an attempt to strip away accumulated falsehoods, an adult process requiring determinati on, self-discipline, and self-knowledge.98 Theoretically, this denuding of mind gave ri se to a childlike innocence with respect to knowledge. But emptiness was not Descartes goal Through disciplined reason, he attempted to build an entirely new philosophy based on the certainty of his cogito ergo sum Childlike simplicity brought clarity and distinctness thr ough the exercise of adult discipline. bases its judgment on fewer instances th an is appropriate, and merely on ava ilable instances, ibid., Book 1, Aph. 105, 83. 96 Ren Descartes, Descartes 1616 Law ThesisEnglish Translation, tr ans. Holly Johnson and Kurt Smith, http://plato.stanford.edu/entrie s/descartes-works/tenglish.html (accessed 12 September 2007). The image of Descartes being nourished in learning parallels the depictio n of nature as the many-breasted Diana of Ephesus. For a seventeenth-century example linked to natural philosophy, see Stukelys image of Diana holding a medal depicting Newtons head, Patricia Fara, Newton: The Making of Genius (New York, 2002), figure 2.5. 97 One of the paragraph headings (part 1, paragraph 71) of Descartes Principles of Philosophy is: That the principal cause of errors proceeds from the prejudices of our childhood, Ren Descartes, Principles of Philosophy trans. Valentine Rodger Miller and Reese P. Miller (Boston, 1983), 32. 98 I procrastinated for so long that I would henceforth be at fault, were I to waste the time that remains for carrying out the project by brooding over it. Accordingly, I have today suitably freed my mind of all cares, secured for myself a period of leisurely transquillity, and am withdrawi ng into solitude. At last I will apply myself earnestly and unreservedly to this general demolition of my opinions, Ren Descartes, Meditations on First Philosophy, in Discourse on Method and Meditations on First Philosophy trans. Donald A. Cress (Indianapolis, 1993), 59. 44

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Overview & Summary The present study is divided in to six chapters. In the following chapter, Chapter 2, I examine Pascals life emphasizing his earliest re lationships in the Parisian community of mathematicians. Pascals participation in the Me rsenne Circle represents a pivotal period in his live when he served his mathematical appr enticeship, which exte nded and enriched the education he received from his father. The purpos e of Chapter 2 is to link Pascals experience as the protg of the Mersenne gr oup to the attitudes of its centr al members on education and children. It uncovers the backgrounds in peda gogy shared by several key members of the acadmie toute mathmatique, including Mersenne and ties these educational concerns to a vision for the future of mathematical studies. As a rising New Archimedes, linked in this way to another key seventeenth-centu ry mathematician Christiaan Huygens, Pascal represented a bright, young hope for Mersenne. The vision for th e future of mathematics would be carried to completion by identifying and training undiscovered ta lent. This new but la tent talent would in turn be perfected through discipline and exercise. Chapter 3 relates Mersennes strategy for the de velopment of talent to Pascals early works in mathematics and natural philosophy. It demonstrates Mersennes in sistence on the importance of developing natural inclina tions through concerted effort, and it shows how Pascal uses language that parallels Mersennes ideas about talented musicians. This chapter focuses largely on Pascals early adulthood in Rouen, time spent outside the French capital. Using Pascals writings about his arithmetic machin e and the Preface of his proposed Treatise on the Void Chapter 3 analyzes Pascals attempt to enter the highest echelons of learne d society. He did so, the evidence suggests, by drawing contrasts between his own work and the productions of artisans, children, and beasts. Eschewing child ishness, Pascal distanced himself from his own childhood, actively seeking to assume his Archimedean position. 45

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Chapter 4 identifies a period of struggle when competing forces of Pascals past and present sought to control his lif e. In particular, this chapte r addresses the tension between Pascals growing religious inte rests and his earlier role as Mersennes Young Archimedes. Pascals struggle manifested itself in a growi ng rift between mature virtues, so prominently displayed in Pascals earlier work, and the lim itations of his scholarly pursuits, expressed by both his religious and worldly friends This critical period of str uggle ended in 1654 with Pascals Night of Fire conversion. Pascals new role as a devout savant is id entified and evaluated in Chapter 5. A key concern in developing Pascals role as devout savant is to draw para llels between childlike virtues and mature virtues from Pascals early life and relating them to his efforts on behalf of an Augustinian Christianity. Employing both the Provincial Letters and a lesser known work, which deals with baptism and catec hetical instruction, this chapter illustrates the duality of agerelated virtues in Pascals religious productions Importantly, while bot h works have religious themes, they also both address issues of pedagogy. Pascals involvement with Port-Royals petite coles offers additional evidence for his interest in issues of childlikeness and maturity. Finally, Chapter 6 addresses the relationship between Pascals life at Port-Royal and his scholarly life in Paris. The key concern of this chapter is to examine how Pascal applied virtues sharpened among his friends at Port -Royal to his scholarly life in Paris. Near the end of his career Pascal returned briefly to the mathematical pursuits of his youth, this time as an intellectual diversion. This fina l chapter shows how characteristi cs of the child and the adult converged in Pascals last mathem atical exercise, the contest of the roulette. The debate that unfolded illustrates the uneasy re lationship between Pascals success as a child prodigy and his failure as an adult scholar. Pascals final math ematical offering represents unresolved conflicts. 46

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47 In the end, his contribution and comportment were thought to conflict with core values of the Parisian learned community.

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CHAPTER 2 PASCAL IN THE TEMPLE: A NEW ARCH IMEDES AND HIS EARLY TRAINING Mersenne and His Circle The Essai pour les coniques launched Pascals mathematical career. Printed in the first months of 1640, it sketches on a single page Pascals proposal for an ambitious project.1 The planned work would build upon the three defini tions and three lemmas presented in the Essai in order to prove theorems universally true of a ll types of conic secti ons (circles, ellipses, parabolas, and hyperbolas). Pascals Essai boldly labels this future work as des lments coniques complets, a description captur ed in the Latin title of the work, Conicorum opus completum .2 Pascal never gave this complete work a finalized form, however, and no copies are known to exist. 3 Nevertheless, Pascals work on conics propelled him to a prominent position in Pariss elite circle of geometers, Marin Mersennes acadmie toute mathmatique. 1 Only two copies of this page have been found. One, consulted by Leibniz, remains in the fonds Leibniz at Hanover, Mathematik. XXXV; volume XV, I, Pascaliana. The other is at the Bibliothque Nationale, Paris, Dpartement des Imprims, Rserve, V 859-860, Part 1, Number IV. Information a bout the location of Pascalrelated manuscripts and printed works is Mesnard OC esp. 1:262-397. See Catalogue des ouvrages de Pascal conservs au Dpartement des Imprims ed. Marie Thrse Do ugnac (Paris, 1935). 2 Essai pour les coniques; The title Conicorum opus completum is stated in Pascals wr itten report to a group of mathematicians meeting at Paris, Celeberrimae matheseos academiae parisiensi. Pascal describes the treatise as encompassing the conics of Apollonius and innumerable others [from] a nearly unique proposition, completed at the age of 16, Mesnard OC :1034. In her biographical narrative, Pa scals sister refers to the work as the Trait des coniques Vie de Monsieur Pascal, Mesnard OC 1:576. 3 The information about the structure of the larger work comes from Leibniz. He obtained copies of Pascals manuscripts on the conics from Pascals family by 1676 What remains of the treatise are Leibnizs notes and a letter to tienne Prier, Pascals nephew, from Le ibniz. This collection of materials is in the fonds Leibniz in Hanover, Mathematik. XXXV; volume XV, I, Pascaliana folio 1ro (Conica Pascaliana); folios 4-9 (Generatio Conisectionum); folio 11ro (Ms. de M. Pascal. Coniques); folio 12ro (Hexagrammum Pascalianum, mysticum ut vocat). A copy of Priers letter is folio 3ro-vo, and although quoted at length is not printed in its entirety in Mesnards OC It is printed in Brunschvicg OC 2: 2, 220-224 and in Blaise Pascal, Oeuvres Compltes ed. Michel Le Guern (Paris, 1998-2000), 1:129. The manuscripts Leibniz reviewed were in fragmentary form and not yet put into a full treatise. However, they we re deemed by Leibniz assez entires et finis pour paratre la vue du public and en tat dtre imprim, Le Guern OC 1:129, 131. Leibniz arranges those he considers to be part of the originally planned treatise as follows, mostly with titles created himself: 1) Generatio conisectionum tangentium et secantium (Pascals title); 2) De hexagrammo mystico et conico ; 3) De quatuor tangentibus ; 4) De proportionibus segmentorum secantium et tangentium; 5) De tactionibus conicis Le Guern OC 1:129-130. 48

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For the Mersenne Circle, as it is often called, the Essai was a sign of the possibilities of a young and talented mind. Pascal needed encour agement, exercise, and discipline, and this educationally-minded group was in a unique positi on to shape Pascals career. For Mersenne, Pascal was an example of the undiscovered talent th at he sought to cultivate in order to fulfill a religious vision for the sciences. From his t eenage years, Pascal was given a catechetical instruction in geometry, with th e Parisian mathematicians as his godfathers. He was groomed with great expectation for the role that he would play in the perfection of knowledge through mathematics. Pascals early work in geometry provides a po int of contact with the individuals and vision of the Mersenne group. The beginning of his math ematical career reveals the way that this informal group embodied an alternative educational model by which a talented prospect could be cultivated. Mersennes stated goa ls include the completion or perfection of mathematics. One way this goal could be fulfilled was by nur turing young individuals (such as Pascal) who demonstrated mathematical promise. The edu cational atmosphere of Mersennes self-styled acadmie emerged out of the interests and expe riences of its members, many of whom were specifically involved with pedagogi cal concerns. These educational approaches informed the groups attitudes toward the development of th e young Pascal, who would always recognize this school as the locus of his mathematical appren ticeship. This chapter makes the case that the Mersenne acadmie was a school whose si ngular pupil was Pascal The educational backgrounds of the key members and their shared vision for the completion of mathematics (the unfolding of its divine, infinite potentialities on the mode l of ancient mathematics) are central to understanding Pascals views of mathema tics, education, and spiritual growth.4 4 The idea of the completion of mathematics expressed in Mersennes work is considered below, pp. 53-62. 49

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The Mersenne Circle: Its Organizer, Members, and Purpose Mersenne was a monk of the Minim order who li ved most of his adult life at a convent near the Place Royale in Paris. Besides being the secretary of Europe, one of his greatest accomplishments was regrouping and animating th e principle amateurs of science of the capital.5 His letter to Peiresc in May 1635 makes the defining announcement of the existence of the noblest academy in the world which was form ed a short time ago in this town. It is, Mersenne specifies, entirely mathematical.6 In a later letter, Mersenne lists the members of the group: tienne Pascal (Blaises father), Cl aude Mydorge, Claude Hardy, Gilles Personne de Roberval, Girard Desargues, the ab b of Chambon, and some others.7 As the organizer and host of the group, Mersenne was in a unique position to provide structure and purpose. His pedagogical experience, then, is particularly im portant for investigating this academy as the school from which Pascal received impetus for his mathematical career. On 25 December 1639, Descartes wrote a letter in response to a communication from Mersenne: I do not find it strange that th ere are some who demonstrate conic sections more easily than Apollonius, for he is extremely l ong and burdensome, and all that he has demonstrated is itself quite easy. But there are other things that could also be proposed, regarding conic sections, th at a child of 16 years woul d have difficulty untangling.8 5 Taton, Les origines de lacadmie royale franaise 13. 6 Mersenne to Peiresc (23 May 1635), Marin Mersenne, Correspondance du P. Marin Mersenne 17 vols., ed. Cornlis De Waard (Paris, 1945-1986), 5:209. 7 This list should not be considered as exhaustive, as we shall see. Armand Beaulieu adds Jacques Le Pailleur, Jean Beaugrand, Pierre Petit, Pierre de Carcavy, and Pierre Gassendi (to whom the information in the letter to Peiresc was to be relayed), Beaulieu, Mersenne: le grand minime (Brussels, 1995), 177. 8 Je ne trouve pas estrange quil y en aye qui demonstrent les coniques plus aysement quApollonius, car il est extremement long et embarrass, et tout ce quil a demons tr est de soy assez facile. Mais on peut bien proposer dautres choses, touchant les coniques, quun enfant de 16 ans auroit de la peyne demesler, Ren Descartes to Marin Mersenne, 25 December 1639, Mersenne, Correspondance 8:697. 50

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The letters timing and its content make clear that the subject is Pascals Essai pour les coniques Descartes comments attest indi rectly but clearly to Mersennes desire to promote the early efforts of this emerging geometrical talent. But Mersennes efforts were not used only on behalf of Pascal; they represent one expression among many of his intere st in undiscovered talent, a pedagogical concern that molded a nd benefited Pascal during his formative years. His evidently positive comparison of Pascal with the legendary Apo llonius of Perga, author of a brilliant thirdcentury BCE work on conic sections, suggests Me rsennes hope that Pascal and others would bring the work of the ancients to completion.9 For Mersenne, this perfection of mathematics was a religious goal and its pur suit was a sacred vocation. Mersennes Educational Goals and the Order of the Minims The Order of the Minims was founded in the fifteenth century. Unlike the Jesuits, the Minims were not dedicated to teaching but preaching.10 For Mersenne, however, preaching took an unconventional form. In his cl everly titled intellectual biography, Mersenne: le grand Minime Armand Beaulieu argues that Mersennes superiors rec ognized that his vocation consisted in the defense of the faith by pen and by conversation even more than through 9 Apolloniuss Conics was central in mathematics and the development of planetary astronomy. Keplers work on planetary movement, with its use of conic sections, is deeply indebted to Apollonius. A recent English translation of the first three books of the Conics is Apollonius, Apollonius of Perga: Conics, Books I-III ed. Dana Densmore, trans. R. Catesby Taliaferro (Santa Fe, NM, 1998). A key recent study of this work is Michael N. Fried and Sabetai Unguru, Apollonius of Pergas Conica : Text, Context, Subtext (Leiden, 2001). Only the first four books of the Conics were available in Europe until just prior to Pascals death. Books V-VII had survived only in Arabic translation, and were first translated into Latin in 1661 in Florence, G. J. Toomer, Apollonius of Perga, in Dictionary of Scientific Biography ed. Charles C. Gillespie, vol. 1 (New York, 1970), 180, 191-192. Apollonius, Apollonii Pergaei conicorum lib. V, VI, VII, paraphraste Abalphato Asphahanensi, nunc primum editi. Additus in calce Archimedis assumptorum liber. Ex codicibus arabicis mss trans. Abrahamus Ecchellensis, ed. Giovanni Alfonso Borelli (Florence, 1661), is available in several copi es at the Bibliothque Nationale in Paris. Book VIII of the Conics is not extant. 10 The standard English-language source on the Minim order is J. P. S. Whitmore, The Order of Minims in Seventeenth-Century France (The Hague, 1967). For general attitudes of the order toward intellectual pursuits, including educational endeavors, see Part III, Chapter I, Studies, 111-119. 51

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preaching.11 Robert Lenoble, Richard Popkin, and Peter Dear have each sought to identify Mersennes goals.12 All three agree that Mersenne sought to undermine arguments of the faithless or unfaithful, which threatened all forms of knowledge, includ ing revealed truth. Significantly, Beaulieus account of Mersennes life and work takes seriously his religious vocation and the demands and values of the Minims. And while the Minims were not a teaching order in the strict sense, J. P. S. Whitmore argues that a broader definition demonstrates the importance of such pur suits to the monks of the black cowl: If, however, the term education be taken in a wider sense than the mere giving of instruction in classes, the Order plays not an insignificant role in the education of the seventeenth century. A few of their members played an important part in the diffusion of new ideas and in the teaching of specific skills such as book illustration, turning, the construction of sun-dials and othe r bits of scientific apparatus.13 Mersennes duties as a Minim introduced him to teaching young men. From 1615-1617, Mersenne taught philosophy at Ne vers to those destined to be monks, and in 1618, he taught theology for another year. 14 It was during his sojourn at Nevers that Mersennes future biographer, Hilarion de Coste, became his pupil. This first recorded teaching experience 11 Beaulieu, Mersenne, 22. 12 Lenoble argues that Mersenne embraced mechanism in an attempt to save the reaction against scholasticism from the libertine, unbelieving snare of Rena issance Naturalism, Robert Lenoble, Mersenne ou la naissance du mcanisme (Paris, 1943), 5ff. P opkin labels Mersenne a mitigated skep tic, accepting the basic caution of the skeptics while seeking to establish convincing or pr obable truths about app earances, Richard Popkin, The History of Scepticism: From Savonarola to Bayle (New York, 2003), 112. Dear expressed Mersennes goal as the desire to establish knowledge of nature as a cumulative acquisition e xperimentally or observationally ratified facts made into demonstrative science through the techniques of mathem atics, and this in order to prevent the success of unorthodox religions and attack s on the social order, Dear, Mersenne and the Learning of the Schools (Ithaca, NY, 1988), 3, 237-238. 13 Whitmore, Order of Minims 117. Furthermore, Whitmore emphasizes a general trajectory from polemic to instruction in the writing of the Minims of the seventeenth century. The precise meaning behind this differentiation of approach is left unclear, but the key aspe ct is the move toward a reconciliation of science with the tenets of faith. The teaching of sk ills is closely linked to the question of the relationship between science and art/technique in Chapter 3 of this dissertation. I am unsure as to the role of the Minim monks mentioned in dispersing knowledge about turning, sun-dials, and scientif ic apparatus, but it seems that if taught to novices, this could be considered a particular aspect of their spiritual training and education. 14 Mersenne, Correspondance 1:xxv. 52

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provides a backdrop to Mersennes interest in the training an d instruction of the young, which was clearly recognized by the editors of Mers ennes correspondence. Beaulieu, one of the collaborators in that project, summarizes: There is an aspect of Merse nnes activity about which little has been said, [and] that is his interest in youth.15 Beaulieus research highlight s Mersennes propensity for identifying and encouraging young provincial talent. It is, he ar gues, an expression of his ident ity and of the responsibilities of his religious vocation. In this pedagogical task, Mersenne, un moine passionn de musique, de sciences, et damiti, reconciled his penchant for intellectual studies with the ambivalent view of profane work held by his order.16 He believed that a completed knowledge of the sciences was a task of devotion and that undisco vered talent would help accumulate it. Central to Mersennes vision was mathematics. A key to its accomplishment was young talent. The Beatific Completion of Ma thematics: Mersennes Vision Mathematics as Epistemological Foundation Peter Dear, in his Mersenne and the Learning of the Schools describes what he calls Mersennes mathematical agenda for natural philosophy.17 At its core, it was an alternative mathematical natural philosophy to replace essentialist physics.18 A critical part of scholastic education during the early modern period was th e certainty and utility of mathematics. According to Dear, Mersennes educational experience at La Flche, and these views of mathematics in particular, shaped the traject ory of his career. For Mersenne, mathematics 15 Il est un aspect de lactivit de Mersenne dont on a a ssez peu parl, cest celui de son intrt pour la jeunesse, Mersenne, Correspondance 15:35. 16 The quotation is from the title of an article, Armand Beaulieu, Un moine passionn de musique, de sciences et damiti: Marin Mersenne, XVIIe sicle 41 (1989): 167-193. 17 Peter Dear, Mersenne and the Learning of the Schools (Ithaca, NY, 1988), 47. 18 Dear, Mersenne, 72. 53

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(including arithmetic, geometry, music, and astron omy) was paradigmatic, the most useful for grounding other types of knowledge. In Mersennes La vrit des sciences contre les sceptiques ou Pyrrhoniens (1625), mathematics plays the central role in overcomi ng the arguments of the skeptics, who deny the possibility of certain knowledge. He calls mathem atics the sciences very -certain and very-true in which suspension [of judgment ] does not at all find a place.19 For most of this dialogic work, the Christian Philosopher (the voice of Mersen ne) answers the questions and challenge of the Skeptic about the foundati onal status of mathematics.20 Mathematics, Mersenne argues, is necessary to understand philosophy, medicine, al chemy, cabalism, politics and jurisprudence, and mechanics.21 One may not neglect the study of this discipline, the Christian Philosopher claims, without risking exclusion from the genui ne community of the learned, just as Plato refused entry to his academy to those ignorant in geometry.22 The importance of geometry was not only classical but Christian. Knowledge of mathematics is the characteristic trait of the only voice in the book labeled Christian. Mathematics, especially geometry, provides uniq ue access to the divine: as an analogy for God and as a mirroring of Gods thoughts. Mathematic s is an aid to religious maturity. The mid1630s organization by Mersenne of the so-ca lled acadmie toute mathmatique is the manifestation of a belief in both the suprem acy and orthodoxy of mathematical knowledge. 19 Marin Mersenne, La vrit des sciences contre les septiques (Paris, 1625). 20 Mersenne considers such diverse areas as the ratio of th e elements in the world and the analogy between different types of ratios and different political systems. 21 Mersenne, La vrit des sciences 235-247. 22 Let us now see its necessity [i.e., mathematics], and its utility, which are so great that Plato would not admit anyone to his Academy [Acadmie] who was not a Geometer ;this is why he sent away someone who would be his disciple, for you do not have the handles [ anses ] (that is, the knowledge of Mathematics, which is necessary to understand Philosophy) they lead the understanding to the truth, soften it, tame it, excite it, lead it, raise it, and transport it to the contemplatio n of abstract, intellectual, and divine things, ibid., 233. 54

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Mathematics as Divine Science God and mathematical objects Although Mersenne emphasized the importance of mathematics as a foundation for human knowledge, he also directly links God and mathematics, stressing connections between God and mathematical objects. In La vrit des sciences for example, Mersenne develops an analogy between God and unity. Both, he st ates, are able to generate an infinite number of elements from their ultimate simplicity. Mersennes analogy is linked to a theological issue of a particularly enduring quality. A strict, or thodox monotheism must emphasize Gods unity. Ontologically, he is without parts and cannot be separated. Yet God is also considered the source of the plenitude of creation. The problem of the Many arising fr om a simple, complete one created perennial theological difficulties, not least of which what Arthur O. Lovejoy has called two antithetic kinds of being.: a complete God absolutely in dependent of creation an d the God that has a need of the world as the emanation of his goodness.23 Neoplatonic notions of the world as an emanation of God were translated with difficulty into an account that made sense within the Genesis account of creation ex nihilo Through the mathematical analogy, Mersenne gives an example of how a simple entity is capable of engendering a creative mu ltiplicity, an approach that mirrors Nicolas of Cusas appr oach toward the One-Many problem.24 And since mathematics is separate from material reality, it represents the intelle ctual productivity of God 23 Arthur O. Lovejoy, The Great Chain of Being: A Study of the History of an Idea (New York, 1936), 315. 24 John H. Gay, Four Medi eval Views of Creation, The Harvard Theological Review 56 (1963), 265-270. In his article, Gay compares the views of Augustine, Pseudo-Dionysius, Thomas Aquinas, and Nicolas of Cusa on the unity-multiplicity question. 55

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and maintains the freedom of the Creator to actualize only the intellectual manifestations that he chooses.25 Mersenne claims that the correspondence betw een God and unity, representing as it does both parsimony and plenitude, is a fitting way to approach the perenn ial difficulty of the Christian doctrine of the Trinity.26 Another similar mathematical -theological correspondence is between the circle and God. Like the circle, God is always uniform and has neither end nor beginning, for he is eternal.27 These most basic mathematical objects of arithmetic and geometry demonstrate the proximity Mersenne pe rceives between mathematical properties and the transcendent truths of Christianity and s uggest that the creative work of enunciating the principles of mathematics is an act in imitation of the Creator. God the transcendent geometer The infinite generativity of unity and the ci rcle are evidence that Mersenne uses to demonstrate the transcendence of mathematic s. Transcendence is not limited to what mathematics and the divine create. Mathematic al objects also transcend human understanding, 25 Cusa also uses mathematical analogy in order to escape the problem of material multiplicity. Cusa highlights the importance of the unity of the straight line, triangle, circle, and sphere when considered to the point of infinity: The learned ignorance uses the analogy of mathematics, wh ich, already free from materiality, leads to the perfections of infinity. For instance, the straight line, triangle, circle and sphere, when allowed to expand without limit, are one at infinity, ibid., 266. 26 [I]t is very right to compare unity to God, in as much as unity eminently contains all the perfections which are in numbers, as God contains all the perfections of the creatures and nonetheless unity is simple and unique, as God is very simple and very unique in his essence, notwithstanding that he is three in persons, Mersenne, La vrit des sciences, 669. 27 Dieu est tousiours vniforme & na ni fin ni comme ncement, car il est ternel, ibid., 762. Cusa describes the Trinity in terms of geometrical analogy, again leading back to ultimate simplicity. He gives a specific explanation for Gods threeness, as Gay explains: There mu st be three and only three persons in the Trinity, since the triangle is the plane figure with the minimum number of sides, and is the simplest plane figure which coincides with the unity of the straight line at infinity. Moreover, th e Unity in Trinity contains all things because the circle is the polygon with an infinite number of sides, and becomes a straight line when its radius becomes infinite, Gay, Four Medieval Views of Creation, 267. 56

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setting the stage for belief in a God who is beyond sense experience and human imagination. The figure of the circle serves as an example em phasizing the eternity of God and his simplicity. The goal is in part apologetic, as it suggest s the necessity of a divine mind superior and incomprehensible to the human mind.28 The clearest demonstrati on of the transcendence of mathematics is the failure of the many attempts to find the exact proportion between the diameter and circumference of the circle a nd, therefore, the square that equa ls the area of the circle. This human inability to discover the quadrature of the circle, despite the pursuit of so many great minds, serves to point to someone more savant than all men. This sort of potential mathematical knowledge, which exceeds the power of human beings, proves the existence of a power or active understanding which could know them.29 Knowledge of the quadrature of a circle, Mersenne claims, is found in this powerful active understanding (i.e., God, the Divine Ge ometer). During the seventeenth century, a quotation from the Book of Wisdom often served to reinforce Gods geometrical tendencies: God made all things in numb er, weight, and measure. The language of Gods two books (the book of revelation and the book of nature) ex tends this same theme. The book of nature, Galileo claimed, is written in the language of mathematics.30 The two books of God, read side 28 Cf., Pascals statement in the Penses, Brunschvicg, no. 267: La dernire dmarche de la raison est de reconnatre quil y a une infinit de ch oses qui la surpassent, Brunschvicg OC 13:196. 29 [I]l faut necessairement quil y ayt quelquvn plus savant que tous les hommes, qui la cognoisse, car pourquoi ces difficultez auroient elles vne puissance passiue pour estre cognus, sil n[] y auoit aucune puissance, ny aucun entendement actif qui les peut cognoistre? Mersenne, La vrit des sciences 764. 30 Philosophy is written in this grand bookI mean the universewhich stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth, Galileo Galilei, The Assayer (Rome, 1623), in The Controversy on the Comets of 1618 trans. Stillman Drake (Philadelphia, 1960), 183-184. 57

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by side, could yield a fuller picture of Gods creation.31 Exploring this composite picture and perceiving Gods role as Geometer could, as Johannes Kepler beli eved, reveal the deep wisdom of the Creator. For Kepler and others, the cosmos must be seen as designed according to a rational, mathematical plan. Ke pler was convinced that the five regular geometrical solids were essential for understanding planetary movements. No unschooled artisan could construct such a system, for it required a mathematical design. Like the Demiurge in Platos Timaeus Keplers God created the world according to mathematical patterns. But Plato saw the Demiurge as a divine artisan following a preexisting pattern in an ideal world of forms and limited because of the recalcitrance of that matter. For Kepler, th e Creator is also the Di vine Geometer, out of whose mind come geometrical principles. Gods geometrical design trumps the limitations of matter. Geometry was indispensible for the im itation of God in genuine ly creative endeavors.32 Mathematics as Imitation of God Apprenticeship to a divine artisan Just two years prior to his writing of La vrit des sciences Mersenne wrote Lusage de la raison. Here he argues that human beings are capable of imitating Gods essence by imitating his actions, a theme that he would deve lop specifically for mathematics in La verit des sciences The goal of the soul is perfec tion, and it is attained by becoming an apprentice to the Divine Master: I do not want to stop myself at the essence of these faculties, let us pass to their operations, which seem to represent more from life [realisti cally as in a painti ng] the eternal secrets 31 Kenneth J. Howell describes Mersennes view of the two books with respect to the Minims Quaestiones celeberrimae in Genesim : Genesis gave truth about nature, but only science can detail the structure of nature through empirical inquiry, Gods Two Books: Copernican Cosmology and Biblical Interpretation in Early Modern Science (Notre Dame, IN, 2001), 37. Howells work focuses on how theologians during the early modern period handled scripture when dealing with the question of planetary theories, such as those of Nicholas Copernicus and Tycho Brahe. 32 Arthur Koestler provides a brief, documented description of Keplers Pythagorean impulses in Arthur Koestler, The Watershed: A Biography of Johannes Kepler (New York, 1960), 59-65. 58

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of divinity; for I perceive nothing in this infi nite essence, that our soul cannot imitate, and know nothing through which it can perfect itself further, than through this imitation, since its perfection consists in rendering itself si milar to this immense archetype, as the perfection of an apprentice consists in imitating the canvas, the example, the edifice, or the painting of his master, until he makes his work similar to the prototype, which has been proposed to him.33 Mersenne depicts God as Master Artisan, whose masterpiece (the universe) is on display to human beings. The human being approximates Gods perfection by reasoning and working in ways that mirror the operation of Gods own faculties. For Mersenne, as we have seen, the si mplicity, complexity, fruitfulness, and incomprehensibility of mathematics help reveal God to humans. But applying oneself to the problems, solutions, and uses of mathematics al so moves the mind to a self-transcendence that approximates the divine nature: For there is no Science, after Theology, which proposes to us, and makes us to see, so many marvels as Mathematics does, which elevates the mind above itself, and forces us to recognize a divinity; for Statics, Hydraulics, and Pneumatics produce such prodigious effects, that it seems that men can im itate the most admirable works of God.34 Through the imitation of the Master Geometer, individuals who exerci se their capacity for mathematics come closer to the perfection of God. 33 Je ne veux pas marrester lessence de ces facultez, passons leurs operations lesquelles semblent representer plus au vif les secrets eternels de la divinit; car je napperoy rien dedans ceste infinie essence, que nostre ame ne puisse imiter, et ne say rien par quoy elle se puisse perfectionner davantage, que par ceste imitation, puis que sa perfection consiste se rendre semblable cet immense ar chetype, comme la perfection dun apprentif consiste imiter le tableau, lexemple, ledifice, ou la peinture de son maistre, jusq ues ce quil face son ouvrage semblable au prototype, qui luy a est propos, Lusage de la raison 79-80. 34 Car il ny a point de sciences, apres la Theologie, qui nous proposent, & nous fassent voir tant de merueilles comme font les Mathematiques, lesquelles leuent lesprit pa r dessus soy-mesme, & le forcent de reconnoistre vne diuinit; car la Statique, lHydraulique, & la Pneumatique produisent des effets si prodigieux, quil semble que les homes puissent imiter les oeuures les plus admirables de Dieu, Mersenne, preface to La vrit des sciences n.p. [6]. 59

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Actualizing the infinite potentialities of mathematics Linguistically, perfection and completion are closely related.35 For Mersenne, as for most early modern Europeans, perfection was th e potentiality that has become actuality. The mathematician who uncovers a multiplicity of pr opositions and applications is actualizing the infinite potentialities of ma thematics in the human realm. The accumulation of these mathematical accomplishments progressively approximates the perfection of Gods own geometrical reasoning. As med iator and intelligencer wi thin the seventeenth-century learned community, Mersenne encouraged the colle ctive attainment of th is perfect knowledge. Mersennes great contribution to the science of his generation, according to contemporaries and historians, was his ability to pos e questions and to promote research of theory, instrumentation, and application. In so doing, he also promoted th e religious task of assi sting the Master in the technical education of humanit y. His collection and dissemination of the work of scholars, including those formerly unknown, created a cas cading effect of multiplied results, moving progressively toward a perfected mathematics. Approximating the heavenly state For Mersenne, there is a clearly religious sign ificance in the pursuit of the mathematical sciences. In seeking this perf ection, one draws closer to the st ate of beatitude. This is the religious grounding for encouraging others.36 He suggests this motivation in La vrit des sciences in a discussion of a nu mber theory problem: 35 Oliva Blanchette provides an analysis of perfectum as it relates to the work of Thomas Aquinas and his views on the perfection of the universe. At its heart, perfection is the end-point of a process of becoming: It is not becoming alone that gives us the idea of per-fection, but a becoming that has reached a certain completion, where nothing of the process remains to be done, Blanchette, The Perfection of the Universe According to Aquinas: A Teleological Cosmology (University Park, PA, 1992), 42. For a detailed analysis of the term, especially as it relates to the work of Aquinas, see Blanchettes Chapter 1, The Original Meaning of Perfection, ibid., 41-73. 36 Robert Lenoble writes: surtout la science nest-e lle pas lannonce et comme les prmisses de la batitude? Mersenne ou la naissance du mcanisme (Paris, 1943), 75. 60

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I would strongly desire that some excellent Mathematicians would study to find some method by which one could find the root of each number, only se eing the number of characters, in order that as one knows by th e number of points s ubscribed how many characters the root ought to have I belie ve that this understanding, and this method is not impossible, and that it is contained in the perfection of the science, just as the quadrature of the circle, and the Geometric invention of two mean proportional lines are contained in the science of Geometry: conse quently, the Angels know all these difficulties perfectly, and we will likewise know them when it pleases God to take us to the ranks of the blessed.37 For Mersenne, even the pursuit of seemi ngly esoteric mathematical knowledge is important in itself. In an ever-increasing comprehensiveness, this work approximates the ultimate heavenly state of the blessed. The approximation and multiplication imitates the handiwork of the Divine Artisan.38 Mersennes proposal for the spiritual task of geometry was put into practice by members of his mathematical academy.39 37 Or ie desirerois fort que quelques excellens Mathema ticiens sestudiassent treuuer quelque methode, par laquelle on pet treuuer la racine de chaque nombre la seule ve du nombre des characteres, afin que comme on sait par le nombre des points souscrits combien la racine doit auoir de caracteres . Ie croy que cette cognoissancce, & cette method nest pas impossible, & quelle est contenu dans la perfectio[n] de la scie[n]ce, aussi bien que la quadrature du cercle, & linuentio[n] Geometrique de deux ligne moye[n]nes proportionelles est contenu dans la science de la Geometrie; par consequent les Anges sauent parfaictement toutes ces difficultez, lesquelles nous cognoistrons pareillement lors quil plaira Dieu nous mettre au rang des bien-heureux, Mersenne, La vrit des sciences 666-667. Also regarding the state of beatitude engendered by geometry, Mersenne writes: You tell me perhaps that sciences do not treat infinite things: but I respond to you that the Geometer does not make a habit of discoursing on the imperfect infinity of these part s, or of these points of quantity, he contents himself with the magnitude that is finite, nonetheless restricting himself only by eternity itself, to which he cannot attend; this is why, if he is wise, he will in this way treat gently his ope rations, and all his labor, that he will connect all to this eternity, in order that after having pourmen his mind among the finite country of its propositions, and of its problems, and having served God in his art of making lines, he enters into this new world, which has no restrictions but eternity, in which there is more contentment in a moment, than he could have here of it in an infinity of years, ibid., 729-730. 38 Later in his life, Mersenne would publish a series of three works that are an expression of this attempt to give an all-encompassing picture of areas of investigation in physics and geometry and to uncover Gods vast canvas of natural philosophy. A series of three works gives a summary of all the fields for which Mersenne advocates further study, Marin Mersenne, Cogitata Physico Mathematica (Paris, 1644); idem, Universae geometriae mixtaeque mathematicae synopsis (Paris, 1644); idem, Novarum Observationvm physico-mathematicarvm, tomus III (Paris, 1647). 39 An example is the work of Claude Mydorge, one of the original members of Mersennes mathematical academy. Mydorges Trait de gomtrie is a manual of geometrical constructions. The author demonstrates how the geometer may, with compass and straightedge, construct progressively more complex figures. Among over one thousand figures for which Mydorge gives instructions ar e a tetradecagon (a fourteen-sided figure) and an egg shape, which Mydorge labels orbe difforme. The comple xity of these instructions demonstrates how necessary it was that geometers be a talented manual worker with a compass, Bibliothque Nationale, Paris, fonds franais 656. 61

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The motivation for moving towards Gods perfec tion in mathematics is important because it brings together the technical pursuit of mathematics (the solving of individual problems and types of problems) and the broader pursuits of the Christian Philosopher, who seeks above all the establishment of the faith through knowledge and behavior. Mersenne believed deeply in the virtue of seeking comprehensiveness that appr oximates Gods completion. Pascals years of apprenticeship with the Mersenne Circle taugh t him about the unbreakable link between virtue and the proper practice of the savant.40 For Mersenne, the mathematician who seeks the state of beatitude (that comes with the discovery of all th e results of a particular proposition) is engaging in the same virtuous work as the penitent enga ged in true repentance. By claiming that the exercise of mathematics led to beatitude, Mersen ne could answer questions about the importance of technical mathematics to spirituality. As Pas cals life shows, however, later experiences led him to a significant parting of ways with Mersen ne on this matter. Subsequent to Mersennes death, as this study will show, Pascal reevaluated this rela tionship and ultimately labeled mathematics as only a mtier.41 Finding Talent in Unexpected Places Recruiting the Best Minds to Pe rfect Mathematical Disciplines Mersenne expresses his desire for the comple tion of mathematics by articulating his hope that potential talents not yet involved in the proj ect would come forward. Th is is evident from an expression of Mersennes hopes for music, one of the Pythagorean quadrivium of mathematics. In the dedication of the treatise Des orgues in his Harmonie universelle, Mersenne exhorts tienne Pascal, Blaises father, to use his skill in music to give it a so lid learned foundation. He 40 The relationship between virtue and scholarship during the early modern period has been pursued, among other studies, in Peter N. Miller, Peirescs Europe (New Haven, CT, 2000). See note 27 in this chapter for further consideration of virtue and spirituality in connection with mathematics. 41 See below, pp. 327-333. 62

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urges tienne to put the final touches [ mettre la dernire main] to music as an expression of his hopes for its perfection: I hope that the rare experiments [Fr. expriences ] that you meet in this book will convince you to seek the reasons for them, for they mer it the study of the best minds, in addition to which you possess to such a high degree all th e hidden resources of the most subtle analysis This is why I dare to promise to all those who cherish the Muses that you will soon put the final touches to this part of philosophy, so that it might no longer fear to appear before the most learned [Fr. plus savants ] in the company of the other sciences It longs to be a participant in the certitude of geometry and arithmetic, if possible, so that its principles might not be able to be contested by Pyrrhonians and doubters.42 Mersenne believed music deserved to be perfected like the other branches of mathematics. Music was important because it imitated divine works in several ways. Perhaps most obviously, Mersenne saw musics unmatched potential for influenc ing human affections and behavior. This capability of music to have profound, even spiritual effects on human beings particularly animates Mersennes Harmonie universelle. It is an expression of a Pythagorean tradition that stretches unbroken from antiquity.43 The Pythagorean tradition stressed the powerful psychological influence of music, with le gends of Pythagoras and others illustrating the ancients mastery of musical manipulation.44 Pythagorass heirs, in cluding Ficino, continued to highlight these effects, musics abilit y to move people toward the divine.45 42 Jespre que les rare expriences que vous rencontrez da ns ce livre vous convieront en rechercher les raisons, car elles mritent ltude des meilleurs esprits, joint que vous possdez un si haut point tous les ressorts de la plus subtile analyse . Cest pourquoi jose promettre tous ceux qui chrissent les Muses que vous mettrez bientt la dernire main cette partie de la philosophie, afin que lle ne craigne plus dsormais de paratre devant les plus savants dans la compagnie des autres sciences . Elle dsirerait dtre participante de la certitude de la gomtrie et de larithmtique, sil tait possible, afin que ses principes ne lui puissent tre contests par les pyrrhoniens et les doutants Mersenne, Harmonie universelle Trait des instruments chordes, Dedicatory letter for the Trait des orgues, excerpted in Mesnard, OC, 2:121. 43 The tradition includes Augustine, who, Brian Brennan ar gues, saw music as the pattern for a well ordered life, Augustines De musica, Vigilae Christianae 42 (1988), 270. 44 Yates, French Academies 38. One of Mersennes correspondents, Jean-Baptiste Doni, wrote to Mersenne, arguing that the abilities of the ancients in this regard was so great that the moderns can never hope to achieve it, Jean-Baptiste Doni to Marin Mersenne, 27 February 1636, Mersenne, Correspondance 6:30. 45 Yates, French Academies 40. 63

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Mersenne had also been inspired by the sixt eenth-century musical academy of Baf. He sought what he believed to be a divine goal of using music to bind together mathematical knowledge of the world.46 The Pythagorean tradition stressed the harmony embodied in music as guiding the design of the cosmos, thus mirroring its structure and providing a portal to divine knowledge. It was therefore a fitting instrume nt for the communication of all types of knowledge. If there appeared a perfect musician, Mersenne argued, that individual could invent dictions, and a perfect language which naturally signifies things.47 Music was universally constitutive of natural tr uth because of its relationship to God as divine designer, who works according to harmonies and ratios. Mersennes Harmonie universelle quotes the passage from the Book of Wisdom to argue that music, like the rest of mathematics, is capable of comprehendi ng all knowledge of the physical world: It is again quite easy to c onclude that one can represent all that is in the world, & consequently all the sciences by means of Sounds, for since all things consist in weight, in number, & in measure, & [since] Sounds represent these three propertie s, they can signify all that one could wish.48 Nature, written in the language of mathema tics, may be communicated through music, and this dissemination of knowledge was linked to the sp iritual importance of the effects of music. It 46 Yatess description of Mersennes in tellectual pursuits highlights the importance of Baf to the Minim. Yatess Mersenne was primarily motivated by the desire to establish a Bafian academy of music to unify knowledge, but these hopes were disappointed. While Yates mentions Me rsennes large informal academy of acquaintances, her examination of Mersenne ends with the year 1635 and the founding of the Acadmie Franaise She does not acknowledge (perhaps for lack of the later volumes of Mersennes Correspondance ) the acadmie toute mathmatique, announced in 1635 and that seems to have been a smaller, more organized cadre of individuals, Yates, French Academies, 284-290. 47 Marin Mersenne, Harmonie vniverselle contenant la theorie et la pratiqve de la mvsiqve (Paris, 1636), Book 1, De la nature & de proprietez du Son, 43. 48 Il est encore bien ays de conclure que lon peut repr esenter tout ce qui est au monde, & consequemment toutes les sciences par le moyen des Sons, car puis que toutes choses consistent en poids, en nombre & en mesure, & que les Sons representent ces trois proprietez, ils peuuent signifier tout ce que lon voudra Mersenne, Harmonie universelle Book 1, De la nature & de proprietez du Son, 43. Yates sees this idea of Mersennes as a clear link between Mersenne and the academies of the sixteenth centu ry, which envisioned music as the image of the whole encyclopaedia, Yates, French Academies 87, 285. 64

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is not only intellectual knowledge that is communicated in this way. Human beings are musical creatures because they are sp iritually linked to the unified cosmos.49 The effects of music were spiritual, not just ps ychological. Human beings could resonate with music as a part of the created order, experiencing moral amelio ration and even oneness with God. They could reach a state of blessedness. Mersennes wri tings are replete with references to possible devotional uses of music.50 Mersenne pled for tienne Pascal to make us e of his particular ap titude for the study of music, therefore, based on an appeal to the religious ends of the culmin ation of mathematical knowledge. Mersenne clearly stated his hopes for a nd the expectations that he had of the elder Pascal, whom he considered one of the best minds [ meilleurs esprits ]. He represented tienne Pascal as the advocate for an important cause. In his dedication to the elder Pascal, Merse nne presented the image of music as one among a number of conferees in the company of the sciences, and this designation underscores Mersennes goal to bring every area of mathematics to a state of fulfillment. By working for the completion of all of the subdiscip lines of mathematics, the certai nty of the entire domain would be actualized. Throughout his li fe, Mersenne expressed the hope that music would become a 49 There is here the continuation of the macrocosm/microc osm idea that is articulated at length in medieval and Renaissance literature about position of humanity within God s creation. Ernst Cassirer sees Nicolas of Cusa as an important point of departure, being followed in turn by Marsilio Ficino, Pomponazzi, and others, The Individual and the Cosmos in Renaissance Philosophy (New York, 1963), 40, 64, 109ff. 50 For example, Mersenne writes in a dedicatory letter in his Harmonie universelle : That it fills with joy those who are already carried to rejoicing, comforts those who are in sadness and, what is further, it explains through a marvelously efficacious eloquence the myster ies of Religion in singing the praise s of God, which is the sole means that we have been able to invent in order to express the recognitio n of the benefits that we receive from his liberal hand and the only thanks that we can say to him for it, Mersenne to Coutel (September 1627), Dedicatory letter to Mersenne, Harmonie universelle Book 2, in Mersenne, Correspondance 1:577. 65

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certain field of knowledge.51 He appealed to tienne Pascal as one whose talent had not yet been put to full use. Recovering Ancient Analysis: Se arching for New Archimedeses Mersennes description of wha t is necessary in order to be an excellent Geometer, in Book IV of La vrit des sciences provides further evidence for hi s approach to perfecting all of mathematics. As with music, the baseline is the ancients. Mersenne states that being an excellent Geometer begins with knowledge of a large number of ancient mathematical works. The final aim, he states, is to comprehend al l of the works (31 books total, including ones by Euclid, Apollonius, Aristae, and Eratosthen es) and combine them into a summary and reconstitution of the so-c alled Analyse des anciens. The di scovery of this analytical method, or the means by which the ancients discovered results, would complete what was available through the synthetic presentation of those ideas in their works. With such knowledge would come the ability to solve all sorts of problems in what pertains to corporeal & visible things, & to their properties.52 The process begins with ones unders tanding all of the component parts of ancient geometrical knowledge. Then, one must attempt to simplify and perfect them through the discovery of general methods and theorems, which may then be used to solve a multitude of problems. A recovery of this ancient method of anal ysis was pursued, among others, by Franois Vite, that pioneer in algebrai c notation, and his disciple, Alexander Anderson. Both of them died, Mersenne says, before bringing the project to fruition. The langua ge Mersenne uses to describe these two individuals suggests their pos ition as modern-day prophets in the divine 51 Numerous letters within Mersennes correspondence a ttest to Mersennes status as Un moine passionn de musique, Beaulieu, Un moine passionn. 52 en ce qui appartient aus ch oses corporelles, & visibles, & leur proprietez, Mersenne, La vrit des sciences 749. 66

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cause of the perfection of mathematics. Much like biblical prophets, however, their work was rejected. By way of response, God removed these sources of revelation: [T]hese torches having been extinguished at ne arly the same moment that they had begun to explode through the universe, as if the ni ght of our ignorance, or the ingratitude & misunderstanding of men had been unworthy of being enlightened by such excellent lights.53 The loss of these great men was due to the gene ral unresponsiveness of th eir time; nevertheless, it left the learned [ savant s] in regret, the faithful remnant in the cause of completing the ancients.54 Mersenne, a representative of this little mathematical band, invokes a divinely ordained nativity of successors to the cause: May it please God to cause to be born again in this century some new Archimedeses, who [will] lead Mathematics to th eir last perfection, & who [will] impose an eternal silence on the many ignorant [people] who want to pe rsuade the world through their sophisms, & paralogisms, that they have found the quadrature of the circle, the duplication of the cube, the trisection of the angle and have recognized several errors in the definitions & propositions of Euclid, even though most of th ese reckless [ones] not know either the very first terms of Geometry, or the [proper] way of speaking about it.55 Mersenne is thus alert for ta lent that might contribute to th e perfection of mathematics and thereby provide a strong weapon ag ainst the skeptics. When th is talent is discovered, as Mersenne later makes clear, it must be employez and caressez through patronage. 53ces flambeaux ayant est quasi aussi to st esteints, quils ont commenc clatter par lvniuers, comme si la nuict de nos ignorances, ou lingratitude, & mescognoissance des hommes eust est indigne destre esclaire par de si excellentes lumieres, ibid., 750. 54 [I]ls ont laiss vn regret aus sauans, & une perte forte signale a toute lEurope, ibid. 55 Plaise Dieu de nous faire renaistre en ce si ecle quelques nouueaux Archimedes, qui conduisent les Mathematiques iusques leur derniere perfection, & qui imposent vn silence ternel quantit dignorans qui veulent persuader par leurs sophismes, & paralogismes, quils ont treuu la quadrature du cercle, la duplication du cube, la trisection de langle & reconu plusieurs erreurs dans les definitions, & propositions dEuclide, bien que la pluspart de ces temeraires ne scachent pas seulement les premiers termes de la Geometrie, ni la maniere den parler, ibid., 750. 67

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Throughout his life, Mersenne le nt intellectual support to tale nted individuals through his letters and writings. In his acadmie, he solidified a group of i ndividuals that could be recognized as authoritative by those with political power and influence.56 Moreover, the group could be an instrument through which his proj ect of expanding upon the methods and work of ancient Greek mathematicians could be propagated. The project would unite learned mathematicians in common cause. But it woul d exclude those who ignorantly and rashly claimed superiority over Euclid and other ancients.57 By including a young man such as Pascal, Mersennes academy prepared for the future elaboration of its mathematical goals. Mersennes desire to find new Archimedeses indicates not merely those whom he already considers to be fine mathematicians, but also those, such as Pascal, who were not yet known.58 His attitudes toward those lo cated in the provinces and his involvement with young people highlight the import ance he accords to harvesting undiscovered talent. Promoting Provincial Talent Mersenne was well-acquainted with a numbe r of individuals throughout France and his epistolary exchanges reveal the value he assign ed provincial savants. Some of his learned correspondents were renowned scholars: Gassen di, Fermat, Peiresc, and Florimond de Beaune (at Blois). But he also exchanged ideas and encouraged the work of a host of less well-known 56 This recognition was already begun by the time of Mersennes announcement to Peiresc, for it was among these individuals that were chosen the mathematical experts for the official judgment of Morins method of obtaining longitudes. 57 Mersenne follows the precedi ng passage with a direct stat ement of exclusion: Cest pourquoy ie scay fort bon gr aux excellents Geometres de ne vouloir pas conferer au ec eux, ni mesme les couter, de peur que par ceste condescendence on croye quils approuent lignorance de ces temeraires, Mersenne, La verit des sciences 750. 58 Mersenne writes of the current crop of mathematicia ns: Nous auons maintenant quantit de personnes qui pourroient faire quelque chose de bon touchant la resolution, & la composition, mais il ny a personne, qui les employe, & qui leur fournisse ce qui est necessaire pour venir bout dvn tel oeuvre, Mersenne, La vrit des sciences, 751. 68

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individuals, among them Christophe Villiers at Sens (particularly interest ed in music) and L. Meyssonier at Lyon (medicine). Mersenne communicates his admiration of provincial intellects in a letter written to Peiresc in 1635: I have seen a short time ago two men, one rais ed with the Toulousia ns since 12 years of age, although Champenois [by birth], and the other from Bar-sur-Seine, who have through their discourse confirmed me in my opinion, that there are often from small towns some gentlemen who surpass nearly all those that are esteemed knowledgeab le, particularly in certain parts of the arts and sc ience, which they have found th rough their fine genius rather than in books.59 Mersenne was already convinced that there was geni us ripe to be harvested in the provinces, and he cites as evidence these two men who were gifted in the connections between music and mathematics. The intellectual ability to undertake and solve co mplex and important questions does not require living in Paris, usually viewed as the center of learned society. Mathematical learning was not native to a particular region and natural talent coul d not fully impart the characteristics necessary to progress in mathematics. Mersenne wrote that what these provincial s attained was accomplished primarily through personal initiative and was superior to many who were taught in schools.60 Self-education through experience and reason was the result of concerted applicati on and was preferable, Mersenne stated, to the bookish learning emphasized in the schools. The training of Pascal, it will become clear, followed this informal mode of training. It stressed the compatibility of individual inclination with purposef ul study and disciplined exercise. 59 Jay veu depuis peu deux hommes, lun nourri avec les Toulousains depuis lage de 12 ans, quoyque Champenois, et lautre de Bar-sur-Seine, qui mont confirm par leur discours dans mon opinion, quil y a souvent es petites villes des gens qui surpassent quasi tous ceux qu on estime savoir particulierement en de certaines parties des arts ou des sciences quils ont plustost trouvees par leur bon genie quapprises dans les livres, Marin Mersenne to Nicolas-Claude Fabri de Peiresc, 15 July 1635, Mersenne, Correspondance 5:301. In his footnote, Cornlis de Waard identifies the probable identity of the two men of whic h Mersenne writes: Jean le Maire and Jean Gall, n. 2, 3. 60 Mersenne to Peiresc, 15 July 1635, Mersenne, Correspondance 5:301. 69

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For those who lived in Paris conferences such as those hosted by Mers enne were a central form of communication. For i nhabitants of the provinces, boo ks served as one means to organize learned culture.61 A form of communication not cons idered by Eisenstein is personal correspondence, such as that carried on by Mers enne. It could communicate essential problems with greater currency than print, and could also be used as a gauge of potential, still unknown savants. 62 This undiscovered talent was not depend ent on bookish learning, Mersenne suggests in his discussion of provincials. Results and qu ality of mind were the determinate factors for significant contributors to learning and specifically to mathematics. Mersenne hoped that the matu ration of knowledge would occu r through the application of fine minds to an array of signi ficant questions. He guided indivi duals to those questions through his correspondence and published works. Pascal would write, after Merse nnes death, that he has provided the occasion for several fine discov eries, which perhaps would never have been made if he had not excited the savants to them.63 The talented child was the ar chetype of those whose knowledg e was, as Mersenne wrote, through their fine genius rath er than learned in books.64 Who more appropriate to excite to fine discoveries than the young, whose interest s and talents may more readily be shaped?65 61 Elizabeth Eisenstein has provided the most provocative statement of the importance for print culture on the emergence of new views of nature, Eisenstein, The Printing Revolution in Early Modern Europe (New York, 1983), 187-254. 62 J. L. Pearl emphasizes the significance of letters, providing a corrective for Eisensteins narrow focus on books in J. L. Pearl, The Role of Personal Correspondence in the Exchange of Scientific Information in Early Modern France, Renaissance and Reformation 8 (1984): 106-113. 63 The full quotation from Pascals Histoire de la Roulette reads: Il avait un talent tout particulier pour former de belles questions; en quoi il navait peut-tre pas de semblabl e. Mais encore quil net pas un pareil bonheur les resoudre, et que ce soit proprement en ceci que consiste tout lhonneur, il est vrai nantm oins quon lui a obligation, et quil a donn loccasion de plusieur s belles dcouvertes, qui peut-tre nau raient jamais t faites sil ny et excit les savants, Histoir e de la roulette, Mesnard OC 4:214. 64 Mersenne to Peiresc, 15 July 1635, Mersenne, Correspondance 5:301. 70

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Mersennes Investment in Youthful Talent Mersennes metaphorical description of music seeking to be accepted in the company of the other sciences provides a clue to his approach to undiscovered talent. Up to the time of his dedicatory letter to tienne Pa scal, Mersenne contends, music could only be considered as a junior member of the conference of the sciences because it was not yet a participant in the certitude of geometry and arithmetic.66 While clearly showing promise, music awaited a publication (e.g., from the elder Pasc als pen) that would articulate its principles and uses with a rigor not yet fully achieved. The personification of music as an understudy to other more certain disciplines parallels the position of the younger Pascal, who was viewed as a mathematical apprentice, not yet fully proven. The member s of the Mersenne Circle groomed him to participate fully in the scope of its activities and in its prestige. But young talent had to be protected and cultivated Mersenne did both. Mersenne expressed his int rt pour la jeunesse on bot h religious and intellectual levels.67 From a religious perspective, the youthf ul tendency to spiritual deviancy awoke Mersennes concern. Libertinage, in both belief and behavior, held a particular attraction for youths and made them susceptible to the impiety of the deists. 68 In fact, recognizing that some youths are attracted to impious beliefs because they see that this is the sentiment of the 65 Mersennes approach to exposing promising minds to important problems seems to prompt Robert Mandrous description of him as no less a teacher than a savant, Mandrou, From Humanism to Science, 1480-1700 (New York, 1978), 191. 66 Mersenne, Harmonie universelle Trait des instruments chordes, Dedicatory letter for the Trait des orgues, excerpted in Mesnard, OC, 2:121 67 The phrase is Beaulieus, Mersenne, Correspondance 15:35. Beaulieu considers Mersennes relationship with young people more extensively in Beaulieu, Un moine passionn, 181. He explor es the characterization of Mersenne as pedagogue in idem, Mersenne 50, 120-121, 129, 157, 294-295. 68 The theme of godless youths is repeatedly found in Marin Mersenne, Limpiet des deistes, athees, et libertins de ce temps combatu, & renuersee de point en point par raisons tirees de la philosophie, & de la theologie (Paris, 1624). 71

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most learned [ savans], Mersenne made a particular effort to demonstrate the compatibility of learning and religion.69 The literature of early modern Europe has many references to this youthful vulnerability to both mo ral and intellectual excess. Those sent away from home to study need oversight to protect them from the licenses of youth. Mers enne was keenly aware of this need. Indeed, when Descartes first me t him in Paris, Mersenne s guidance helped to detach him from the habits that he had for gaming and useless pastimes.70 Worldly diversions were but a single step from religious libertinage. Beaulieus work on Mersenne also mentions fr equent visits to th e Minim convent by the young Andr Pineau, nephew of Andr Rivet, in order to deliver le tters from the Dutch savant.71 While there is no evidence to s uggest a particularly close acqua intance between Mersenne and Pineau, Mersenne was certainly willing to sacrifice time for the young man: I have seen and entertained Father Mersenne for the space of two good hours.72 Thanks to the esteem in which the monk held his father, Claude Rivet (known as de Montdevis) also received Mersennes attention. Their relationship was close enough th at Mersenne could repr imand Claude for not showing respect to his father.73 At the moment of their meeting, Mersenne was 40, Rivet 26. Besides these passing but meani ngful interactions, some also saw Mersenne as one who might take pains to locate a pl ace of service for talented youth. In 1624, Claude Bredeau made appeal to Mersenne on behalf of an e ducated young man whose father had died: 69 voyent que cest le sentiment des plus savans, ibid., 122. 70 le dtacher des habitudes quil avoit au jeu et aux passe-tems inutile, Baillet, Vie de M. Descartes (Paris, 1691), 1: 37. 71 Beaulieu, Un moine passionn, 181. 72 [J]ay veu et entretenu lespace de deux bonne heures le P. Mersenne, Andr Pineau to Claude Rivet, 21 December 1646, Mersenne, Correspondance 14:694. 73 Marin Mersenne to Andr Rivet, 17 September 1632, Mersenne, Correspondance 3:332. 72

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[H]is mother believed that because of the frequent meetings that you have with so many learned [ doctes] and rare persons, you could easily find work for him, where by doing service, he could augment the unders tanding that God has given to him.74 Jean-Baptiste van Helmont also wrote to Me rsenne about his young sons unusual talent for artistically cutting paper with sc issors, believing that Mersenne would find it fascinating. He was not disappointed.75 Two New Archimedeses: Pasc al and Christiaan Huygens The above examples provide episodic eviden ce of Mersennes eye for potential young talent. They are suggestive enough to have been noticed by Mersenne scholars, but incomplete enough to be questionable as a key factor in the narrative of his biogr aphy. But when one considers the role of Mersenne and his acadmie in Pascals youth, and the parallels to Mersennes mentoring of Christiaan Huygens, the pattern of circumstances stands out. Pascal and Huygens (two bright, young Archimedeses) were the incarnations of Mersennes hope for carrying out the project of the completion of mathematics. For both of these men, Mersenne was a challenging voice, an encouragi ng mentor, and a tireless promoter. Mersenne and the youthful Pascal Mersennes acquaintance with Blaise Pas cal began in 1635. Around this time, according to Pascals sister and biographer, Gilberte Pri er, tiennes unexpected discovery of his sons 74 sa mere a creu que pour la frequentation que vous avez avec tant de doctes et rares personnages, facilement yous pourriez luy trouvez pa rty, o en faisant service, il pourroit accroistre ce que Dieu luy a donn dentendement, Claude Bredeau to Marin Mersenne 11 December 1624, Mersenne, Correspondance 1:186. 75 Van Helmont is himself unclear about the boys age in the first letter, he says he is twelve; in the second, only eleven. The first passage is from a letter dated 12 January 1631: je dis que les jolits que mon petit garon dun capriccie taille, nest pas pour en tirer prouffict, mais ce nest qu une rarit en un enfant de douze ans, sans patron et sans art, quil couppe cela, signe qu il seroit propre desseigner, Jean Baptiste Van Helmont to Marin Mersenne, 12 January 1631, Mersenne, Correspondance 3:31. The second letter reads: Mon petit eag de 11 ans prend dune main le ciseau et de lautre une lopp e de papier ou parchemin sans estre deline ou pourtraict, coupe selon lidee luy proposee, soit une histoire ou aultre phantasie. Et nest merveille que lon ne le croid pas, veu que les painctres dAnvers le sont venu voir, ne croyant pas possible; toutefois il leur couppoit lhistoire dActeon, Jean Baptiste Van Helmont to Marin Mersenne, 30 January 1631, Mersenne, Correspondance 3:53. 73

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aptitude for geometry led to his attending mee tings where all the able gentlemen of Paris assembled to bring their works or to examine those of others.76 Undoubtedly, this account refers to the Mersenne Circle. According to his sister, Pascal s oon began submitting his own works to the group, while offering observations a nd critiques of others productions. Sometimes, she writes with obvious pride, h e has discovered faults which the others had not perceived.77 The problem of taking Gilbertes account of Pascals life at face value is obvious when one considers the narrative as a whole and its attempts to sanctify every as pect of his character. It is possible that Pascals performance was less thor oughly astounding than she portrays. In any case, Pascals attendance at the meetings at that early age seems unproblematic. By the time of his Essai pour les coniques he was clearly held in high regard by Mersenne. Blaises father facilitated hi s entry to the group and his intr oduction to Mersenne. tienne Pascal was associated with several of Mersenne s circle before the time at which Blaise supposedly joined them in their weekly meetings The affair of Jean-Baptiste Morins supposed discovery of a new method for calculating longitudes (1634-1635), reve als tiennes close contact with Claude Hardy, Roberval, Le Pail leur, and Montmor, among others. Finally, the dedication of Mersennes Trait des orgues in the Harmonie universelle (1635/1636) to tienne, demonstrates a significant acqua intance between the two, especially since the elder Pascal was not a published writer. The first recorded evidence of Mersennes knowle dge of Blaises work is in late 1639, just prior to the printing of the Essai pour les coniques (1640). In a letter to Descartes (November 1639), the response to which is cited early in this chapter, Mersenne praises the young mans 76 o tous les habiles gens de Paris sassemblaient pour porter leur ouvrages ou pour examiner ceux des autres, Vie de Pascal, Mesnard, OC 1:575. 77 il a dcouvert des fautes dont les autres ne st aient point aperus, Vie de Pascal, Mesnard, OC 1:575. 74

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efforts in projective geometry. Though now lost, the content of this letter likely parallels another sent approximately one year later to Theodore Haak: [W]e have here a young man, a folio of whose Coniques I believe that I sent to you, who is such an excellent geometer, being only 18 y ears old, that he has brought together all the conic sections and the Apollonius in a single proposition, fr om which he derive 400 corollaries in such a way that not one depend on the other, but all, the last as well as the first, from that one proposition.78 Mersenne expresses in this passa ge the outlines of a project that is in harmony with his own goal to complete mathematics through seeking principles that encapsulate the massive learning of the ancients. In his later Cogitata physico-mathematica Mersenne states that Pascals contribution to geometry is his all-encompassing method: [O]ne may note that Pascal the younger has found a general method by means of which one ends by understanding what ratio the spaces limited by straight lin es and conic curves have among them.79 In his response to Mersennes letter, Descar tes, the great advocate of the algebraic method, minimizes the significance of the young Pascals accomplishments. Mersenne had been enthusiastic about the authors ag e; Descartes was lukewarm. In the letters to Descartes, Haak, and one to Constantin Huygens, Mersenne ma kes prominent mention of Pascals youth.80 Descartes, in contrast, downplays the positive co mparison to the propositions of Apollonius. The 78 [N]ous avons ici un jeune homme, dont je crois vous avoir envoy une feuille des Coniques lequel est si excellent gomtre, nayant que 18 ans, quil a compris toutes les sections coniques et l Apollonius dans une seule proposition, de laquelle il drive tellement 400 corollaires que pas un ne dpend lun de lautre, mais tous, aussi bien le dernier que le premier, de la dite proposition, Mersenne to Theodore Haak (18 November 1640), Mesnard, OC 2:239. A similar characterization of Pascals work is given in Mersenne, Cogitata Physico-Mathemtica who says that Pascal the son has through a single most general propo sition, armed with 400 coroll aries, the entire Apollonius is embraced, preface to Hydraulica, pneumatica, arsque navigandi n.p. [11]; cf., French translation in Mesnard, OC 2:299. 79 notare possis juniorem Paschalem generalem methodum invenisse, cuius beneficio innotescat quam inter se rationem habeant spatia quaecumque lineis r ectis et curvis conicis comprehensa, Ballistica et Acontismologia in Cogitata physico-mathematica in quibus tam naturae quam artis effectus admirandi certissimis demonstrationibus explicantur 102; cf., French translation in Mesnard OC 2:299. 80 Mersenne also sent a copy of the Essai to John Pell, though the letter with which it was delivered is no longer extant. Mersenne makes reference to it in Marin Mersenne to John Pell, 7 March 1640, Mersenne, Correspondance 9:184. It may be imagined that Mersenne would also have mentioned Pascals age to Pell. 75

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real accomplishment would be taking on even more difficult problems in conic sections, which Descartes could propose and that a child of 16 years would have di fficulty untangling.81 Descartes restraint underscores Mersennes enthusiasm for those whom he perceived as having talents that could serve his mathematical goals. In the case of Pascal, as the young man matures, Mersennes admiration grows. A few year s later, when Pascal was in the throes of his work on the arithmetic machine, Mersenne hopefully declares Blaise as one from whom can be expected marvelous discoveries not only in pure, but in mixed mathematics.82 Pascals promise for the present and the future was obvious. Because the interactions between Mersenne and Pascal were primarily face-to-face, rather than through correspondence, it is impossible to know pr ecisely Mersennes hopes and expectations. Mersenne makes br ief references to Blaises work in his published books as well as in his correspondence.83 But one particularly fruitful approach to the question of the Mersenne-Pascal relationship appears indir ectly, through Mersennes correspondence with Constantin and Christiaan Huygens. These exchanges indicate that Me rsenne drew a close connection between Blaise Pascal and Christiaan Huygens. In both prodigies he saw the aptitude necessary to further the progre ss of mathematics. By labeling each Archimedes, Mersenne drew them into his vision for mathem atical perfection, as foreshadowed in La vrit des sciences Mersennes relationship with Huygens shed s light on his interactions with Pascal. 81 Descartes to Mersenne, 25 December 1639, Mersenne, Correspondance 8:697. 82 mira possis expectare cum in puris, tum in mixtis Mathematicis, Ballistica et Acontismologia in Cogitata physico-mathematica 102. 83 These are considered in the current chapter and in Chapter 3. 76

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Pascals counterpart: Christiaan Huygens Christiaan Huygens was born at The Hague on 14 April 1629. He was thus nearly six years Pascals junior. Like Pascal, his intr oduction to Mers enne came through his father, though in this case through correspondence. When he was seventeen, the age at which Mersenne had praised Pascals Essai pour les coniques Christiaans father wrote: I proceed to copy a letter that the younger (17 years of age) writes on th e subject of his mathematical studies in which this boy succeeds admirably.84 Mersenne responded by sending several problems to Christiaan and asking for his clarification of a questi on regarding the fall of bodies, mentioned by Constantin in his letter. Merse nnes initial contact with Christia an, then, was a simple favor to his father, as his tone in the firs t letter suggests. He certainly do es not coddle him for his fathers sake: As I greatly honor Monsieur your father, and I believe it will give him pleasure [for me] to speak to you about your propositions of wh ich you say you have the demonstration, I will tell you only about the last [of them], that I do not believe that you have the demonstration of it, if I do not see it.85 Mersenne proceeds to outline the difficulties he finds in the proposition in question. He thus begins the relationship by issuing a challenge and offering suggestions of possible angles to consider. He tests the mettle of his young correspondents mind. For Pascal, the familial biography offers only h azy details regarding his early participation in the Mersenne group. It is reasonable to infe r, however, that like Huygens, he too had to demonstrate his perceptiveness and strong reasoni ng to Mersenne and his friends. Between his 84 [J]e faij copier une lettre que le cadet (aag de 17 ans) escrit sur le subject de ses estudes mathematiques o ce garcon reuscit marueilles, Constantin Huygens to Marin Mersenne, 12 September 1646, Mersenne, Correspondance 14:451. 85 Comme ihonore grandement Monsieur vostre pere, et que ie croy luy faire plaisir de vous parler de vos propositions dont vous dites auoir la demonstration, ie vous diray seulement sur la derniere, que ie ne croie point que vous en ayez la demonstration, si ie ne la voy, Marin Mersenne to Christiaan Huygens, 12 October 1646, ibid., 538. 77

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entry into the group around 1635-1636 and the Essai pour les coniques of 1640, Pascals status changed. He went from an unexpected talent, at tested by an influential father, to one whose work earned consideration from the learned world. Christiaan Huygens impressed Mersenne with his response to the queri es of his Parisian correspondent. In a letter to Constantin, Me rsenne described the young man as clear-sighted [ clair-voyant].86 But he was particularly interested in Christiaans age. 87 Constantin had mentioned it in the first letter about his boys, but Mersennes request fo r confirmation indicates how important it was to him.88 Constantin obliges with his reply: He has entered into his 17th Year and in keeping with what he knows promises me very much. Do not fear that I hurry him [when it comes to his] mind [ le presse desprit ]: I have never done so with my children, no more than my parents [did] to me.89 Constantin Huygens, like tienne Pascal, was keenly aware of his sons talents and took charge of his education and intellectual formation. Me rsennes evident concern that Constantin not presse desprit his son may reflect Mersennes experiences as Pascals mentor. Pascals father followed the dictates of humanis tic pedagogical theory, which warn ed that a child should only be exposed to the learning for which his mind had ac quired readiness. As such, tienne tried in vain to keep Blaise from mathematics. According to Blaises sister, this was because their father 86 According to Constantins letter, Mersenne made this characterization. But Mersenne does not use this term in any extant letter. Perhaps the letter to which Constantin refers has been lost. This is even more probable because none of Mersennes extant letters asks for Christiaans age either. 87 Vous prenez la peine de demander laage de mon fils et luy faictes trop dhonneur, Constantin Huygens to Marin Mersenne, 19/26 November 1646, Mersenne, Correspondance 14:637. 88 Constantin had written in his 12 September 1646 letter: I have two young galants, my eldest and he who follows him, who have great desire to see your quadrature of the hyperbola and your centers of percussion. And in order to tell you that they are capable of judging of it, I make to copy a letter that the younger one (aged 17 years) wrote to his said Elder (who is here in charge with me) on the subj ect of his mathematical studies where this boy raises some marvels, Const. Huygens to Mersenne, 12 September 1646), ibid., 451. 89 Il est entr dans sa 17e Anne et laduenant de ce quil sait me promect beaucoup. Ne craignez pas que je le presse desprit: jamais je ne lay faict mes enfans, non plus que mes parens a moij, Const. Huygens to Mersenne, 19/26 November 1646, ibid., 637. 78

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knew the all-consuming nature of mathematical studies But it could also be attributed to a belief that such studies might affect health.90 By 1646, at the age of twenty-three, Pascals health was already failing. 91 For Mersenne, the personal compar ison between the two mathematical prodigies had already begun. The response from Constantin reassured Mers enne that he could further encourage him about his sons talent without e ndangering Christiaans well-bei ng. In a letter of 3 January 1647, Mersenne makes an important prediction connect ing Huygens to the geometrical invocation in La verit des sciences : I do not believe that if he continues, he will not someday surpass Archimedes, relative of King Gelon.92 Constantin had until this time referred to his son as my scholar and my little mathematician.93 Henceforth, following Mersennes lead, his favorite moniker for Christiaan would be my Archimedes.94 A few days later, Mersenne writes to Christiaan with the same complimentary comparison: 90In 1635, a tutor of an aristocratic young man writes to th e mother of mathematics, to which I havent yet dared to introduce him, for fear of straining his mind, which weaken s with too much work Chamizay to Madame de Trmoille, 16 May 1633, Archives Nationales, Se ries 1 AP, 648, quoted in Jonathan Dewald, Aristocratic Experience and the Origins of Modern Culture: France, 1570-1715 (Berkeley, CA, 1993), 95. Samuel Sorbire gives a warning to Abb Tallemant regarding the danger to health involved in the over-stimulation of the mind in the area of languages, Samuel Sorbire to Abb Talemant 1 June 1659, Bibliothque Nationale, Paris, fonds franais 20612, folio 221 recto. 91 In the biography, Blaises sister writes: il nous a d it que depuis lge de dix-huit ans [1641] il navait pas pass vn jour sans douleur, Vie de Pascal, Mesnard, OC 1:577. Certainly by fall 1647, when Descartes made his visit to him, Blaise was in poor health to require attentive care and a great deal of bed-rest, as attested by Jacqueline Pascal to Gilberte Prier, 25 September 1647, Mesnard OC 2:480-482. 92 Je ne croy pas sil continue, quil ne surpasse quelqu e jour Archimede, cousin du Roy Gelon, Marin Mersenne to Constantin Huygens, 3 January 1647, Mersenne, Correspondance 15: 17. 93 Const. Huygens to Mersenne, 19/26 November 1646, ibid., 14:635; Constantin Huygens to Marin Mersenne, 23 December 1646, Mersenne ibid., 14:717. 94 U. Frankfourt and A. Frenk also recognized this as the turning point for Constantins identification of his son as Archimedes, Frankfourt and Frenk, Christiaan Huygens trans. I. Sokolov (Moscow, 1976), 45. For mon Archimedes in letters from Constantin to Mersenne, see Constantin Huygens to Marin Mersenne, 14 January 1647, ibid., 15: 46; Constantin Huygens to Marin Mersenne, 6 April 1648, ibid., 16: 219; Constantin Huygens to Marin Mersenne, 3 May 1648, ibid., 16: 296; Constantin Huygens to Marin Mersenne, 20 July 1648, ibid., 16: 430; Constantin Huygens to Marin Mersenne, 14 August 1648, ibid., 16: 477. For the elder Huygenss mention of his son to other correspondents, see Constantin Huygens to J. J. Stckar, 13 October 1654, Huygens, OC 1:298; 79

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I ask God, Monsieur, to keep you this entire year in very good health and that be the Apollonius and the Archimedes of our days, or rather of the century to come, since your youth could give you an entire century.95 The above passage reinforces the link between Mersennes hope for some new Archimedeses and his interest in young talent, including Huygens. To be sure, it is not unusual for Mersenne and other early modern authors to offer the hyp erbole of comparison with Archimedes or some other ancient figure.96 Father Mersenne gives similar adulation, for example, to Roberval and Fermat.97 But Huygens belongs in a category reserv ed for those who show potential in youth. Because of his age, he has vn siecle entier to contribute to Mersennes hope for the completion of mathematics. Mersenne was deeply enthusiastic about the prospect of young mathematicians capable of extending his agenda beyond his lifetime. The assertion that Mersenne makes a mental parallel between Huygens and Pascal is not based solely on circumstantial similarities. Pasc als shadow falls decidedly across Mersennes correspondence with the Huygenss. In a subseq uent letter to Consta ntin, Mersenne draws attention to this other mathematical talent: Constantine Huygens to Princess Palatine Elisabeth, 25 December 1654 Christiaan Huygens Oeuvres compltes de Christiaan Huygens 22 vols. (The Hague, 1888-1950), 1:313, hencefort Huygens OC [vol#]: [page#]. 95 Je prie Dieu Monsieur, de vous conseruer toute cette anne en tres bonne sant, et que vous soyez lApollonius et lArchimede de nos iours, ou plustost du siecle venir, puisque vostre jeunesse vous peut donner vn siecle entier, Marin Mersenne to Christiaan Huygens, 8 January 1647, Mersenne, Correspondance 15:34. 96 Archimedes is a much more likely candidate than Apolloni us as a historical figure for comparison. Archimedess life was more thoroughly documented in narrative form. Biographical information about Apollonius is virtually nonexistent. Archimedess extant work was also of greater breadth and volume, with surviving work in both pure and applied mathematics. Nevertheless, it should be note d that Apollonius was called The Great Geometer by an early commentator (Geminus), Fried and Unguru, Apollonius of Pergas Conica, 5. A number of early modern mathematicians judged their own works against those of Apollonius, Jean Dhombres, La culture mathmatique au temps de la formation de Desargues: Le monde des coniques, in Desargues en son temps ed. Jean Dhombres and J. Sakarovitch (Paris, 1994), 62. 97 For the comparison between Fermat and Archimedes, see Bonnel to Marin Mersen ne, April 1646, Mersenne, Correspondance 14:252. For a comparison between Roberval an d Archimedes, see Pierre Desnoyers to Gilles Personne de Roberval, 18 March 1648, ibid., 16:186. 80

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If your Archimedes comes with you, we will cause him to see one of the finest treatises of geometry that he has ever seen, which ha s come to be completed by the young Paschal.98 In a postscript to the same later, Mersenne adds: Your Archimedes will see here the invention of the said Pascal to calculate without pain and without knowing anything.99 Significantly, of the extant letters from to Consta ntin, Mersenne only uses the designation your Archimedes [ vostre Archimedes] in these two passages. In both cases, Mersenne is writing about Pascal. Is Mersenne implying that these youngsters represent two great possibilities for the future of mathematics? The co-identity implied in their earlier correspondence is finally made explicit in a letter written in May 1648. Mersenne writes to Chri stiaan of Sieur Pascal, who is another Archimedes.100 There remains no doubt, then, of Merse nnes conscious pairing of Pascal and Huygens. These two Archimedeses, whose y ears of birth (1623 for Pascal and 1629 for Huygens) bracket the pub lication of Mersennes La vrit des sciences (1625) are thus neatly linked to his vision that there would be born again in this century some new Archimedeses.101 Both Pascal and Huygens were conscious of the debt they owed Mersenne for encouraging their mathematical potential. While Huygens never met Mersenne personally, he acknowledged later the part that Mersenne played in his first apprenticeship: Father Me rsenne honored me with his correspondence in order to incite me to the study of mathematics, to which he saw me 98 Si vostre Archimede vient auec vous, nous luy ferons veoir lun des plus beaux traitez de geometrie quil aye jamais v, qui vient destre achev par le jeune Paschal, Marin Mersenne to Constantin Huygens, 17 April 1648, ibid., 16: 230. 99 Vostre Archimede verra ici linuention dudit Pascal pour suputer sans peine et sans rien scauoir, Mersenne to Const. Huygens, 17 April 1648, ibid., 232. Mersenne refers here, of course, to Pascals arithmetic machine. 100 Sieur Pascal, qui est un autre Archimde, Marin Mersenne to Christiaan Huygens, 15 May 1648, ibid., 314. 101 Mersenne, La vrit des sciences 750. See above, p. 67. 81

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naturally inclined [ il me voyoit port naturellement ].102 Pascal had a more personal relationship with the Minim monk and Mersennes formul ation of unsolved problems profoundly shaped Pascals work. Mersennes influence mark s his efforts in geometry, number theory, combinatorics, physics, and perhaps even apologe tics. Pascal is spar ing in his praise of Mersenne as a mathematician, but lauds him, with Huygens, because he has provided the occasion for several fine discoveries, which would ha ve never been made if he did not excite the savants to them.103 The Mersenne Circle and Pascals Mathematical Apprenticeship Pedagogical Interests and Activi ties of the Participants Pascals training as a mathematician was not accomplished by the Minim alone. The members of Mersennes mathematical academy co llectively participated in the education of Pascal. Having recognized his talent, they sought ways to encourage him, through discipline and exercise, to cultivate that geomet rical talent. A number of scholars have examined Pascals debts to the members of the Mersenne Circle. Pierre Humberts work is pa rticularly important. Humbert argues against an interpretation of Pascal as a loner, emphasizing instead his connections with other mathematicians and philosophers of the time. As evidence, Humbert excavates Pascals mathematical and philosoph ical influences not merely through textual analysis, but by attending to th e personal connections develope d through the Pascal family. Among those most prominent within the group, and personally connected with Pascal, are Girard Desargues, Gilles Personne de Roberval, Jacque s Le Pailleur, and of course tienne Pascal. 102 Le Pere Mersenne mhonoroit de sa correspondance pour minciter a lestude des mathematiques a la quelle il me voyoit port naturellement, Christiaan Huygens to Pierre de Carcavy, 1 June 1656, Huygens, OC 1:428. 103 il a donn loccasion de plusieurs belles dcouvertes, qui peut-tre nauraient jamais t faites sil ny et excit les savants, Histoire de la roulette, Mesnard OC 4:214. 82

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Desargues: self-taught master Pascals debt to Girard Desargue s is clear from his earliest work.104 It was obvious enough to Descartes on the reading of the Essai pour les coniques : [H]aving read only half of it, I judged that he had learned from Mons ieur Desargues, which was confirmed to me at once through the confession that he [P ascal] himself makes.105 Pascals Essai praises Desargues as one of the gr eat minds of our time and in it he admits that I owe the little that I ha ve found on this matter to his writings.106 Pascal especially refers to Desargues Brouillon Projet, published not long before the Essai .107 Pascals work follows the example of Desargues in using geom etrical projection to generalize properties and results from conic sections.108 The connection is so strong that Ren Taton remarked that Pascal is shown to be the first and the only true discipline of Girard Desargues in the field of geometry.109 Jean Mesnard examines Pascals use and expansion of Desargues in depth. Desargues influence is not only evident in pr ojective geometry, Mesnard argues, but in the 104 Desargues was born 21 February 1591 in Lyon and died October 1661. The best source of introductory information on his life is Ren Taton, Girard Desargues, in Dictionary of Scientific Biography ed. Charles C. Gillespie, vol. 4 (New York, 1971), 46-51; see also Marcel Chaboud, Girard Desargues, Bourgeois de Lyon, Mathmaticien, Architecte (Lyon, 1996). 105 [A]vant que den avoir lu la moiti, jai jug quil avait appris de Monsieur Desargues, ce qui ma t confirm incontinent aprs par la confession quil en fait lui-m me, Ren Descartes to Marin Mersenne, 1/2 April 1640, Mesnard OC 2:238-239. 106 Nous dmontrerons aussi cette proprit, dont le premier inventeur est M. Desargues, Lyonnais, un des grands esprits de ce temps [J]e dois le peu que jai trouv sur cette matire ses crits, Essai pour les coniques, Mesnard OC 2:234. 107 Girard Desargues, Brouillon Project dune Atteinte aux Evenemen ts des Recontres du Cone avec un Plan was published in 1639, in Girard Desargues, Oeuvres ed. Nol-Germinal Poudra, vol. 1(Paris, 1864), 103-230. Pascals Essai pour les coniques was printed in early 1640. 108 Pascal avoids, however, the abstruse terminology that prompted criticism of the Brouillon Project 109 [Pascal] se rvle comme le premier et le seul disciple vritable de Girard Desargues dans le domaine de la gomtrie, Ren Taton, Loeuvre de Pascal en gomtrie projective, Loeuvre scientifique de Pascal ed. Pierre Costabel (Paris, 1964), 20. Robert Allard, La jeunesse de Pascal: de la lgende lhistoire (Paris, 1994), argues with this traditional conclusion, stating that Philippe de la Hire was the vritable continuateur of Desargues work, 70. 83

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geometrical elements of philosophy, incl uding the importance of the infinite.110 The relationship between the Desargues and Pascal, Mesnard co ncludes, furnishes perhaps a one-of-a-kind example of fertilization of one mind by another.111 Significant claims of influence as ide, Pascals language in the Essai only directly suggests a familiarity with Desargues writings. He ma kes no mention of a personal relationship with his master in projective geometry. Yet if Pascal was a regular attendee of the Mersenne group, as seems likely, then he also would have had a mo re personal acquaintance with the work of the Lyonnais mathematician. His familiarity with Desargues work was gleaned from the oral giveand-take of conferences instead of simply read in a book. If contemporary accounts of the groups activities are accurate the attendees, including Pascal, would have discussed the contents of the book at their meetings. Alexandre Koyr addresses th e personal relationship between Desargues and Pascal, characterizing the latter as a student of the former. In hi s seminal article, Pascal Savant, Koyr writes: I am inclined to think that the influence of Desargues is exercised through personal contact. I do not believe, in fact, that a nyone, even a genius like Pascal, would have been capable of understanding and assimilating the ideas and the methods of the great Lyonnais geometer by a simple reading of the Brouillon project.112 110 Pour en venir lessentiel, et reprendre un terme qui na cess de simposer nous, la grande invention de Desargues a t celle dune gomtrie de linfini, ou de lapplication de lide dinfini la gomtrie pure, Jean Mesnard, Desargues et Pascal, in Desargues en son temps ed. Jean Dhombres and J. Sakarovitch (Paris, 1994), 98. Later in the article, Mesnard writes: Si lon aborde la mtaphysique de la gomtrie, un rapprochement trs prcis simpose entre Desargue s et Pascal, ibid., 98. 111 [Il] fournit un exemple peut-tre unique en son genre de fcondation dun esprit par un autre esprit, ibid., 99. 112 Je suis enclin penser que linfluence de Desargues s est exerce dans un commerce personnel. Je ne crois pas, en effet, que quiconque, mme un gnie comme Pascal, ait t capable de comprendre et dassimiler les ides et les mthodes du grand gomtre lyonnais par la simple lecture du Brouillon project Koyr, Pascal Savant, 262. 84

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Koyr continues by claiming that we can see in Pascal a true student of Desargues.113 Importantly, the supposed teacher-student re lationship is used by Koyr as evidence against the received tradition of Pascal as ch ild prodigy and mathematical genius. Koyr provocatively suggested the marginality of Pascal to the contributions of seventeenth-century science and, in turn, his position in the history of science. K oyr downplayed the deterministic role of inborn talent and thereby encouraged consideration of the influences that developed that talent.114 Koyrs argument that Desargues educat ional influence was central to Pascals success is convincing. His iconocl astic tendencies serve as a he lpful corrective to an overly optimistic view of Pascals inborn talents, though it also remains clear that Pascals work in geometry was creative, not just derivative.115 Desargues own educational background and his writings harmonize with a concern for pedagogy. The first thirty years of his life are ob scured by lack of documentation. His two older brothers became avocats at the Parlement of Paris. 116 It is possible, t hough never recorded, that he too received some kind of university education. According to the opponents of his Brouillon Project, however, Desargues went about saying everywhere that he owed his instructions only to his particular studies that he read no work.117 His insistence on his absolute self-education 113 [N]ous pouvons voir dans Pascal un vritable lve de Desargues, Koyr, Pascal Savant, 262. Likewise, Andr Bord writes: Blaise restera li Roberval et Carca vy, mais il se considrera comme le disciple de Desargues . La mort de son matre, en septembre 1661, dut affecter Pascal, Andr Bord, La vie de Blaise Pascal: une ascension spirituelle; suivi dun essai, Plotin, Montaigne, Pascal (Paris, 2000), 200. 114 Here Koyr provides a subtle reinforcement of Mersennes view about the relationship between natural talent and disciplined exercise, Koyr, Pascal Savant. See below, pp. 111-116. 115 Descartes avait certainement tort de douter ainsi loriginalit de cet Essay ; si Pascal reconnat trs objectivement que Desargues inspira ses recherches, il est incontestable que certaines des ides nouvelles quil prsente sont de luimme, Ren Taton, Loeuvre mathmatique de G. Desargues (Paris, 1951), 34. 116 What little that is known about Desargues early life is summarized in Ren Taton, Desargues et le monde scientifique de son poque, in Desargues en son temps ed. Jean Dhombres and J. Sakarovitch (Paris, 1994), 25-26. 117 [Il] allait disant partout quil ne devait son instruc tion qu ses tudes particuli res, quil ne lisait aucun ouvrage, Desargues, Oeuvres de Desargues ed. Poudra, 1:12. 85

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is not surprising or unique. His detractors were claiming that he had plagiarized other writers on perspective, and Desargues stat ement represented a hyperbolic de fense technique. The ideal of learning mathematics through ones own genius is characteristic of the seventeenth century in general, but is especially important to the core members of the Mersenne group. Desargues interest in education did not cease with autodidacticism. It extended to the development of pedagogical methods. In Harmonie universelle (1636), Mersenne writes: I begin thus through a very easy method, whic h Monsieur des Argues, [an] excellent geometer, has given in some terms that he ha s recognized as proper fo r insinuating it into the mind of children, and in or der to make it be understood in little time and with much facility.118 Desargues interest in disc overing the best way to instru ct children reinforces the pedagogical element of the Mersenne Circle. He is particularly concerned to formulate language appropriate for the young, anticipating his use of terminology in the Brouillon Project. In that work, Desargues introduces a naive terminology based upon the natural world, using words such as tronc (trunk), rameau (branch), and souche (stump) to refer to geometrical elements.119 Ironically, the new terms that he used in projec tive geometry made his work not more, but less accessible to experienced mathematicians. The cons cious effort to create parallels between the visible natural world and abstract geometrical entities seems to signal a conscious attempt to instruct beginners.120 118 Je commence donc par une mthode fort aise, laquelle Monsieur des Argues, excellent gomtre, a dress en des terms, quil a reconnu propres pour linsinuer dans lesprit des enfants, et pour la faire comprendre en peu de temps avec beaucoup de facilit, Mersenne, Harmonie universelle De lart de bien chanter, 331. 119 Desargues nineteenth-century editor, Nol-Germinal Poudra, even compiles a list, Vocabulaire des termes employes par Desargues dans cet ouvrage, Oeuvres de Desargues ed. Poudra, 99-102. 120 Descartes describes the distinction between mathematical writing for mathematicians and for the curious, Ren Descartes to Girard Desargues, [4] January 1639, Ren Descartes, Oeuvres de Descartes ed. Victor Cousin, vol. 8 (Paris, 1824), 67-69; see also, Dominique Descotes, Blaise Pascal: littrature et gomtrie (Clermont-Ferrand, France, 2001), 57-58. On the reception of Desargues Brouillon Project by French mathematicians generally, see Taton, Desargues et le monde scientifique, 39-40. 86

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Desargues insistence on the ro le of the mathematician in the perfection of architecture and perspective is a further extension of his c oncern with pedagogy. Desargues portrays the geometer as the teacher; practical architects and artists are students.121 He sees geometry as the disciplinary pedagogue of the ar ts of drawing and design. On the other hand, Desargues recognized inherent limitations associ ated with his own lack of tec hnical dexterity. With this in mind, he cultivated a student, Abraham Bosse, who had superior technical skills. Bosse was assigned the task of bringing to fruition Desar gues whole system of techniques based on the theoretical geometry of perspective. Desargues writings and hi s attempts to reform practical arts demonstrate the prominence of the teacher-student relationship for Desargues. These links between Desargues and pedagogy do not provide direct evidence of a teacherpupil relationship with Pascal. This association, however, st rengthens the link between the members of the Mersenne Circle and an interest in pedagogical theory and practice in various realms. Such connections provide indirect s upport for the claim that the groups training of Pascal was not merely an unintende d by-product, but an assumed goal. Roberval: university connection Gilles Personne de Roberval, another major participant in the Mersenne group, is more closely linked to formal educational practices. One historian labels him a pedagogue living a precarious existence on the proceeds of his lessons.122 Before his arrival in Paris in 1628, he gave private lessons to Francois du Verdus, among others, in orde r to support himself. 123 His 121 Chapter 3 examines the hierarchical relationship between theory and practice suggeste d by Desargues, comparing it with Pascals own relationship with practitioners. 122 D. T. Whiteside, Un savant mconnu: Gilles Personne de Roberval (1602-1675): Son activit intellectuelle dans les domaines mathmatique, physique, mcan ique et philosophique (Book Review), Isis 54 (1963), 303. 123 Kokiti Hara, Gilles Personne de Roberval, Dictionary of Scientific Biography ed. Charles C. Gillespie, vol. 11 (New York, 1975), 486. 87

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personal education was not in a tr aditional university setting. Instead, he attended classes while in his role as itinerant tutor.124 In 1632, he attained the positi on of professor of philosophy at the Collge de Matre Gervais. Two years later he won the competition for the Ramus chair of mathematics at the Collge Royal in Paris, a positi on of great prestige that he held until death. Later, he filled the chair of mathem atics left vacant at Gassendis death.125 Roberval did not receive his position in the university community because of family status, having been born and raised, as he says, inter multos .126 Like the provincials fo r whom Mersenne expressed admiration, Roberval acquired his mathematical expertise not through birth, but through the concerted effort of self-education. Roberval demonstrates his ski ll as a teacher, argues Lon Auger, through the large number and prominent status of individuals who atte nded a presentation that he delivered in 1658.127 Gassendi recommended Roberval as his successor to the chair in mathematics based on the observation that he teaches this fi ne science with so much success.128 On the other hand, his competition for the chair may not have been extrem ely fierce. One of his fellow competitors in 124 Pierre Costabel and Monette Martinet, Quelques savants et amateurs de Science au XVIIe sicle : Sept notices bibliographiques caractristiques (Paris, 1986), 21. Costabel and Martinet especially note Robervals attendance at Bordeaux. 125 Lon Auger, Un savant mconnu: Gilles Personne de Roberval (1602-1675), Son activit intuellectuel dans les domaines mathmatique, physique, mcanique et philosophique (Paris, 1962), 151. Augers work is a key work concerning the biographical elements of Robervals life, including his chapter, Roberval, Professeur au Collge Royal de France, ibid., 149-153. See also, Costabel and Martinet, Quelques savants et amateurs de Science au XVIIe sicle 21-31, especially the bibliography. 126 Hara, Roberval, Dictionary of Scientific Biography, 11:486. 127 Auger, Un savant mconnu, 152. Augers book on Roberval is the only published work entirely devoted to this important seventeenth-century mathematician. The r ecent publication of Gilles Personne de Roberval, lments de gomtrie ed. Vincent Jullien (Paris, 1996), signals a welcome interest in his career and work. 128 [Pierre Gassendi] eut soin en mourant de recommander sa chaire de Professeur du Royaux Mathematiques, pour M. de Roberual Geometre, qui enseigne cette belle science auec tant de succez, Michel de Marolles, Les memoires de Michel de Marolles vol. 1 (Paris, 1656), 275.On Robervals success as a teacher, see also Costabel and Martinet, Quelques savants et amateurs de Science au XVIIe sicle 22. 88

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1659 drew the ridicule of the jury when he simply read from Euclids lments when asked to give a lesson.129 Robervals eloquence, however, had its limits. Some who heard his address to inaugurate his position in Gassendis chair remarked that he was as bad at oratory as he was good at geometry.130 As a university professor, Roberval operated in a culture that thrived on debate and disputation. This suited his di sposition, as Robervals constant, virulent contentiousness with Descartes clearly demonstrates. At universities, theses were customarily announced and then debated by a number of eminent individuals. Pascals Essai pour les coniques a single sheet of paper in which he merely outlines the work (d efinitions, lemmas, and propositions), bears some resemblance to a university thes is print, as Mesnard observes.131 On another level, Roberval habitually kept his work secret exposing it only to initiates among his friends, such as the inner circle of the Mersenne gr oup. This behavior suggests para llels with the secret knowledge of guilds and crafts, with which the or igins of the university are associated.132 As Chapter 6 will attempt to show, the Roberval-l ike secrecy that would characte rize Pascals last efforts in mathematics distanced him from the rest of the learned community of the late 1650s.133 129 Auger, Un savant mconnu, 150. 130 Abraham du Prat to Thomas Hobbes, 1 April 1656, Mersenne, Correspondence 1:246. 131 On pourrait comparer l Essai avec les placards de thses. Aussi bien lopuscule de Pascal est-il appel thse en 1670 par le thoricien de la perspective Grgoire Huret Plus significative encore lexpression les thses de M. B. P. employe par Beaugrand, da ns une lettre imprime du 20 juillet 1640, Mesnard OC 2:220, n. 3. 132 Pamela O. Long, Openness, Secrecy, Authorship: Technical Arts an d the Culture of Knowledge from Antiquity to the Renaissance (Baltimore, MD, 2001), argues that the simple a ssociation of secrecy with craft traditions and openness with learned communities is inadequate and that elements of both openness and secrecy are evident in the burgeoning scientific community of the seventeenth century. The questions of artisanal knowledge and its relationship to theory is also of importance to this disserta tion. On questions of this relationship, see below, pp. 128148. 133 See below, pp. 339-341. 89

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Le Pailleur: fatherly poet Robervals polar opposite is Jacques Le Paill eur, who would become the mid-1650s host of the remnants of the original Mersenne gatherings.134 Robervals intensity and technical proficiency stand in stark contra st to the light-hearted Le Pail leur, who was skilled in music, poetry, and humor. Ren Pintard labels him: Honnte homme playful, pleasing singer and distinguished dancer, [a] no less practiced poet, especially in humorous verse.135 He was close friends with Charles Vion Dalibray, the celebrate d poet of libertinism, who wrote a number of poems to his friend Le Pailleur.136 Dalibrays light-hearted, bacc hanalian behavior, which seems to extend to Le Pailleur, is playful and good-natured. Unlike Roberval, Le Pailleur ev idently had little formal traini ng in mathematics. With his varied interests and the emphasis th at he placed on his social life, he is the clearest example of the honnte homme among Mersennes mathematicians. Like Pascal, he demonstrated mathematical aptitude from a young age. Tallem ant des Raux, one of his long-time friends, writes: He was devoted to mathematics from his child hood: he learned it by himself. He had only twenty-nine solz when he began to read the books of this science, and he exchanged the books [for others] as soon as he had read them.137 134 Michel de Marolles records the existence of this group: chez feu Mons. le Pailleur, il y en auoit vne autre tous les Samedys, pour parler des Mathematiques, o iay v Mess. Gassendi, Boillaud, Pascal, Roberual, Desargues, Carcaui, & autres illustres en cette science, Marolles, Memoires de Michel de Marolles (Paris, 1656), 272. Taton clearly believes that this gathering was a continuation of that which had been begun with Mersenne, Taton, Les origines 21. 135 Honnte homme, badin, plaisant chanteur et danseur mrite, rimeur non moins exerc, surtout en vers pour rire, Ren Pintard, Le libertinage rudit dans la premire moiti du XVII sicle (Paris, 1943; repr., 1983), 349. 136 See Charles Vion Dalibray, Oeuvres potiques du sieur de Dalibray ed. Ad. Van Bever (Paris, 1906), 97-100. 137 Il sestoit addonn aux mathematiques dez son enfance: il les appris tout seul. In navoit que vingt-neuf solz quand il commena lire les livres de ce tte science, et il eschangeoit les livres mesure quil les lisoit, Tallement des Raux, Historiettes 2: 101. 90

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tienne Pascal, understanding that Le Pailleur would be sympathetic to his sons blossoming attraction to mathematics, went to his old fr iend first when he disc overed Blaise drawing geometric figures on the playroom floor. 138 Blaise acknowledged both Le Pailleurs talent in mathematics and his influence over his own career. In a letter written to Le Pailleur during the controversy concerning the void in the 1640s, Pascal calls him an excellent geometer w ho has as much skill in discovering the faults of reasoning as [he has] strength to avoid them.139 His combination of the art of conversation with careful reasoning could have provided Pasc al with a model for bringing together careful reasoning and the art of conversati on. Moreover, Le Pailleurs re lationship with Blaise was both personal and intellectual, just as it had been with his father. Pascal affi rms this when he writes that through him, I was always raised with an uncommon method and care [that was] more than paternal.140 tienne Pascal The fatherly figure of Le Pailleur was a double of his close friend tienne Pascal. He was, properly speaking, both Pascals tuto r and confidant. Gilberte Prier, in her biography, claims that tienne resigned his post as President of the Cour des Aides in Clermont and moved to Paris for the sole benefit of his sons education: As he had no other son than that, this quality of only son, and the gr eat marks of intellect [Fr. esprit] that he recognized in this child, gave him such great affection for him that he could not determine to commit his education to another, and resolved to instruct him 138 Le Pailleur and the elder Pascal had already been friends for a number of years by the time Pascals geometrical talent manifested itself. tienne Pascal calls Le Pailleur un de mes intimes amis, depuis trente ans et plus, tienne Pascal to tienne Nel, April 1648, Mesnard OC 2:587. 139 un excellent geomtre [qui a] autant dadresse pour dcouvrir les fautes de raisonnement que de force pour les viter, Blaise Pascal to Jacquels Le Pailleur, February 1648, Mesnard OC 2:569. 140 [J]ai t toujours lev avec une mthode singulire et des soins plus que paternels, Pascal to Le Pailleur, February 1648, Mesnard OC 2:576. 91

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himself, as in fact he did, my brother having never entered a collge and having never had any master but my father.141 This account of tiennes attitude as with the rest of the deta ils provided by Prier, must be considered with some caution. In particular, P riers dedication to the educational values of Port-Royal certainly influenced this memory. Nevertheless, all the indicators suggest that Pascal was never formally schooled. The memoires of Blaises last confe ssor, Father Beurrier, offer an explanation of tiennes own educat ional background and thus of his choice of education for his son: He had learned, through his own father [and] without having had anot her master, the Greek and Latin languages, philosophy, mathematics, history, canon and civil law, and especially positive theology through the reading of the Bible and the Holy Fathers.142 Being thus himself a man educated by his father, he chose a similar path for Blaise. The Acadmie as an Educational Alternative Few would dispute that tienne was Blaises only master, in th e sense of dire ctly guiding his education. As has been shown, however, Pascal may also be viewed as Desargues pupil, at least in the important sense of his technical training in projec tive geometry. In his overall preparation for a mathematical and natural philosophica l career, the Mersenne Group also played a collective role as an informal educational institution. For some, this meant simply allowing him to interact as a junior member of the disc ussion circle, facilitating his self-study. Others, such as Claude Mydorge, may have seen their ro le as more active. Mydorge writes that in 141 [C]omme il navait point dautre fils que celui-l, ce tte qualit de filz unique, et les grandes marques desprit quil reconnaissent en cet enfant, lui donnrent une si grande affection pour lui quil ne put se rsoudre de commettre son ducation un autre, et se rsolut ds lors de linst ruire lui-mme, comme il a fait, mon frre nayant jamais entr en pas un collge et nayant ja mais eu dautre matre que mon pre, Mesnard OC 1:571. 142 [I]l avait appris par son propre pre, sans avoir eu autr e matre, les langues grecque et latine, la philosophie, les mathmatiques, lhistoire, le droit canonique et civil, et surtout la thologie positive par la lecture de la Bible et des Saints Pres, Mesnard, OC 1:870. 92

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mathematics, one cannot learn without a tutor [ precepteur], because of the Demonstrations that one must contemplate and to keep in proportion.143 Blaise recognizes the role that the Mersenne Circle played in his training in a brief summary of mathematical and physical work written in 1654.144 It is addressed to a new group that had supplanted Mersennes after his death, which met weekly at Le Pailleurs home.145 He acknowledges his indebtedness for th eir investment in his formation: I confess in fact as yours what I would not have made mine, if I had not been educated in your midst.146 Later in the same paragraph he goes to on to acknowledge the benevolence that has sustained me from my youngest years in this le arned School [Lyceo]. 147 Labeling the group a learned School [ erudito Lyceo ] could be viewed as merely an honor ary nod to the savants who graced it. However, when Mersenne chose to use the word acadmie to describe to Peiresc the group of learned men who gathered regularly in Paris, he invoked rich intellectua l connotations, including those associated with the uni versity and with the arts. 143 ne se peut apprendre sans precepteur a cause des Demonstrati ons qu[]il faut faire cont empler et proportionner, Mydorge, Trait de gomtrie BN, Paris, fonds franais 656, 2. 144 There are two extant copies of this Latin piece, one by Leibniz in the fonds Leibniz at Hanover and another by Father Guerrier in a private collection. Leibnizs bears the title Celeberrimis matheseos professoribus but Brunschvicg and Mesnard have agreed that the original designation of the work was likely that of the other copy: Celeberrimae matheeseos academ iae parisiensi, Brunschvicg OC 3:293, 305; Mesnard OC 2:1022. The text of the piece is in the original Latin in Brunschvicg OC 3:305-308 and in Latin and a French translation in Mesnard OC 2:1031-1035. 145 There has been some debate about the identity of th e group to whom the piece is addressed. Brunschvicg believed that it was written to the Acadmie de Montmor b ecause of a mistaken date fo r Le Pailleurs death (1651), Brunschvicg OC 3:296-297. Subsequent research has establishe d Le Pailleurs death in 1654 and thus Mesnard argues that the piece was addressed to the group meeting in his home, the mo st direct successor to Mersennes acadmie mathmatique, Taton, Les origines, 21; Jean Mesnard, Pascal lAcadmie Le Pailleur, in Loeuvre scientifique de Pascal ed. Pierre Costabel (Paris, 1964), 7-16; Mesnard OC 2:1022-1023. 146 vestra enim esse fateor quae non, nisi inter vos educatus, mea fecissem. Mesnard OC 2:1031. 147 benignitas quae me a junioribus annis in erudito Lyceo sustinuit. Mesnard OC 2:1032. 93

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When Mersenne announced his group to Peiresc, he called it la plus noble acadmie du monde. (the noblest academy in the world).148 The most obvious reason for him to give it the label acadmie is that the Acadmie Franaise was instituted by Cardinal Richelieu in that same year. Perhaps Mersenne had the founda tion of this governmentally-sponsored group in mind when he wrote to Peiresc. The designation could be viewed as the expression of a desire for the legitimation that the literary community had received in the political arena. It is a mistake, however, as Simone Mazauric makes clear, to consider French academism of the seventeenth century only in term s of governmental institution of learned conferences. To do so is to privilege a later definition of the wo rd acadmie, with the foundation of various academies such as the Acadmie Royale des Sciences.149 Jean-Robert Armogathe avers that Mersennes group should not, in fact, be labe led an acadmie, as it does not have the formalized structure and rules that such a name indicates.150 But this opinion, if accepted, would devoid the word of some of the educational co nnotations it undoubtedly had in the seventeenth century. When Pascal addressed his 1654 work to the Celeberrimae matheseos academiae parisiensi there was a suggestion of formality. The name invokes the educational institution of the University of Paris, known as academiae parisiensis. But when Peter-Eckhard Knabe writes in his Lhistoire du mot Acadmie, that French makes a strict distinction between 148 Marin Mersenne to Nicolas-Claude Fabri de Peiresc, 23 May 1635, Mersenne, Correspondance 5:209. 149 [D]uring the whole first half of the century, the contemporaries of Louis XIII have used in a very much larger sense and concurrently with other term s with similar acceptance/understanding in order to designate any sort of relevant meeting of private initiative, a meeting more or less regular, more or less regulated, more or less formalized destined to favor the commerce of minds, Simone M azauric, Aux origines du mouvement acadmique en France: Proto-histoire des acadmies et gense de la sociabilit savante (1617-1666), in Acadmies et socits savantes en Europe ed. Daniel-Odon Hurel and Grard Laudin (Paris, 2000), 36-37. 150 Jean Armogathe, Le group de Mersenne et la vie acadmique Parisienne, Dix-Septime Sicle 44 (1992), 136. 94

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acadmie and universit ,151 he offers chronologically indistinct data that does not take account of its cultural connotations, including its use as the Latin desi gnation of the university. Knabe argues for the distinction, and even opposition, of these two words, based largely on an entry from the Encyclopdie of 1734. A strict distinction between the Latin academiae and the French acadmie, however, is misleading. Knabes argument that the word acadmie is used for organizations arrayed in opposition to tradi tional educational institutions reinforces the supposition that these informal groups worked to displace the university, while maintaining similar goals. Frances Yatess study of sixtee nth-century French academies argues that they were the heirs of the projects of Ficino and Ramus.152 Ficinos famed academy had borrowed the terminology of Platos own educational endeavor s to refer to what may well have been an informal school where the Florentin e Neo-Platonist tutored students.153 In 1567, Ramus called on the memory of Ficinos work in Florence in an attempt to convince Catherine de Medici to help sponsor his reform of the universities.154 Thus, while acadmie is not, as Knabe correctly asserts, a synonym of universit it maintains associations with an educational agenda. These connotations are further attested by de velopments in sixteenth and seventeenthcentury France. Yates points out the wide-rang ing educational undertakin g of Bafs musical 151 [L]e franais opre une distinction st ricte entre acadmie et universit, Peter-Eckhard Knabe, Lhistoire du mot acadmie, in Acadmies et socits savantes en Europe ed. Daniel Odon Hurel and Grard Laudin (Paris, 2000), 30. 152 The relationship between the Italian academies (beginning with Ficino) and those of sixteenth century France is the subject of Yates, French Academies Chapter 1, 1-13. 153 James Hankins presents a critique of the traditional understanding of Ficinos Academy as a center of Florentine intellectual life, arguing instead that the documentary evidence suggests that the academy was an informal gymnasium or school attended by his pupils, and highlights Ficinos unofficial role at the university at Florence, in James Hankins, The Myth of the Platonic Academy of Florence, Renaissance Quarterly 44 (1991), 448-449; 454; 454, note 85. Hankins also discerns seven different categories of meaning for the Latin academia in the Renaissance, ibid., 433-436. 154 Yates, French Academies 20-21. 95

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academy, which included a general study of mathematic s. Mersenne provides an account of this academy in his early commentary on Genesis.155 This royally-sponsored musical academy provided a model for Mersenne to follo w, a model that stressed education. The schools for French gentlemen, which adopted the designation of acadmies and appeared during the late sixteent h and early seventeenth century, provide further evidence of the educational connotations of the term.156 These schools taught pr actical arts, such as horsemanship, fencing, and dancing. In addition, many instructed th eir pupils in the basics of mathematics. Such knowledge was a prerequisi te for the art of for tification, which those destined to the military would undertake. In these academies, the emphasis was on practical rather than pedantic knowledge, in opposition to the universities. But instruction for young men remained their focus. In Italy, likewise, academ ic terminology was allied with the teaching of the crafts, perfected through the appl ication of theory to practice: Painters form, together with glass-makers, e ngravers, cabinet-makers, and even saddlers and stationers, a corporati on, placed under the patronage of Saint Luke and which has responsibility for the training of apprentices. Alberti and Leonardo da Vinci demand, in their treatises on painting, a fundamental modi fication of practical teaching both scientific and theoretical. It is this require ment that engenders the corresponding acadmies In 1577, the corporation of Saint Luke of Rome becomes an acadmie .157 155 Yates, French Academies 23-25. Yates provides an English translation of Mersennes passage from Quaestiones celeberrimae in Genesim (1623) and argues for its importance as a sour ce for information about Bafs approach to his musical academy. 156 See Knabe, Lhistoire du mot acadmie, 31; H. C. Barnard, The French Tradition in Education: Ramus to Mme Necker de Saussure (Cambridge, 1922), 116; Philippe Aris, Centuries of Childhood: A Social History of Family Life trans. Robert Baldick (New York, 1962), 203-208. 157 [L]es peintres forment avec les verriers, les doreurs, les benistes et mme les selliers et les papetiers une corporation, place sous le patronage de saint Luc et laquelle incombe la formation des apprentis. Alberti et Lonard de Vinci rclament dans leur traits sur la pein ture une modification fondamentale: que le fondement de lenseignment pratique soit une formation scientifique et thorique. Cest de cette exigence que naissent les acadmies correspondantes. En 1577, la corporation de saint Luc de Rome devient une acadmie, Knabe, Lhistoire du mot acadmie, 32-33. 96

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Academies devoted to specific arts or crafts, such as those of Baf s, the gentlemen of France, and the craftsmen of Italy, informed Merse nnes understanding of the term. In this vein, Mersenne suggests, in La vrit des sciences the formation of an academy of alchemists in each province so that they might be wellguided by the master of their craft: But I desire that this art was treated more fa ithfully, and with a fine r order than it is: and that there would be raised up in each Realm, or even in a town of each province, an academy for alchemy, as well as for the other arts and that the master of the Academy, and the magistrate, take care that the Alchemists point out all that coul d serve the health of man, for whom God has created the heavens and the earth. This would be the means of preventing the abuses which are committed in this art, and to punish all of the charlatans, who run throughout all the towns, so that no one may be ruined, and lose time in huffing and puffing, that each one ought to be employed in serving God, the King, and the public.158 Like the proposed alchemical group, Mersennes acadmie thus provided a means for continuing legitimate mathematical activity. The Minim sought to provide intellectual encouragement and guidance to those who worked toward the completion of mathematics in its diverse forms. Without governmental support for his academy, Mersenne served as organizer and master. As the example of Pascal demonstrates, Mersennes academy also served as an informal place of training based on cooperative research. This community of savants, as other academies of its time, played a role de supplance, as Jean Mesnard argues, to provide for the lack in universities.159 It was, indeed, a new form of education160 one whose substitution was preferable both morally and intellectually: 158 Mais ie desirerois que ct art ft traitt plus fidelleme[n]t, & auec vn plus bel ordre quil nest pas: & quon dresst vne academie pour lAlchymie dans chaque Royaume, ou mesme dans vne ville de chaque prouince, aussi bien comme pour les autres arts, & que le maistre de lAc ademie, & le magistrat eussent soin que les Alchymistes remarquassent tout ce qui pourroit seruir la sant de lhomme, pour lequel Dieu cre le ciel & la terre. Ce seroit le moyen dempescher les abus qui se commettent dans ct ar t, & de punir tous les charlatans, qui courent parmy les villes, afin dempescher quaucun ne se ruint, & perdt le temps souffler, quvn chacun doit employer seruir Dieu, le Roy, & le public, Mersenne, La vrit des sciences 105-106. 159 Jean Mesnard, Le XVIIe sicle, p oque de crise universitaire, in La culture du XVIIe sicle: enqutes et synthses (Paris, 1992), 103. Another informal group, with a so mewhat different audience, also met during the first half of the seventeenth century. Thophraste Renaudot viewed his weekly conferences, which drew a wide crowd of amateurs, as the most profitable means of providing instruc tion. In the conference en titled Of the conference and if 97

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There issued from the Mini ms Mersenne faithful friend, A savant man, wise and outstandingly good. His cell was to be prefer red to all the schools. (All of the masters [there] are swelled with ambition). Around Mersenne turned, as around an axis, each star of knowledge in its proper sphere.161 Pascals Model of Mathematical Success The evidence in this chapter concerni ng the educational ba ckground and pedagogical experiences of several members of the Mersenne Circle provides support for the argument that, in its relationship with Pascal, the group manife sted specifically educa tional tendencies. The training of the young cannot be viewed as the primary or perhaps even a major motivation of this early scientific society. But there is ample reason to believe, especially in the case of Pascal, that the group attempted to cultivate and promote someone who represented its future. This is further attested by Adrien Baillet, in his Vie de M. Descartes regarding the prodigy who appeared around the same time among the Mathematicians of Paris:162 it is the most instructive type of teach ing (4 March 1641), various views are put forward about teaching. The final states that the conference is most amenab le to learning because it places all of the options before a group, leaving the decision of the correct one to the silent votes of the company, Thophraste Renaudot, De la petite fille velue et autres confrences du Bureau dAdresse (1632-1642) ed. Simone Mazauric (Paris, 2004), 13-17. A recent work has examined the format and subject matter of the conferences, Kathleen Wellman, Making Science Social: The Conferences of Thophraste Renaudot, 1633-1642 (Norman, OK, 2003). 160 une forme nouvelle deducation, Mesnard, Le XV IIe sicle, poque de crise universitaire, 110. 161 Adfuit e Minimis Mersennus fidus amicus; / Vir doctus, sapiens, eximieque bonus. / Cujus cella scholis erat omnibus anteferenda; / Professorum omnes ambitione tument / Illi portabat, si dignum forte porisma / Reppererat quisquam, principiumve novum. / Perspicuo et proprio sermone, carente figuris / Rhetoricis gnomis, ambitione, dolo, / Ille dedit doctis, qui vellent, rursus ut illud / Vel statim possent, vel trutinare domi. / Edidit e multisque inventis optima quaeque; / Signans authoris nomine quidque sui. / Circa Mersennum convertebatur ut axem / Unumquodque artis sidus in orbe suo, Thomas Hobbes, Opera philosophica quae latine scripsit omnia ed. William Molesworth, vol. 1 (London, 1839), xci. 162 le prodige qui parut vers le meme tems parm y les Mathmaticiens de Paris Baillet, Baillet, Vie de M. Descartes, 1:39. 98

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The prodigy was that a young boy of sixtee n years had composed a Treatise on Conic Sections, which was a cause of astonishment to all the old Mathematicians to whom it had been shown.163 When Descartes replied somewhat indifferently to the copy of the Essai sent by Mersenne, Baillet continues, M. de Roberval, M. le Pailleur, & the other friends of Messieurs Pascal exclaimed against an opinion which did not appear to them [to be] obliging enough for a child of such rare merit.164 If Mersenne and the amis de Messieu rs Pascal were too enthusiastic about Pascals achievements, Baillets account of thei r reaction to Descartes nevertheless reiterates their concern to see their young protg succe ed within the larger savant community. Pascals early life is inextricably tied to both the educational approach of his father and the clear interest of the Mersenne group in nurtu ring and encouraging the talent of a teenage mathematician. His experiences as a youngster in the group would provide a core identity as he progressed through his mathematical and natural philo sophical career. He made every effort to move beyond his identification as a promising child, but the members of the Mersenne group would continue to consider him as their protg. Pascals involvement in the weekly Parisian ma thematical conferences also signals that the development of posterity was a concern of at least part of the nascent scientific movement. Little effort has been made to understand how learned co mmunities viewed their fu ture, especially as it involved educating a new generati on. The foundation of the official Acadmie Royale des Sciences included a group of members known as lves, but little research has been carried out on these individuals or the role that they played in the daily life or long-term strategy of that 163 Le prodigetoit quun jeune garcon de seize ans avoit compose un Trait des Coniques, qui faisoit le subjet de ltonnement de tous les vieux Mathmatic iens qui on lavoit fait voir, ibid. 164 M. de Roberval, M. le Pailleur, & les autres amis de Messi eurs Pascal se recrient cont re une opinion qui ne leur paroissent assez obligeant pour un enfant dun si rare mrite, ibid., 40. 99

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100 institution.165 Within the different manifestations of the Mersenne group, Pascal continued to be an important participant and symbol. His early mentors would continue to promote and protect him, even after he had achieved scientific stardom. For Pascal, the Mersenne group offered a vi sion of what it meant to be learned, and equally, a model of what it meant to train in a part icular field. Coming of age in this atmosphere, Pascal was reminded of the privileges he had r eceived, the intellectual gifts, the nurturing exercise, and his responsibility to honor those privileges. While he was praised as a promising young geometer, Pascals education combined di sciplined work with natural talent and inclination. Throughout his life, notions of childhood, matu rity, and hard work played a key role in every phase of his intellectual life, from mathematics and physics to philosophy and religion. Pascals early training within the Mersenne group laid the foundation for his mathematical career and his spiritual life. When he left Paris with his family in 1640, he took with him the sense of mission he learned as an apprentice to the Parisian mathematicians. 165 David Sturdy is able to give brief summaries of the work of some of the lves, but also notes the paucity of study on them, Sturdy, Science and Social Status: The Members of the Academie des Sciences, 1666-1750 (Rochester, NY, 1995), 127-137. Of the goal of training new scientists, Sturdy writes: It may also have been assumed that as they gained experience within the Acadm ie they would eventually provide the core of the next generation of academicians. If this aspiration indeed wa s held by Colbert and by senior members of the Acadmie then it was realised only in part, for two of the lves, Pi vert and La Voye-Mignot, made so little impact that even today almost nothing is known about them, ibid., 127.

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CHAPTER 3 PAINFUL LEGITIMATION: NATUR E, DISCIPLINE, EXERCISE The previous chapter showed that Mers enne saw Pascal and Huygens as new Archimedeses poised to contribute to the perfec tion of mathematics. This potential was based on sound training from their father s, Mersenne recognized, not just on raw talent. This chapter will seek to show that Mersenne recognized that Pascal and Huygens required continued hard work and clear direction to be consummated as Archimedeses. I argue that Mersennes works dealing with music demonstrate his belief that training in the arts a nd the sciences is as important as natural inclination, the influence of bodily humors, or power s exerted by stars at birth or conception. Building on this background of his early mentor and other contemporary sources, the chapter goes on to argue that Pascals wr itings about craftsme n in Rouen and about opponents of his views on the void resonate with th e primacy of discipline and exercise (rather than nature) expressed by Mersenne. During this period, this chapter suggests, Pascals writings highlight the virtues of maturity in ways that, although in harmony with Me rsennes views of the acquisition of learning, distance him from the childlike role that had characterized his identity in the Mersenne group. This chapter will begin with a brief consideratio n of the early modern notion of intellectual inclinations. This will provide a backdrop to th e consideration of questions of the relationship between nature and nurture in the work of Me rsenne. Then, Mersennes general views on the limitations of natural inclinations will be explored with a subsequent deta iled investigation of his evaluation of the relative importance of natu ral inclination and concerted application in the realm of music. These first two sections define the set of pr oblems and issues that will be discussed vis-vis Pascals life. The balance of the chapter consis ts of an analysis of Pascals work and writings 101

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dealing with the arithmetic machine and the prob lem of void, in order to uncover patterns of expression that support the hypothesis that Pascals position as an emerging star prompted him to seek legitimation by placing himself in cont rast with those who worked only by natural inclination or instinct. Inclinations and Intellectual Pursuits in Context Classification of Inclinations In seventeenth-century France, references to inclinations were multifaceted. The stillpredominant Aristotelian worldview was teleological ly oriented, with all things (rocks, animals, human beings, heavenly bodies) having inclinations according to their respective natures. As it refers to human beings, inclination was seen as a general category of in ternal factors affecting behavior. Pascals contemporary, Marin Cureau de la Chambre (1594-1669), wrote a work entitled Lart de connoistre les hommes in 1659. One of the chapters of the work is Des inclinations. In it, Cureau de la Chambr e describes inclination as seated within the appetit of the human soul, where it brings about a dispos ition to be moved to a particular action.1 He continues by stating that an inclination is a disposition [that is] constant and which has spread long and deep roots in the soul.2 Such constant dispositions come from nature or habit. If the origins of dispositions were multifarious so were the actions to which inclination disposed one. Cureau de la Chambre subdivides inclinations into those that ha ve to do with the body, mind, or moral actions. This chapters content is relate d to the significance of bodily and intellectual inclinations. The question of mo ral inclinations will be pursued in Chapter 5, in the context of Pascals later association with Port-Royal. 1 Marin Cureau de la Chambre, Lart de connoistre les hommes (Paris, 1669), 64, 60. 2 Ibid., 61. 102

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The first set of inclin ations was understood to be rooted in the body. Inclinations of the body may be instinctual, as in the case of sheep, which butt heads even before they have sprouted horns. These inclinations were though t to be morally neutral and tended only to the continuation of the natural order of things.3 But they might also be learned through habit, as with the disposition of an artisan effectively to use a tool.4 Such actions could be motivated by good or evil intentions and could be used well or poorly. As this chapter will show, Pascal saw little difference between th ese two types of bodily inclinations. In his writings on the arithmetic machine, he equated the habitual inclinations of the body with the instin ctual inclinations of animals. By doing this, he stressed the inferi ority of craft knowledge compared to creative, mathematical inventions. Neither of these bodily inclinations, he suggests, is sufficient for developing the expertise of a savant. Intellectual Inclinations and the Choice of Career Huartes Examen and types of esprit Attitudes about intellectual inclinations are particularly important for understanding Pascals efforts to assume the role of a new Archimedes. Such inclinations were believed to be those that led individuals to pursue different kinds of knowledge and that determined an individuals potential for success in some field. One of the work s that influenced seventeenthcentury thinking most was Juan Huartes Examen de ingenios para las ciencias Huarte (15301592), a physician, first published his work in 1575 in his native Spanish. By the middle of the seventeenth century, there were editions in Italian, Latin, English, Dutch, and French.5 By 3 Other examples that Cureau de la Chambre gives are of snakes that bite before having venom and birds that try to fly before their wings are ready, ibid., 64. 4 Ibid., 63. 5 The different editions are catal ogued in Gabriel A. Prouse, LExamen des esprits du docteur Juan Huarte de San Juan: sa diffusion et son influence aux XVIe et XVII3sicles (Paris, 1970), 217-218. 103

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Pascals death, the work had appeared in sevent een French editions by two French translators: Gabriel Chappuis (twelve edit ions between 1580 and 1633) and Charles Vion Dalibray, poet friend of the Pascal family (f ive editions between 1634 and 1661).6 The subtitle of Huartes work attests to its purpose: in which is s hown the differences of Minds [ Esprits ], which are found among men, and to what ty pe of science in particular each one is suited.7 Huarte argues that some people are suite d by nature to the study of oratory, some to law, some to theology, some to medicine or anot her discipline, while others are not fit to any type of learning.8 Drawing on the work of Galen con cerning humors and their qualities, he insists that From these three Qualities alone, Heat, Moisture, and Driness, proceed all the differences of Wit [ esprit] observd among Men.9 Thus, natural qualities are absolutely necessary for proficiency in any subject, and any attempts to train someone contrary to these natural inclinations will be Vain and Fruitless.10 The role of the teacher, argues Huarte is to 6 Dalibrays translation would appear in four more editions before the end of the seventeenth century, Prouse, Lexamen des esprits 218. 7 Juan Huarte, Lexamen des esprits povr les sciences, ou se mons trent les differences desprits, qui se trouuent parmy les hommes, & a quel genre de science chacun est propre en particulier trans. Charles Vion Dalibray (Paris, 1645). 8 The titles of some of the chapters, in Juan Huarte, The Tryal of Wits, Discovering the great Difference of Wits among Men, and what Sort of Learning suits best with each Genius trans. Edward Bellamy (London, 1698), include: What Wit is, and what Differences of it are ordinarily observed among men (Chapter 1), 1; That the Theory of Divinity belongs to the Understanding, and Prea ching (which is the Practic) to the Imagination (Chapter 12), 214; That the Theory of Laws pertains to the Memory; Pleading Causes and Judging them (which is Practic) to the Understanding; and Governing of a Commonwealth to the Imagination (Chapter 13), 244; The Differences amongst men unqualified for Sciences (Chapter 2), 22. 9 Huarte, Tryal of Wits (1698), 129 (Chapter 18 title). Carlos G. No rea, Notes and Discussions: Juan Huartes Naturalistic Humanism, Journal of the History of Philosophy 10 (1972), includes a ch art that associates the predominance of the qualities of Humidity, Heat, and Dryness with particular intellectual endeavors: 1) Humidity (Memory)Languages, Theory of Law, Positive Theology, Geography, Arithmetic; 2) Heat (Imagination)Poetry, Eloquence, Music, Practice of Medicine, Politics; 3) Dryness (Intelligence)Theology, Theory of Medicine, Philosophy, Practice of Law, 73. 10 This is in spite of Ciceros examples of philosophers, who seemed slow and inept in their childhood yet by the hard work of their masters became important thinkers in those fields that had once confounded them: if the Youth has not a pregnant Intellect susceptible of proper Rules and Precepts appropriated to the Art he Studies, even the 104

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open the way to Learning based on natural capacit ies and inclinations, a nd students who seek a master to instruct them in something for which they do not have the right esprit do but plague themselves and their Teachers.11 Central to Huartes educa tional philosophy, then, was th e discovery of a persons temperament at a young age: [I]t is convenient before the Child be sent to School, to discover his Inclination, and the tendency of his Parts, to find out what Study is most agreeable to his Capacity, so to order Matters, that he wholly apply himself to that.12 Such a discovery would be beneficial for the state as well as the individual.13 Such a procedure was followed in the utopia of Tommaso Ca mpanella (1568-1639), an Italian Dominican theologian and philosopher, and sometimes considered a child prodigy.14 In his City of the Sun Campanella writes that children are evaluated for th eir potential prof iciency in arts and sciences by exposing them to different su bjects one after the other: In order to find out the bent of the genius of each one, after their seventh year, when they have already gone through the mathematics on the walls, they take them to the readings of all the sciences.15 Bartoli and the relationship between inclination and effort The Jesuit Daniel Bartoli, in his The Learned Man Defended and Reformd, published in Italian in 1645 (transla ted into French in 1654 and English in 1660), approves of a pedagogical Roman Orators diligent care of his Son, as also all the Prudence of the best of Fathers prove Vain and Fruitless, Huarte, Tryal of Wits (1698), 34. 11 Ibid., 35. 12 Ibid., 37. 13 Ibid., 38. 14 Campanellas early years, including the evidence of his precocious intellect, his life-shaping illness at 13, and his training at a Dominican monastery ar e described in John M. Headley, Tommaso Campanella and the Transformation of the World (Princeton, 1997), 14. 15 Tomaso Campanella, City of the Sun, in Famous Utopias, ed. Charles McLean Andr ews (New York, 1901), 284. 105

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practice similar to Huartes and Campanellas. Bartoli, a teacher of mathematics, emphasized the role of discipline and hard work, as subseque nt evidence will show. Bu t he also stressed the importance of uncovering inclinations to arts a nd sciences at an early age. The method of encyclopedic exposure to different types of la bor may be traced, Bartoli claimed, to ancient Greece: The Wise Athenians esteemed it a foundation of never knowing any thing, not to know from the beginning to apply ourselves to that for which Nature designd us. Thence it was that before they applyed their children to a ny profession, they curious ly inquired into their Inclinations; of which the Desires commonly are Truth-telling-Interpreters: and that they did, by laying before them the implements of all the Arts.16 For Bartoli, inclination must be the point of departure for the pursuit of the status of an individual learned in ar ts or sciences: it is necessary to consult the Genius and from its inclinations to take directions.17 According to Bartoli, those attempting to work contrary to their inclinations are like planets moving in retrograde, they make but small progress.18 On the positive side, Bartoli asserts, some i ndividuals are so particularly inclined to a single type of work not by the elec tion of the Will but by instinct of Genius that denying them such an activity would remove an essential aspect of them.19 [O]therwise they have nothing considerable, and indeed seem Monstrous.20 For Bartoli, it is imperative to discover these natural tendencies. To study in one area while ha ving natural talent in an other is self-defeating and produces misshapen knowledge. It is a warp ing of God-given purpose and an insult to the Creator. On the other hand, the inha bitants of Thomas Campanellas City of the Sun for 16 Daniel Bartoli, The Learned Man Defended and Reformd trans. Thomas Salusbury (London, 1660), 275-276. 17 Ibid., 274. 18 Ibid., 274. 19 Ibid., 297. 20 Ibid., 297. 106

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example, produce good work and it gives them pleas ure, because they are trained in precise accordance with their inclinations: Since from childhood they are chosen according to their inclination and the star under which they were born, therefore each one working according to his natural propensity does his duty well and pleasantly, because naturally.21 The Ratio studiorum and selection through inclination The Ratio Studiorum the guiding document of early-mode rn Jesuit schools, is less overt about the necessity of well-match ed inclinations, yet the judgment of students talents is an integral part of the educati onal program. A ccording to the Ratio those who exhibit certain abilities should be given specific opportunities. For example, while all second-year philosophy students are required to attend a fo rty-five minute public lecture in mathematics, if some have some abilities and the inclination for this study, they will exercise themselves after the course in private lessons.22 In the same way, the rule appoints t wo or three men eminent in letters and eloquence in each province with the task of identifying individuals with the abilities and inclination conducive to the positio n of master of humanities. This cultivation of natural talent will provide, the rule states, a so rt of harvest of good professors.23 Mersenne and the Limits of Intellectual Inclinations Mersennes attempts to develop th e talent of Pascal and Huygens should be seen in light of the evidence that exists regarding his views on the re lative importance of natural inclination and the development of that inclinati on through training and in tellectual application. Mersenne does not fully explain his perspective on this relationship in his writings. His pos ition may be explored, 21 Campanella, City of the Sun, 300. 22 Adrien Demoustier, Julia Dominique, and Marie-Madeleine Compre, eds., Ratio Studiorum: Plan raisonn et institution des tudes dans la Compagnie de Jsus trans. Lone Albrieux and Dolors Pralon-Julia (Paris, 1997), 82. 23 Ibid., 83. 107

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however, through some of his opi nions regarding Naturalism and by making some cautious generalizations from Mersennes views on inclination and application in music. Mersennes Rejection of Determinism for Intellectual Inclinations Astrological determinism Robert Lenobles massive study, Mersenne ou la naissance du mcanisme situates the Minims philosophy between Renaissance Naturalism and Scholasticism, both of which he rejected for a kind of mechanism. Mersenne could not accept the deterministic character of sorcery and Kabbalah. The spells of sorcery and the correspondences of Kabbalah, with their emphasis on hidden, ineluctable processes, threaten ed the place of divine providence and human free will.24 More to the point, Mersenne rejected the determinism of judicial astrology as embodied in the work of Girolamo Cardano ( 1501-1576), who argued that Christs birth and other miraculous events were the resu lt of the natural forces of astrology.25 Mersenne could not accept deterministic astrology, but such previous Christian thinkers as Augustine and Thomas Aquinas had allowed the infl uence of the stars over human temperament, which influences human possibilitie s, but leaves room for freedom.26 Without contradicting key Christian axioms, then, he could endorse an astrologically-influenced version of Huartes temperamental scheme regarding types of mind. Mersenne remained cautious about astrology, 24 Car, et cest l le suprme danger de la Cabale, dans luniverselle correspondance qu elle imagine entre les noms, les astres, les lments et les personnes, la destine hu maine nest plus quun lment de lhistoire cosmique, Lenoble, Mersenne 108. 25 Marin Mersenne, Limpit des distes, athes et libertins de ce temps (Paris, 1624), 212. Lenoble provides an analysis of Mersennes view s on astrology in Lenoble, Mersenne, 128-133. Astrological nativities are but one small aspect of early modern astrology, claiming to be able to predict the future of a person based on the alignment of the planets at the moment of thei r birth. This most extreme claim for astrological determinism may be compared with the more general, widely-accepted view in early modern Europe, that the heavenly bo dies somehow influenced the course of terrestrial events; see Lynn Thorndike, The Place of Astrology in the History of Science, Isis 46 (1955): 273-278. The classic work on the history of astrology is Lynn Thorndike, History of Magic and Experimental Science 8 vols. (New York, 1923-1958). 26 Lenoble, Mersenne 128-129. 108

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however, because of its associations with determinism, but also b ecause of the lack of decisive evidence for connections, a problem that had prompted some empirical investigation.27 His caution echoed a similar hesitancy on the part of Huarte. For Huarte, the acceptance of astrological causes of different types of mind would destroy his project of attempting to show how parents might shape the intellectu al inclinations of their children. 28 Mersennes questioning of astrol ogical predictors wa s expressed in the context of music, but with an argument that could be generally applied to other endeavors. In the first question of his Preludes de lharmonie unive rselle ou questions curieuses (1634), Mersenne asks whether or not a talented musician is determined by the in fluence of stars and planets. He provides a detailed description of three different nativi ties that astrologers claim might produce this perfect Musician. He explains the rationale used by those who claim th at such talent arises through the particular stella r configurations present at the time of birth. He then objects to each nativity, demonstrating its manife st ambiguity. He argues that the combined influence of the planets is so complex that the same positions of the stars that seem to portend the perfect musician also countermand that possibility. Astrology is self-contradictory, Mersenne claims, untrustworthy in predicting someones inclination to an occupation or science. He does not 27 Ibid., 132-133. A manuscript in the Bibliothque Natio nale, Paris, fonds franais 1 2293, attributed to JeanBaptiste Morin, provides a number of diagrams and descripti ons of the nativities of individuals of renown, including tienne Pascal, who appears with Desargues preceded by the following description: esprit des hommes principalement ceux qui son plus destaches des employs comme mathematiciens poetes musicians. The entire collection is presented as a collection of empirical data to test questions of the influence of nativity, which the author seems to doubt: il y a Dans Vn de mes manuscrits Vn traict que J[]ay faict de mes opinions sur Lastrologie et en son prambule mes sentiments de la medecine et de La Chim ie et mes experiences. ce discours est pour preuuer que les astres nagissent que par les qualites naturelles, et que les Iugements nen peuuent estre que generaux et Incertains, encore que L[]examen nen puisse estre trop exacte, f. fr. 12293, folio 6r. 28 The Astrologers hold, that the Child being born under su ch an Influence of the Stars will be Wise, Witty, Well or Ill-conditiond, happy or unhappy, with a thousand other qualities, and properties, whic h we see and observe every day among Men. But if this were true, we could not here prescribe any Rules; for all would depend on Chance, and not be our Choice, Huarte, Tryal of Wits (1698), 443. Huarte argues that parental nutrition, the timing of intercourse, and other physical factors relating to the pare nts bodies determine the type of child that will be produced. 109

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dismiss Judicial Astrology enti rely, probably because of Thomas Aquinass endorsement of it, but he concludes that a simplistic determination of effectiveness in music through the stars is not a satisfactory hypothesis: I would say that it seems that nothing assu red may be predicted about the inclinations or perfection of the child, because of the ma tter of which its body is formed, the milk and the meat with which it is nourished, the air that it breathes, the diverse company among which it is raised, and a thousand other circ umstances, which are gr eatly significant, and more than sufficient to prevent all the predic tions of the Astrologers, even if these had a perfect knowledge of nature and the effects of all the St ars, which they never have.29 Temperament and inclination Mersenne agreed with Huartes dismissal of astrological determinism, but he also went a step beyond it. He did not agree with Huarte about the determinative influence of the qualities of heat, dryness, and humidity. The argument (fro m the same source as the passage above) deals with music, but his appeal to empirical comple xity could well be applied to other pursuits. Mersenne argues that there is no one temperament suited to the Perfect Musician. It is impossible, he states, to determine who will be able to compose or play good music based on theories of bodily composition. This conclu sion seems obvious, experience causing us to see excellent Musicians of all sorts of temperaments.30 He thus denies that the whims of nature 29 Je diray quil semble quon ne peut rien predire dasseur des inclinations, ou de la perfection de lenfant, raison de la matiere, dont son corps est form: du laict, et de s autres viandes, dont il est no urry; de lair quil inspire, des diverses compagnies parmy lesquelles il est lv, et de mille autres circonstances, qui sont grandement considerables, et trop suffisantes pour empescher toutes les predictions des Astrologues, encore quils eussent une parfaite connoissance de la nature, et des effects de t ous les Astres, laquelle ils nauront jamais, Mersenne, Questions inouyes; Questions harmoniques; Questions thologiques; Les machniques de Galile; Les prludes de lHarmonie Universelle (Paris, 1634; repr. 1985), 560. Jean Mesnard takes note of a set of lists of individuals compiled perhaps between 1650-1660 (origi nally associated with Jean-Baptiste Morin) that consiste chercher, aprs coup, le rapport qui peut exister entre la desitne d un homme et la position des astres sa naissance, puis, par comparaison de plusieurs cas, dgager des constantes, des lois, One of the people mentioned in these lists, under the category Esprit des hommes, principalement ceux qui sont plus dtachs des emplois, comme mathmaticiens, potes, musiciens, etc., car les autres sont partout so us les autres chapitres, et principalement des honneurs is tienne Pascal: Monsieur Pascal, excellent en mathmatique musique, esprit prompt, subtil, entendu aux affaires, Mesnard OC 459-460. 30 lexperience nous faisant voir d excellents Musiciens de toutes sortes de temperaments, Mersenne, Questions inouyes, 601. 110

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produce learning or exclude it. Mersenne claims that the responsibility fo r success is not with the parents, as Huarte had asserted, but with th e individual acting in perfect freedom. Mersenne claims that application of the mind makes a successful musician in th e same way that selfdiscipline creates the possibility of a morally righteous life: It is very easy to conclude from all of th e preceding discourse, th at the temperament and the humours do not so dominate reason that it does not keep its freedom or cannot overcome vices and imperfections, for it is as easy to correct the temperament or inclination that moves one to theft or some other bad action as it is for the melancholy Musician to compose songs, and ga y tunes; he does this throu gh the rules of art, which arm reason against sense, and mind against temperament.31 Nature, Discipline, Exercise: Necessary Components for Learning Another passage that deals with music furthe r develops Mersennes ideas about the place of personal initiative in acquiring expertise. In a section of his monumental work Harmonie universelle (1636), Mersenne borrows a section from a treatise by a Parisian lute teacher named Basset, which develops the principles needed for skill in playing the instrument. His analysis of the project of becoming skilled, however, is generalized: Most of those who have considered the arts & sciences require three conditions to acquire the perfection of them, that is, Nature, Discipline, & Exercise, without which one cannot arrive at the end that one proposes for oneself.32 This statement helps justify, to a degree, the gene ral parallel that this chapter tries to draw between Mersennes approach to musical proficie ncy and Pascals application to mathematical 31 Il est tres-ays de conclurre de tout le discours precedent, que le temperament, et les humeurs ne dominent pas tellement la raison, quelle ne demeure dans sa libert, et quelle nen puisse surmonter les vices, et les imperfections, car il est aussi ays de corriger le temperament, ou linclination, qui porte au larrecin, ou quelquautre mauvaise action, comme il est ays au Musicien melancholique de composer des chants, et des airs gays; ce quil fait par les regles de lart, qui arment la ra ison contre le sens, et lesprit contre le temperament, Mersenne, Questions inouyes 602-603. 32 La pluspart de ceux qui ont traict des arts & des scie nces, requierent trois conditions pour en acquerir la perfection, sauoir la Nature, la Discipline & lExercice, sans lesquelles on ne peut arriuer au but que lon sest propos, Mersenne, Harmonie universelle Livre second des instrumens, 76. 111

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learning. Caution is warranted in making the le ap, but with the further development of the argument it is hoped that the connection will appear plausible, if not compelling. The discussion of musical talent and applic ation by Basset recognizes the existence of a natural inclination that makes for an easier path in musical accomplishment. Some individuals have such a sensitive ear, Basset argues, that they are able to hear the dis tinctions in notes, thus having an advantage in learning music.33 In another passage, Merse nne considers the gift of a fine voice, linking it to other gifts given by God, including the intellectual skill of an Aristotle: There is no difficulty in teaching those w ho have a good voice [to sing], because it is within them [naturally] to imitate, and to do all that is wanted; which happens similarly with all other Apprentices, w ho have more need of a brake than a spur, as was said of Aristotle, when he was still a student: from there comes the Latin proverb gaudeant ben nati [rejoice you well-born], because of the good quali ties that nature & birth give to some & that they deny to others; which one must attribute to the order of Divine Providence.34 Nevertheless, Mersennes writings on music i ndicate that he was not willing to accept the view that nature preselected those that would be talented at singing, playing the lute, or composing music: The Art of making good Songs on all sorts of subjects does not depend only on the genius, whim, & inclination of thos e who make them, but also on the judgment that ought to provide guidance to Composers, as to other Artisans, in all that they undertake, in order that they be able to give th e reason for the chords, the degrees, the intervals, the passages, & the trills that they em ploy in their compositions.35 33 loreille si delicate, Mersenne, Harmonie universelle Livre second des instrumens, 77. 34 Il ny a nulle difficult enseigner ceux qui ont vne bonne voix, parce quils se portent deux-mesmes imiter, & faire tout ce que lon veut; ce qui arriue semblablement tous les autres Apprentifs, qui ont plus besoin du frein [brake] que de losperon [spur], comme lon disoit dAristote lors quil estoit encore escolier: de l est venu le Prouerbe Latin gaudeant ben nati raison des bonnes qualitez que la na ture, & la naissance donnent quelques vns, & quelles denient aux autres: ce que lon doit rapporter lordre de la Prouidence Diuine, Mersenne, Harmonie universelle Embellissement des Chants, 2: 354. 35 LArt de faire de bons Chants sur toutes sortes de sujets ne dpend pas seulement du genie, de la caprice, & de linclination de ceux qui les font, mais aussi du iugement qui doit seruir de conduite aux Compositeurs, c me aux autres Artisans, en tout ce quils entreprennent, afin quils puissent rendre la raison des chordes, des degrez, des interualles, des passages, & des tremblemens, quils employent dans leur compositions, ibid., 2: 360. 112

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Mersenne stresses in this passage the importance of an intellec tual capacity (judgment) that should be exercised in order to have success in composition. Such an application of mind would ostensibly help to improve t hose who were already talented. Perhaps even more significantly, the passa ge by Basset disputes the idea that the naturally talented have an unquestionably privil eged position. But those who lack such traits could take heart: As the most sterile earth is made fertile by the care and diligence of the laborer, so those who believe themselves to be incapable of lear ning this art ought to be assured that they can overcome the defects of nature, & inclin ation, by putting into practice the teachings that we set forth.36 The language in the passage evokes the figure of cultivation that was often a part of describing the educational process. Growth comes through the diligence of both teacher and pupil. Even if nature has granted advantages to some, the pa ssage suggests, those without such advantages could become accomplished. The talents, or the deficiencies, of the child had to be improved and matured in order to attain perfection. Only the lack of proper learning and exercise the above passage s uggests, would finally disqualify someone as a lute player. The need for application rather than dependence on natural inclination may be linked to the broader theme of a rejection of ignorants. Although the topic is addressed in his writings on musi c, it also appears in other wo rks. Considering these works together helps to provide a sense of the relative importance attached to hard work and studied effort to attain to ones full potential. 36 [C]omme la terre la plus sterile est rendu fertile par le soin & la diligence du laboureur, ainsi ceux qui croyoient estre incapables dapprendre cet art, doiuent sasseurer quils peuuent surmonter les defauts de la nature, & linclination, en mettanten pratique les ense ignemens que nous allons donner, Mersenne, Harmonie universelle Livre second des instrumens, 76. 113

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In his Questions harmoniques Mersenne addresses a claim made by some of his contemporaries that the tr uth is found by the ignorant and not by the savants. 37 According to this opinion, the ignorants were those who relied on the simp le judgment of the senses in the practice of an art, believing th at the application of the opini ons of the ancients were an unnecessary burden. They believe that those who apply themselves diligently to principles of the art are most often preoccupied with and have th eir minds so attentive to the authority of the Ancients.38 It is the senses, the ignorants declare, through which it would be necessary to begin to reestablish the scie nces if they were lost.39 Even mathematicians, according to the claim recorded by Mersenne, have had to admit this and submit to the notion of common sense.40 Mersennes critical response to this opinion upholds the impo rtance of becoming learned. He emphasizes that specialized fields are the re sult of time and effort. While the common person or child who is unlearned in an ar t or science may be able to dis cern the most banal principles of that art or science, Mersenne claims that there are limitations to the final ability-level of these ignorants : The light of reason, which is nearly all alone in the mind of th e ignorant, could well give to them some light tincture of th e truth, but it is not great enough to make them penetrate into particular truths, which contain very many difficulties, as are t hose which serve as object to the arts, and to the sciences, and which have need of several experiences/experiments. From there it comes that they are mistaken the most often when they want to extend too much the little knowledge that they have, being similar to those who believe to be able to uncover all this that there is in a town, or in a large country with the light of a little candle, 37 Mersenne, Questions inouyes 171. 38 [Ils] sont le plus souvent preoccupez, et ont lesprit tellement prevenu de lautor it des Anciens, ibid., 167. 39 par lesquels il faudroit commencer rtablir le s sciences si elles estoient perdes, ibid., 170. 40 The privileging of the ignorants over the savants is ironically, a characteristic of both libertine and devout. The libertine quotes Lucien: Le meilleur mode de vie une vie toute dor, est celui des ignorants et des simples particuliers, Theophrastus redivivus III, Libertins du XVIIe sicle vol. 2, 331; think also to the title of a dialogue by La Mothe Le Vayer: De lignorance louable. Some devouts, for their part, blasment ou mesprisent les sciences sous pretexte de pit, Mersenne, Harmonie universellem, De lutilit, 20. 114

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where a thousand torches would not be sufficien t; or to those who judge colors in the shadows, or by the light of the fire, which are constrained to be withdrawn in the clear light of day: for the knowledge of the sava nts with respect to that of the ignorants is as the light of day and of the Sun compared to that of a candle, or of a shiny piece of glass.41 Mersennes claim against the praise of the i gnorant ties the discussion in the context of music to other comments that he makes about mathematics. In La vrit des sciences for example, Mersennes Christian Philosopher di stances himself from those who claim to be learned in mathematics, but do not have th e proper training. He describes them as: the many ignorant [people] who want to pe rsuade the world through their sophisms, & paralogisms, that they have found the quadrature of the circle, the duplication of the cube, the trisection of the angle and have recognized several errors in the definitions & propositions of Euclid, even though most of these reckless [ones] know neither the very first terms of Geometry, nor the [proper] way of speaking about it.42 Mersenne argues that such foolish ones shoul d not have any attention given to them by geometers, for fear that by such condescension it would be believed that they approve of these reckless [ones].43 Ignorance is, for Mersenne, a state of nature. It is the unimproved stat e. The analysis of lute-playing in Harmonie universelle summarizes this view in its assertion that without the aspects of Discipline and Exercise nature is imperfect and blind.44 Mersenne sought to safeguard the claim to learning from the flock of ignorant [people] who speak as parrots in a 41 Mersenne, Questions inouyes 175. 42 quantit dignorans qui veulent persuader par leurs sophismes, & paralogismes, quils ont treuu la quadrature du cercle, la duplication du cube, la trisection de langle & reconu plusieurs erreurs dans les definitions, & propositions dEuclide, bien que la plus part de ces temeraires ne scachent pas seulement les premiers termes de la Geometrie, ni la maniere den parler, Mersenne, La vrit des sciences 750. 43 de peur que par ceste condescendence on croye quils aprouuent lignorance de ces temeraires, ibid. 44 Mersenne, Harmonie universelle Livre seconde des instrumens, 77. 115

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cage, often without knowing what they say.45 For Mersenne, nature is clearly limited in its ability to comprehend the fu ll range of knowledge of an art or a science. Mersennes mathematical academy provide d a forum for establishing legitimate specialized learning. The group would provide, by way of its exclusivity, an endorsement to those who were within its ranks. They woul d be one of the group of our Geometers [ Nos Geometres] mentioned so often in their letters. Me rsenne sought to estab lish the role of the savant in mathematics so that they might ultima tely be financially protected and patronized by governmental authority.46 But in order to do this, he had to counteract those who claimed that it is worth as much to say this is a Mathema tician, as if one sai d, this is a fool.47 Many people viewed mathematics as being unrelated to practical matters. It was abstract and few of its claims could be verified by the senses. Mathematics was the epitome of uselessness, and this created a lower status for mathematicians. It was precis ely the division between mathematics and physical reality that Galileo sought to overcome by combining the roles of philosopher and mathematician under the courtly patronage of the Grand Duke of Tuscany.48 Mersenne also worked for legitimacy, for himself and for his circle of frie nds. He desperately sought to overcome the perceived uselessness of mathematics in La verit des sciences 45 Mersenne, Limpit des distes 187. 46 Mersennes attempts to establish a means of legitimtion in seventeenth-century France is rooted in issues similar to those that troubled Italian mathematicians during the fifteenth and sixteenth centuries. Mario Biagioli considers the questions of how mathematicians sought to gain more social legitimacy in Biagioli, The Social Status of Italian Mathematicians, 1450-1600, History of Science 27 (1989): 41-95. Biagioli stresses the attemps of mathematicians to reiterate the certainty of their di scipline as a means to well-defined prof essionalization measures, ibid., 54. Mersennes emphasis on mathematics in La verit des sciences is an echo of this concern. 47 Mais vous nauez pas rpondu ce que iauois dit des autres sciences naturelles, particulierement des Mathematiques, qui me semblent de pures rueries, cest pourquoy ce nest pas sans suiet quon appelle ceus qui sen meslent, Maistres Mates, car ils sont quasi tous fols, & vaut autant dire cest vn Mathematicien, comme si on disoit, cest vn fol, Mersenne, La verit des sciences 66. The argument is attributed to one of the oppositional voices (The Skeptic) in Mersennes book. 48 Mario Biagioli, Galileo Courtier: The Practice of Science in the Culture of Absolutism (Chicago: University of Chicago Press, 1993), 105-106, 203-209. 116

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Becoming Archimedes: Working for Legitimacy During the years that Pascal li ved in Rouen (1640-1647), he expr essed himself in ways that emphasized his mathematical learning. In this section I argue that du ring this period Pascal emerged out of the shadow of the Parisian group and that he worked to move beyond his position as an apprentice to one of legitimacy in his own right. Through his work on the arithmetic machine and the experiments on the void, he was moving from potential young star to accomplished savant. He was becoming Archimedes. During this period of self-legitimation, Pa scals writings emphasized that his work depended on concerted practice and intellectual a pplication. As this section will show, Pascal expressed a contrast between hi mself and his opponents that suggest an attempt to move away from being identified as child-prodigy. In his wo rk with the arithmetic machine, lack of manual skill forced him to cooperate with artisans, but he vehemently maintained the superiority of the savant theoretician to the habituated worker. In his experiments a nd writings on the void, by contrast, Pascal battled established scholars who unblinkingly relied on the expertise of the ancients to decide a physical question. In the fi rst case, he upheld the master-servant relationship of the super-natural mathematician and the nat ural artisan. In the second, he opposed those who denied the cumulative aspects of physical k nowledge. They thereby preferred the state of the beasts, or the natural state, to that of the human being, m ade only for infinity. In both cases, through the disciplined and trained imitation of God s works (the mind through the arithmetic machine, the display of a void in the tube) he interacted with pedagogical nature. By learning from nature, through his interaction with obs erved phenomena, he transcended the original, unimproved state of nature. Pascal became a full-fledged savant during th e Rouen period, which will be attested by changes in the ways members of the learned comm unity referred to him. During this time, he 117

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used mathematics to create amazing effects and to promote philosophical reflection. In short, he displayed the God-imitating quality of the learne d mathematician, not the animal-like quality of those who focused on shaping matter or those who i dolized the ancients. In his youth, Pascals mentors were amazed by the mature thinking of the child. During this period, this section will propose, Pascal left childhood behind in favor of maturity and expertise. Imitating the Creator: Pasc als Calculating Machine Narrative summary In March 1638, tienne Pascal was marginally involved in an uprising of those who were owed payment for rents on the Htel de Ville. The rents were unpaid by the government because the war with Spain had drained the coffers. Seve ral individuals who were involved in this event were arrested including some fr iends of tienne, and tienne went into hiding in the Paris area and probably also in Clermont, Pascals town of origin.49 tienne bided his time, awaiting the return to Richelieus favor. Meanwhile, the Pasc al children remained in Paris, probably under the care of the family nurse, Louise Delfault. In April 1639, the tide turned for tienne. On e of the elder Pascals friends, an actor named Montdory, spent time talking with Cardinal Richelieu, specifically pleading the innocence of tienne in the affair of the rents. Not long after, the youngest of the Pascal children (Jacqueline) performed a ro le in a play, entitled Lamour tyrannique at Richelieus home. After the play, Jacqueline, then thirt een years of age, approached th e cardinal, who received her with the exclamation, Here is the litt le Pascal! He showered aff ection on her and heard her pleas on behalf of her father. He consen ted to her requests, te lling her, Go, I agree to all that you have 49 This and subsequent events in the Pascals lives are record ed by Gilberte Prier in her Vie de Jacqueline Pascal, Mesnard OC 1:660-662. 118

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asked of me; write to your father that he may return in entire safety.50 Shortly thereafter, by fall 1639, tienne was appointed as deputy commissary in Normandy for the collection of taxes associated with the sustenance of troops there. In the spring of the following year, the family was reunited in a house in Rouen. When Blaise left Paris, the seedbed of his savant career, only a few individuals (including the Mersenne Circle and some of Mersennes correspondents) knew of hi s mathematical work. As Chapter 2 showed, there is little evidence of great enthusiasm for Pas cals earliest project, except among the small group with whom he met on a weekly basis. Du ring his time in Rouen, however, Pascal initiated work on his arithmetic machine and on his experiments and writings on the void. These two projects would establish his learned reputation during his lifetime and until the posthumous publication of his other works. Pascals name became well-known first becaus e of his machine calculer, sometimes referred to as the Paschaline. Its invention was directly related to his fathers employment in Normandy. tienne oversaw the collection of taxes in the region and, as such, had to make large arithmetic calculations. These calculations we re extremely time-consuming using the traditional methods. In 1643, the work and strain of these calcul ations were such that hi s letters to his eldest daughter (now married and living elsewhere) were irregular. He writes to her: My good daughter will excuse me if I do not wr ite to her as I would desire, having no leisure to do so. For I have never been burdene d by the tenth part of what I am now In the past four months I have not gone to bed six times before two oclock in the morning.51 50 Allez, je vous accorde tout ce que vvous me demandez: crivez votre pre quil revienne en toute sret, Jacqueline Pascal to tienne Pascal, 4 April 1639, Mesnard OC 2:211. See also Gilberte Prier, Vie de Jacqueline Pascal, Mesnard OC 1:661-662. 51 Ma bonne fille mexcusera si je ne lui cris comme je dsi rerais, nayant aucun loisir. Car je nai jamais t dans lembarras la dixime partie de ce que jy suis present . [I]l y a quatre mois que je [ne] me suis pas couch six fois devant deux heurs aprs minuit, tienne Pascal to Gilberte Prier, 31 January 1643, Mesnard OC 2:283. 119

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Blaise began work on his arithmetic machine in order to ease tiennes load and perhaps his own, since Blaise probably helped his father with these duties: The length and difficulty of the ordinary means that are used having made me think to some quicker and easier assistance, in order to help me in the great calculations with which I had found myself consumed for some years in several affaires related to the employ with which it pleased you to honor my father for the service of His Majesty in Haute Normandie.52 Since Blaises father was so busy with his work that he could not go to bed until after midnight, it seems unlikely that he did much to continue his scientific or mathematical interests. There are likewise no extant letters or treat ises to suggest that Blaise advanced his work with conic sections or other areas of abstract geometry. It was up to Blaise to put his talent to work. He applied himself to an engineering task: the creation of a machine to assist his father. Pascal henceforth entered a new phase of hi s career. In the writings of this time he increasingly distanced himself from his image as a child with adult-like intellectual skill in several ways that this chapter will show. In his writings, he c ontrasted his own knowledge with the artisans craft, which he characterized as similar to natural, animal instinct. He described his projects as having put into practice the talents of his nature and applied the principles and methods that he had obtained through good instruction. In so doing, Pascal earned renown in the circles of French intellectual culture.53 Pascal tells the story of the arithmetic mach ines creation in two documents, written after a number of exemplars of the machine had been cr eated. Blaise began work on the machine when 52 Les longueurs et les difficults des moyens ordinaires dont on se sert mayant fait penser quelque secours plus prompt et plus facile, pour me soulager dans les grands calculs o jai t occup depuis quelques anns en plusieurs affaires qui dpendent des emplois dont il vous a plus honorer mon pre pour le service de Sa Majest en la Haute Normandie, Blaise Pascal to Ch ancellor Sguier, 1645, Mesnard OC 2:332; John R. Cole has suggested, in his psychoanalytic study of Pascal, that the arithmetic machin e should be seen as an offering to the father, Cole, Pascal 49. 53 [J]employai cette recherche toute la connaissance que mon inclination et le travail de mes premires tudes mont fait acqurir dans les mathmatiques, B. Pascal to Sguier, 1645, Mesnard OC 2:332. 120

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he was nineteen years old (1642-1643). By the ag e of twenty-one, while visiting Paris, Pascal succeeded in making an appointment, through the me diation of Pierre Bourdelot, to show the prince de Cond a prototype.54 Following up on this meeting, a dedicatory letter for the machine was written to Chancellor Sguier in 1645, and a Notice necessary for those who may be curious to see the arithmetic machine, and to make use of it [ Avis ncessaire ceux qui auront curiosit de voir la machine arithmtique, et de sen servir ] was printed in Paris a short time afterward. These two sources, the additional info rmation drawn from the privilege itself, and contemporary writings about the machine suggest Pa scals attempt to establish himself as a fullfledged savant. The privilege that was eventually granted to Pascal as the sole inventor of the machine provides the best description of its inner workings. There are various ways that the machine might be constructed to do what Pascal wanted, but the main principles of the mechanism seem to be the same in each.55 The key to its operation was the in terlocking of toothed wheels. These wheels were aligned so that a full turn would e ngage the next wheel in the line, causing it to move one place, thus counting the turns of th e first wheel. Then, when the second wheel had turned through a full revolution, it would likewise engage the next wheel and move it a single position. For example, with a decimal version of the machine, as are the two examples now located in Clermont and in Dresden, there woul d be a number of wheels (between six and ten), 54 Pierre Bourdelot to Blaise Pascal, 26 February 1644, Mesnard OC 2:297. 55 The privilege that was granted to Pascal for the making of his machine in 1649 describes a number of the different ways in which the machine was attempted: De laquelle machine il aurait fait plus de cinquante modles, tous diffrents, les uns composs de verges ou lamines droites, dautres de courbes, dautres avec chanes; les uns avec des rouages concentriques, dautres avec excentriques, les uns mouvants en ligne droite, dautres circulairement, les uns en cnes, dautres en cylindres, et dautres tout diffrens de ceux-l, soit pour la figure, soit pour le movument; de toutes lesquelles manires diffrentes linvention principale et le mouvement essentiel consiste en ce que chaque roue ou verge dun ordre, faisant un mouvement de dix figures arithmtiques, fait mouvoir sa prochaine dune figure seulement, Privilege, Mesnard OC 2:713. 121

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each of which have nine arms extending from its center.56 The spaces between the arms are associated with each of the digits 1-9 and the wh eels represent the various powers of ten. The far right wheel represents ones, the next to the left tens, the next hundreds, and so on. When the operator wishes to add a number, he inserts stick or pen into th e appropriate space on the wheel and turns it. When the wheel fo r the ones has rotated th rough an entire circuit, its tens wheel, which moves a single position, and the machine i ndicates a single ten. If the ones wheel makes another full circuit, the tens wheel moves to the second position, representing two tens, or twenty. The machine displays the cumulative total on drums labeled 1-9, which rotate in connection with the wheel when the opera tor moves it with a quill pen or stick. The interlocking parts of this type of machin e had to be made with precision, requiring cooperation between the theorist Pa scal and local artisans. While in Rouen, Pascal enlisted the mechanical skills of clockmakers. Clockmaking had been an important tr ade in Rouen since the fourteenth century. As such, the talent pool from which Pascal could draw was deep. When he enlisted artisans to implement his design, however I met obstacles as great as those that I wanted to avoid.57 Trouble with clockmakers Pascals initial difficulty was the difference in skills of the theorist and the artisan. Unlike the neat interlocking of wheels that Pascal envisioned in his machin e, the linkage of practical and theoretical knowledge in this complex task required a nearly impo ssible fine tuning of communication and personal relationship: 56 Some other versions of the machine include wheels that indicate monetary values. For a detailed description of the machines function, see Vernon Pratt, Thinking Machines: The Evolution of Artificial Intelligence (New York: Basil Blackwell, 1987), 48-53. 57 B. Pascal to Sguier, 1645, Mesnard OC 2:332. 122

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Not having the skill to handle metal and hammer as [I do] pen and compass, and artisans having more knowledge of practice of their art th an of the sciences on which it is founded, I saw myself reduced to quitting my entire undertaking, through which there came to me only very much fatigue, without any good success.58 Pascal does not detail the difficulties he encounter ed but his writings suggest possible factors. Because Pascal could not use the proper tools to create the gears and box and other parts of this machine with sufficient precision, he had to rely on the artisans handiwork. But because the artisans were not trained in mathematics, mechan ics, and physics, Pascal would have to attempt to communicate to them the means of making th ese parts without using the customary language of the theorist. He implies that the artisans lacked the intellectual savvy to understand the complex functioning of his machine. It would be ineffective to use the comprehensive design strategy as a means to communicate the technical requirements for the individual parts. Instead, Pascal had to work in piecemeal fashion with hi s clockmakers. He established rules (with the dual meaning of measurement and method) fo r the artisan to follow in the making and assembling of parts. The standards for the individual parts were created by Pascal through his knowledge of theoretical disciplines.59 The artisans had only to follow the rules. At the heart of Pascals challenge were the workers customary mode of learning and the scope of their training, both of which were rooted in habit rather than original thought. A clockmakers apprentice learned to use a hammer, a lathe, or a file through bodily repetition. This repetition, combined with instruction from the master, instilled a set of guidelines that governed the workers movements when he made particular common objects, such as the gears of a clock. In the case of a new invention such as the arithmetic machin e, Pascal argues, the 58 Nayant pas lindustrie de manier le mtal et le marteau comme la plume et le compas, et les artisans ayant plus de connaissance de la pratique de leur art que des sciences sur lesquelles il est fond, je me vis rduit quitter toute mon entreprise, dont il ne me revenait que beauc oup de fatigues, sans aucun bon succs, ibid. 59 He had, he writes, to give [to the artisan] the measures and the proportions of all the pieces of which it [the machine] ought to be composed, Mesnard OC Avis, 2: 339. 123

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worker (even a master) lacked the hands-on experi ence and inherited rules requisite to proceed unaided. Theory provided the rules by which th e physical piece was made. Furthermore, while the function of each piece of a cl ock is firmly fixed through repeat ed custom, the fabrication of parts for the arithmetic machine was a first-time ev ent. Only when continual exercise has given to the artisans the habit of follo wing and practicing these rules [of theory] with assurance is the worker able to craft the parts of the new invention without assistance.60 In multiple senses, then, the craftsman is regl. In the first place, he follows essential instructions that have been passed along by an authority. As such, he is also regl in his status. Just as artisans did not belong to the ruling class, so in th e realm of knowledge, they must submit to an authoritative power. No matter thei r level of experience, apprentice and master alike were pupils of the theorist. Technicians and theorists in the work of Desargues The idea of technician as disciple or as pupil to the theoretician also appears in the work of Desargues, Pascals mentor in projective geometry. Like Pascal Desargues is often praised for his brilliance in both abstract and applied mathem atics. He wrote treatis es on the technique of perspective in painting, the making of sundials, and architectural practic es (e.g., shaping stones for buildings).61 In a controversy that took place between 1640 and 1644, he was accused of 60 Avis, Mesnard OC 2:338. 61 Girard Desargues, Mthode Universelle de mettre en perspective les ob jets donns rellement ou en devis, avec leurs propositions, mesures, loignemens, sans employer aucun point qui soit hors du champ de louvrage in Oeuvres de Desargues 1: 55-84; idem, Maniere Vniuerselle de tracer au moyen du style plac, tous quadrans plats dheures gales au soleil, auec la reigle, le compas, lequierre et le plomb in Oeuvres de Desargues, 1: 352-358 (plus plates); and (using the same beginning of title as his original work on conics), Brouillon projet dexemple dvne maniere vniuerselle du S. G.D. L. [Sieur Girard Desargues de Lyon] touchant la pratique du trait a preuues pour la coupe des pierres en larchitecture; et de les claircissement dvne maniere de rduire au petit pied en perspective comme en gomtral, et de tracer tous quadrans plats dheures gales au soleil in Oeuvres de Desargues, 1:305-358. For a scholarly look at Desargues pr actical works, see Antoine Picon, Girard Desargues ingnieur, in Desargues en son temps: 413-422; Franois-Rgis Cottin, Larc hitecte et larchitecture Lyon au temps de Desargues, in Desargues en son temps 425-432; Jol Sakarovitch, Le fascicule de stromtrie: entre savoir et mtiers, la fonction de larchitecte, in Desargues en son temps : 347-362. 124

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plagiarism, pride, and practical ineptitude. To answer the last charge, Desargues was forced to argue the pedagogical du ties of a theorist.62 In his defensive treatises, Desargues portrayed himself as a master to those who practiced the arts of drafting architectural plans and cutting stones. Os tensibly, the desire to aide practitioners motivated this in structional role. The word ai de also appears in Pascals description of his work on the arithmetic machine and the assist ance he had to give to the workers and suggests the similarity of the two mathematicians attitudes toward workers.63 Desargues help took the form of a simplificatio n of the instruction that the artisans received from their masters: I was touched by the desire to understand, if it were possible to me the foundations, and the rules of their [the stonecutters] practice, such as one would fi nd them and see them when in use; I noticed ther eby that those who gave themselves to it, had to burden themselves with the memory of a great number of diverse le ssons for each of them; and which through their nature a nd condition, produced an incred ible encumbrance in their understanding, and far from causing them to have diligence for the execution of the work, caused them to lose time there.64 Desargues belief that craftsmens nature a nd condition made learning a vast number of lessons difficult is central to his self-styled positi on as a teacher of artisa ns. Mersenne similarly suggests the mental inferiority of technical workers when he attri butes the limitations of bell size in part to the imbecilit de lartisan.65 Pascal reemphasizes the sa me trait in his arithmetic 62 A helpful account of the main lines of this extended controversy is found in Ren Taton, Loeuvre mathmatique de Desargues 48ff. 63 [I]t is likewise absolutely impossible to all the simple artisan s, as able as they be in their art, to put to perfection a new piece which consists, as this, in complicated movements, without the help [ aide ] of a person who through the rules of theory gives to him the measures and the proportions of all the pieces with which it ought to be composed, Avis, Mesnard OC 2:338-339. 64 Reconnaissance de M. Desargues, in Desargues, Loeuvre de Desargues 1:487-488. 65 Mersenne, Harmonie universelle, Livre septiesme des instrumens de percussion, 3. 125

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machine writings when he identifies an artisan as a simple-minded man.66 Desargues, Mersenne, and Pascal do not clea rly indicate what they mean in declaring artisans to have inferior intellects by nature. It is probable, however, that there was a significant social factor involved and that the shared char acteristics of artisan al classes had to do with a complex of typical educational patterns a nd habituated subservience. Desargues compares the artisans of the bu ilding industry to children. Their lack of capacity is primarily related to their style of learning, which wa s habitual and based on simple rules, therefore not developing the memory. De sargues method of teaching children to sing, recorded in Mersennes Harmonie universelle, likewise stresses the limitations of his young students. Desargues sought to simplify the skill by stressing the imitation of sounds of either the masters voice or an instrument the master played: The advantage that comes from this way of l earning to read & make the notes of Music is that the understanding is greatly assisted by it, [while] memory and sight are not employed very much, & [it is] almost as if only the hear ing and the voice of the Disciple are at work, when he exerts himself thus on a book of Music; from which it arises that the mind is not disheartened in the long exercise necessary for the apprenticeship of the Arts, as it is disheartened when it has several difficulties to combat & to overcome at the same time, as [occurs] in the ancient way of learning to sing, with the subtleties & diverse names that each note receive; such does not occur in this method.67 Both child and artisan, then, require a method th at is not complex but sufficiently simplified by his superiors. The artisan parallels the child in that both are unlikely to memorize a great deal. 66 Avis, Mesnard OC 2:339. 67 Lauantage que lon reoit de cette maniere dappren dre lire & entonne les notes de la Musique est, que lentendement sen trouue grandement soulag, la memoire & la veu ny ont pas beaucoup demploy, & ny a quasi que loye & la voix du Disciple qui trauaillent, lors quil sexerce ainsi dessus vn liure de Musique; do vient que lesprit ne se rebute pas dans le long exer cice necessaire lapprentissage des Arts, c me il se rebute lors quil a plusieurs difficultez combattre & surmonter en mesme temp s, comme en la faon ancien ne dapprendre chanter cause des muances & diuers noms que chaque note reoit: ce qui ne se rencontre point dans cette methode icy, Mersenne, Harmonie universelle Art de bien chanter, 2: 341. 126

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By nature and condition, both worker and child are hindered by limited capacity for memorization. The adult practitioners whom Desargues sought to instruct in pers pective did not agree with his evaluation of their limitations nor were they desirous of becoming pupils in Desargues theoretical classroom. It was, one critic raile d, as if Desargues believed that all the painters who appear there [in Paris], a nd of which this great city know s the works, understand nothing of their craft.68 The same critic was appalled that a man that has never practiced their art wants to make himself their master in it.69 Desargues claim to be ab le to teach painting without being a practitioner upset the traditional master-apprentice hierarchy. Desargues defends his invasion of this order by referr ing to another art, in a pa ssage from the preface to his Perspective : For doctors, in order to make themselves sava nt in their profession, neither go to school nor to the lesson of apothecaries who put in effect their ordinances; but on the contrary the apothecaries, in order to make themselves ca pable in their profession, go to the school and to the lesson of doctors, in which the doctors are masters, and the apothecaries disciples; also geometers, in order to be advanced in this science, do not go to the school and lesson of masons, but on the contrary, the masons in order to render themselves capable of the geometrical drawings necessary fo r the practice of their art, a nd to become more capable of making a masterpiece for their mastership, go to the school and to the lesson of the geometers, in which in the same way, th e geometers are masters, and the masons disciples.70 Desargues here sets up a hierarchy similar to that which Pascal expresses in his writings on the arithmetic machine. The theoretician holds the po sition of authority and e xpertise with respect to the individual that uses his hands to fashion the product. The ge ometer, Desargues states, is the one to invent; the mason is the one to trace manually, position and mason the said rocks and 68 Tout Paris sait comme il va publiant partout, que tous les peintres qui y paroissent, et desquels cette grande ville admire les ouurages, nentendent rien en leur mestier, Anon ., Advis charitables sur les diverses oeuvres et fevilles volantes dv sievr Girard Desargues Lyonais, in Loeuvre de Desargues 2: 271. 69 quvn homme qui na iamais pratiqu dans leur art, sy ve uille rendre leur maistre, et les ose faire passer dans les meilleures compagnies pour des ignorants, Anon., Advis charitables, in Loeuvre de Desargues 2:272. 70 Reconnaissance de Monsieur Desa rgues, Place en tte de la Perspective de Bosse, 1618, in Loeuvre de Desargues, 1:491-492. 127

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to learn by memory and effect the rules of practice of the trait [i.e., alignment]71 For Desargues, as for Pascal, the artisan has been trai ned to be, and therefore essentially is childlike, placed under the authority of the theoretical mathematician. The opinions of Mersenne, Pascal, and Desar gues belong to an established tradition that sees theory as superior to pr actice. During the early modern period, however, the theoretician and practitioner increasingly inte racted and experience and experi mentation grew as key values in natural philosophy. As a re sult, the relationship between artisan and theorist grew increasingly ambiguous. Pamela H. Smith explores the implications of this renegotiation of traditional categories in her work, The Body of the Artisan Smith argues for the importance of artisans to the developing epistemology of the Sc ientific Revolution. Their engagement with the natural world provided the ground upon which lim inal practitioners could seek legitimacy.72 One Rouennais artisan attempted to establish his legitimacy by creating an arithmetic machine like Pascals. Pascal writes about his machine primarily to protect his interests from such imitations. Pascals defense According to Pascals Avis, the integrity of his machine was threatened by counterfeits. A false execution of his invention was a ttempted by a worker of the town of Rouen, clockmaker by profession.73 None of the scholarship on th e various exemplars of Pascals 71 Reconnaissance, in Loeuvre de Desargues 1: 492. The term trait is used in architecture to indicate the lines that guide carpenters and masons in their construction. Th e phrase pice de trait, according to the a nineteenthcentury dictionary of architectural terms, refers to [a] piece of which all the parts have been cut according to the rules of the art; it is a masterpiece of cutting, Ernest Bosc, Trait, Dictionnaire raisonn darchitecture et des sciences et des arts qui sy rattachent vol. 4 (Paris, 1880), 348. 72 Artisans or craftspeople were, I believe central in establishing and articulating the epistemology that gave such liminal practitioners authority and that helped brin g about this new philosophy, Pamela H. Smith, The Body of the Artisan: Art and Experience in the Scientific Revolution (Chicago, 2004), 19. 73 un ouvrier de la ville de Rouen, horloger par profession, Avis, Mesnard OC 2: 339. 128

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machine has been able to ascertain the identity of the indicted clockmaker, much less locate the device that he constructed. Pascal himself makes no attempt to iden tify or discuss this worker. He may have withheld the identity of the offendi ng party to ensure that the artisan received no further advertisement and to ensure that pr actitioners did not usur p the position of the theoretician. Perhaps Pascal hi mself was not aware of the name of this clockmaker, a signal of the inherent namelessness of artis anal professions at that time.74 In either case, it is clear that the counterfeiter is in direct c ontrast to Pascal, the discipli ned and learned mathematician. Novelty, rashness, and daring As learned inventor, Pascal corresponds to Mersennes maistre who knows the theory of music and can thus create new compositions. In contrast, the worker is portrayed as the ignorant who presumes to exerci se what is not within the scope of his training. Furthermore, because the training of the worker is based on me morization and habit, the artisan remains in the state of nature. The artisans training and education does not l ead from natural inclination to mature completion, as Mersenne claims for the musical savant.75 Artisan and mathematician alike experience limitations with novelty, but Pascal makes a distinct contrast regarding the possibility of each one overcoming those limitations. The learned 74 Edgar Zilsel cites this lack of recognition during the Renaissance in his important article, Zilsel, The Sociological Roots of Science, American Journal of Sociology 47 (1942): 544-562. The humanist literati mostly ignored workers: If they mentioned them, they did so in an exceedingly careless and inaccurate way. From the present point of view the culture of the Renaissance owes its most important achievements to the artists, the inventors, and the discoverers. Yet these me n entirely recede into the background of the literature of the period, ibid., 551. The education level of these artisans also contributed to name lessness: They were uneducated, probably often illiterate, and perhaps for that reason, today we do not even know their names, ibid., 551-552. Zilsel argues for a profound change that took place by 1600, which brought artist-engineers to gr eater intellectual prominence. He rightly points out the key connection between the emergent inductive me thods and the artisans give-and-take with matter. Nevertheless, as Pascals language shows, the division be tween the work of the savant and of the artisan is still important during the first half of the seventeenth century. 75 I was helped in this distinction between types of edu cation by a section in a paper by Natasha Gill, Second Nature: The Nature/Nurture Debate in Enlightenment Pedagogical Thought, From Locke to Rousseau, http://se1.isn.ch/serviceengi ne/FileContent?serviceID=PublishingH ouse&fileid=4DA8669 A-60E3-77B9-3ABB2B2E6666B645&lng=en (accessed 7 October 2008). Gill explores th e 18th century educational connotations of the relationship between natural inclination and habit/custom 129

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inventor ultimately has the capability to undertak e and execute new works, if he makes a disciplined application of knowledge.76 Such effort would be wasted for the artisan. On the one hand, Pascal calls his own attempt to cr eate the machine a bold action [ une action tmraire ] in which I dared [ os ] to attempt a new path through a fiel d strewn with thorns, and without having a guide to clear the way for me.77 On the other hand, he condemns in similar terms the workers attempts to imitate his creation, sa ying that it represents their ignorance and rashness [ tmrit ]78 of daring [ oser] to undertake more than their equals79 Temerity and daring were virtues for one equipped to take on the challenge of new works, but were vices for the worker. This is based not merely on an ab solute social barrier between theoretician and practitioner or even on what Ba rtoli calls the imprudence of pursuing certain disciplines against the inclination of [ones] Genius .80 The artisans transgression is to make something for which only years of mathematical training would suffice. The imperative that workers remain in their place is an assertion of political and social power, and the attempt to usurp the position of the theoretician is a t ype of social upheaval, similar to the killing of the mistresss cat as recounted by Robert Darnton.81 More importantly for Pascal, it is also a safeguarding of the process through which a person becomes a savant. 76 dentreprendre et dex cuter ouvrages no uveaux, Avis, Mesnard OC 2: 338. 77 [J]ai os tenter une route nouvelle dans un champ tout h riss dpines, et sans avoir de guide pour my frayer le chemin, B. Pascal to Sguier, 1645, Mesnard OC 2: 333. 78 Avis, Mesnard OC 2: 338. 79 doser entreprendre plus que leurs semblables, Avis, Mesnard OC 2: 338. 80 Bartoli, Learned Man Defended and Reformd 274. 81 Robert Darnton, Workers Revolt: The Great Cat Massacre of the Rue Saint-Sverin, in The Great Cat Massacre and Other Episodes in French Cultural History (New York: Vintage, 1985): 75-104.. 130

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Imitating God in the act of creation Pascals reaction to the workers of Rouen is lin ked to the pursuit of Mersennes agenda for mathematical knowledge. Pascal argues that th e artisans should confine themselves to the manipulation of matter rather than dabbling in the complex and creative work of invention, or even the copying of invention. Mersenne had outlined his desire for mathematics to reach perfection and, by extension, for the mathematicia n to imitate the most admirable works of God.82 Pascal tackles this task by attempti ng to imitate the mind through his arithmetic machine. The artisan is fixed in the creatu rely realm of the sec ond nature of habit. The theoreticians God-imitating posture and st atus as master is a part of Mersennes response to those who argue that musical practic e is master of musical theory. Mersennes Questions harmoniques features the voice of an objector to this relationship between theory and art. Desargues painte rs had rejected the mathematicians role as pedagogue. Here, likewise, theory is considered dependent on practice. Mers ennes objector states: the Theoreticians know nothing but what they learn from practiti oners, whose maxims and experiments they presuppose.83 Mersenne counters, in a classical m ove, by linking his own hierarchical scheme to the superiority of Gods contemplation of himsel f. In Platonic fashion, the act of creation is an expression of that contemplation: It is necessary to conclude from all of this that the theory of sciences and of arts, and consequently of Music, which in some way correspond to the inward operations of God, ought to be preferred to pract ice, which corresponds to the works of God, which we call external.84 82 Mersenne, preface to La vrit des sciences n.p. 83 [L]es Theoriciens ne savent autre chose que ce quils apprennent des praticiens, dont ils supposent les maximes, et les experiences, Mersenne, Questions inouyes Questions harmoniques, 184. 84 Do il faut conclure que la theorie des sciences et des arts, et consequemment de la Musique, qui respond en quelque maniere aux operations interieu res de Dieu, et ses divines ides, doit estre prefere la pratique, qui respond aux oeuvres de Dieu, que nous appellons exterieures, ibid., 190. 131

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Thus, Mersenne argues that the Theory of the scie nces is in some way similar to the divine ideas, for it is the exemplary cause of practice.85 Pascals echoing of Mersennes articulation of the master-pupil, God-creature relationship of theoretician to artisan suggests that his self-legitimation in the matter of the arithmetic machine is an expression of the attempt to pur sue a continuation of Mersennes agenda. His invention would prove him to be the new Archim edes, as Mersenne had hoped. In his work on the arithmetic machine, Pascal denies to the cl ockmaker the dignity of the imitation of Gods works. The best that he can do is to reproduce the works already in existence, since he cannot transcend the habits that crea te a second nature unless he ha s someone who has theoretical knowledge to instruct him and inculcate a new habit, which might be called a second second nature. On the other hand, Pascal, by applying ma thematical principles to the creative process, can create a thing new in natu re, which produces effects clos er to thought than anything done by the animals.86 Monstrosities: Trial and error Pascal clarifies the possibility of the theore ticians imitation of God and its impossibility for the artisan in the way that he describes th eir approach to the invention process and their respective aptitude for give-and-take with matter. Pascal describes the artisans attempts to copy the novelty of his machine as hit or miss. He compares them to someone who is drunk. The workers are intoxicated by the false persuasion that they are able to extend themselves beyond the limited scope of their skills with the hamm er, turn, and file. As a result, they work 85 [L]a Theorie des sciences est en quelque faon semb lable aux ides divines, car elle est la cause exemplaire de la pratique, Questions harmoniques Question 4, 186. To be sure, Mersenne does not discount the importance of reducing theory to practice, afin daider le prochain, et de profiter tout le monde, ibid., 187. 86 Vie de Pascal, Mesnard OC 1:576; Brunschvicg, no. 340: La machine arithmtique fait des effets qui approchent plus de la pense que tout ce que font les animaux, Brunschvicg OC 13:258, trans. A. J. Krailsheimer, in Pascal, Penses trans. Krailsheimer, no. 741, 229. 132

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gropingly, a metaphorical ev aluation that suggests how muddled and clumsy the attempts of the workers are in this enterprise.87 In describing the result of bli nd trial-and-error by the artisans, Pascal uses the metaphor of monstrosity to reinforce their lack of correspondence to the cr eator. Pascal considers the mauvaises copies of his machine to be a deformed infant: It happens that after very much time a nd work, either they produce nothing which corresponds to what they have attempted or, at most, they cause a little monster to appear, whose most important parts are missing, th e others being formless and without any proportion.88 Pascal thus suggests that th e monsters or abortions [ avortons ] produced by the artisans were the result of illegitimate unions engendered by a warped nature.89 Pascal uses the language of monstrosity to por tray the direct link of artisans to corrupt, postlapsarian creation, in contrast with the im peccability of original creation, which was an unmarred expression of Gods creative ideas. Although the monste r that was the counterfeit machine looked similar to the genuine article, this very similarity could damage the reputation of the original. This, in turn, w ould threaten Blaises position as an imitator of the perfectly creative God. 87 ils travaillent en ttonnant, Avis, Mesnard OC 2:338. 88 .[I]l arrive quaprs beaucoup de temps et de trava il, ou ils ne produisent rien qui revienne ce quils ont entrepris, ou, au plus, ils font paratre un petit monstre auquel manquent les principaux membres, les autres tant informes et sans aucune proportion., Avis, Mesnard OC 2:338. 89 Pascal calls them avortons illgitimes and contrasts them with children produced from la lgitime et ncessaire alliance de la thorie avec lart, Avis, Mesnard OC 2:340. Bartoli uses the language of monstrosity to argue against those whose natural Genius does not match up with the field to which they apply themselves: [I]f it happen, that the interests of honour, and profit permit not me n to surcease that which they badly began; you shall see as many Monsters in a Learned Academy as in Affrican Lybia: a Poetical Physician, a Phylosophical Historian, a Mathematical Civilian; in which those in-nate Seeds which are derived from the Womb into the Instinct of the Mind confounding and inter-mingling themselves with those, that are acquired by Study ; whilst neither those nor others prevail; by being one and the other; they are neither one nor the other, Bartoli, Learned Man Defended and Reformd 281-282. 133

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From antiquity through the early modern peri od, the question of mons ters haunted those attempting to understand the relationship between God and nature. A monster was a creature or human being that was born with uncommon characteristics that often mixed the traits of a normal creature or human with those of other creatures. They also included animals and people born as conjoined twins, those with en larged body parts, and hermaphrodites. The appearance of these shocking creatures issu ing from animal or human wombs required explanation, in part because it seem ed to implicate God in imperfection.90 Pascal experienced a similar difficulty in his relationship with the worker s. He was the creator of the machine, in the sense of the one who designed it but his own work was impli cated in the failure of the presumptuous artisans to duplicate it: These imperfections, making it ridiculous, never fail to draw the scorn of all those who see it, of whom most unreasonably place the fault on he who has first had the thought of such an invention, rather than clarifying it with him and then blaming the presumption of those artisans who, through a false boldness [ hardiesse ] daring to undertake more than their equals, produce useless abortions.91 Pascal argues that those who, without proper knowledge, presum e to imitate the work of a true inventor will ultimately fail to create a f unctional, well-proportioned instrument. Both the beauty and usefulness of proper proportionality w ill be lacking. A true creator, Pascal suggests, makes viable productions, not still-born infants. A genuine imitator of God produces inventions that derive beauty from their marvelous functi on, not mere outward adornment. For Pascal, the 90 My discussion of monstrosities is especially i ndebted to Lorraine Daston and Katharine Park, Wonders and the Order of Nature: 1150-1750 (New York, 1998), Chapter 5, Monsters: A Case Study, 173-214. On this issue, see also Alan W. Bates, Good, Common, Regular, and Orderly: Early Classifications of Monstrous Births, Social History of Medicine 18 (2005): 141-158; Alan W. Bates, Emblematic Monsters: Unnatural Conceptions and Deformed Births in Early Modern Europe (Amsterdam, 2005); Laura Lunger Knoppers and Joan B. Landes, eds., Monstrous Bodies/Political Monstrosities in Early Modern Europe (Ithaca, NY, 2004). 91 [C]es imperfections, le rendant ridicule, ne manquent jamais dattirer le mpris de tous ceux qui le voient, desquels la plupart rejettent sans raison la faute sur celui qu i, le premier, a eu la pense dune telle invention, au lieu de sen claircir avec lui et puis blmer la prsompti on de ces artisans qui, par une fausse hardiesse doser entreprendre plus que leurs semblables, produi sent ces inutiles avortons, Avis, Mesnard OC 2:338. 134

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pseudo-creations of counterfeiters, on the other hand, appear to have the same function and utility as the genuine article, but are deceitful. An article we ll-made on the outside but without function is comparable to the deceitfulness of an idol, which though externally beautiful is powerless and useless. This problem plagues Pascals nemesis clockmaker: He makes only a useless piece, truly handsome, shaped and well filed on the outside, but so imperfect within that it is of no use.92 In the clockmakers usual line of work, this kind of monster would be akin to the clock that has a wonderfully crafted shell, and an ornate face, but is unable accurately to indicate the time. For Pascal, the non-functionality of the artisans clock is a si gn of inauthenticity and lack of correspondence with the works of God. Lorra ine Daston and Katharine Park have categorized the responses to monstrosities into three complexes of inte rpretation, signifying the various emotional responses to these irregularities.93 Pascals response to th e clockmakers machine is situated between the categories of horror and repugnance. M onsters were a cause of horror by some accounts because they were signs of human sin that presaged divine wrath. This was further reinforced by the fact that these monsters most often died soon after birth.94 For Pascal, the monstrous, malfunctioning machine signified the transgression of the artisan in attempting the work of the mathematical engineer. But his response is also repugnance at the machines falling short of the perfect design of the godlike desi gner. It violated the standards of regularity and decorum.95 92 [N]e fit-il quune pice inutile, propre vritablement, plie et trs bien lime par le dehors, mais tellement imparfaite au-dedans quelle nes t daucun usage,Avis, Mesnard OC 2:339. 93 Daston and Park, Wonders and the Order of Nature 173-177. 94 Ibid., 177-190. 95 Ibid., 202. 135

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Pascals machine, by contrast with the c ounterfeit item, is a worthy imitation of Gods creation because it is both wonderful in functi on and striking in beauty. One may perform, with it alone and without any effort of mind, the operations of all the parts of arithmetic.96 Pascal does not ignore aesthetics. He takes care to match the outward appearance of the machines to their marvelous usefulness. Their simple boxy design does not lack a certain earthy attractiveness and to some of the machines he added particular embellishments. For example, he ordered silver flanges attached to the number wheels of the machine destined for Queen Christina of Sweden.97 But whereas the Rouennais clockmakers focus was on the showy part of the piece (i.e., the box), the elega nce of Pascals machine, as Jean Mesnard assesses it, comes from a desire for beauty that has constant ly inspired the design of the most necessary pieces.98 No doubt much of the credit for the machin es beauty should be gi ven to the artisans who worked for Pascal, since their hands crafted th e pieces under his supervision. In his critique of the clockmakers copy, however, Pascal draws a stark contrast between the outside and the inside of the machine, which symbolizes th e difference between him and the clockmaker. Indeed, Pascal made it simple for someone to examine the inside of the machine. A panel on the underside of the machine, if taken off, revealed the gears. The lack of functionality would be shown physically if the wheels di d not line up correctly with one another. Beauty and function 96 B. Pascal to Sguier, 1645, Mesnard OC 2:332. 97 Here, I follow Jean Mesnards argument that one of the two exemplars of Pascals arithmetic machine found in the Conservatoire des Arts et Mtiers is the one that was sent to Christina. Part of the evidence that he uses to establish this provenance is the unique feature of the silver flanges: les ro ues de cette machine a t enrichies de collerettes en argent: luxe vritablement royal, dont tous les autres exemplaires sont dpourvus, ibid., 2: 324. 98 un dsir de beaut [qui] a constamment inspir le dessin des pices les plus ncessaires, ibid., 2: 326. 136

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should coincide at the interior of the instrument, providing an authenticating stamp to the machine.99 The artisan produces, through dr unken groping, a monstrous sham of a creation, which the royal privilege that Pascal requests should smother before [its] birth.100 The blindness that characterizes the methodology of the second nature of habit is contra sted with Pascals approach to the problem of making the machine, which em erges from mathematical theory. Instead of a random trial-and-error approach, he begins w ith a profound meditation informed by the combination of his natural inclination and his study in mathematics.101 Then, when his original designs encountered difficulties, Pascal writes, it was theoretical knowle dge that enabled their correction: I began the execution of my proj ect with a machine very different from this [one] both in its material and in its form, which did not however entirely satisfy me, so that in correcting it little by little I gradually made a second one, in which, again encountering inconveniences that I could not tolerate, I composed a third as a remedy to them and however, in the process of perf ecting it, I found reasons to ch ange it, and finally I mustered the patience to make more than fi fty models, all different before having attained the accomplishment of the m achine that appears before you now.102 Through successive attempts, Pascals m achine approached optimal performance. Although the project was not without difficult ies, his method of dealing with failure contrasts with the artisans de pendence on trial-and-error. Pa scal emphasizes his ability to 99 In a more tangible effort to mainta in the integrity of his ma chines, Pascal placed writte n certifications of their authenticity on the inside panel of some versions, Jacques Payen, Les exemplaires conservs de la machine de Pascal, in Loeuvre scientifique de Pascal ed. Pierre Costabel (Paris, 1964): 229-247. The inscription reads: Esto probati Intrumenti symbolum hoc., Blasius Pascal aruernus, Inuentor, 20 may 1652. 100 Avis, Mesnard OC 2:340. 101 B. Pascal to Sguier, 1645, Mesnard OC 2:332. 102 Javais commenc lexcution de mon projet par une machin e trs diffente de celle-ci et en sa matire et en sa forme, la quelle ne me donna pas pourtant la satisfaction entire; ce qui fit quen la corrigeant peu peu jen fis insensiblement une seconde, en laquelle rencontrant encore des inconvnients que je ne pus souffrir, pour y apporter le remde, jen composai une troisime et toutefois, en la perfectionnant toujours, je trouvai des raisons de la changer, et enfin jai pris la patience de faire jusques plus de cinquante modles, tous diffrents avant que dtre venu laccomplissement de la machine que maintenant je fais paratre, Avis, Mesnard OC 2:340. 137

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mentally recognize the ways his machine might be improved, so that throu gh theory and with the knowledge that his training provi ded, it would reach perfection. Like Mersennes vision for attaining Gods archetyp al knowledge of mathematics, Pascal s invention of the arithmetic machine was through successive approximations. He corrected and modified. But the ability to discern error is precisely what is missing from the presumptuous worker who brings his monster into the world. The Christian narrative of the fa ll implicated animal, artisan, and intellectual alike. It is only through reas on, Pascal suggests, that inevitab le errors may be superseded. Reason, he says, is the mark of mature humanity.103 Endorsements compared Having contrasted the func tionality of his machine and his methodology with the counterfeit and its maker, Pascals final step was to highlight the difference between the endorsements that he and the worker of Rouen ha d received. The artisa n had gained recognition because of his instruments inclus ion in the cabinet of a curious [ un curieux ] of the same town [i.e., Rouen].104 By contrast with this popular accep tance, Pascals recognition came from his old academy, the learned mathematicians in Paris. The minimization of the importance of the opinion of the curious is puzzling, since Pascals Avis explains, defends, and presents his machine specifically to les curieux. Indeed, the Mersenne Circle was closely allied to the culture of the curious amateur. The majority of them were not members of intellectual institutions such as the university, but were non-professionals that ha d taken up books at their leisure in order to engage in knowledgeable conver sation. In the Avis, Pascal carefully avoids 103 In the Penses written late in his life, Pascal will write of the paradox of human weakness and human greatness: Through space the universe grasps me and swallows me like a speck; through thought, I grasp it, Pascal, Penses, trans. Krailsheimer, no. 113, 29 (Brunschvicg, no. 348, Brunschvicg OC 13:263). He will reiterate this regarding the distinctive character of human beings: All mans dignity consists in thought, Pascal, Penses, trans. Krailsheimer, no. 756, 231 (Brunschvicg, no. 365, Brunschvicg OC 13:278). 104 dans le cabinet dun curieux de la mme ville, Avis, Mesnard OC 2: 339.. 138

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directly insulting the collector of rare and curious pieces. Instead, he invites his dear reader [ cher lecteur ] to demonstrate good judgment by echoing the approval of the machine pronounced by those, such as his own mentors, who had es tablished a reputation of mathematical learning.105 Without undermining his appeal to the curious, then, he urges them to prefer the verdict of those they already recognize as learned to the ta cit endorsement of an anonymous collector. Pascal thus rejects the claim that these collections are an authoritative source of legitimation in the savant world. The requisi tioning of the little abortion by a curious certainly indicated the notoriety that Pascals ge nuine machine had already received in the town, but the acquirer fell short of tr ue learnedness, for the machine ha d essential defects made clear through a testing of its function.106 The inclusion of the non-functioning copy of Pascals machine in the collection of a curious reinforc ed the comparison with natural monstrosities. Daston and Park describe a response to monsters that is rooted in pleasure and even delight.107 But Pascal argues that the true machine calls fo r wonder, while the monstrosity does not. The delightful design can be most cl early appreciated by those who are aware of the theoretical efforts that were involved. He calls on his audience of curiou s readers to defend him against imperfect savants, even of their own nu mber, who do not have adequate skill in mathematically-based disciplines.108 Pascal takes for granted that the reader will re spond favorably to the learned status of his first tutors. Prior to Mersennes announcemen t of the group in 1635, Cardinal Richelieu called 105 Ibid. 106 Ibid. 107 Daston and Park, Wonders and the Order of Nature 190-214. 108 Lors donc que ces savants imparfaits te proposeront que cette machine pouvait tre moins compose, je te conjure de leur faire la rponse que je leur ferais moi-m me sils me faisaient une telle proposition Avis, Mesnard OC 2:336. 139

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upon several of its participants to render a verdict to the govern mental authorities as to the legitimacy of Jean-Baptiste Morin s method of determining longitudes.109 Pascal likewise appeals to the mathematicians of Paris as authoritative. They, more than the run-of-the-mill curious, would be able to judge the merits of hi s machine, because its in vention required facility in geometry, mechanics, and physics. [I]n Pa ris, he writes, those who are the most wellversed in mathematics have not judged it [the machine] unworthy of approbation.110 His work was certified as legitimate because of their approval: I already have the satisfaction of seeing my little work, not only authorized by the praise of some of the principle [individuals] in this true science but even honored by their esteem and their recommendation.111 This excerpt from Pascals dedicatory letter to Chancellor Sguier demonstrates that such an appeal to well-known specialists was potentially effective in ga ining, not only public acceptance, but governmental support. Mersennes hopes of seeing savants officially recognized had begun to succeed. While Pascal appealed to the intellectual auth ority of the group of Parisian mathematicians in general, he reached beyond the learned amateurs to focus more specifically on Roberval, who had an official position as a professor at the Collge Royal. Roberval, he among them whom the greatest part of the others admire always and acquire his productions, agreed to demonstrate 109 The official statement appointing the members of the committee was issued 6 February 1634: Nous souhaittant la connaissance particulire dun si grand secret Nous avons commis, ordonn et constitut, commettons, ordonnons et constituons par ces prsentes Messieurs labb de Chambon, le prsident Pascal, Mydorge, Boulenger, professeur royal de mathmatiques, et Hrigone, aussi professeur, Morin, Diploma Primum, Mesnard OC 2:90. G. Bigourdan gives a brief account of the Morin affair of the longitudes in Bigourdan, La confrence des longitudes de 1634, Comptes rendus hedomadaires des sances de lAcadmie des Sciences 163 (1916): 229-233. See also, Monette Martinet, Jean-Baptiste Morin (1583-1656), in Quelques savants et amateurs de Science au XVIIe sicle: Sept notices biobib liographiques caractristiques ed. Pierre Costabel and Monette Martinet (Paris, 1986), 72-73; 76-77. 110 Avis, Mesnard OC 2:334. 111 [J]ai dj la satisfaction de voir mon petit ouvrage, non seulement autoris de lapprobation de quelques-uns des principaux en cette vritable science mais encore honor de leur estime et de leur recommendation, Lettre Ddicatoire, B. Pascal to Sguier, 1645, Mesnard OC 2:333. 140

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the machine and arrange for its sale to interested parties.112 The endorsement of a professor of mathematics was a far cry from that of an a nonymous curious in Rouen and a step beyond the informal, though clearly attested, expertise of the Mersenne group. Roberval was one of the few in the Parisian mathematical community who atta ined a post in the echelons of formal French education.113 The mere fact that he held the title professor of mathematics would have recommended him to those not knowledgeable in math ematics. He was a particularly useful ally for Pascal because he combined worldly recogn ition with impressive erudition. Robervals authority, together with that of th e rest of the mathematicians in the capital, helped Pascal gain the support and approval of Chancel lor Sguier. With that further endorsement in place, he could impress those who judged savants on the appearance of power, rather th an their intellectual credentials.114 Through the ongoing contrast betwee n artisans and himself, Pascal sought to safeguard his authoritative position as creator of the arithmetic machine. While he admits that with all the theory imaginable he could not have succeeded w ithout them, the workers remained mere tools. In fact, the anonymity of the workers (not a single one is named) indicates their interchangeability and thus their individual dispen sability as unwitting cogs. Pascal views their reliance on habit as like the instinct of beasts. By contrast, his ability to meditate on the 112 celui dentre eux de qui la plupart des autres admirent to us les jours et recueillent le s productions, B. Pascal to Sguier, 1645, Mesnard OC 2:333. 113 There are, of course, other examples. Pierre Gasse ndi, Robervals predecessor to one of his chairs of mathematics, is the best example. 114 Pascal would develop the notion of three orders (bodily, intellectual, spiritual) in his Penses written through the last years of his life. In it, he mentions that it is custom or habit (i.e., second nature) that trains one to consider someone to be important who has a large train of lackeys. Intellectuals should not be judged at this level; nevertheless, sometimes those steeped only in habit do judge based on the honors of those who wield political power, esp. Brunschvicg no. 93, Brunschvicg OC 13: 20-21. 141

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problem, arrive at a solution, a nd provide corrections based upon a plan, emphasizes the function of reason and thus the character of the Creator. The machine as transcendent The coup de grce of Pascals accomplishment, as he sees it, is the use of his creative powers to transcend the limitations of those, like the artisans, whose training is limited. He designed the arithmetic machine to ease the pain of calculation that comes from the effort and habituation needed to pe rform calculations using th e traditional methods of plume (pen) and of jetons (counters): You know how, using the counters [ jeton ], the calculator (especially when he is lacking in habit) is often obligated, for fear of falling into error, to make a long continuation and extension of counters, and how necessity constrains him afterw ard to shorten and to pick back up those which are uselessly extended, which shows two useless inconveniences, with the loss of two [lengt hs] of time You know lik ewise how, in using the pen [ plume ], one is at all moments obligated to re tain or borrow the necessary numbers, and how many errors creep into th ese retentions and borrowings, unless having a very long habituation and, moreover, a profound atten tion and which fatigues the mind in a short time.115 In the methods of plume and of jetons Pascal writes, the mind of the individual performing the calculation is placed under great mental strain.116 Just as Desargues artists and the children learning music had their memory taxed, so the on e calculating with a pen or with counters needed to maintain profound attention. In place of this, Pascal substituted his individual 115 Tu sais, comme, en oprant par le jeton, le calculateur (surtout lorsquil manque dhabitude) est souvent oblig, de peur de tomber en erreur, de faire une longue suite et extension de jetons, et comme la ncessit le contraint aprs dabrger et de relever ceux qui se trouvent inutilement tendus; en quoi tu vois deux peines inutiles, avec la perte de deux temps . Tu sais de mme comme, en opran t par la plume, on est tous moments oblig de retenir ou demprunter les nombres ncessaires, et combien derreurs se glissent dans ces rtentions et emprunts, moins dune trs longue habitude et, en outre, dune attention profond et qui fatigue lesprit en peu de temps, Avis, Mesnard OC 2:337. 116 The methods of jetons and plume are described, some years after the i nvention of Pascals machine, in Jean Franois, Larithmtique ou lart de compter toute sorte de nombres, auec la plume, & les iettons (Rennes, 1653). He knows of Pascals machine, acknowledging its rarity and ultimate failure of utility: The instrument named the Pascaline wheel does them with assurance and promptitude through a small local movement: but the expense of this instrument which is sold for 100 livres, & of the danger that some wheel will fail, & the ignorance that it leaves of Arithmetic makes it very rare, ibid., 22, my translation. 142

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profound meditation on theory and design. For those limited in their expertise and mental strength, the arithmetic machine supplied for the defect of ignorance or of little habit, and all of this without any work of the mind.117 It does not even require the knowledge of how arithmetic operations are performed.118 Gilberte would write that Blaise had discovered the means of doing all the operations [of arithmetic] with an entire certaint y, without any need of reasoning.119 Pascal insists, then, that the machine sta nds as a substitute for the operators thought. Through the mechanism of the gears, the Pascaline approximates human thought, an accomplishment that imitates one of Gods most profoundly mysterious creat ions. A mechanical philosophy that understood natural phenomena by wa y of mathematically-d escribable processes had already begun to emerge by the time that Pas cal created his machine. Machines created by human beings as objects of wonder provided additi onal plausibility to such a view of nature.120 Descartes notion of animals as beast-machines suggested that actions usually attributed to immaterial thought could be reduced to matter in motion. Descartes further articulated a mechanistic model of human sensation and me mory, though he would always maintain the 117 supple au dfaut de lignorance ou de peu dhabitude sans aucun travail desprit, Avis, Mesnard OC 2:337. 118 Ibid. 119 le moyen den faire toutes les oprations avec une entire certitude, sans avoir besoin du raisonnement, Vie de Pascal, Mesnard OC 1:577. Paradoxically, she adds that the work which was meant to reduce the fatigue of others served to undermine his own bodily constitution: Ce travail le fatigua beaucoup, non pas pour la pense ni pour le mouvement, quil trouva sans peine, mais pour faire comprendre aux ouvriers toutes ces choses, ibid. 120 Derek J. De Solla Price, Automata and the Or igins of Mechanism and Mechanistic Philosophy, Technology and Culture 5 (1964): 9-23. De Solla Price writes that simulacra (i.e., devices that simulate) and automata (i.e., devices that move by themselves) offered tangible proof, more impressive than any theory, that the natural universe of physics and biology was susceptible to mechanistic explanation, ibid., 9. 143

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existence and importance of immaterial res cogitans .121 Descartes stopped at the machine-like quality of the human body and Julien Offray de La Mettries Lhomme machine was still nearly one hundred years away, but thinkers began to postulate ways that human thought might be analyzed into constituent parts. Hobbes viewed all thinking as reducible to the four arithmetic operations and Leibniz sought to widen the sc ope of calculating mach ines in his vision (ultimately unrealized) of a machine th at reasons, a thinking machine.122 Pascals later reflections on his calculator in his Penses maintain the limitation of his machine, transcended as it is by the nobility of human will. But while he suggests that it cannot approach the transcendence that is godlike human thought, it is certainly a good approximation to lower-order operations of the human mind, whic h surpass the level of animal thought and the habituated working of the artisan-clockmaker. Furthermore, this machine, the result of the profound deliberation of the godlike engineer, was for Pascal the result of discipline and served to discipline the childlike artisan so that he could find results that were beyond his natural capacities.123 With the arithmetic machine, the effort of mind needed to perform calculations was reduced to the speed of the hand: if you want a s till more specific explana tion of its quickness, I 121 Descartes explained much of human memory as a process of physical imprinting, but objections and problems with the complexity of these processes prompted him to settle for a much more limited conception of mechanistic memory, John Morris, Pattern Recognition in Descartes Automata, Isis 60 (1969): 451-460. 122 Leibnizs vision is in agreement with Mersennes goal s to provide some means of encyclopedic knowledge in a universal language. The importance of Leibnizs place in the history of artificial intelligen ce is highlighted in Pratt, Thinking Machines especially Chapter 5 (Leibniz: Mechanizing Reason), 70-80; Chapter 6 (The Failure of Leibniz Project), 81-90. 123 Carolyn Merchant describes the profound importance of the metaphor of machine as order and power in Merchant, The Death of Nature: Women, Ecology, and the Scientific Revolution (San Francisco: Harper and Row, 1980), 216-235. Merchant suggests that Mersenne sought to replace The Imitation of Jesus Christ by The Imitation of the Divine Engineer 226. The godlike engineer was first and fo remost a mathematician and for Pascal, the control that he exerted was not merely over the work required to do his calculations, but also over the childlike and beast-like artisans. 144

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will tell you that it is like unto the agility of the hand of the one who operates [it].124 The fatigue that Pascal experienced because of his attempts to comm unicate to the workers the proper way to create the machine contrasts sharply with the lack of effort required by its operator. The habituated hand took on an ironic primacy. Pascal the savant had created an invention that could not be imitated by those whose pr imary training was tactile. Thr ough his intellectual application, however, he reduced the task of arithmetic to th e point that those most agile with their hands could use it best. Pa scal superintended [ regle ] his workers in order that he would create, through their hands, what would tran scend the limitations of their habit. The artisans had not been habituated to be good calculators, but Pascal deskilled calculation by removing the element of concentration and memory required for traditional methods.125 By doing so, the skilled arithmetician was placed on equal footing w ith the manually dexterous. If it is only the speed of the hand that determines the speed of calculation, Pascal himself would have performed more slowly than a manual laborer. This levelin g puts an ironic twist on Pascals insistence on the hierarchical relationship between designer and craftsman.126 But Pascals ch aracterization of the artisans skill as habituated and thus less than human prefigures the deskilling that resulted from industrialization. 124 [S]i tu veux encore une plus particulire explication de sa vitesse, je te dirai quelle est pareille lagilit de la main de celui qui opre, Avis, Mesnard OC 2:337. 125 Desargues was ostensibly motivated by this same concern that workers not be taxed in their memory, as he states in Reconnaissance de Monsie ur Desargues, Desargues, Loeuvre de Desargues 1:477-478. 126 The Marxist roots of the term deskilling also highlights the irony, with such a leveling further hardening the socio-cultural distinction between those who have non-duplicatable skills (as Pascal claims for the mathematical savant) and those whose expertise may be imitated by a machine. The terminology of deskilling is especially associated with the indictment of capitalism in Harry Braveman, Labour and Monopoly Capitalism: The Degradation of Work in the Twentieth Century (New York: Monthly Review Press, 1974), although it was already in use in the 1940s, Oxford English Dictionary http://dictionary.oed.com/cgi/entry/50061915?single=1&query_type=word&queryword=deskill&first=1&max_to_s how=10 (accessed 7 October 2008). 145

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Pascal carefully distinguished his role from that of the artisan in order to protect his position as the author of his machine. The distin ction was meant to ensure that he would receive credit for the renown of the machine. But it also served a larger protect ive function for Pascal and the group of mathematicians with whom he was associated. Mersenne had engaged in an argument with those who claimed that the state of the ignorants was sufficient to engage in learned pursuits. Pascals rejection of the capabil ity of artisans to crea te something new served as evidence against this opinion and protected the privileged pos ition of trained theoreticians. Childlikeness and the Arithmetic Machine By classing artisans as non-entities in th e learned world, Pascal parted ways with Mersennes Harmonie universelle, which ascribes moral virtues to their skill. Mersenne writes, for example, that the tool of the manual laborer is such that several have called it one of the principal instruments of wisdom & reason.127 The hand is not merely put at the service of reason, it transcends reason. The movements of th e hand on the strings of th e lute are a case in point, writes Mersenne: They are so marvelous that reason is often c onstrained to admit that it is not capable of encompassing the lightness & quickness, which surpasses the swiftness of the liveliest imagination that may be met, as is experien ced when one wishes to number the sounds that it makes, or the chords that it touches, or its trills [ tremblemens ] during the space of a measure.128 But Pascal gave little credit to the wisdom of the hand that the artisans possess, or to the workers contribution to refining his design. Pascal did not dem onstrate the resourcefulness of 127 [P]lusieurs lont appelle lvn de principaux instrumens de la sagesse & de la raison, Mersenne, Harmonie universelle Livre second des Instrumens, 3:76. 128 [I]ls sont si merueilleux que la raison est souuen t contrainte daduoer que lle nest pas capable den comprendre la legeret & la vitesse, qui surpasse la promptitude de limagination la plus viue que lon puisse rencontrer, comme lon experimente lors quon veut nombrer les sons quelle fait, ou les chordes quelle touche, ou ses tremblemens dans le temps dvne mesure, Mersenne, Harmonie universelle Livre second des Instrumens, 3:76. 146

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Robert Hooke, who exchanged ideas with masterful artisans in the coffee houses of London and appropriated them for his and the Royal Societys use.129 When it came to the presentation of the mach ine to the curious of Paris, Pascal excused himself from giving a full written account of its functioning. He claimed instead that such an explanation is of the number of t hose which can be taught only orally.130 Pascal thus suggests that the physical presence of the machine is necessary for effective teaching about its proportions and use. Learning by ex perience is taken for granted in our historical accounts of the scientific revolution and bears the marks of an artisanal epistemology.131 Pascal associates habits acquired through hands-on t eaching with the need for instru ction from theoreticians, yet the method of instruction in the us e of the machine is strikingly si milar. Pascal admits that he does not employ the usual geometrical method, which is: to represent through figures the dimensions, th e disposition, and the connection of all the pieces, and how each one ought to be placed in or der to compose the instrument, and to put its movement to perfection.132 Finally, when Pascal asserted his imitation of God and denied it to the worker, he upset a traditional analogy of God as Divine Artisan, as Mersenne expresses in Lusage de la raison.133 129 Rob Iliffe, Material Doubts: Hooke, Artisan Culture and the Exchange of Information in 1670s London, British Journal for the History of Science 28 (1995): 285-318. Iliffe argues that Hooke was a strategist and techniquemerchant who was able to capitalize on his ability to co mmunicate with natural philosophers and artisans alike within the space of Londons coffee houses. Hooke was, Iliffe writes, more than a middleman flitting between what have occasionally been portrayed as two rather static realms of the genteel and the artisanal. He was a central player in the exchange of philosophical and technical goods who was uniquely at home in all the spaces and worlds described in the Diary ibid., 317. Hooke also had a unique ability to build relationships with artisans: From the spring of 1674, he was able to interact with Tompion to an extent that is possibly unparalleled by any other combination between a British craftsman and a natural philosopher in this period, ibid., 311. 130 lors tu jugeras que cette doctrine est du nombre de celles qui ne peuvent tre enseignes que de vive voix, Avis, Mesnard OC 2:335. 131 Smith, Body of the Artisan 59-93. 132 reprsenter par figures les dimensions, la disposition et le rapport de toutes les pices, et comment chacune doit tre place pour composer linstrument, et mettre son mouvement en sa perf ection, Avis, Mesanrd OC 2:334335. 147

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Clearly, despite the efforts of Pas cal, Desargues, Mersenne, and others to create a master/disciple relationship between the theorist and the artisa n, complexities problematized identification of savants in opposition to the ignorant, esp ecially those untrained in mathematics. Pascals work on the arithmetic machine cont inued after he left Rouen. He used his inventiveness and industry as leverage to promote his maturity and to demonstrate that he was no mere child genius coasting on natural talent. Ne vertheless, his work continued to require the support of the Parisian community, which he us ed to certify his status as a savant. His dependence on early mentors demonstrates that, de spite his efforts, he remained tied to his previous identity as a child prodigy. Pascals other major project during these years, his experiments and writings on the void, demonstrat e that the same goals and limitations embodied his arithmetic machine permeated his other work. The Controversy of the Void: Neither Beast nor Child Pascals goal to establish himself as a mature savant fortified the contrast between his work and that of artisans. During his involve ment in the conflict about the existence and character of the void, this section will argue, he developed additional contrasts in which he identified himself with disciplined application and philosophical maturity. Again making use of the work of artisans, this time the glassmakers of Rouen, Pascal styled himself an instructor in natural philosophy, through the theatr ical display of the void in tube s. This section also argues that Pascals language suggests that he has taken up his proper position within the adulthood of humanity, moving beyond scholastic infantilism to new opinions that are based on cumulative observation. Finally, in his ha ndling of the polemical exchange with the Jesuit Father Nol, Pascal demonstrates the coupling of childlike deference and mature communication. By the 133 Mersenne, Lusage de raison 79-80. 148

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conclusion of his work on the void, the transition from the young Pascal to the illustrious Pascal was virtually complete. Empty arguments The question of the possible and actual existenc e of a vacuum, empty space, or void, was one of the most controversial topics of the 1640s and 1650s. The conflict was at least as old as the ancient atomists, Democritus and Lucretius.134 The problem was at once philosophical and empirical and especially concerned definitions attached to observed phenomena. The void was not a space filled with invisible matter called air, thus casually called empty. In the context of this controversy, the void lacked any substance. Aristotle had ar gued against the existence of any kind of void, for void was defined as an em pty place into which an object might move; but for Aristotle the notion of place could not be divorced from the dimensions of a body. Aristotles cosmos is a plenum.135 The terminology of the horror vacui natures resistance to empty space, emerged in the Middle Ages to describe a principle noted by ancient Greek pneumatists.136 The horror vacui explained, for example, a devi ce called the clepsydra, which when plugged at the top does not allow liquid to flow out through th e holes in the bottom.137 134 W. E. Knowles Middleton, The History of the Barometer (Baltimore, MD, 1964), 4. 135 Aristotles key discussion of the void, his examination of prior theories, and his arguments against it, are in Physics.IV.6-9.213a11-217b28. The definitive work on the concept of the void in medieval and early modern Europe is Edward Grant, Much Ado about Nothing: Theories of spa ce and vacuum from the Middle Ages to the Scientific Revolution (Cambridge: Cambridge UP, 1981). Grant briefly discusses Aristotles views on this subject in Chapter 1, Aristotle on void space, ibid., 5-8. 136 Grant, Much Ado about Nothing 67-68. The Middle Ages saw the flourishing of this terminology: Although the full significance of this famous principle would be desc ribed and explicated on in the fourteenth century, it had already emerged in the thirteen th, when expressions such as natura abhorret vacuum horror vacui and fuga vacui began to appear. The origin of the principle is, however, unknown. But already in the first half of the twelfth century, Adelard of Bath expressed the fundamental idea of natures resistance to a vacuum Grant, Much Ado about Nothing, 68. 137 Basically a decanting vessel, the clep sydra is characterized by a narrow, open neck and wide body with small holes at the bottom, which is the part first submerged into the liquid to be decanted, usually water or wine. When all the air in the vessel is expelled and replaced by the incoming, rising water, the narrow or ifice at the top is stopped up, usually by covering it with the thumb. Upon lifting the vessel from the water, one observes that the water 149

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While the natural tendency of water is toward the center of the earth, natures tendency to prevent the void is stronger. During the Midd le Ages, most philosophers believed that only through Gods omnipotent power could the horror vacui be overcome, and God had never done so.138 Early-modern consideration of the void bega n in Italy. Hero of Alexandrias work Pneumatica translated into Latin in 1575, provided descriptions of various machines that illustrated this puzzling phenomenon.139 Galileo Galileis work on limits to which water could be raised in a pump for fountains was at the genesis of the Italian preoccupation.140 In 1639 or 1640, Rafaello Maggiotti and Gasparo Berti bu ilt upon Galileos observations, devising an apparatus that used a lead tube closed at th e top by a glass bulb and submerged in a cask of water. With this apparatus, they were able to make a rough estimate of the greatest height (18 cubits) at which water would sta nd in the tube. These observations facilitated discussion of what was at the top of the tube when the water de scended to that height. In 1644, Evangelista Torricelli, a Galilean disciple, substituted mercur y for water, allowing the use of smaller tubes made of glass. Mercury, or quicksilver, remained elevated only to a level of about 19.6 inches. The smaller apparatus, in contrast with the lead pi pe, provided a better view of the entirety of the tube, and the smaller tube facili tated manipulation. For example, the experimenter could move the tube up and down in the basin and observe that the empty space at the top of the tube would grow larger, and vice versa. In June 1644, Torrice lli and Michelangelo Ricci wrote a series of remains in the now elevated clepsydra despite the expectation that it would fall through the tiny holes at the bottom, Grant, ibid., 83. 138 Middleton, History of the Barometer 4. 139 See the important article, Marie Boas, Heros Pneumatica : A Study of Its Transmission and Influence, Isis 40 (1949), 38-48. 140 Significantly, Boas calls Galileo the most important follower of Heros atomism, ibid., 48. See also Mesnard OC 2:346. 150

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letters discussing the demonstration. They co rresponded with one anothe r about its implications for the question of the existence of the vacuum and the relationship between the weight of a liquid and the height of the liquid in the tube.141 French interest in the problem began when Mersenne received fragmentary communication from Franois du Verdus concerning Torricellis work on the void. Mersenne attempted similar demonstrations with no success, because obtaining the necessary quality of glass was difficult in France. Later that autumn, Mersenne depart ed for Italy, where he observed Torricellis demonstration and spoke with several of Torricelli s collaborators. When Mersenne returned to France in July 1645, he was determined to repeat the experiment for himself.142 Mersenne and Pierre Chanut attempted it again in Paris, but once more, the brittle French glass, not as strong as the Italian, broke under the weight of the qui cksilver during the inversion of the tube.143 It is possible that this experiment was discussed dur ing the conferences at Mersennes Minim cell.144 Continued work was further slowed by Chanuts departure to Sweden on a mission from the king.145 Sometime between the summer of 1645 a nd the fall of 1646, Pierre Petit (1594?-1677) became involved with the problem, finally succeeding in an exprience with a smaller tube that left only a small, apparently empty space at its top.146 This was unsatisfying to Petit, since there 141 See the translation of these letters in I.H.B. and A.G.H. Spiers, eds., The Physical Treatises of Pascal: the Equilibrium of Liquids and the Weight of the Mass of the Air (New York, 1937; repr. 1973), Appendix III, Torricellis Letters on the Pressure of the Atmosphere,: 163-170. 142 Humbert, Cet effrayant gnie 71. Consult the important work by Cornelius De Waard, Lexprience baromtrique, ses antcdents et ses explications (Thouars, 1936). 143 Humbert, Cet effrayant gnie 71. 144 Roberval explains the reason Mersenne did not succeed in the exprience as follows: neither this year nor the following, was he able to procure for himself appropriate tube s in Paris, both because they did not make them there, and because, during nearly all that tim e, he traveled in the southern provin ces of the realm of France, De vacuo narratio, Mesnard OC 2:461. 145 He was named rsident de France, OC 2:347. 146 Pierre Petit to Pierre Chanut, 19/26 November, 1646, OC 2:350. 151

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was then a greater chance that this space was onl y an air bubble. He therefore sought a way to make a larger tube that would contain more mercury and create a larger void.147 Pascal joined the debate on the void partly because of where he lived. Rouen was the location of an important French glassworks. In 1598, the French monarchy established it in an attempt to compete with the fine glass being produced in Venice.148 The dAzmar family, with a 250-year history as glassmakers, had run the glassworks since 1619.149 The business benefited from a monopoly in the region granted by roya l authority, and from the surrounding forests, which provided the necessary fuel. It had a prim e location near the Seine River that facilitated transportation to Paris. This combination fact ors made its potential for productivity and sales quite high.150 The type of glass the dAzmar family pr oduced would be especially important for experiments on the void. Their glassworks specialized in Venetian-type cr ystal, and according to a report on the renewal of letters patent in 1642, th ey were the first to introduce this kind of glassmaking to France.151 Claude Mazauric makes a strong ar gument that the Rouen glassworks, in 1646, was not a business of modest artisans, more or less needy, but powerful manufacturers.152 Italian glass, to which Torricelli had access and that was necessary for his 147 Ibid. 148 This account of the history of the Rouen glassworks follows from Claude Mazauric, Note sur la verrerie de Saint-Sever au temps dtienne Pascal, in Les Pascals Rouen, ed. Jean-Pierre Clro (Rouen, 2001): 159-178. 149 Ibid., 172. 150 One can also imagine that the abunda nce of forests in Upper Normandy, notably the forests of ducal origin that had become royal forests, rendered much more sustainable the installation project of an industry of glass, since it is, as everyone knows, an art of fire, a great consumer of combustibles, that is, essentially, wood, ibid., 162-163. For the importance of transportation by water, see Warren C. Scoville, Capitalism and French Glassmaking, 1640-1789 (Berkeley, CA, 1950), 98. 151 The dAzmars were, however, not locals. Their family originally came from Languedoc and only came to Rouen when they took over the glassworks, C. M azauric, Note sur la verrerie, 170, 172. 152 Ibid., 175. 152

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experiments, was superior to anything produced around Paris.153 Pascal lived in a town where conditions were right to produce adequate ma terial for the perfor mance of the Torricelli phenomenon.154 Prompted by a suggestion from Mersenne th at proper glass for To rricellis experiment might be found there, Petit decided to make a st op in Rouen on his way to visit Dippe on other matters.155 While there, he met with tienne and Blai se Pascal, explained hi s desire to perform the experiment, and arranged to procure the glass before his return. Petit recorded the details of the subsequent experiments performance in a letter to Chanut written in November 1646. In that same year, Pascal the son performed the sa me type of demonstration of the void, to which He summoned [as] witnesses the mo st learned men of this town.156 Pascal was not merely giving a theatrical display of a curious phenome non. He stated a clear preference for the view that nature permitted a void. Jacques Pierius, professor of philosophy in the college of the archbishopric of Rouen, wrote a work that ment ions Pascal, the not unworthy son of a very 153 Even in 1660, there were no good glassworks in the Pari s area: besides that, as we have no glassworks in Paris or its neighborhood we could not get appropriate vessels made [for experiments on smoke and sound in the vacuum], Pierre Petit to Henry Oldenburg, 23 October 1660, Henry Oldenburg, Correspondence of Henry Oldenburg, ed. Rupert A. Hall and Marie Boas Hall, vol. 1(Philadelphia, 1965), 398. 154 C. Mazauric, Note sur la verrerie, 177. 155 Roberval says that Mersenne had already written to some friends at Rouen (the Pascals, or someone else?) to ask about procuring some tubes. Of Rouen, Roberval writes: there, indeed, were found greatly celebrated glass and crystal manufacturies, De vacuo narratio, Mesnard OC 2:461. The way to Dippe from Paris often went through Rouen. A work published in 1643 give s an account of a trip thro ugh (among other regions) northern France. The route for this tour includes Paris to Rouen and Rouen to Di ppe. Each leg of the trip is said to take two days hard riding on horseback, Louis Coulon, LUlysse franois, ou Le voyage de France, de Flandre et de Savoye: contenant les plus rares curiosits des pays, la situation des villes, les moeurs & les faons de faire des habitants (Paris, 1643), 328-329; 340-341. 156 Advocavit testes viros hujus urbi s doctissimos, Jacques Pierius, An detur vacuum in rerum natura excerpted in Mesnard OC 2: 361. Pierius was convinced of Aristotles opinions on natures horror of the void, and probably was an attendee at Pascals Rouen demonstra tion. Pierre Guiffart, author of a Discours du vide to be discussed below, likewise writes of the performing of plu sieurs expriences en cette ville en la prsence de tous les plus savants hommes de sa connaissance, Pierre Guiffart, Discours du vide (Rouen, 1647), 7, excerpted in Mesnard OC 2:423. 153

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illustrious and very learned father, as an objector to his own theory that the space at the top of the tube was occupied by vapors from the quicksilver.157 Pieriuss An detur vacuum in rerum natura may have prompted Pascal to respond by expanding his simple duplication of the Torricelli e xperiment. Pascal aimed to demonstrate what he called natures limited horror of the void through a number of demons trations using various apparatus, including syringes, bellows, and tubes of various shapes and sizes.158 Pierre Guiffart (1597-1658), provided another Rouennais response to Pieriuss crit ique that was supportive of both Pascals experiments and hi s arguments about the void. Guiffart, a physician in the town, had attended some of the expe riments and public discussions.159 Meanwhile, in Paris, Roberval and Mersenne became aware of Pascals work with the void, and attempted their own versions of the expe riments, apparently with apparatus received from Rouen.160 Roberval also communicated with Pie rre Desnoyers, Secretary to the Queen of 157 illustrissimi et doctissimi patris non degener filius, Pierius, An detur vacuum Mesnard OC 2:360-361. 158 A description of the expriences and apparatus used in them are recorded in Blaise Pascal, Experiences nouuelles touchant le vide (Paris, 1647), 1-18. Alexandre Koyr argued that these were only thought-experiments, Koyr, Pascal Savant (1956), 276. Since th en, Shozo Akagi and Kimiyo Koyanagi have undertaken to consider the question of whether the experiments were actually performed by Pascal, Akagi, Comment interprter les Experinces nouvelles touchant le vide, in Pascal Port-Royal Orient Occident: Actes du colloque de lUniversit de Tokyo, 27-29 septembre 1988 ed. Thrse Goyet et al. (Paris, 1991): 199-209; Koyanagi, Cet effrayant livret Expriences nouvelles touchant le vide de Blaise Pascal, in Les Pascals Rouen ed. Clro: 137-157. The expriences in Pascals 1647 work also provide examples for Peter Dear in his discussion of the relationship between English and French attitudes toward miracles an d the ordinary course of nature, Dear, Miracles, Experiment, and the Ordinary Course of Nature, Isis 81 (1990): 663-683. 159 Guiffart, Discours du vide excerpted in Mesnard OC 2:421-433. Guiffart advocated Harveys theory of the circulation of the blood in idem, Cor vindicatum, seu tractatus de cordis officio (Rouen, 1652). In 1654, he wrote a work that recounted his reasons for converting from the Protestant to the Catholic faith, idem, Les Vrits catholiques, ou les Justes motifs qui ont oblig le Sr Guiffart, de quitter la religion prtendue rforme pour se ranger lglise catholique, apostolique et romaine (Rouen, 1654). For biographical information about Guiffart and especially his work on circulation and on religio n, see See Ren Le Clerc, Un medecin thologien, Notices, mmoires et documents 27 (1909): 17-35. 160 See letters from Auzout and Hall de Monflaines to Mersenne. 154

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Poland, where the question of the void subsequently became a hot topic.161 Roberval sent him a Narration regarding the developments in France on this issue, including Pascals Rouen activities. He also transmitted copies of Pascals Expriences nouvelles touchant le vide to Desnoyers, who praised it to Heve lius. Hevelius, in turn, requested a full copy of the work, which furthered Pascals recognition.162 The main goal of Pascals experiments in R ouen was to test the possibility of creating a void. Upon his return to Paris in the summer of 1647, however, he re ad the correspondence between Ricci and Torricelli and shifted his focus to the raison des effets of the experiments (i.e., the weight of the air). In Paris, Pascal also engaged in a lively polemic with tienne Nol, a Jesuit, who criticized Pascals Expriences nouvelles and eventually published an oppositional treatise entitled Le plein du vide. This exchange, including Pascals response to Nol, his letter to the old family friend Le Pailleur, and tienne Pascals attack of the Jesuits treatise constitute key primary sources the discussi on and analysis that follows. Pascals illness during this tim e curtailed his activities and writing. Despite difficulties, however, he arranged for his brother-in-law to perform the celebrated experiment of the Puy-deDme, which accounts for the only mention of Pa scal in most textbooks. In September 1648, Florin Prier took measurements in a glass tu be at the bottom and at the top of a mountain situated at Pascals natal town of Clermont. This experiment helped to establish the principle of the weight of the air, which Robert Boyle later cited as an experimentum crucis for the spring of 161 In particular, the Capucin Valerian Magni wrote a work describing an experiment identical to that performed by Torricelli, Magni, Demonstratio ocularis (Warsaw, 1647), discussed in Mesnard OC 2:455-459. 162 Pierre Desnoyers to Johannes Hevelius, December 18, 1647, Mesnard OC 2:454; Johannes Hevelius to Pierre Desnoyers, 17 January 1648, Mesnard OC 2:454. 155

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the air.163 It was not decisive, however, for all those w ho constituted the learned circles of Paris. Boulliau, for example, wrote of those who attributed the phenomena observed on the Puy de Dme to air pressure: I believe that they are mist aken, and that it is necessary to have recourse to other reasons.164 Furthermore, Descartes questioned wh ether the idea for the experiment was Pascals own, claiming he had suggested it during meetings with Blaise in the autumn of 1647. Despite debates during the past century, Pascal re tains his place as the original mastermind of the test. New roles, old roles: childlikeness and maturity in the question of the void The time during which he worked on the question of void was the most active period of Pascals scholarship, though it was punctuated by periods of ill health. Although these times of infirmity prevented voluminous publication, the e xperiments that he performed and suggested were central to the discussions that took place in Paris. Pascal was also becoming increasingly well-known outside Paris. While praise of his geometrical work as a teenager came from the Mersenne Circle in Paris, his work on the arithmetic machine and hi s experiments with the void gained attention from around Europe. Several savants mention Pas cals machine during this time, including Petit, who praised it to Jacques Buot (162?-1675?) as a Piece truly invented with as much good 163 In his Defense Against Linus: such an Experimentum cCucis (to speak with our Illustrious Verulam) is afforded us by that noble Observation of Monsieur Pascha ll, mentioned by the famous Pecquet, and out of him by our Author: namely, that the Torricellia n Experiment being made at the foot and in divers places of a very high Mountain, (of the altitude of five hundred fathom or three thousand foot) he found, that after he had ascended a hundred and fifty Fathom, the Quicksilver was fallen two Inches and a quarter below its station at the Mountains foot; ande that at the very top of the Hill it had desce nded above three Inches below the same wonted station. Whence it appears that the Quicksilver being carried up towa rds the top of the Atmosphere, falls down the lower, the higher the place is wherein the observa tion is made: of which the reason is plain in our Hypothesis, Robert Boyle, The Works of Robert Boyle ed. Michael Hunter and Edward B. Davis, vol. 3 (London, 1999), 50-51. 164 Decipi ipsos puto, et ad alias rationes confugiendum esse, Boulliau to Hevelius (11 December 1648), Mesnard OC 2:700. Just prior to this comment, he provides a brief description of the phenomena observed during the Puy de Dme experiment, ibid. 156

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fortune and speculation as its au thor has of mind and knowledge.165 Jean Franoiss 1653 published work on arithmetic also mentions the Pascaline.166 Both Petit and Franois express reservations about the producti on cost of the machine, but even their qualified praise demonstrates the calculators widespread recognition. But these notices of Pascal pale in comparison with the accolades receiv ed by Pascals work on the void. The learned reception of Pascals work demons trates a dual characte r that highlights the tension between Pascal the child and Pascal the mature savant. On the one hand, he continued to be recognized by some primarily for his youthful tale nt. In part, his father s status as a learned man overshadowed the sons adult progress. On the other hand, he was beginning to earn his own identity, a mature respectab ility that distinguished him from his father and his now burdensome reputation as a child prodigy. Once a promising genius, Pascal was now illustrious in his own right. When Petit wrote the initial letter to Pierre Chan ut regarding his performance of the experiment on the void in Rouen, he gave priority of place to tienne Pascal, since he was, as Petit writes, 165 Pice vritablement invente avec autant bonheur et de spculation que son auteur a desprit et de science, Pierre Petit to Jacques Buot, 23 September 1646, Mesnard OC 2:345. Buot was probably approximately Pascals age and had similar interests. He taught and wrote on mathematics and introduced a device known as the Roue de proportion for arithmetic calculations just two years prior to the granting of the privilege for Pascals machine. He would become a member of the newly-formed Acadmie des Sciences in 1666, Sturdy, Science and Social Status 111. Petit demonstrated knowledge of mathemati cal tools prior to this letter, in Pierre Petit, Lusage ou le moyen de pratiquer par une rgle toutes les oprations du compas de proportion (Paris, 1634). Interestingly, Petits letter to Buot calls the machine merely la bote ou instrument de M onsieur Pascal, rather than de Monsieur Pascal le fils or de Monsieur Pascal le jeune, Petit to Buot, 23 September 1646, Mesnard OC 2:345. This is striking because in his letter to Pierre Chanut two months later his references to Monsieur Pascal are to the father while he makes a separate, distinct reference to the son, P. Petit to Chanut, 19/26 November 1646, Mesnard OC 2:350-351. Was Petit perhaps under the impression, during his brief visit to Rouen, that the machine was of tiennes invention? Alternately, this difference may be the result of the addressees level of ac quaintance with the Pascals. Perhaps Buot was unfamiliar with the elder Pascal, while Chanuts knowledge of him required Petit to make the distinction. 166 The instrument named the Pascaline wheel does them [arithmetic operations] with assurance and promptness through a small local movement: but the expense of this instrument which is sold for 100 livres, & the danger that some wheel will come to fail, & the ignorance that it leaves of Arithmetic renders it very rare, Franois, Larithmtique ou lart de compter 22. 157

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your good friend and mine.167 It is tienne, Petit claims, that for a long time has admitted the [existence of] the void.168 Furthermore, the six-folio le tter mentions the young Pascal only once, though in that context he suggests the sophisti cation of Pascals grasp of the nuance of experimental interpretation.169 Pierius, who opposed Blaises interpretation of the experiment, identifies him as Monsieur Pascal the younger, a not so unworthy son of a very illustrious father, thus making refere nce to tiennes reputation.170 But his description of Blaise in An detur vacuum in rerum natura (1646) also suggests admiration of th e son as distinct from the father: most celebrated and in all types of scie nces well-versed, more than his age would seem to allow. 171 Clearly, Pieriuss praise of Pascal was based largely on Bl aises learning in light of his youth. As with his first effo rts at geometry, he was praised for the quality of his work, but more specifically because of his precocity.172 Pierre Guiffart, unlike Pierius, basically agrees with Pascals verdict on the void. Ironically, however, he does not gi ve the same kind of personal praise as Pascals opponent. Instead, he focuses his favor on Blaises experi ments, which play a prominent role in the 167 [J]en fis le rcit, en passant Rouen, votre bon ami et le mien, Monsieur Pascal, P. Petit to Chanut, 19/26 November 1646, Mesnard OC 2:350. 168 Monsieur Pascal fut ravi dour parler dune telle exprience, tant par sa nouveaut que parce que vous savez quil y a longtemps quil admet le vide, ibid., 2:350. According to Petit, tiennes belief in the void was encouraged through the reading of, among others, Hero of Alexandria. The elder Pascal was longtemps persuad de cette opinion de Hron et de plusieurs autres philosophes, ibid., 2:354. For the importance of Hero, see Boas, Heros Pneumatica 38-48. 169 le fils de Monsieur Pascal objectait que les simpliciens pourraient dire que cet espace qui paraissait vide tait de lair, lequel, pour viter le vide, aurait pntr le verrre et serait entr par ses pores, P. Petit to Chanut, 19/26 November 1646, Mesnard OC 2:352. 170 Dominus Paschal junior, illustrissimi patris non degener filius. Pierius, Ad experientiam 13, excerpted in Mesnard OC 2:642. 171 nobilissimus et in omni scientiarum genere plusquam ejus aetas pati videretur versatissimus, Pierius, An detur vacuum 2, Mesnard OC 2:361. 172 As Pascal was, by this time, already in his mid-tw enties, this reference to wisdom beyond his years seems somewhat puzzling. It should be borne in mind, however, that early modern culture drew on a notion of adolescence and youth that extended through ones twenties. 158

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argument of Guiffarts treatise: Those w ho are philosophers cannot see them without admiration, and those who are not become so by considering them.173 Guiffart, however, appended to his treatise a poem by Jean-Baptiste Por e. In his celebration of Guiffarts work, Pore refers to Blaise as the ingenious Pascal who establishing the Void / Has filled our minds with a sweet astonishment.174 Pascals early mentors also added their voices of affirmation during this period. Roberval refers to him as the most celebrated Mr. Pascal and the most expert Mr. Pascal in his first Narration on the void, which was addressed to Des noyers and passed along to others, including Hevelius.175 Roberval expands on thes e designations in the second Narration. Pascal, he states, fulfilled the needs of the occasion pr esented by the question of the void: [What is] necessary is a man not only shar p and zealous for the truth, but especially magnificent and capable in his search for what is true, in order to pr operly organize all the expenses which would be justified: we have found such a person for this affair in the person of noble Mr. Pascal.176 Desnoyers, in turn, refers to the Expriences nouvelles touchant le vide as very fine and very well reasoned.177 Pascals virtues are praised; his youth is not mentioned. 173 Ceux qui sont philosophes ne les peuvent voir sans admiration, et ceux qui ne le sont pas le deviennent en les considrant, Guiffart, Discours du vide excerpted in Mesnard OC 2:427. 174 Lingnieux Pascal tablissant le Vide / A rempli nos es prits dun doux tonnement, ibid., 2:423. Guiffarts openness to novel ideas is clear from his ready acceptance of Ha rveys theory on the circul ation of the blood, despite opposition by many physicians in the town, Guiffart, Cor vindicatum (1652). Le Clerc, U n mdecin thologien, records a number of excerpts from Guiffarts works, incl uding a statement concerning his own legitimacy: depuis vingt-cinq ans que je la professe [le medecin], lenvie la plus industrieuse na pu jusques icy trouver de lgitime matire pour mimputer ngligence, ignorance ou temerit quelque malheureuse ressite, quoted in Le Clerc, Un medecin thologien, 19. 175 nobilissimo viro D. de Paschal; solertissimus D. de Paschal, excerpted in Mesnard OC 2:462, 469. 176 sed idem ut exhibeatur, virum requirit non sagacem m odo ac veritatis studiosum, sed praeterea magnificum, et qui inquirendo vero quosvis sumptus bene impensos statuerit; qualem hoc in negotio habuimus nobilissimum virum Dominum de Pascal... Narratio ad nobilem virum dominum, excerpted in Mesnard OC 608. 177 fort beau et fort bien raisonn, Desn oyers to Hevelius, 18 December 1647, Mesnard OC 2:454. 159

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In his Novarum observationum physico-mathematicarum (1647), Mersenne continued his promotion of Pascal, begun in the late 1630s, men tioning him several times with reference to the question of the void. He grants him a designatio n reserved for learned men of the time: the most illustrious man M. Pascal.178 Just three years earlier, in his Cogitata physicomathematica Mersenne identified him with referen ce to his father, as Pascal the younger.179 Pascal does not escape connection with his father in Mersennes later work, but Novarum observationum uses language that suggests equality: t he two Pascals, excellent geometers and philosophers.180 Blaise is his fathers colleague, not his pupil. Mersenne also touts the young man as the one who has made more observa tions on this void than any other and assures the reader that if Blaise would print his work in a treatise as planned, he will oblige the philosophers to himself.181 With this final remark, Mersenne indicates his belief that Pascal is coming of age and ready to assume his place among the philosophes who elucidate the principles of natural phenomena. Gassendi also lent his voice to the general acclamation of Pascals success, though for this older savant Pascals age was still worth men tioning. Among the savants living in Paris in the 1640s, few were as well-respected as Gassendi. From 1628-1632 he lived in Paris, where he made a number of learned friends. Gassendi was fully involved in the intellectual life of Paris during his residence in the 1640s, and had particularly close acqua intances with Boulliau and Mersenne. He refers to Pascal as the am azing adolescent Pascal when writing about the 178 clarissimo viro D. Paschal; when both he and his father are mentione d together, they are clarissimo D. Paschali, Mersenne, Novarum Observationvm Physico Mathematicarvm 218. 179 The Latin phrase reads juniorem Paschalem, De Ballistica et Acontismologia sev de Sagittarvm, Iacvlorvm et Aliorvm Missilivm ,, Mersenne, Cogitata Physico Mathematica, 102. 180 The original Latin reads Paschalium, eximios geometras et philos ophos, first preface to Mersenne, Novarum Observationvm Physico Mathematicarvm folio 2v; cf. French translation in Mesnard OC 2:487. 181 [S]i faciat satis clarissimus Paschalius ph ilosophos sibi maxime obstricturus est, Mesnard OC 2:489. 160

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quicksilver experiments performed in Rouen.182 In the context of the Puy de Dme experiment, he refers to Pascal, this outstandi ng, or rather inco mparable, young man [ adolescente ].183 Gassendis praise of Pas cal using the Latin term adolescente is noteworthy fo r the classical connections that it invoked. Th is term referred to a time of life that extended through young adulthood and indicated associati on with great ancients, such as Cicero, who saved Rome while still an adolescente .184 Gassendis praise for Pascal demonstrates what Valerian Magni (who claimed his own preeminence in the experiment on the void) also recognized by the middle of 1650: Pascal was a man of eminent reputation in France.185 Pascal owed his fame, however, not simply to his great abilities, but to the general interest in his subject matter. For Jean Pecquet, whose interests centered on medicine, Pascal was important becaus e he did put in all th e Devotaries of true wisdome through all Europe an eager desire to try the Experiments of Vacuity.186 Pascals 182 mirifico adolescente Pasc halio, Pierre Gassendi, Animadversiones in decimvm librvm Diogenes Laertii, qvi est de vita, moribus, placitisque Epicvri, vol. 1 (Lyon, 1649), 426. Gassendi calls him mirificus Paschalius again, this time without a reference to his youth, Pierre Gassendi to Franois Bernier, 6 August 1652, Pierre Gassendi, Opera omnia vol. 6 (Stuttgart-Bad Cannsta tt, 1964), 318, col. 2. 183 eximii, seu incomparabilis potius adolescentis PASCHALII, Gassendi, Animadversiones, vol. 1, Appendix, III. See also, Simone Mazauric, Gassendi, Pascal et la querelle du vide (Paris, 1998). 184 The Latin word adolescentewas still in use positively to speak of an individual, while in French this word seems to have been used as an insult, as is suggested by Le Maistres desire in 1636 that Balzac not refer to him with such a term, since it is said only in an ironic way of speaking, from which he [Le Maistre] is quite glad, by your good pleasure, to save himself, avowing certainly that, in the Latin sense, it would be too glorious for him that you you had spoken of him in such a way, as he knows up to what [point] the limits of adolescence went for the Romans, and reminds himself that Cicero, somewhere, is credite d with saving Rome while still an adolescent, Jean Chapelain to Guez de Balzac, Fe b. 17, 1636, Jean Chapelain Lettres de Jean Chapelain de lAcadmie Franaise vol. 1 (Paris, 1968), 108. 185 vir inter Gallos praecipuae nobilitatis, Valerian Magni, Principia et specimen philosophiae (Cologne, 1652), 90-91. 186 Jean Pecquet, New Anatomical Experiments of John Pecquet of Diep (London, 1653), 102. 161

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experiments on the void were important for their clarity and for challenging the scholastic view of nature.187 The foregoing testimonies are not unusually adulatory for the seventeenth century. Descriptors such as marvelous and illustrious were used to maneuver and advance socially in the learned world. Nevertheless, that he received praise from significant sources indicates that Pascal had effectively taken his place among savants in France. De scartes increased interest in Pascals work provides no small evidence to th e greater position of influence that Pascal had acquired in the learned community. Descartes had once dismissed Pascals work on conic sections as a mere aping of Desargues, but by the fall of 1647 he considered Blaises work signi ficant enough to pay him two personal visits. The meetings are recorded by Jacqueline, Pa scals younger sister, in a letter to Gilberte, his older sister. Jacqueline clearly perceived the honor of the visit and wanted to share her pride with the family. Descartes desire d to visit Pascal, Jacqueline writes, because of the great estimation that he had always heard peop le make of Monsieur my father and of him.188 The mention of tienne reiterates the relationship between Pascals status as savant and as son. It also points to a key claim of this study. The traj ectory of this part of Pascals career suggests both a continued childlike dependency on his elders a nd an assertive drive to validate his identity as a mature savant. While some scholars view this period in Pascals life as an assertive drive 187 Pascals role as a challenger of scholasticism is a part of the traditional narrative of his experiements on the void. Alexander William Stewart Baird, Pascals Idea of Nature, Isis 61 (1970): 296-320, describes Pascals simultaneous rejection of the Aristotelian animism of nature as emobodied in the horror vacui and his maintenance of nature as an active principle. Pascals critique of Aristotle, Baird argue s, does not lead him to the reductive mechanism of Descartes. Inst ead, his idea of nature falls between Renaissance hylozoism, which regards nature as something divine and self-creative, and the Cartesian idea of the world as a sort of giant clockwork, ibid., 318. 188 M. Descartes, son compatriote et intime ami, lui avait fo rt tmoign avoir envie de voir mon frre, cause de la grande estime quil avait toujours ou faire de Monsieur mon pre et de lui, Jacqueline Pascal to Gilberte Prier, 25 September 1647, Mesnard OC 2:480. 162

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for glory, it is clear that Pascals ill health and his childhood in fluences placed him in a position of dependence.189 Descartes meetings with Pascal provide an ex emplary episode of Pas cals dependency that also reflects the possessiveness of one of his ment ors. Pascals health had recently suffered in part, as Gilberte suggests, because of assiduous application to his arithmetic machine. He was so infirm that he had to remain in his bed while talk ing with Descartes. Also present at the meeting was Roberval, a central member of the Mersenne group and one of tienne Pascals old friends. Roberval likely helped to demonstrate the cal culator for the invalid Blaise, and thereafter, discussion turned toward the void. Descartes and Pascal exchanged a few words about their conflicting interpretations of Blaises experiment s. In the midst of this discussion, Roberval jumped in to finish Blaises thoughts, ostensibly because he believed the young man would be caused pain by speaking because of his illness, disputing Descartes theory of subtle matter heatedly.190 At this point in the conversation, Pascal be came a mere bystander. The record suggests that Descartes bristled impatiently at Robervals interruption, saying that he would talk to Blaise as much as he wanted because he spoke with re ason, and that he would not talk with Roberval, who spoke with preoccupation.191 These words did not serv e their stated purpose, but 189 Cousin remarks on Pascal, who adored glory, and who was as head-strong as Descartes. Cousin views Descartes as Pascals archrival, Victor Cousin, tudes sur Pascal (Paris, 1876), 80-83. Mesnard depicts a Pascal for whom his scientific work was a source of pride and which had to be abandoned at his conversion, Jean Mesnard, Les conversions de Pascal, in Blaise Pascal, lhomme et loeuvre ed. M. A. Bera (Paris, 1956): 46-63. Strowski recognizes Pascals project of the arithmetic machine as driven by the expecta tion of glory and fortune, Fortunat Strowski, Pascal et son temps 3 vols. (Paris, 1921), 2: 57. Of particul ar importance for Pascal as assertive and driven is Nelson, Pascal, Adversary and Advocate 190 M. de Roberval, croyant que mon frre aurait peine parl er, entreprit avec un peu de chaleur M. Descartes, J. Pascal to G. Prier, 25 Sept 1647, Mesnard OC 2:481. 191 [Descartes] lui rpondit avec un peu daigreur quil parlerait mon frre tant que lon voudrait, parce quil parlait avec raison, mais non pas lui, qui parlait avec proccupation, ibid. 163

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escalated the verbal conflict betw een Pascals talented elders. Jacquelines letter describes how the rivals argued their way out th e door and into a carriage, wher e they continued their heated dispute on their way to a mutual lunch da te undoubtedly fraught with indigestion.192 While Jacqueline characterizes Robervals actions as motivated by concerns for Blaises health, the exchange also indica tes that Pascals identity as protg of the Mersenne group continued into adulthood. Roberv al demonstrates a sense of owne rship over Pascals person and ideas, while Descartes also seeks to align hims elf with the young mans reasonableness. The image is striking. Two great representatives of learned Europe stood ove r Pascal, the dependent child, arguing to claim a commodity (Pascals genius) caught between two warring factions. Pascals deferential approach is even more prominently displayed in a conflict with the Jesuit father, tienne Nol. Nol initiated a correspondence with a letter to Pascal, in which he stated several arguments against the Expriences nouvelles touchant le vide Pascals lengthy reply to Nols points prompted a further riposte from the Jesuit. Nol suggested through his courier that he did not want to endanger Pascals already fragil e health. He was urged by Nol not to respond to his letter. Not long after, however, Father Nol published a work entitled Le plein du vide which essentially expanded on the arguments that he had made in his second letter to Pascal. This transformed their differences from a private to a public deba te. It was an affront to Pascal as savant. Nols work suggested that Pa scals lack of response to his letter was an admission of defeat. Significant issues of re putation were at stake. Jacques Le Pailleur, one of the Pascals old friends and one of the original participan ts in the Mersenne group, showed his concern 192 [Descartes], voyant sa montre quil tait midi, il se leva, parce quil tait pri de dner au faubourg SaintGermain, et M. de Roberval aussi, si bien que M. Descartes ly mena dans un carrosse o ils taient tous deux tout seuls, et l ils se chantrent goguettes, mais un peu plus fort que jeu ce que nous dit M. de Roberval, ibid. 164

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through a letter to Pascal, in which he asked th e reason for his silence. In a more offensive tactic, tienne Pascal wrote a scathing epistle to the Jesuit, in which he took him to task for both the disingenuous treatment of his son and for the ph ilosophical deficiencies in Nols work. As father and teacher, he intercedes on behalf of his son and pupil. tiennes letter to Nol presents Blaise as childlike in his humility and innocence and mature in his virtue. By contrast, Nols outward marks of learni ng, tienne suggests, are combined with childish rhetoric a nd natural ignorance. In the letter, tienne portrays Pascal as a meek figure. When wronged in this heated discussion, he had s een two possibilities: either to answer the Jesuit in a similarly ironic tone or, practicing the instructi on of the Gospel, to confront Nol in a direct and brotherly way.193 However, Blaise considered neither of these appropriate. Instead, his father continues, he assumed the role of the inferior party, citing the disparity between your age and his.194 In his response to Nol, according to tienne, Blaise exhibited submissiveness. He also showed that he continued to entrust matters of his learned career to his father: He has considered it more appropriate to ask me, as he has done, to take the pain to practice for myself the command of the Go spel, causing you to understand his just complaint, having provoked him without reason, and the lack of an appropriate correspondence between the type of writing th at you have used and the condition that you profess, judging that you will receive that more readily from me than from him.195 The young Pascal was probably wise to respond to Nol as he did. He certainly could not have written the scathing letter penned by his father. The acids of tiennes critique had to be 193 en pratiquant le prcepte de lvangile, Pas cal to Nol, April 1648, Mesnard OC, 2:587. The Provincial Letters demonstrate conclusively that Pascals ability to be irenic was matched by his ability to be ironic. 194 [Il] [a] eu gard la disparit de votre ge et du sien, ibid. 195 il a estim plus propos de me supplier, comme il a fait, de prendre la peine de pratiquer moi-mme ce prcepte de lvangile, vous fa ire entendre sa juste plainte de lavoir, sans occasion quelconque, provoqu, et le peu de convenance quil y a entre le genre dcrire dont vous avez us et la condition que vous professez, jugeant que vous recevrez cela avec plus dagrment de ma part que de la sienne, ibid., 2:587-588. 165

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delivered from a position of social power.196 His status was already secured within the learned circle of Paris, and as a former President of the Cour des Aides at R ouen, within the political hierarchy of the governing class. In responding to tienne Nol, tienne Pascal first confront s the Jesuit because of his style of writing. He uses invective in his work to such an extent, tienne remarks, that It is difficult to judge if you have invented invective because it was useful for continuing the allegory, or if you have inve nted the allegory in order to ha ve a reason let this invented invective creep in.197 Blaises father suggests that Nol is quite proud of himself for being able to insult the work and thus the person of the younger Pascal in various ways. But such pride is misplaced: What glory can a man of honor claim from the art of invective, which is in itself nothing but a pure weakness, and so natural to man that it is almost as if one has the need to study in order to become ignorant of it.198 Pascal presents Nol as having, like the artisans of Rouen, dem onstrated himself to be in a state of unlearned nature. In the attempt to establish his eloq uence and learning, he had instead proven that he had not unlearned a weakness for giving insu lts. The heavy-handed correction that the elder Pascal offers in th is letter is remarkably like the hard discipline of the pedagogue to his students. Indeed, tienne give s the Jesuit a lesson in antithes is, complete with examples and counterexamples, to show the unlearned nature of the title of Nols work: Le Plein du Vide 196 The indispensibility of the patronage of someone in soci al power is a theme of earl y modern science and culture more general and is the subject of a vast literature. Li sa T. Sarasohn, Nicolas-Claude Fabri de Peiresc and the Patronage of the New Science in the Seventeenth Century, Isis 84 (1993): 70-90, reiterates the importance of intercessory writing in the learned culture of seventeenth-century France. 197 [I]l est difficile juger si vous avez invent les invectives pour trouver expdient de continuer lallgorie, ou si vous avez invent lallgorie pour prendre sujet dy faire glisser ces invectives inventes E. Pascal to E. Nol, April 1648, Mesnard OC 2:598. 198 [Q]uelle gloire peut un homme dhonneur prtendre de lart dinvectiver, qui, de soi-mme, nest rien quune pure faiblesse, et tellement naturelle lhomme que tant sen faut quil ait besoin dtude pour y devenir ignorant, ibid., 2:601. 166

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Furthermore, he provides a subtle educational commentary suggesting that the traditional School was too indulgent toward s the natural state of man: [The title of the work] would tr uly be acceptable in the Schools [ dans lcole ], where it is not just permitted, but necessary (so much is the nature of man imperfect) to begin by doing ill, in order to lear n little by little to do good.199 By contrast, in the world, where nothing is excuse d, Nols title would be rejected because it lacked any perfect sense.200 The traditional schools compromise with the natural state of humanity, and do not discipline it enough, Pascals father asserts. Amon g the world (i.e., the broad group of the learned public) the schools had little respect because of this lack of true intellectual discipline. The Jesuit fathers positi on as a teacher (he had instructed Descartes at La Flche) did not prevent him from being fundamentally ignorant, at least in the judgment of tienne. The elder Pascals criticism of Nol ironically expresses what he considers a key truth: that while tiennes son was hesitant to approach his older offender, the Jesuit was more of a child than Pascal. When provoked, Blaise did not retaliate but had recourse to a more mature response: And certainly, my Father, a lthough I am not so happy as to have the benefit of your understanding, I cannot conceal from you that you have been quite fortunate to have undertaken, so cheaply, to carry out these type of injuries against a young man who, finding himself provoked without reason-I sa y without any reason-could, through the bitterness of the injury and through the ras hness of his age, endeavor to push your invectives back onto you in terms that would be capab le of causing you to eternally repent . You have not been unfo rtunate to have been involved with a young man who, through a moderation of nature which is not always in agreement with that age, 199 [Le titre] peut vritablement passer dans lcole, o il est non seulement permis, mais aussi ncessaire (tant la nature de lhomme est imparfaite) de commencer par faire mal, pour apprendre peu peu faire bien, ibid., 2:591. 200 [M]ais certainement dans e monde, o lon nexcuse rien, elle ne saurait passer, puisque par elle-mme elle na point de sense parfait, ibid 2:591. 167

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instead of coming to these extremities-disa dvantageous to both of you, but very much more to you-has taken another way in order to have you hear his complaint.201 According to tienne, Nol had acted the part of the youngster, surrendering to the slightest test of nature. Blaise, by contrast, had demonstrated the restraint associated with maturity. He exemplified precocity in manner and bearing, not just in natura l philosophy and mathematics. Thus, paradoxically, by assuming the role of the meek child in this quarrel, Pascal demonstrated maturity. He had not remained in the state in which nature created him, but had exercised the art of self-control. Pascal exhibited characteristics of childlik eness and submission in his disagreement with Nol about the void. At the oppos ite end of the spectrum, howev er, his father asserted his maturity by claiming that Blaises self-discip line distinguished him fr om his opponents. His work on the void was characterized in similar terms as had been his work on the arithmetic machine during the same period. He was not a mere prodigy but a mature savant. Pascals Preface: mature thinking After recovering from the bout with illness that had plague d him during the meeting with Descartes and probably during his debate with No l, Pascal worked to complete a lengthier treatise on the void, which he had promised in the 1647 text of Expriences nouve lles touchant le vide. Only fragments of the body of this treatise rema ins, but a draft of the preface to the treatise survives and provides, as Eric Koch suggests, Pascals most extensive statement on the New 201 Et certainement, mon Pre, quoique je ne sois pas assez heureux pour avoir le bien de votre connaissance, je ne puis vous dissimuler que vous lavez t beaucoup davoir entrepris, si bon march, de vous commetre en style dinjures contre un jeune homme qui, se voyant provoqu sans sujet, je dis sans aucun sujet, pouvait, par lamertume de linjure et par la tmrit de lge, se porter repousser vos invectives en termes capables de vous causer un ternel repentir . Vous navez pas t malheureux davoir eu affaire un jeune homme, lequel, par une modration de nature qui ne saccorde pas toujours avec cet ge, au lieu den venir ces extrmits dsavantageuses lun et lautre, mais beau coup plus vous, a pris une autre voie pour vous faire entendre sa plainte, ibid., 2:590. 168

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Science.202 The preface reflects Pascals views on the structure of different types of knowledge and has close connections with ideas of Fran cis Bacon. The essay uses the language of pedagogy to describe interactions with nature and suggests the cont rast between instinct and true learning, between childishness and maturity. A co mparison of the preface with Pascals account of the clockmakers abortive inventions and Mersennes Harmonie universelle concerning the limitations of nature in the art of playing the lu te, shows the common themes that Pascal used to secure his legitimacy. The purpose of the preface is to validate Pasc als consideration of the void by establishing the acceptability of novelty in physics. He therefore reiterate s a division between knowledge established by authority and knowle dge established by sense and r eason. He seeks to discredit those who confound the two categories. Unwilli ng to dismiss authority altogether, Pascal acknowledges authority in questions of sim ple facts or divine or human institutions.203 This is the case in history, geography, jurisprudence, lang uages, and especially theology. But authority must not decide questions in mathematics, physics, architecture, and, indeed, all the sciences, which are self-evident to the senses and to reasoning.204 Many of his contemporaries, Pascal claims, have reversed the relationship with author ity. Novelty is acceptable in theology, but it is rejected in physics.205 Pascals main concern is, of course, the simple acceptance of the 202 Erec R. Koch, Pascal and Rhetoric : Figural and Persuasive Language in the Scientific Treatises, the Provinciales and the Penses (Charlottesville, VA, 1997), 38. Mesnard argues for a date of 1651 for the fragments and the preface, based on a letter written by Pascal which refers to the work in progress, Mesnard OC 2:773, 786. The text of the preface is in Mesnard OC 2:777-785 and the fragments are in Mesnard OC 2:787-798. Both were published for the first time in Blaise Pascal, Oeuvres ed. C. Bossut, vol. 4 (La Haye, 1779). 203 Fragment of a Preface to the Treatise on the Vacuum, in Great Shorter Works of Pascal ed. mile Caillet and John C. Blankenagel (Philadelphia, PA, 1941), 51. 204 Ibid., 51-52. 205 the misfortune of our world is such that we encounter many new opinions on theology that were unknown to antiquity, but which are now upheld with obstinacy and received with applau se. On the other hand, though their number is small, new opinions advanced in physics seem perforce to be convicted of error as soon as they shock 169

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authoritative opinion of Aristotle and other ancient authorities that nature will not suffer a void, or at least that n ature abhors the void. Pascal attempts to clarify the mistake of revering the ancients by drawing on a developmental analogy that had become popular among advocates of the New Science. To this purpose, he uses Bacons no tion of humankind as a single i ndividual, growing in knowledge from the beginning of its existence up to the pres ent, so that the same thing happens in the succession of men that happens in the different stages of an individual.206 Pascal further argues, Those that we call ancients were veritably ne w in all things, and actually constituted the childhood of mankind.207 This parallel between the accumu lation of all of human knowledge and the development of an individual was a pedagogical and not an organic metaphor: In such a way that the whole of mankind, durin g the course of so many centuries, ought to be considered as the same man, who always remains and who continually learns . Those that we call ancient we re truly new in all things, and made up the childhood of man properly speaking, and as we have joined to their knowledge the experience of the centuries that have followed them, it is in us th at one can find the antiquity that we revere in others.208 Pascals use of a pedagogical metaphor for th e development of human knowledge emphasizes, once again, the contrast between undeveloped na tural inclination and its augmentation through exercise. Pascal argues that t hose who consider ancient opinions in physics as authoritative are accepted opinions. It is as if the respect we have for ancient philosophers were a duty, and the respect we have for the most ancient of the church father s were merely a courtesy, ibid., 52. 206 Ibid., 54. Bacons statement of this idea is in Francis Bacon, Novum Organum book I, chapter LXXXIV. Foster E. Guyer, Cest nous qui sommes les anciens, Modern Language Notes 36 (1921): 257-264, traces the expressions of this notion from ancient Greece throug h the eighteenth century and makes the case for Pascals reading of Bacon. See also Mesnard OC 2:772-777 and LeGuern OC 1:1094-1097. 207 Fragment of a Preface, in Great Shorter Works 54. 208 De sorte que toute la suite des hommes, pendant le co urs de tant de sicles, doit tre considre comme un mme homme qui subsiste toujours et qui apprend continuellement . Ceux que nous appelons anciens tait vritablement nouveaux en toutes choses, et formaient lenfance des hommes proprement; et comme nous avons joint leurs connaissances lexprience des sicles qui le s ont suivis, cest en nous que lon peut trouver cette antiquit que nous rvrons dans les autres, Prface sur le trait du vide, Mesnard OC 2:783. 170

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attempting to sidestep the normal road to knowle dge. They were following the opinions of the childhood of humanity even t hough chronologically they bel onged to its age of maturity. But this natural state of the intellect, Pascal claims, is ch aracterized by blindness. He suggests that those who misunders tand the place of authority and use it in improper contexts have faulty sight. He laments the blindness of those who rely on authority alone for proof in physical matters, in place of reasoning or experiences.209 This is similar to the point that Mersenne made concerning th e perfect lute-player in Harmonie universelle Natural inclination to such an art (or to a science) without discipli ne and exercise is blind and imperfect. This same accusation is present in Pascals descript ion of the Rouennais artisan who copied his arithmetic machine. The worker did not have the resources necessary to complete the project successfully because he relied on habit or seco nd nature. Fumbling like a drunken man, he could only create a misshapen mass. Pascals description of author itative teaching about physics, stated in his preface, shares other features with Mersennes statements about nature and lute-playing. Mersennes Harmonie universelle had argued that, in playing an instrume nt, good instruction and practice would make up for a lack of musical inclina tion. The naturally-talented musi cian with a delicate ear might believe that his own talents were the only guide needed to perfect his art, but inborn deficiencies believed to determine the perfect musician were in fact improved by discipline. In a similar, though more extreme case, Pascal stated that the artisan of Rouen, excellent as he was in the habituated art of clockmaking, could not create a properly working mach ine without instruction in mathematics and physics. The artisan falsely presumed that he could draw on his natural 209 Ibid., 2:779. 171

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abilities and thereby short-circuit the cumula tive effects of instruction in mathematics, mechanics, and physics. For the artisan, the musician, and the natural philosopher, remaining in ones natural state co-opts the individual created in G ods image. As Pascal states, it is to treat the reason of man unworthily, and to put it alongside the instinct of the animals.210 Memory and accumulation of skill allow the human being to transcend the limita tions of nature. For someone who wishes to play music well, writes Mersenne, the most st erile earth is rendered fertile by the care and diligence of the laborer. Thus, one can overcome the defects of nature.211 In the case of physics, as Pascal points out, humanitys impr ovement is a process that takes place throughout the life of the individual and throughout human history. But knowledge wa s not viewed as built in a strictly linear fa shion. It is bu ilt indirectly, through facts and expriences .212 Reasoned analysis eventually leads to simple principles that make sense of those expriences .213 Pascals handful of principles for deali ng with conic sections elegantly produced numerous theorems. Similarly, many experiences derive from an eleg ant principle in physics. In physics, as in mathematics, such a discovery is a true imitation of the Creator. It is thinking his thoughts after him.214 210 Nest-ce pas indignement traiter la raison de lhomme, et la mettre en parallle avec linstinct des animaux, Ibid., 2:781. 211 Mersenne, Harmonie universelle Livre second des Instruments, 77. 212 The French exprience indicates both experience and experiment. The use of the word here arises from the goal of portraying both as essential to humanitys learning over time. 213 The similarity between such simple rules and the rules of thumb of artisans is important for the development of inductive method. Zilsel argues of the Renaissance artist-engineers: their quantitative thumb rules are the forerunners of the physical laws of science, Zilsel, Sociological Roots of Science, 553. Pascals relationship with the Rouennais artisans, however, demonstrates a recognition that, although feedback fro m the artisans was necessary for its construction, only the savant could reason properly about that feedback. 214 This quotation is attributed to Johanne s Kepler, though its origins are obscure. 172

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To show deference to authority in certain su bject matters, such as physics, the Preface argues, is to renounce true humanity, as a bearer of Gods creative im age. It is lik e the action of animals. Pascal illustrates his point with a par ticular example from the world of the beasts. Bees, he observes, have constructe d their hives with the same leve l of perfection for thousands of generations.215 Nature he writes, instructs to th e extent that necessity presses them.216 But like the lute-player who relies on imparfait natural inclination, the hive-making of bees remains at a restricted perfection, imposed by nature.217 This truth does not, however, minimize the marvelous beauty and exactness of honeycombs. But the bee operates within natural constraints and despite indications to the contrary it doe s not have genuine theoretical knowledge of construction.218 It does not have the same capacity to construct a lutes and glass tubes as does a man. Pascal asserted this same type of restrict ion in his account of workers at Rouen. Artisans who attempt to build an arithmetic machine like Pascals, but without his help, undertake more than their equals219 Their apprenticeship confines them to skills that have been learned through habit. Pascal claims that their limitation, at he art, is the inability to handle all of the proper theory and thereby determine the proportions of a large number of interconnected parts. The bee and the naturally skilled musician re ceive without study their respective gifts for hive-making and lute-playing.220 The artisan likewise receives his skill in working with tools 215 Les ruches des abeilles taient aussi bien mesures il y a mille ans quaujourdhui, et chacune delles forme cet hexagone aussi exactement la premire fois que la dernire, Mensard OC 2:781. 216 La Nature les instruit mesure que la ncessit le s presse, Preface sur le trait du vide, Mesnard OC 2:781. 217 The French reads, perfection borne, P reface sur le trait du vide, Mesnard OC 2:782. 218 In delineating the various failures of esprit, Huarte refers to Aristotles labeling of those who speak by Natural Instinct, and say more than they know as Brute-b east-like, Huarte, Tryal of Wits (1698), 30. 219 plus de leurs semblables, Avis, Mesnard, OC 2:338. 220 Comme ils [les abeilles] la reoivent sans tude, ils nont pas le bonheur de la conserver; et toutes les fois quelle leur est donne, ell le ur est nouvelle, Preface sur le trait du vide, Mesnard OC 2:782. 173

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through repetition and not through st udy. Restricted to the resour ces of unimproved nature, there is no possibility, Pascal suggests, of accumulating improvements that approach perfection. But while nature restricts the bee absolutely, the na tural philosopher, made in Gods image, has his memory to draw advantage not only from his own experience but even from that of his predecessors, because he always keeps in his memory the knowledge that he has once acquired.221 The effectiveness of the analogy between bees and the man who trusts authority in the question of the void relies upon the assumption th at human nature and animal nature are essentially distinct. Mersenne us es the word nature in his disc ussion of lute-playing to indicate an individuals inclination toward music. Inclination might co me from the keenness of ones sense of hearing, the relative con centration of ones humors, the position of the stars at ones birth, or even the type of people encountered in ones developmental years. But even in such cases, nature is not the final word for the human being. The limitations Pascal and Mersenne ultimately deride are self-imposed. In Pascals opinion, as expressed in the Preface to a Treatise on the Void and elsewhere, the key trut h about humanity is that it is made only for infinity.222 By contrast, the nature of anim als exists in limited perfection. [ perfection borne ].223 Animals will not regress but neither will they progress. 221 [Lhomme] tire avantage non seulement de sa propre exprience, mais encore de celle de ses prdcesseurs, parce quil conserve toujours dans sa mmoire les connaissan ces quil sest une fois acquis es, Preface sur le trait du vide, ibid. On the cumulative nature of music, Me rsenne writes in his second book of Instruments in the Harmonie universelle : Encore que les siecles passez ayent produit des hommes tres-excellens en toutes sortes darts & de sciences, & particulierement en celuy dont nous traitons, lon peut neantmoins dire quelles se perfectionnent dautant plus quelles vont plus en auant: comme is est ays de prouuer par lvsage des tremblemens, qui nauoit iamais est si frequent quil est maintenant, Mersenne, Harmonie universelle Livre second des instrumens, 3:79. 222 Il nen est pas de mme de lhomme, qui nest produit que pour linfinity, Preface sur le trait du vide, Mesnard OC 2:782. 223 [L]a nature nayant pour objet que de maintenir les animaux dans un ordr e de perfection borne, Preface sur le trait du vide, ibid. 174

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When Pascal writes that Nature instruct s animals, he refers to a one-time lesson administered at birth. For human beings, instru ction by nature is quite a different story. Nature, in the external sense of the universe (not an internal state of nature) unveils itself. Revelation may occur through reading or hearing a bout a predecessors experiences. It may take the form of autodidacticism th rough ones own experiences. And the process is both active and passive. On the one hand, human beings actively participate in the multiplication of experiences (or experiments). On the other, Pascal depicts external nature not merely as yielding to the discoveries of man but as an active pedagogue: The secrets of nature are hidden; although it always acts, one does not always uncover its effects: time reveals them from age to age, and although always equal in itself, it is not always equally known.224 Humanity in general and individuals in particular must be attentive to natures lessons in order to gain the knowledge sh e actively distributes. But the learned natural philosophe r, Pascal claims, is not mere ly a student. Those who are learned in physics are qualified to detect what nature teaches and to structure experiences of nature as knowledge. The Expriences nouvelle s touchant le vide seeks to structure natures lessons in proper order to a llow others access to knowledge.225 Similarly, Pascals work on the void in Rouen included a public de monstration in the court of the glassworks, similar in style to 224 Les secrets de la nature sont cachs; quoiquelle agisse toujours, on ne dcouvre pas toujours ses effets: le temps les rvle dge en ge, et quoique toujours gale en elle-mme, elle nest pas toujours galement connue, Preface sur le trait du vide, ibid., 2:780-781. 225 The importance of the order of the experiments is stressed in Jean-Paul Fanton dAndon, Lhorreur du vide: exprience et raison dans la physique pascalienne (Paris, 1978) and Dominique Descotes, La rhetorique des expriences sur le vide, in Les Pascals Rouen: 237-261. Descotes argues that the presentation of the experiments in their particular order as baaed in a dramatic strategy, comparing the Nouvelles expriences to the tragedies of Racine, Descotes, La rhetorique des xperiences sur le vide, 250-261. 175

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theaters of medical demonstration.226 Here Pascal dramatically allowed the spectators to see natures lessons by using fo rty foot tubes of glass. Pascal thus acted the part of intermediary between nature and humans. He played the active role of the natural philosopher that complemented natures work as pedagogue. He used his mathematical training and hard work to draw conclusions about the prin ciples of nature, thus securing his legitimate place as a savant. He no longer received acclaim as a youthful boywonder. He pushed beyond natural talent. The true savant, as Pascal presents himself, transcends nature in two ways. He does not rely on natural inclination as a valid means to knowledge; instead, he overcomes the limitations of natures pedagogy by ordering experiences to reveal the principles of the universe. Pascal underscored that he was human, not a pa ssive animal, by imitating the Creator. He used apparatus (tubes, syringes, and bellows) to transcend the mere observance of nature and to actively re-create the void, which he believed was consistent with nature. Guiffart writes of the experiences of Pascal in this way, emphasizing the controlled display of a natural phenomenon: In them is seen a miniature abridgement of the world, in which keeping the elements enclosed in our hands and at our disposal, they allow us to understand what they are and what they can do.227 In this godlike demonstration, Pascal creates an outside-l ooking-in perspective of the phenomenon and creates effects with in the tube at will. The e xperiments on the void are thus a means by which Pascal imitates the Creator a nd distances himself from mere creatures. 226 A scene from such an anatomical demonstration is pictured on the title page of Andreas Vesalius, De fabrica (Basel, 1543). 227 En elles on voit un petit raccourci du monde, dans lequel tenant les lments enferms entre nos mains et notre disposition, ils donnent connatre ce quils s ont et ce quils peuvent faire, Guiffart, Discours du vide excerpted in Mesnard OC 2:427. 176

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Pascals opponents argued that this God-imitatin g re-creation yielded an absurdity. Instead of a creation out of nothing ( ex nihilo ), it was a creation of nothing. If Pascals work had come to nothing, was this not a pitiful task for the im itator of the Creator? Pascal believed that a display of the effects of creation was equivalent to re-creatin g natures works. For the imitator of God, this was a pedagogical tool, an exhibition of the wonders of the world. In his defense against the argument of creating nothing, he claims that he merely makes a negative hypothesis: that this space is void, until such time t hat one has shown that some matter fills it .228 Pascal thus balances an assertion of creativ e possibilities with humble skepticism. Pascal, however, used a similar tactic to critic ize Father Nol during their exchange. In an ironic tone, he accuses the Jesuit of having cre ated a kind of Cartesian subtle matter. But while the true creation of matter belongs only to God and requires great power, Nol effortlessly creates this matter with just his imagination: Imagination has that proper to itself that it produces with as little effort and time the greatest things as the smallest; some have ma de it [i.e., the substan ce filling the void] of similar substance as the heavens and the elem ents; and others, of a different substance, following their fantasies, because they use it as if it were their own work.229 Pascal portrays the fruits of Nols imagina tion as ridiculous, comparing him to a bungling creator. Like the artisan who worked on the c ounterfeit arithmetic machine, the Jesuit cobbles together the efforts of earlier phi losophers to identify the matter th at fills the apparent void. He thereby makes a monster of nature.230 This monster is made up of the great number of 228 que cet espace est vide, jusqu ce que lon mait montr quune matire le remplit Blaise Pascal to Jacques Le Pailleur, [February 1648], Mesnard OC 2:560. 229 [L]imagination a cela de propre quelle produit avec aussi peu de peine et de temps les plus grandes choses que les petites; quelques-uns lont faite de mme substance que le ciel et les lments; et les autres, dune substance diffrente, suivant leur fantaisie, parce quils en disposai ent comme de leur ouvrage, Blaise Pascal to tienne Nol, 29 October 1647, Mesnard OC 2:522. 230 Car on ne peut les croire toutes ensemble, sans faire de la nature un monstre, et comme la raison ne peut pencher plus vers une que vers lautre, cause quelle les trouve galement loignes, elle les refuse toutes, pour se dfendre dun injuste choix,ibid., 522-523. 177

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different opinions and is a divi ded body, of which the contrary members tear each other apart from the inside out.231 As with the clockmakers calculato r, the contradictory aspects of the concepts that make up Nols notion of subtle ma tter show it to be unintelligible. Neither the artisans machine nor Nols subtle matter func tions in the way that their creators had hoped. Both have ill-fitting parts. Nols attempts to imitate the Creator, Pascal ar gues, result in a ridiculous monster. Pascal clearly indicates that Nol has presumptuously invented new matter. He writes, for instance, of the matter with which the Father fills it [the void] and of the matte r that he puts in the tube.232 Furthermore, unlike the Creator, who opera tes in harmony and order, the Jesuit creates and destroys matter at random: But I would indeed like to know from this Father where his ascendancy over nature comes from, and this dominance that he exercises so absolutely over the elements, which serve him with so much dependency that they cha nge properties in the same measure that he changes thoughts, and that the universe accomm odates its effects to th e inconstancy of his intentions. I do not understand wh at blindness could be to the proof of this light, and how one could give assent to some belief in things that are made to arise and are destroyed with an equal facility.233 Pascal suggests that Father Nol mirrors creatures acting according to blind instinct, not God. By accepting various ambiguous accounts of the void from his predecessors, Nol does no more than the bees, which simply operate accordi ng to their instinctive hive-making. He thus 231 Aussi est-il trange de voir parmi ceux qui soutiennent le plein le grand nombre dopinions diffrentes qui sentrechoquent; Ils composent un corps divis, dont les membres contraires les uns aux autres se dchirent intrieurement, B. Pascal to Le Pailleur [February 1648], Mesnard OC 2:575. 232 Ibid., 2:566; 570. He also writes: vous voyez que le P. Nol place dans le tuyau une matire subtile rpandue par tout lunivers ibid., 2:571. 233 Mais je voudrais bien savoir de ce Pre do lui vien t cet ascendant quil a sur la nature, et cet empire quil exerce si absolument sur les lments, qui lui servent av ec tant de dpendance quils changent de proprits mesure quil change de penses, et que lunivers accommode ses effets linconstance de ses intentions. Je ne comprends pas quel aveuglement peut tre lpreuve de cette lumire, et comment on peut donner quelque crance des choses que lon fait natre et que lon dtruit avec une pareille facilit, ibid. 178

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abdicates his place as a human be ing who is made for infinity and who is capable of learning from reason. The letters of Pascal and his father against No l, the preface to the treatise on the void, and the writings on the arithmetic machine all pl aced emphasis upon Pascals maturity. This commonality demonstrates, in part, the way that Pascal and his circle defined themselves as savants. The development of legitimate learning, they believed, required improving on natural inclination. Neither inbo rn talent nor the inte llectual instinct of ignorants sufficed to attain perfection in a discipline, whether in music, geometry, mechanics, or physics. A perfect musician may have natural talent, but few of the musically gifted reached perfection. The geometrical wunderkind produced disciplined work in order to be recognized in the Parisian mathematical academy. The inventor of the arithmetic machine, through his efforts at the frontier of theory and practice, blazed a trail through a fiel d strewn with thorns.234 The natural philosopher, with very mu ch expense, pain, and time, re-created natures processes and organized them to reveal truths about the universe. This period of Pascals life demonstrates that childlike characteristics continued to be central to Pascals identity. Bl aises illness and his history as the protg of the Mersenne group helped reinforce relations of dependency. While this had the potential of undermining Pascals assertions of full-grown maturit y, his father transformed it into another device for legitimacy by characterizing his sons innocent ap proach to disputation with Nol as maturitys hallmark. The tension between dependency and assertion is also displayed in the ambiguous relationship between Pascal and the artisans, with Pascal creating clear contrasts yet still relying on the 234 [J]ai os tenter une route nouvelle dansun champ tout hriss dpines, B. Pascal to Sguier, 1645, Mesnard OC 2:333. 179

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180 workers skill. With the artisans, Pascal had admitted his limitations. He attempted to emphasize the importance of overcoming a restr icted perfection but the tension remained. It will be argued in the following chapter that although Pascal por trayed himself as a mature, sophisticated mathematician, in time he had to come to terms with limitations attributed to his work by religious and wo rldly friends. This transformation unfolded under the continuing influence of earlier roles: the childhood protg of the Mersenne group and his fathers only son. The issue of dependency lingered. Pascals association with chil dhood remained multifaceted and tenacious, despite his attempts to distance himself from it. Through his involvement with the religious movement of Port-Royal, however, his views on the relationship between childhood and maturity shifted focus. A new phase of development slowly emerged, a new view of restricted perfection that reflected the biblical complementarity of the two poles of age-related virtues. His new identity was religious savant.

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CHAPTER 4 A MAN BETWEEN : THE ST RUGGLE FOR A YOUNG TALENT (1647-1654)1 Pascal returned to Paris from Rouen in 1647 with his sister Jacqueline. By the late 1640s, as we have seen, savants throughout learned Europe knew of Pascal s work. The attempts that he made to justify his position showed some succ ess. He had establishe d his position as savant through his favorable comparison of himself with t hose of mere natural inc lination. But as this chapter will show, by this time Pascal had alr eady begun to reconsider his identity as a mathematician and the status of reasoning, mathem atical and otherwise. Chapter 2 shows that Mersenne had viewed the perfection of mathem atics as a goal in itself and as an effective defense against the threats of the skeptics. Th is chapter highlights the ways that Jansenism provided resources whereby Pascal came to understand the limitations of the field of mathematics. Meanwhile, his status as a ma thematical savant placed him in a position of leadership within the Le Pailleur Circle, which continued the work of Me rsenne. This chapter claims that Pascals fathers friends supported his con tinued efforts in mathematics as the best use of his natural talent and as a continuation of the hopes they had for him when he was young. But Pascals new religious influences suggested that he needed to lay aside the expectations of his earthly childhood and to assume his position as a child of God. When he accepted the vocation of the religious devout instead of the mtier of mathematician, Pascal had to embrace the humility of the child while continuing to exercise the discipline of the savant.2 1 The title is taken from a quotation by the Chevalier de Mr, see below, p. 232, n. 146. 2 The French mtier originates in the tradition of manual laborers and designates a particular type of craft. 181

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Encountering the Limits of Savant Pursuits Experiments on the Void Part of the genesis of Pascals questioning of the sufficiency of mathematics probably arose from the controversy of the void. When Bl aise began his research into the question in 1646, he left the abstract but logical ly tight geometrical realm of his Essai pour les coniques for the ambiguities of natural philosophy, especially physics [ la physique ]. Doctors, philosophers, and theologians hotly debated the question and Blaise was therefore forced to interact at that level. During the first experiment in Rouen with his father and Petit, Blaise demonstrated his ability to grasp the nuances of the philosophical ob jections that might be raised. But Pascals first work on the void ( Experiences nouvelles touchant le vide ) offers only a few comments about the philosophical implications of his experiments. It is di fficult, especially within the works introductory note, Au l ecteur, to distinguish between th e voice of the father and the voice of the son. Blaise writes th at his consideration of the ex periments confirmed me in the thought that I had always ha d that the void was not a th ing impossible in nature.3 The statement is a close parallel to Petits comment to Cha nut concerning tienne Pascals own prior antischolastic belief. The elder Pascal was, Petit wrote in 1646, for a long time persuaded of this opinion of Hero and several other philosophers that is, of the existence of the void.4 It is not surprising, considering tiennes close supervision of his sons firs t studies, that Blaise adopted many of his opinions. Moreover, the Expriences nouvelles is dedicated to Blaises father, who 3 [E]lle me confirma dans la pensee o iauois tousiours est, que le vuide nestoit pas vne chose impossible dans la Nature, & quelle ne le fuyoit pas auec tant d horreur que plusieurs se limaginent, Pascal, Experiences nouuelles Au lecteur, n.p. [2]. 4 P. Petit to Chanut, 19/26 November, 1646, Mesnard OC 2:354. 182

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probably backed the project financially.5 Pascals natural philosophy began as a continuation of his fathers. While the Expriences nouvelles is relatively aphilosophi cal, the seeds of foundational questions about knowledge are clearly present. Within the public forum of the glassworks, he had to interact with individuals about their questions. He tried out different means of persuasion and sought to anticipate the responses of his listeners.6 His involvement pushed him beyond the safely demonstrative bounds of mathematics in to regions of cautious hypothesis, reasoned argument, and intellectual appeal.7 He had to lock horns with th e authoritative presence of the ancients, instead of merely perf ecting them, as he had done in his geometrical work. He had to make arguments for the legitimacy of the a ugmentation and fundamental correction of accepted ancient views on physics. Jansenism and the Evalua tion of Mathematics Pascals work on physics helped introduce a phi losophical dimension to his life that would continue to develop during th e stormy period between 1646 and 1654. However, he experienced another powerful influence during the same year. For it was in 1646 that the Pascal family met the Deschamps brothers and, through their in fluence, had a personal experience with the spirituality of Port-Royal. 5 This is Mesnards opinion, Mesnard OC 2:495. 6 Consider, for example the experiment w ith the water and the wine, in which he had his auditors predict whether the wine or the water would descend further in the tube. 7 Pascals contribution to a method of scientific inquiry has sometimes been described by describing his careful performance of experiments and his unwillingness to accept questionable hypotheses, Dijksterhuis, Mechanization 450-451; Hooykaas, Fact, Faith, and Fiction, 347. 183

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Jansenism: the first conversion In January 1646, tienne Pascal took a fall on some ice and broke his leg.8 He required medical care and was in recovery from the accident for three months. Monsieur Pascal hired two talented doctors, the Deschamps brothers.9 These brothers had been converted to a particular type of spirituality, associated with Corneliu s Jansenius, which had an Augustinian emphasis on penance and on the necessity of grace for conversion and Christian living. After their exposure to Jansenism, the brothers had begun to live lives of exemplar y piety and to perform acts of charity on behalf of the poor, including the opening of two hospitals in wh ich they cared for the sick.10 The example of their lives and the books of Jansenist piety that they brought to the Pascals house prompted the family to consider their need of a new appr oach to Christianity.11 Prior to their association with the Deschamps, the Pascals were far from irreligious. If the accounts of the family members post-conversion ar e believed, Blaises life had no hint of libertinage, either morally or re ligiously. He was preserved, th rough a particular protection of 8 According to Margurite Prier, tienne Pascal was on hi s way to witness a duel that was about to occur in one of the faubourgs of Rouen, Mmoire sur Pascal et sa famille, Mesnard OC 1:1098. 9 One brother had the title Seigneur des Landes, the ot her Seigneur de la Bouteillerie, Henri Gouhier, Pascal et les humanistes chrtiennes (Paris, 1974), 12. For very brief biographical entries on Adrien Deschamps de la Bouteillerie (dates unknown) and Jean Deschamps des Land es (?-1688), see Frdric Delforge, Adrien Deschamps de la Bouteillerie, in Dictionnaire Port-Royal ed. Jean Lesaulnier and Antony McKenna (Paris: Honor Champion, 2004), 324; Frdric Delforge, Jean Deschamps des Landes, in Dictionnaire Port-Royal 325. 10 They had from their youth studied perfectly in medicine, in surgery, and in anatomy, in order to not take a chance, by trusting their instinct, of making a mistake, for want of understanding the general rules and the formation of the human body. When these two Messieurs had resolved to give themselves entirely to God, each one of them determined to build a little hospital at the end of their park where their lands touched one another. M. Deslandes, who had ten children, put ten beds in his hospital, and M. de La Bouteillerie, who had no children, put in twenty, Jacqueline Prier, Mmoire sur Pascal et sa famille, Mesnard OC 1:1098; Delforge, Jean Deschamps des Landes, in Dictionnaire Port-Royal 325. 11 They were further instructed in their religious devotion by Guillebert, the Jansenist cur of Rouville. For this detailed account of the Pascal convers ion, from a verbal family tradition r ecorded by Blaises niece Margurite Prier, see Mmoire sur Pascal et sa famille, Mesnard OC 1:1097-1099. Jean Guillebert (1605-1666), met Antoine Arnauld during his studies at the Sorbonne. Arnauld, in tu rn, placed him in contact with Jean Duvergier de Haranne, the abb de Saint-Cyran; see Jean Lesaulnier, Jean Guillebert, in Dictionnaire Port-Royal 495-496. 184

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God, from all the vices of youth.12 The father tienne taught him to differentiate between what can be known by reason and what can be known by faith. tienne Pascal was a virtuous man, though according to Blaises niece Jacqueline Prier, he did good works out of a moral virtue, but not at all from a Christian virtue.13 Through their exposure to Jansenist sp irituality, however, tienne and his family received true piety.14 Jansenism and the quest ion of priorities An important aspect of Jansenist spirituality was the reevaluation of priorities. While Blaise attempted to establish himself as a ge ometrical and inventive savant, the Deschamps believed that such knowledge was ultimately worthl ess. They considered its results (ironically, given Pascals recent work) as nothingness and the void [ nant et le vide ].15 Nevertheless, as Pascals niece recounts, the Deschamps were ve ry much impressed by the beaux talents that were being misused.16 They sought to enlist Pascals mind in the pursuit of pious goals, for it would be unfortunate if he only used it in what they considered the ephemeral productions of mathematics. The 1646 conversion is only one moment in the transformation of his religious perspectives and his way of life. Even the familial accounts of his life mark several key changes. Most scholars accept at least tw o distinct conversions. The firs t is the conversion to Jansenism with his family in 1646. The second is the mys tical 1654 Night of Fire which confirmed for 12 La vie de Pascal, Mesnard OC 1:578. This, of course, further suggests a view of Pascal as being mature, or adultlike, even in his youth, which was generally considered a time of dissolution. 13 Mmoire sur Pascal et sa famille, Mesnard OC 1:1097. 14 Mmoire sur Pascal et sa famille, Mesnard OC 1:1097. 15 Mmoire sur Pascal et sa famille, Mesnard OC 1:1099. It is possible that Margu rite Prier uses this phrase in order to highlight some spiritual connection between Pascals endeavors in physics and his religious devotion. 16 Mmoire sur Pascal et sa famille, Mesnard OC 1:1099. 185

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him the importance of recognizing the God of Abraham, God of Isaac, God of Jacob, not of philosophers and savants .17 Many biographers construct a na rrative in which the interval between the two consists, in part, of a worldly period, out of which Pascal emerges with the Night of Fire. I would argue, however, that the period of 1646-1654 was a time in which Pascal was negotiating the terrain of his identit y. It was a time of personal upheaval, with his fathers death and his sisters determination to enter a convent. He was in a process of choosing a mode of living. It was also a time of uncerta inty for the mathematical community of Paris, which lost Mersenne, while the political specter of the Frondes heightened a sense of fear and instability. During this period, Pascal experienced a variety of tensions that shaped his career. Historians of science have often simplified his ca reer in one of two ways. Some have examined his views of mathematics and natural philosophy and stopped there, thus ignoring the evolution of his ideas about his scientific work. Others have focused attention on his renunciation of mathematical work because of his religious c onversion. Shunning both of these simplifications, this chapter seeks to highlight the ways that Jansenism provided resources whereby Pascal came to understand the limitations of the field of mathematics. Pascal had spent his formative years under the in fluence of those who praised the virtues of mathematics and the life of the savant. He would later write: From hearing people praise these trades [ mtiers ] in our childhood and running down all the others we make our choice.18 But as an only son of a widower, he had also matured under the strong influence of his father, and while tienne was recognized by savants of all of Europe, he was also a public official and a man 17 Le Mmorial, Mesnard OC 3:50. A third conversion is also often ascribed to Pascal near 1660, after which he performed no more work in mathematics. My interpretation contests this notion of a third conversion. For further treatment of Pascals Memor ial, see below, pp. 239-242. 18 Pascal Penss, ed. Krailsheimer no. 634, 209. 186

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concerned with the future of his family and the strength of his financial assets.19 Thus, Blaise represented the hope for a Mersennien completi on of mathematics, but he also embodied the future of the Pascal familys reputation and ma terial goods. Furthermore, his close relationship with his sister Jacqueline and the evolution of her religious devotion kept Pascal under the questioning influence of Port-Royals spiritual values. Each of these factors affected the way Pascal viewed his previous work and the relati onship between his natural inclinations and his concerted efforts. Much of Pascals work on the void occurred after his exposure to Jansenism, and coincided with issues raised by this religious community about learning. The previous chapter focused on ways that Pascal asserted his legitimacy as a savant through these writings and his ability to transcend the limitations that hi ndered those who relied on ancien t authorities. But the later writings on the void demonstrate Pascals concerns with even mo re basic restrictions on the reach of knowledge. In particular, the preface to Pascals planned treatise on the void makes distinct claims regarding the reje ction of novelty in theology: it is necessary to confound the insolence of these rash [ones] who produce novelties in theology.20 And while he maintains his ability to overcome the restric ted perfection of na tural philosophic hivebuilding, he admits a higher-order boundary: [Theologys] principles are above nature a nd reason, and, the mind of man being too weak to arrive there through its own efforts, it cannot manage to this high understanding if it is not carried there by an all-pow erful and supernatural force.21 19 pitaphe dtienne Pascal, Mesnard OC 2: 843. Pascal had been supported by his fathers assets during his life and would live from those assets and the investments that he made with them, including his business venture (late in life) of the first omnibuses in Paris. 20 [I]l faut confondre linsolence de ces tmraires qui produisent des nouveats en thologie, Prface sur le trait du vide, Mesnard OC 2:779. 21 Ibid., 2:778-779. 187

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On the one hand, then, Pascal again emphasizes th e folly of reliance upon natural capacity. In this case, however, he indicates the futility of humanitys attempts to improve upon this ignorance through its own efforts. The applica tion of mathematical skill cannot bring mature understanding in this realm. Instead, humanity must accept its position as a child and submit to be carried to such knowledge by God. The Boundaries of Orthodoxy: The Saint-Ange Affair Pascals critique of religious novelty had r oots in his experiences. His preface does not identify the names of those who hold ver y many new opinions in theology, unknown to all antiquity, sustained with obstinacy and received with applause.22 It is likely, however, that one of the individuals that he had in mind was a man named Jacques Forton, also known as sieur de Saint-Ange. Pascals personal involvement in a controversy involving this theologically novel clergyman exposed him to the pitfalls of atte mpting to establish theological truths through reason.23 Saint-Anges self-proclaimed expertise, and his belief that children could gain theological knowledge by providing them with a prefabricated structure of religious reasoning, jolted Pascal. He was able to recognize and di smiss Saint-Anges theolo gical errors in part because Pascal had specific views on the acqui sition of physical knowledge. In physics, SaintAnge claimed that knowledge of the natural wo rld was accessible through a process of reasoning from theological truths. The pathway was not one of religious reas oning of well-planned experiments, and the use of mathematical reasoni ng. Saint-Anges claim to be dually-learned in theology and natural philosophy could not therefore, be taken seriously. 22 Ibid., 2:779-780. 23 Because it is the way that most scholars and contemporar ies referred to him, as a rule I will employ the name Saint-Ange. 188

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Background to the Conferences Saint-Ange, a former Capuchin monk who in 1647 anticipated receiving a clerical benefice in Rouen, was the author of works entitled La conduite du jugement naturel (16371641) and Discours sur lalliance de la raison et de la foi, (1642).24 In these works, Saint-Ange offered a comprehensive view of the universe thr ough reasoning from theological first principles. He believed that the theologica l doctrine of the Trinity could be proved through reason and that from this single truth, decidedly less clear and distinct than Descartes cogito all of Gods decrees regarding the natural world could be determined. By this means he claimed to know the secrets of the physical universe and purposed to dispense them to enlighten the ignorant. Saint-Ange arrived in Rouen in early 1647, a year after tiennes accide nt on the ice and in the midst of Pascals continuing work on the void. The primary source for what is known as the Affaire Saint-Ange is a document recounting tw o conferences in which Saint-Ange, Pascal, and two of Pascals friends participated.25 The two friends, Adrien Auzout and Raoul du Mesnil (also known as Hall de Monflaines), were a pproximately the same age as Pascal and each would be involved with the natural ph ilosophical argument concerning the void.26 The document that the three young men pr oduced describes the conferences in detail, as a means of 24 Jacques Forton, La conduite du jugement naturel o tous les bons esprits de lun et lautre sexe pourront facilement puiser la purit de la science 2 vols. (Paris, 1637-1641). The work is in two part. For the first part, published in 1637, the authors name is given by the initials S. D. S. A. This was made more transparent with the publication of Part Two in 1641, which provides the authors name as Sieur de Saint-Ange Monteard, cf., Jacques Forton, Discours sur lalliance de la raison et de la foy (Paris, 1642). Later there would be even further authorial identity: M. Jacques Forton, sieur de S. Ange, in Jacques Forton, Discours sur lalliance de la raison et de la foi, ensemble les questions de toute la philosophie et de la thologie, rpondues par les escoliers de Monsieur de S.Ange-Monteard (Paris, 1653). These works are ra re, with editions at the Bibliothque Nationale in Paris. The authorial distinctions, in the case of La conduite may suggest a hesitancy about publishing his opinions under a name by which he was easily identifiable, progressively offering more information. 25 This document is entitled Rcit de deux confrences ou entretiens particuliers tenus les vendredit premier et mardi cinquime fvrier 1647. The original, preserved by Fa ther Guerrier, is in the Bibliothque Nationale, Paris, fonds franais 12449, 559-595. Citations in this dissertation are from Mesnard OC 2:376-394. 26 Auzout would later be a member of the Acadmie des Sciences. Both of these yo ung men corresponded with Mersenne about the void. For this correspondence, see Mesnard OC 2:622-632. 189

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supporting accusations of theological novelty that they brought agai nst Saint-Ange. Despite the main aim of the document, Saint-Anges natura l philosophical opinions, which astonished the young thinkers, are integral to the account. Saint-Anges Religious Reasoning The first shock to Pascal and his friends was Saint-Anges rejection of experience as the basis of reasoning about the physi cal universe. He begins hi s departure from the young natural philosophers views by questioning connections between causes and effects. He argues that explanations of the effects expe rienced in the world should be ba sed not on efficient, natural causes but on final causes, the decrees of God: thus, in order to understand the effects it is necessary to understand the decrees.27 To ascertain the decrees, he continues, only the doctrine of the Trinity is needed. Saint-Ange portrayed himself as a prophet, to whom God had entrusted this method of finding the truth. 28 According to him, his theo logical knowledge of the Trinity gave him ultimate mastery over the other sciences, for they all depended upon that one key principle. He claimed: [I]t is necessary to understand the Trinity before having other knowledge [ les autres sciences ], that it was its antecedent and that on this understanding depended his theology and his physics.29 27 [D]onc que, pour connatre les effets, il fallait connatre les dcrets, Rcit de deux confrences, Mesnard OC 2:376. 28 Gouhier, Pascal et les humanistes chrtiennes 31. 29 [I]l fallait connatre la Trinit devant que davoir les autr es sciences, quelle tait son antcdent et que de cette connaissance dpendait sa thologie et sa physique, Deux confrences, Mesnard OC 2:377. Saint-Anges use of a single principle from which all the processes of the univ erse flow reflects a general approach to natural philosophy that focuses on Gods omniscience as opposed to his omnipotence, as Margaret Osler has suggested. The omnipotence viewpoint, recognizing God as the ultimate freely acting being, limits itself to the particulars which such a God might produce in Creation. The former, on the other hand, em phasizes Gods eternal reason. The natural philosopher could hypothetically discern underlying principles about creation by which predictions may be made. 190

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What seems to have most shocked Auzout, M onflaines, and later Pascal, was that SaintAnge began his deduction of the natu re of the universe with a theolo gical truth that seemed to be the most mysterious one of all: the Trinity. Pascal was not at all opposed to the abundant fruitfulness that a single principle or proposition coul d have. Mersenne praised Pascal, for example, for his ability to distill the work on conic sections into a single proposition from which he thus derives 400 coroll aries, which do not depend on one another but all on the single proposition.30 Indeed, Pascal would refer to the figure which embodied this proposition, and was so fruitful for its many productions, as the mystic hexagon.31 For Pascal and his mentors, mathematics was a way to imitate the works of the Creator and to plumb the depths of God the geometer. But these efforts to discover the hidden thoughts of God did not extend to understanding the mysteries of G ods decrees or of the Trinity. The record of the conferences illustrates how Saint-Anges attempt to avoid the truly difficult work of physics by deducing all of it from theology yielded absurd results. Like the artisan of Rouen, who could only create a monstrous machine because of his limitations, SaintAnges methods were so faulty th at his opinions we re ridiculous. Failure of Saint-Anges Appeal for Legitimacy Although it was Saint-Anges religious claims that prompted the three friends accusations to authorities, his opinions in physics gave fu rther evidence of how un founded his claims to learning were. His preposterous natural philosophical claims woul d have led to his rejection by the three friends, even if his re ligious opinions were not so pecu liar. For Pascal, Auzout, and Monflaines, Saint-Anges arguments were like th e ranting of a silly child. He claimed, for 30 Marin Mersenne to Thodore Haak, 18 November 1640, Mesnard OC 2:239. 31 For a French translation and introductory notes to Leibni zs notes, see Pierre Costabel, Traduction franaise de notes de Leibniz sur les Coniques de Pascal, in Loeuvre scientifique de Pascal ed. Pierre Costabel (Paris, 1964), 85-101. On the mystic hexagr am, see especially Harrington, Pascal philosophe, 12. 191

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example, that the universe had a certain amount of masse corporelle and that all of it eventually had to be united with spirits to make human beings. [A] geometer, he therefore stated, could calculate approxima tely the number of men who ought to be from the beginning of the world until the end.32 His listeners responded by turning away in laughter, as much as civility would permit.33 He also stated an analogy between men and bottles floating in the sea which, when broken, return their common matter to the ocean of universal matter. Once again, the young men were not in rapt aw e of his clever comparison. In stead, they sarcastically poked fun at him: This thought elicited shared laughter, and some pleasant words were said about this comparison between men and bottles.34 Finally, he claimed that a grown man did not contain more substance than a young chil d, but only appeared larger. At this, the group could not keep from laughing at all this strange discourse, an experience which repeated itself when SaintAnge denied that child ren received substan ce from their parents.35 Thus, Saint-Anges attempts to impress the three friends by his excited claims of astonishing knowledge backfired. With each new audacious claim they only found more at which to shake their heads and smile to themselves. He was the polar opposite, for them, of the respectable, mature savant. Saint-Ange also tried to argue that he had the support of savants, much as Pascal did in appealing for a privilege for his arithmetic mach ine. The sieur de Sain t-Ange boasted of the initial incredulity of the audiences in Paris w ho had eventually been converted to his views, 32 Il dit donc ensuite de cela que un gomtre pourrait supputer peu prs le nombre des hommes qui devaient tre depuis le commencement du monde jusques la fin, Rcit de deux confrences, Mesnard OC 2:382. 33 [T]ournant en rise, autant que la civilit le pouvait pe rmettre, cette proposition, on lui fit quelques doutes sur cela, ibid. 34 Cette pense excita une rise commune, et on dit quelques mots agrables sur cette comparison des hommes et des fioles, ibid., 2:383. 35Ibid., 2:391; in the second case, th e groups reaction to Fortons statemen t is recorded as follows: Tout cela acheva de surprendre la compagnie, quoi lon ne se put empcher de tourner en rise, autant que la civilit le permettait, tous ces tranges discours, ibid., 2: 392. 192

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including the Augustinian scholars Monsieur Hallier and Hersent.36 More importantly, perhaps, he also dropped the name of M. Petit, which like ly was Pierre Petit, with whom Pascal first performed the experiments on the void.37 According to Saint-A nge, after making a public mockery of his philosophy, Petit had been won to his side through argument and the supposed claimed that he had never heard anything so powerful.38 Saint-Anges clearest attempt for legitimacy in Pascals eyes was his mention of an appearance in a company at which there was a great deal of to-do made about the said sieur Pascal.39 While there, he had heard about the latters recent experiments at Rouen. Pascal was likely significantly ch agrined when Saint-Ange claimed that they supported Saint-Anges unus ual views on the behavior of the masse corporelle that is discussed a bove. Saint-Ange had unwisely a ttempted to equate his learned credentials with Pascals. From the events that followed, it is clear that Pascal and his friends were not impressed by these references and were hard-pressed to believe that he had received approval for his ideas from aut horitative centers of learning. Knowledge without Effort Perhaps the most troubling aspect of Saint-A nges philosophy, however, was his claim that the deep secrets of his knowledge could be easily communicated and learned. In his Discours sur lalliance de la raison et de la foi Saint-Ange argues that at th e original creation faith and 36 For the career of Franois Hallier (1585-1659), see Louis Ceyssans, Franois Hallier, Bulletin de lInstitut Historique Belge de Rome 40 (1969): 157-264. Charles Hersent (?-1660) is described as un enfant infidle of the Oratorians in Pierre Feret, La facult de thologie de Paris et ses docteurs les plus clbres vol. 5 (Paris, 1907): 343-352. 37 Henri Gouhier, Jean Mesnard, and Michel Le Guern all agree that it is to this Petit, and not to a Petit who was a theologian, as Brunschvicg and Urbain had claimed. Gouh ier writes: connaissant les recherches des Pascal sur le vid il peut juger habile dajouter le tmoignage dun homme de science, Gouhier, Pascal et les humanistes chrtiens, 141, note 10; Mesnard OC 2:377, note 4; Le Guern OC 1:1114, note 3. 38 Rcit de deux confrences, Mesnard OC 2:377. 39 [Il] dit quil avait entendu parler de cette exprience [du vide] Paris, devant que de venir en cette ville, en une compagnie o on avait fait trs grand tat dudit sieur Pascal, Rcit de deux confrences, ibid., 2:382. 193

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reason had a marriage that allowed for perfect knowledge of the world and of God. This was the state of knowledge of the first man. When sin entered the wo rld, however, the union between faith and reason was dissolved. It is this fatal dissolution [funeste dissolution ] that caused the difficulties of attaining true knowledge. 40 This original union may be restored by simply asking God for wisdom. And although Saint-Ange em phasized that the human beings request constituted working to attain wisdom, once it was received l earning was extremely easy. For those who, like Pascal, were tr ained in savant culture, this confounded theological and natural philosophical truth, and clearly represented an invalid and ineffective means of becoming truly learned. Saint-Ange demonstrates this confus ion of spiritual and intellectual maturity by illustrating his point through the examples of Sain t Catherine, Saint Teresa, and the originally unlearned and ignorant twelve apostles. For Sain t-Ange, maturity and learning were attained through a method that restored the original state of Adam, who was born fully-grown. Even a child could attain maturity in knowledge of religion and other sciences if a proper method was followed. Saint-Ange thus sought to catechize children in his system in an attempt to amaze others with a maturity gained with ease and whic h lifted children to a position of intelligence, understanding, and even expertise that was far beyond their years. His goal was both scientific and religious pedagogy. The purpose of Saint-Anges Discours sur lalliance de la raison et de la foi was to make clear his plan of having his Scholars have an experience of a short and easy 40 Ceust est l lheureux estat de tous les esprits, si ce diuin mariage [entre raison et foy] eust est indissoluble tout fait, mais comme Dieu ne lauoit fait qu condition que la liaison nen dureroit que iusques la mort dvn des deux mariez, le memse moment qui vid le pech des Anges & des hommes en vid vne funeste dissolution, Forton, Discours sur lalliance 26. 194

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method that God had given to him to teach the sciences of Philosophy and Theology.41 He explicitly claims that he has the shortcut to knowledge that Pascal decr ies during this period: If [his method] finds complete minds [ esprits ] & [those] in which the judgment is solid, it produces fruits as ripe as one could pluck from them through great and long work.42 Saint-Ange believed that he could demonstrate the success of this easy method through a trial before learned individuals. According to the preface of the work, Saint-Anges group of young scholars thoroughly impressed the attendees of the Viscountess dAuchys academy. Allowing those present to question these youngsters, th ey responded beyond what one could hope from the little time that they had spent with him [Saint-Ange].43 The language used here is strikingly similar to admiration of Pascal as a savant, l earned beyond his years, suggesting Saint-Ange had created child prodigies through his method. By contrast Tallemant des Raux, in one of his Historiettes narrates a much less admiring scene of a very similar gathering featuring Forton and his charges. He interprets Saint-Anges work teaching children philosophy and theology as like that of an animal trainer: In order to finish the histor y of the academy of the Viscountess dAuchy, I will say that lEsclache, who gives philosophy in French, spoke there often. That made one named Saint-Ange (who proved, according to his clai m, the Trinity by natural reason, and who whistled for young children on Philosophy and Theo logy, and made them respond in return in French), to want to introduce himself also among the Viscountess. Several persons, men and women, went to hear thes e parrots; but M. de Paris, having by chance some business 41 [Son] dessein de faire voir dans ses coliers une exprience dune mthode courte et facile, que Dieu lui a donn pour enseigner les sciences de Philosophie et de Thologie, Forton, Discours sur lalliance, preface, quoted in Gouhier, Pascal et les humanistes chrtiennes 31. 42 Si elle [ce mthode] trouue des esprits faits & dont le iugement soit solide, elle y produit des fruits aussi meurs quo[n] en puisse cueillir, par de gra[n]ds & de lo[n]gs trauaux, Forton, Discours sur lalliance 40. The fruits of labor analogy is a long-standing one, and is used by Pas cal in his address to the Parisian academy, see below, p. 227. 43 Forton, Discours sur lalliance preface, quoted in Gouhier, 31. 195

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with the Viscountess, was there one day when Saint-Ange and his little disciples were babbling.44 Des Raux, like Pascal, disapprove s of this manner of teaching as merely habituating children like beasts. Philosophy and theology, like the mathematics and physics required for the arithmetic machine, cannot, Pascal believed, be re legated to the beastly realm of mere habit and repetition. The claim that one may become savant without the requisite effo rt was a betrayal of intellectual order. And like the Rouennais artisan, the theo logical and philosophical adepts created through Saint-Anges acceler ated course were counterfeit. Franois du Verdus, using the metaphor of des Raux, links such natural appr oaches to knowledge with the rejection of geometry: These philosophers who belong to certain schools, I mean these sophists, or rather, these parrots who have been whistled into their cages, without ever thinki ng about the intentions of the pedants, their masters, who have beguiled them into captivity in order to keep them for a long time under their rods, these people ha te a philosopher who is a geometer more than one can imagine.45 The unthinking students of Saint-Ange, mere b abblers, thus paralleled Pascals blind groping clockmaker from Rouen. They may ind eed have had the capacity to vocalize reasoning that sounded learned beyond their years. However, the ridicul ous natural philosophical views and the dangerous doctrines revealed during Sain t-Anges meeting with Pascal and his friends revealed the monstrosity of their education, bo th from the standpoint of a mathematician and from that of an adherent of Jansenist spirit uality. Pascal was con cerned for these children because Saint-Ange boiled religious truth down to a series of propositions. For Pascal, religious 44 Pour achever lhistoire de lacademie de la viconte sse dAuchy, je diray que lEsclache, qui monstre la philosophie en franois, y parloit souvent. Cela fit envie un nomm Saint-Ange (qui prouvoit, ce quil disoit, la Trinit par raison naturele, et qui siffloit de jeunes enfans sur la Philosophie et Thologie, et les en faisoit respondre en franois), de sintroduire aussy chez la Vicontesse. Plusieurs personnes, hommes et femmes, alloient entendre ces perroquets; mais M. de Paris, ayant par hazard quelqu e affaire avec la Vicontesse sy rencontra un jour que Saint-Ange et ses petits disciplines babilloient, Tallemant des Raux, Historiettes 1: 135-136. 45 Franois Du Verdus to Thomas Hobbes, 23 December 1655, in Thomas Hobbes, The Correspondence, Volume 1: 1622-1659 ed. Noel Malcolm (Oxford, 1994), 223-224. 196

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truth, unlike physics and mathematics, transcends reasoned statements. Even though theological truth is authoritatively delivered, as Pascals preface argues, Christianity is primarily about virtuous response to God that cannot be produced thr ough a natural, habitual repetition of words. Saint-Anges approach was, therefore, dangerous for childrens souls. In deed, Gilberte Priers account of her brothers involvement in the Saint-Ange affair sugge sts that he was motivated in his denunciation of the priest by his concern fo r the children whom Sain t-Ange might catechize in his clerical position.46 Saint-Anges approach to knowledge is, in pa rt, an attempt to demonstrate the ease of becoming learned in philosophy and theology. Pas cal emphasized the difficulty, time, and effort that his major projects required of him and therefore Saint-Anges results proved unlearned. However, Saint-Anges suggestion of a childs ability to be theologically learned beyond his years necessitated a thoughtful response, since Ch ristian teaching commande d childlikeness. In this regard, Pascal had to sepa rate intellectual learnedness from religious devotion. He had to continue to argue for his di sciplined learning while recogni zing the importance of humble submission in both religion and science. As the rest of this chapter wi ll show, his experiences opened new windows to the relationship between childlike limitations, submissiveness, and the efforts of maturity. Forging a New Identity: Une Personne Qui Nest Plus Mathmaticien Awareness of Limitations The letter that recounts Descar tes visits to Pascal in 1647 suggests that by that time he was already considering the possibl e limitations of mathematics. His fathers friends, including 46 Ils [Pascal and his two friends] voulurent contredire [Saint-Ange], mais il demeura ferme dans ses sentiments; de sorte quayant co nsidr entre eux le danger quil y avait de laisser la libert dinstruire la jeunesse un homme qui tait dans des sentiments errons, ils rsolurent de lavertir premirement, et puis de le dnoncer sil rsistait lavis quon luy donnerait, La vie de Pascal, Mesnard OC 1:579. 197

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Roberval, sought the continued pr eeminence of his scie ntific and mathematical work. But the letter also indicates that he had begun to shed the notion of mathematics as his mtier or craft, without devaluing its importanc e. Jacqueline writes in the letter to her sister: Say to M. Dumnil, if you see him, that a person who is no longe r a mathematician, and others who have never been so, kiss their hands to one who is one anew. M. Auzoult will explain all that to you, I have ne ither the time nor the patience.47 No previous communication betw een Dumnil (i.e., Hall de M onflaines) and Pascal exists, leaving the occasion for this passage in mystery.48 That the person who is no longer a mathematician is Pascal, however, there can be little doubt, as Mesnard affirms. But Mesnard further remarks that this sentence suggests Pascal s desire to renounce the sciences after his first conversion in Rouen, and this is perhaps a bit to o extreme. To be unwilling to be identified as merely a mathematician does not imply that he gave those occupations no value whatsoever. To interpret the line as such perhaps hews too clos ely to Pascals earlies t biographers by reading into events of the 1640s an attitude toward the world that existed only beginning in the mid1650s, if indeed it ever did. Nevertheless, Pascals abandonment of his principal identity as mathematician is significant. The letter also recounts the subject of Pascal s conversation with Roberval, which suggests Pascals continued movement toward a focus on theological matters. On the afternoon of Descartes second visit, Roberval and Pascal disputed a long time concerning very many things 47 Dis M. Dumnil, si tu le vois, quune personne qui nest plus mathmaticien, et dautres qui ne lont jamais t, baisent les mains un qui lest tout de nouveau. M. Auzoult texpliquera tout cela; je nai ni le temps ni la patience, Jacqueline Pascal to Gilberte Prier, 25 September 1647,, Mesnard OC 2:482. 48 As Auzout is a co-resident of Rouen, and supposed to be able to explain the cryptic sentence, he is the likely source of the anecdote to which Jacqueline refers. 198

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which appertained as much to theology as to physics.49 The clear interest in new avenues of thought and his unwillingness to be identified as a mere mathem atician suggests a move away from a Mersennien view, in which the mathem aticians contemplation and proliferation of geometrical propositions was a spiritual work in itself. The influence of Port-Royal helped facilitate a shift in the relationship: from the discipline and exercise of the mathematician to those of the devout believer. Discovering Restricted Perfect ion: Port-Royal Spirituality In the months following the visit from Descarte s, Blaise placed himself under the tutelage of those associated with Port-Roya l. In so doing, he continued to encounter criticisms for the scourge of his mathematical tale nt. In January 1648, Blaise wrot e to Gilberte to recount his several meetings with Monsieur de Rebours of Port-Royal. During one of their first conversations, Pascal suggested that he had idea s for writing against the Jansenists opponents: I said to him then that I thought that followi ng the same principles of common sense, one could show very many things that the adversarie s [of the Jansenists] say are contrary to it, and that well-directed reasoning leads one to believe them, although it is necessary to believe them without the help of reasoning.50 But Rebours discouraged Pascal in his attempt to embark on a project as a religious savant, as one who sought to express his devotion through st udy and discipline. Rebours believed him to be motivated by an intellectual pride that claimed too much strength for itself. A large part of this suspicion came from the fact that Pascal, although already eschew ing the label of 49 il parla fort toute la journe, le matin M. Descartes, et laprs-dne M. de Roberval, contre qui il disputa longtemps touchant beaucoup de chos es qui appartiennent auta nt la thologie qu la physique, Jaccqueline Pascal to Gilberte Prier, 25 September 1647, Mesnard OC 2:481. 50 Je lui dis ensuit que je pensais que lon pouvait, suivant les principes mmes du sens commun, montrer beaucoup de choses que les adversaires disent lui tre contraires et que le raisonnement bien conduit portait les croire, quoiquil les faille croire sans laide du raisonnement, Blaise Pascal to Gilberte Prier, 26 January 1648, Mesnard OC 2:555. This project would only finally commence with the 1656 printing of the first of the Provincial Letters 199

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mathematician, was known by Rebours to have been involved in the study of geometry.51 This suggests that Rebours considered it misguided for geometry to hold a significant place in spiritual exercises. By meeting with Rebours, Pascal took minci ng steps toward submission to Port-Royal and inched away from his early mathematical apprenti ceship. He also made an abortive attempt to bring forth a fruitful exercise in defense of a Jansenist position. He was unsuccessful in his attempt to earn legitimacy through exercising c ommon sense in the defense of Port-Royal. Instead of convincing Rebours, he reinforced the sp iritual directors belief that worldly desires and pride underlay Blaises religious project. Pascal remained too assertive in spiritual matters. He must be more like a child. The Coexistence of Childlikeness and Maturity Blaise nevertheless continued his quest to atta in a new level of learning in Jansenist piety. In a letter dated 1 April 1648, and co-authored with his sister Jacqueline, Blaise expressed this desire using language that mirrors his arguments in his work on the arithmetic machine and in physics.52 The beginning of the letter mentions that the two have been reading a letter by Saint-Cyran on vocation and through it have reached a new zenith of zeal. Their letter describes in detail the condition of the fallen human being and ones responsibilities toward God. In Pascals works on the machine and the void, he contrasts the limited skills of the artisans and the restricted perfection [ perfection borne] of those who yield to an cient authorities with the 51 Blaise Pascal to Gilberte P rier, 26 January 1648, Mesnard OC 2:555. 52 The letter is incomplete in the copy made by Father Guerrier and Mesnard assumes this is a result of an incomplete original, Mesnard OC 2:580. Guerriers copy is preserved in a Collection particulire, as Mesnard states (labeled Le Premier Recueil Guerrier), Mesnard OC 1:309. This copy has b een virtually inaccessible to twentieth-century scholars, who do not mention the name of the collections owner, only a simple statement that it remains in the hands of descendents of Madame de Bella igue, who received it from Guerrier. Le Guern writes of the letter: Nous avons localis le manuscrit, mais sans pouvoir en obtenir la communication, Le Guern OC 2:1097. Mesnards and Le Guerns publication is based on the original publication in Blaise Pascal, Penses, fragments et lettres de Blaise Pascal ed. Armand Prosper Faugre, vol. 1 (Paris, 1844), 7-11. 200

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intellectual breadth and efficacy re presented by savants in mathematics, physics, and mechanics. While he acknowledges his need fo r skilled artisans, the characte r of their productions and the moral degeneracy of their repugnant plagiarism de monstrate their ultimate inferiority. They are wrong to reach higher than their position warrants. The Pascal siblings st ate that the Christian, however, must accept limitations while reachin g beyond his natural state to perfection: [T]hose whom God, through regeneration, has graci ously retrieved from sin (which is true nothingness, because it is contrary to God, who is true being) in order to give to them a place in his church which is his true temple, after having graciously retrieved them from the nothingness at the point of their creation in order to give a place in the universe, have a double obligation to serve him and to honor him, since as creatures they ought to keep themselves in the order of the creatures and not profane the place that they fill, and that as Christians they ought ceaselessly to aspire to make themselves worthy to take part in the Body of Jesus Christ. But while the creatu res which compose the world are acquitted of their obligation by keeping th emselves within a restricted perfection, because the perfection of the world is also restricted, the children of God ought not to put any limits on their purity and their perfection, because they take part in a body entirely divine and infinitely perfect; as one sees that Jesus Christ does not at all limit the commandment of perfection, and that he proposes to us a model where it is found to be infinite, when he says: Therefore be perfect as your heavenly Father is perfect. Also it is a very detrimental and very ordinary error among Ch ristians, and even among those who make a profession of piety, to persuade themselves that there is a certain degree of perfection in which one has assurance and that it is not necessary to surpass, since there is nothing at all which would be evil if one stops there, and in which one can avoid falling only by climbing higher.53 The Pascals letter is significant, in part, be cause the spiritual values it expresses parallel language and ideas similar to those used by Blaise in his interactions with the artisan of Rouen and his preface to the treatise on the void. While the two scientific writi ngs stress the way that one develops skills in the mathematical scie nces, the above passage indicates a developing understanding of the characteristic s of someone who wishes to m ake a profession of piety, to be learned in religion. The pa rallel expressions of limitatio n and transcendence provide a 53 Blaise and Jacqueline Pascal to G ilberte Prier, 1 April 1648, Mesnard OC 2:583. 201

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context in which to consider Pascals comparison of the mtier of mathematics with the vocation of the religious. In the first place, the Pascals describe the Christian as having a dual nature. The limited, creaturely nature that resemble s the ignorance of a child coexists and yet contrasts with a potential super-nature that strives for the ma turity of perfection. The creaturely aspect of human existence cannot properly ev aluate the physically created world. The one who lacks the supernatural light of God cannot attain the transcendent vision and the possibility of perfection that are revealed in creation.54 Instead, they grope for knowledge with brutal blindness, but succeed only in the idolatrous substitution of mate rial things, the images of their liberator, for the reality of God. The limitations of this natural state parallel the strivings of the ar tisan of Rouen. The worker, unlike Pascal, lacked the lights of geometry, physics [ la physique ], and mechanics [ la mcanique].55 The counterfeit arithme tic machine, undertaken without heed to limitations, thus represented an idol. It was well-f iled on the outside, but a nonfunctional, useless monstrosity.56 Pascals genuine creation, on the other hand, mirrors the knowledge of God gained by looking at the world with the he lp of a supernatural light. His training in mathematics, physics, and mechanics facilitated his striving for perf ection. His recognition that he could not proceed, like the artisans, from natural skill alone, kept him from fruitlessly groping in the 54 De sorte que nous devons nous considrer comme des criminels dans une prison toute remplie des images de leur librateur et des instructions ncessaires pour sortir de la servitude. Mais il faut avouer quon ne peut apercevoir ces saints caractres sans une lumire surn aturelle; car, comme toutes choses parlent de Dieu ceux qui le connaissent, et quelles le dcouvrent tous ceux qui laiment, ces mmes choses le cachent tous ceux qui ne le connaissent pas, ibid., 2:582. 55 Les lumires de gomtre, de la physique et de la mcanique men fournirent le desse in, B. Pascal to Sguier, 1645, Mesnard OC 2:332. 56 bien lime par le dehors, Avis, Mesnard OC 2: 339. 202

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dark. As a result, the machine transcended its physical form and imita ted the thought processes of the human mind. Pascals writings on the void also mirror the Pa scals statements about the efforts toward perfection made by the Christian who refuses to rest in his natural state. In his preface, Pascal equates trust in ancient authority to unwillingn ess to improve upon natural inclination. Unlike the beasts, man is produced only for infinity and thus can advance from day to day in the sciences.57 Furthermore, the ancients are not supe rior to the moderns because the individual human being can surpass the limitations of his own life span by assimilating the body of experiences recorded by his pred ecessors. Likewise, as childre n of God, who partake of a body entirely divine and infinitely perfect (i.e., the sacrament of Ch rists body), Christians ought not to put limits on their pur ity and on their perfection.58 The Pascals claim the possibility of transcending limitations in an approximation to moral perfection. This co ntrasts with the very detrimental and very ordinary error held even by some who make profession of piety, that an individual is utterly determin ed by his natural inclinations.59 The movement toward perfection is continuous and gradual, just as Pascals work on the arithmetic machine had been. The lights of ge ometry, physics, and mechanics enabled Pascal to design his arithmetic machine with reasonable hopes of success.60 His ultimate success, however, only occurred through correcting it little by little and perfect ing it, even to the point of creating more than fifty models.61 Similarly, the supernatural light [ lumire 57 Prface sur le trait, Mesnard OC 2:782. 58 B. and J. Pascal to G. Prier, 1 April 1648, Mesnard OC 2:583. 59 Ibid. 60 Les lumires de la gomtrie, de la physique, et de la mcanique men fournirent le dessein, et massurrent que lusage en serait infaillible, B. Pascal to Sguier, 1645, Mesnard OC 2:332. 61 Avis, Mesnard OC 2:340. 203

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surnaturelle ] enables one to perceive in the world the good images with which God originally filled it.62 These illuminated images serve as a continually present lesson, providing correction so that human beings may transcend the imprisonment, blindness, and sin of their natural condition.63 Like Pascals approximation of mechani cal perfection, spiritual maturity is a continuous process, for we avoid falling only by rising higher.64 There is a resonance, then, between Pascals vision of the one who is savant in mathematics and the one who is learned in relig ious devotion. Neither can rest upon natural inclination, but must strive for further but grad ual perfection. However, the Pascals letter of April 1648 places importance on the Christian recogni zing his continuous status as a creature, and not making efforts to rise a bove that status. True spiritual ity did not mean simply rising above the limitations of the natura l state. It required that strivings for perfection be accompanied by a constant recognition of ones creatureliness and weakness. The Christian, write the Pascals, must be childlike, yet growing to maturity.65 The intellectual realm was a key area of human 62 [N]ous devons nous considrer comme des criminels dans une prison toute remplie des images de leur librateur et des instructions ncessaires pour sortir de la servitude. Mais il faut avouer quon ne peut apercevoir ces saints caractres sans une lumire surnaturelle ; car, comme toutes choses parlent de Dieu ceux qui le connaissent, et quelles le dcouvrent tous ceux qui laiment, ces mmes choses le cachent tous ceux qui ne le connaissent pas, B. and J. Pascal to G. Prier, 1 April 1648, Mesnard OC 2:582. 63 Cest pourquoi nous devons bien mnager lavantage que la bontde Dieu nous donne de nous laisser toujours devant les yeux une image des biens que nous avons perdus, et de nous environner, dans la captivit mme o sa justice nous a rduits, de tant dobjets qui nous servent dune leon continuellement prsente, ibid. 64 [O]n puisse viter de tomber quen montant plus haut, ibid., 2:583. 65 William J. Bouwsma explores the relationship between the Christian idea of adulthood and the imperative to childlikeness in Bouwsma, Christian Adulthood, in Adulthood ed. Erik H. Erikson (New York, 1978): 81-96. Most of Bouwsms article focuses on the importance of growth in maturity in both biblical and historical Christianity. But he also explores the paradoxical childlik e/mature duality. [T]he ideal of Christian adulthood is not control but spontaneity, which is related to childhood. Furthermore, Childhood assumes growth, and it is in this respect fundamentally different from childishness, which rejects it; in this sense childhood is a model for adulthood, ibid., 89. For the Christian adulthood, matur ity should be characterized by a capacity for growth, ibid., 87. 204

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limitation. As the meeting with Rebours had suggeste d, this was a less-thansubtle indictment of Pascals early devotion to mathematical perfection. Pascals journey toward religious devotion is very closely linked to his relationship with his sister, who seems to have led the way. By the time of the April 1648 letter that the two cowrote, Jacqueline was already clearly committed to the idea of entering the convent of PortRoyal. The letter is a testimony to the strength of those nascent desires. Later in the year, Jacqueline would seek permission fr om her father to take a religious retreat at Port-Royal. From their still-extant corre spondence, it appears that tienne was against any such designs.66 Jacqueline nevertheless persiste d and was able to carry out her plan, albeit in hiding. Blaise evidently supported his sisters plan, in her designs, although his fath ers disapproval would likely have been deeply troubli ng to his only son. In fact, following tiennes death in 1651, Blaise opposed the entry of his sister into the convent, at least for a time. It finally took place on 26 May 1652. Pascals Continuing Role as Protg Mathematician Blaises own movement toward the rigors of progressing in spiritual expertise was not steady and not without setbacks. He altern ately expressed great enthusiasm for it and demonstrated resistance, as hi s foot-dragging over Jacquelines vocation demonstrates. These uneven strivings coexisted with continued efforts to improve upon his work on the void and to establish his arithmetic machine as a worthwhile device in the eyes of savants and those in powerful positions. tiennes friends seconded and encouraged these attempts at self-promotion and thereby probably helped to forestall Blaise s commitment to Port-Royal. His continued 66 All of the extant correspondence is written from th e children to their father. Very little of tiennes correspondence still exists. One has to wonder, given the care displayed toward Blaises personal writings, whether tiennes opposition to the religious ambitions of Blaise and Jacqueline prompted certain letters to be destroyed. 205

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position of apprentice to his original mentors, ironically reinforced his attempts to assert himself in mathematics and natural philosophy, and thus to distance himself from his identification with the natural talent of that childhood. Influence of the Mersenne Circle The influence of Pascals fathers friends during this period is suggested in Jacquelines letter of 25 September 1647, recounting the visits of Descartes. Chapter 3 describes Robervals attempts to maintain control of the young mans tale nt against his rival, De scartes. Jacquelines letter also mentions Dalibray, a companion of tiennes long-time friend Le Pailleur and a neighbor of the Pascals. Dalibray spent time with Pascal on the day of Descartes first visit. By 1653, he had written two adulatory poems to Pas cal, encouraging him and praising him in his efforts on the arithmetic machine and in physics.67 In the sonnet that celebrates the arithmetic machine, Dalibray recognizes the universal attraction his inven tiveness should have: Your mind [ esprit] is like unto th is second soul Which flows everywhere in the world And presides over and supplie s all that is done there68 By substituting his own genius for others effo rts to calculate sums, writes Dalibray, Pascal allowed them to partake of his talents as a mathematical genius. The machine, Dalibray continues admiringly, is Of a ma rvelous genius a durable proof.69 His praise of Pascals work was a reminder to the young man of his need to pursue the fields to which he was most naturally suited. Dalibray had been recently occupied with the Spanish author Juan Huartes Lexamen des esprits, which he translated in 1645, and of wh ich re-editions would be published in 1650 67 Dalibray, Les Oeuvres potique de Sr Dalibray (Paris, 1653), 31-33. The poems are entitled, A Monsieur Pascal le Fils sur Son Instrument pour lArithmtique and Au Mme sur le Vide. 68 Ton esprit est semblable cette me seconde / Qui va sinsinuant par tout dedans le monde / Et prside et supple tout ce qui sy fait, ibid., 31. 69 Dun merveilleux gnie une preuve durable, Sur son instrument pour larithmtique, ibid. 206

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and 1655. Huarte (1530-1592) insisted that an i ndividual should not divide his efforts but give himself to the bent of his esprit. The thought of encouraging Pasc al to make focused use of his mathematical mind may have been a contribu ting motive in Dalibrays poems about Pascal.70 On the afternoon of his first meeting with Des cartes, Pascal asked Dalibray to inform Le Pailleur to let his drinking co mpanion know of the planned sec ond meeting with Descartes that would occur the following morning.71 tienne Pascal was the fr iend to whom tienne had gone when he discovered Blaises mathematical genius. He would also take up Mersennes mission at the latters death in 1648.72 Pascals request and the presen ce of Dalibray and Roberval drive home his continued tendency to consult with his fathers friends. They visited his home even during the time when tienne did not live in Paris. Pascal con tinued to have respect for his fathers friends and they had an unyielding influen ce over his life. Their e xpectation was that he would continue the work he had begun in his youth. Pascals close contact with members of the savant community would have been a strong reinforcement to Pascal as he pursued recognitio n for his work. These designs would have been only further strengthened, and the religious ones moderated, by tiennes return to a life in Paris from Rouen beginning in August 1648.73 tiennes acerbic attack on Father Nol at the beginning of 1648, discussed in Chapter 3, proves his interest in his sons reputation as a savant. 70 Huartes influence on seventeenthcentury thought was significant. Mi chel Le Guern highlights Huartes influence over Bacon and Jansenius regarding the souls faculties, Le Guern OC 1:1095. See also, Prouse, Lexamen des esprits :sa diffusion For further treatment of this subject, including remarks on Pascal and Huarte, see Jean Molino, Lducation vue travers Lexamen des esprits du docteur Huarte, in Le XVIIme sicle et lducation: colloque de Marseille (Marseille, 1971), 105-115. 71 The close relationship between Dalibray and Le Pailleur is explored in Pintard, Libertinage rudit 349. 72 Marolles mentions Le Pailleurs Academie, in Marolles, Mmoires de Michel de Marolles, 272. Mesnard establishes Le Pailleurs academy as the direct continuation of Mersennes through the mi d-1650s, Mesnard, Pascal lAcadmie Le Pailleur, 7-16. Tallement des Raux gives a brief description of Le Pailleur, with some episodes from his life, in Des Raux, Historiettes 2: 99-101. 73 tienne was not irreligious, but we have already seen his opposition to Jacquelines entry into Port-Royal. He would probably also have opposed a move toward a closer relationship between Blaise and the Jansenists. 207

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The letter was written about the same time as Blaise s letter to Le Pailleu r defending his silence. Le Pailleur had written to Pascal, concerned ab out the damage his silence would cause. Both reactions to the Father Nol situation unders core the perceived importance of reinforcing Pascals reputation as a precocious talent in mathematics, in physics, and in moral character. Buoyed by the support and endorsement of his fathers old friends, including Mersenne, Roberval, Le Pailleur, and Dalibray, Pascal pursued projects that demonstrated his legitimacy in mathematics and physics. In 1649, he was finally awarded a privileg e for his arithmetic machine. It strengthened the reputation that Pa scal had for capacity in several sciences, and especially mathematics. Furthermore, it gave an official royal e ndorsement and expressly sought to excite him to communicate more and more of the fruits of it to our subjects. 74 Pitching the Pascaline and Himsel f: The Letter to Queen Christina In 1652, Pascal promoted his work further by presenting it to Queen Christina of Sweden, a great supporter of learned scie nce in the seventeenth century. Pierre Bo urdelot, through whom Pascal presented his machine to Prince de C ond in 1644, also managed to introduce it to the queen.75 In a letter to Queen Christina about the machine, Pascal draws on the language of two empires of greatness: one of political power and the other of savant intelligence. Christina, Pascal claims, embodies them both. By the way that he describes the relationship between the 74 Privilge pour la machine arith mtique de M. Pascal, Mesnard OC 2:713. 75 Pierre Bourdelot (1610-1686), personal physician to the Prince de Cond and later of Queen Christina, was labeled as an exemplar of seventeenth-c entury libertinage rudit in Pintard, Libertinage rudit 219-220, 353-355. Bourdelot had organized an informal academy that met at the home of the Prince de Cond sometime during the early 1640s. With his move to Swed en, this Parisian academy was suspended, but resumed in 1664 with his return, continuing until his death. Pascal may have visited this academy, especially as Bourdelot was one of those who addressed the question of the void, Ren Pintard, Autour de Pascal: lAcadmie Bourdelot et le problme du vide, in Mlanges dhistoire littraire offerts Daniel Mornet (Paris, 1951): 73-81. On the Acadmie Bourdelot and its relationship to the Acadmie des Sciences, see Taton, Les origines de lAcadmie des Sciences, 16-17, 28. Some of the conversations held at the later meetings are published in Gallois, Conversations Acadmiques tires de LAcadmie de Monsieur lAbb Bourdelot 2 vols. (Paris, 1674). 208

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two empires and the queens place within them, Pa scal expresses thoughts th at also apply to his life, especially the relatio nship between inborn traits and disciplined endeavor. In his letter to her, Pascal praises Queen Christina. She is a special individual who combines temporal power and strength of mind. She received her position as queen not because of any virtue, but through the natural process of birth. On the other hand, Pascal emphasizes that intellectual prowess does not come as some claim, through birth or through fortune, as can the power of earthly rulers. Instead, it is imparted a nd preserved through merit.76 Although throughout the letter Pascal takes the expected role of the dependent, submissive, and inferior servant, he strategi cally manages to stress his own concerted exercises in the realm of the mind.77 For example, he reminds the queen of t he pain and the time that new productions cost, especially when inventors want to bring them to th eir final perfection.78 In another place, he characterizes his work as a great effort of mind.79 He thus communicates to the queen that he is not devoid of the merits of learning. 76 Ce second empire me parat mme dun ordre dautant plus lev que les corps, et dautant plus quitable quil ne peut tre dparti et conserv par le mrite, au lieu que lautre le peut tre par la naissance ou par la fortune, Blaise Pascal to Queen Christin a of Sweden, [June 1652], Mesnard OC 2:924. 77 Pascals expressions of Christinas power highlight his own sense of the importance of savant accomplishments: Reign therefore, incomparable princess, in an entirely new manner; let your genius subjugate all that is not submitted to your arms . For me, not being born under th e first of your empires, I want the world to know that I glory to live under the second; and it is to testify of it that I dare to raise my eyes to my queen, giving to her this first proof of my dependency. It is this, Madame, which has inclined me to give this present to Your Majesty, although [it is] unworthy of her. My weakness has not astonished my ambition. I figured that even though the mere name of Your Majesty seemed to distance from itself all that is dispro portionate to it, it nevertheless does not reject all that is inferior to it; otherwise its greatness woul d be without homage and its glory with eulogies. It is content to receive a great effort of mind, without requiring that it be the effort of a mind as great as hers. It is through this condescension that she deigns to enter into some comm unication with the rest of men, B. Pascal to Queen Christina, Mesnard OC 925. 78 Votre Majest nignore pas la peine et le temps que cotent les productions nouvelles, surtout lorsque les inventeurs les veulent porter eux-mmes la dernire perfection, ibid., 2:923. 79 Ibid., 2:925. 209

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Pascal sought Christinas r ecognition of his machine, whic h would provide him with the backing of power and perhaps financial support.80 In praising her characteristics, he created an indirect parallel with himself. He had been a young man talented beyond his years and Christina was a young queen, in whom the advantage of exprience is brought together with the tenderness of age, who thereby furnishes to the universe this unique example which it lacked.81 Pascals desire to make a place for himself within the world of the best minds is thus expressed in his praise for the queen who might be able to le nd temporal legitimacy. If she wondered whether he had the wherewithal to cont ribute significantly to science, his machine would be the proof. In addition, she could take the word of Bourdelot, the queens personal physician and one of Pascals old acquaintances: You are the clearest and most penetrating mind I have ever se en. With the diligence that you have for work, you will surpass both the anci ents and the moderns, and will leave to those who follow you a marvelous ease of learning.82 Nothing certain is known of the queens reaction to Pascals letter and his machine. But Pascals verbal and physical offerings reveal a man whose desire to be r ecognized as a mature savant was not yet utterly satisfied. 80 Queen Christinas patronage extended to intellectuals and artists, including Ren Descartes (whose death in 1650 has been attributed to Christinas demands for early morning philosophical discussions) and Gian Lorenzo Bernini. Lilian H. Zirpolo, Christina of Swedens Patronage of Bernini: The Mirror of Truth Revealed by Time, Womens Art Journal 26 (2005), 38-43, provides an overview of intellectual patronage and an in-depth look at the patronage of Bernini. Bourdelot encourages Pascal about the possib ility of the queens support: vous tes un de ces gnies que la reine cherche, Pierre Bourdelot to Blaise Pascal, 14 May 1652, Mesnard OC 2:919. 81 Cest Votre Majest, Madame, qui fournit lunivers cet unique exemple qui lui manquait, B. Pascal to Queen Christina, Mesnard OC 2:925. 82 Vous tes lesprit le plus net et le plus pntrant que j aie jamais vue. Avec lassiduit que vous avez au travail, vous passerez galement les anciens et les modernes, et la isserez ceux qui vous suivront une merveilleuse facilit dapprendre, Bourdelot to B. Pascal, 14 May 1652, Mesnard OC 2:919. 210

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Defending Work on the Void Pascal also sought to promote and protect hi s work in physics. In late 1647 Pascal commissioned his brother-in-la w to perform the barometric experiment on the Puy-de-Dme around the same time that he was pursuing his in terviews with Rebours at Port-Royal. Further writings in physics, including an unfinished work on the void and two other treatises that remained unpublished until after his death ( Trait de lquilibre des liqueurs and Trait de la pesanteur de la masse de lair) followed in the ensuing years.83 The subject of the void and its expansion to the question of the weight of th e air became one of the hot topics of natural philosophy in the French capital a nd was the subject of most wide spread interest among Pascals former mentors. It particularly occupied Me rsenne and Roberval, who devised and performed different experiments.84 As news of the work being done in Paris spread throughout learned Europe, Pascals priority and originality were challenged. He countered by emphasizing not only his hard work and effort, but also his virtue. One of the key purposes of Pascals Expriences nouvelles touchant le vide was to secure the results of his experiments against the unvirtuous. Like the artisan of Rouen, they could attempt to profit from his work even though they were not as knowledgeable and had not expended the efforts that he had: Having made these experiments with very much expense, pain, and time, I was afraid that another who has not employed neither time, m oney, nor pain, anticipating me, would give to the public some thing that he had never seen, and which consequently he could not 83 Mesnard calls the unfinished work Fragment dun Trait du Vide The text is in Mesnard OC 2:787-798. 84 Mersenne continued to procure tubes from Rouen through Hall de Monflaines and Adrien Auzout. Furthermore, he tried to commission Jacques Le Tenneur to perform the experiments on the Puy de Dme that Pascal had envisioned. Roberval recounts a number of experiments that he performed on the void in his Narratio to Desnoyers. 211

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report with the exactness and the order that ar e necessary in order to recount them as is required.85 Likewise, in his Rcit de la grande exprience he emphasized how the virtue of his method contrasted with that of the opponents of his interpreta tion of the void. His method consisted of the little by little distancing from the anci ents through the force of the truth and the evidence of expriences that uncover the hidden truths of nature.86 His opponents espouse chimerical causes for the apparent void, which serve only to cover the ignorance of those who invent them.87 To be virtuous in natural philosophy requires hard work, not vain invention. Pascal versus the ignorant: correspondence with Ribeyre Pascal displayed his defense of virtue in a number of different writings between 1648 and 1654. A particularly vigorous example appears in his response to writings by Father Mdaille, a Jesuit at the college of Clermont. On 25 June 1651, Mdaille sustained theses at the college regarding the experiments on the void, and dedica ted these theses to Monsieur de Ribeyre, President of the Cour des Aides in Clermont-Ferrand, Pascals natal town.88 Mdaille raised the accusation, which had already been circulating, that Pascal had claimed Torricellis experiments for himself. In an initial letter to Ribeyre, Pa scal cites his relationship with the savants of Paris 85 [A]yant fait ces expriences avec beaucoup de frais, de peine et de temps, jai craint quun autre qui ny aurait employ le temps, largent, ni la peine, me prvenant, donnt au public des choses quil naurait pas vues, et lesquelles par consquent il ne pourrait pas rapporter avec lexactet et lordre ncessair e pour les dduire comme il faut, Pascal, Experiences nouuelles Au lecteur, n. p. [5]. 86 Ie ne le fais quen cedant la force de la verit, qui m y contraint. Iay resist ces sentiments nouueau, tant que iay eu quelque pretext pour su iure les anciens . Aussi ie ne les ay quittes que peu peu, & ie ne men suis esloign, que par degrez, Blaise Pascal, Recit de la grande experience de lequilibre des liqueurs (Paris, 1648), 19. Pascals reference to les veritez caches is in the paragraph which precedes, ibid. 87 Il en est de mesme de lantiperistase, & plusieurs autres causes Chimeriques, qui napportent quvn vain soulagement lauidit quont les ho mmes, de connoistre les veritez caches, & qui loing de les descouurir ne seruent qu couurir lignorance de ceux qui les inuentent, & nourrir celle de leurs sectateurs, ibid., 18-19 88 The author of a manuscript attributed to a M. Lamy gives the name of the Jesuit as Jean-Paul Mdaille, the younger brother of Jean-Pierre Mdaille, the founder of the Sisters of Saint-Joseph, who spent most of his adult life of ministry in Clermont and the surrounding towns of Auverg ne. No traces of the theses written by P. Mdaille have been found, as Mesnard notes, Mesnard OC 2:804, note 1. 212

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and those of Clermont, and claims that they may a ttest that I have never failed to say that this exprience came from Italy, and that it is of the invention of Torricelli.89 He does not stop at defense. He reiterates his legitimate claim to learning in physics by recalling the efforts of numerous learned individuals to spread his Expriences nouvelles throughout Europe. Mersenne, for example, not being content to se e it all over France, asked me for several [copies] to send them, as he did, to Sweden, Holland, Poland, Germany, Italy, and in all directions.90 With the support of well-known savants, Pascal had given his self-defense and produced evidence of renown. Having established this, he questions Mdailles legitimacy in learned matters because of his evident ignorance of the Expriences nouvelles and thus Pascals public acknowledgment of the Torricelli experiment: Thus I believe that this good Father of Mont ferrand is the only one among the curious of all of Europe who has not had knowledge of it. I do not know through what misfortune, unless it is that he flees the commerce a nd the communication of sa vants, for reasons I cannot fathom.91 Pascal therefore suggests the importance of bein g a part of learned co rrespondence networks for claims to learning. In support of this criterion, Pa scal adds later that if Mdaille had a little more commerce with Paris he would understand that it would be as absurd for him to claim credit for the invention of the mercury experiments as it would be to claim that he invented the telescope.92 89 [J]e nai jamais manqu de dire que cette exprience est venue dItalie, et quelle est de linvention de Torricelli, Blaise Pascal to Ri beyre, 12 July 1651, Mesnard OC 2:806. 90 Et enfin le P. Mersenne, ne se contentant pas den voir par toute la France, men demanda plusieurs pour les envoyer, comme il fit, en Sude, en Holla nde, en Pologne, en Allemagne, en Italie et de tous les cts, ibid., 2:809. 91 De sorte que je crois que ce bon Pre de Montferrand est le seul entre les curieux de toute lEurope qui nen a point eu de connaisance. Je ne sais par quel malheur si ce nest quil fuie le co mmerce et la communicatioin des savants, pour des raisons que je ne pntre pas, ibid. 92 Ibid., 2:810. 213

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Pascal, endorsed by the savants of France a nd known by all of learned Europe, offers a striking contrast to Mdaille, who was comp letely unknown in these communities. Indeed, Pascal had never heard of him: I do not conceal from you, Monsieur, that I wa s marvelously surprised to learn that this Father, whom I do not have the honor of knowi ng, of whom I do not kno w the name, that I have no memory of having ever seen whatso ever, with whom I ha ve nothing at all in common, neither directly, nor indirectly, nine or ten months after I left the province, when I was distanced from it by one hundred league s, and when I think of nothing less, has chosen me for the subject of his discussion.93 In addition to being unknown by the great minds of Europe, Pascal suggests that Mdaille does not even know the work of the most important thinkers of the time. Pascal admits no such ignorance. He cites Roberval, professor of ma thematics, who used my book as an indubitable proof against Valerian Magni, th e Polish Capucin who claimed to have repeated the Torricelli experiment prior to Pascal.94 If the Jesuit does not know the wo rk of Roberval, who happens to be Pascals close friend, he cer tainly does not deserve a hearing. In fulfill ment of the hopes of Mersenne for a new Archimedes, Pascal seeks to impose an eternal silence on one who is ignorant of geometry:95 If this Jesuit Father of M ontferrand knows M. de Roberval, it is not necessary that I accompany his name with the praises which ar e due him, and if he does not know it, he 93 Je ne vous cle point, Monsieur, que je fus merveilleusement surpris dapprendre que ce Pre, que je nai point lhonneur de connatre, dont jignore le nom, que je nai aucune mmoire davoir jamais vu seulement, avec qui je nai rien du tout de commun, ni directement, ni indirectem ent, neuf ou dix mois aprs que jai quitt la province, quand jen suis loign de cent lieues, et lorsque je ne pense riens moins, mait choisi pour le sujet de son entretien, ibid., 2:805. 94 M. de Roberval, professeur aux mathmatiques, qui se servit de mon imprim comme dune preuve indubitable, Mesnard OC 2:811. In the discussion of Roberval, Pascal also drops the name of another savant: M. Desnoyers, secrtaire des commandements de la Reine de Pologne, homme trs savant et trs digne de la place quil tient auprs de cette grande princesse, ibid., 2:811. 95 See the discussion in Chapter 2 of the i nvocation of a new Archimedes in Mersenne, La vrit des sciences 750. 214

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ought to abstain from speaking of these matters, since this is an indubi table proof that he has no entry into high fields of knowledge, neither of physics, nor of geometry.96 Geometry overcoming limits Pascals letters to Ribeyre demonstrate th at virtues and learning go hand in hand. And although by 1651 he had long previously made the cl aim to be no longer a mathematician, he continued to appeal to the cap acity of mathematics to establish truth and to maintain the exclusionary nature of the mathem atical community. In the treatise Lquilibre des liqueurs unpublished during Blaises lifetime, Pascal points to a particular proof as one that will be able to be understood by geometers alone, and can be bypassed by others.97 Those who have not exercised themselves in mathematics are excluded from an important aspect of the argument offered by Pascal. He makes a similar statement w ith reference to a proof that liquids weigh in proportion to their height and not their width: [T]he demonstration of it would be easy, by in scribing in the one and in the other several little regular tubes Those who are accustomed to the inscriptions and circumscriptions of geometry will have no pain to understand that; and it would be very difficult to demonstrate it to the others at least geometrically.98 In both Lquilibre des liqueurs and an accompanying treatise entitled La pesanteur de la masse de lair Pascal presents evidence to show that his explanation of the void is mathematically comprehensible in ways that othe rs are not. The height of the mercury in the tube, he states, is proportiona l to the amount of air above th e basin in which the tube is 96 Si ce Pre Jsuite de Montferrand connat de M. de Roberval, il nest pas ncessaire que jaccompagne son nom des loges qui lui sont dus, et sil ne le connat pas, il se doit absentir de parler de ces matires, puisque cest une preuve indubitable quil na aucune entre aux hautes connaissances, ni de la physique, ni de la gomtrie, B. Pascal to Ribeyre, 12 July 1651, Mesnard OC 2:812. 97 Voicy encore une preuve qui ne pourra estre entendu que par les seuls Geometres, & peut estre passee par les autres, Pascal, Trait de lquilibre 10. 98 Et la demonstration en seroit facile, en inscriuant en lvn & en lautre plusieurs petits tuyaux reguliers . Ceux qui sont accotumez aux inscriptions & aux circonscriptions de la Geometrie, nauront nulle peine lentendre cela; & il seroit bien difficile de le dmontrer aux autres au moins Geometriquement, ibid., 18. 215

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submerged. Thanks to this explanation, he says there is no longer any need for recourse to explanations (e.g., that nature has a horror vacui ) that use terms that personify nature. Through mathematical acuity and exercise one moves be yond naive beliefs about natures passions and transcends the beast-like or chil dish reliance upon the ancients th at Pascal opposes in his preface to the treatise on the void. A mathematical approach to nature also su rpasses the limited knowledge of artisans. Artisans, ancients, and the unsound philosophers who follow them, have ascertained unsound mechanical principles from their own circumscri bed experiences. They could not recognize that the created nature that they observed also had limits to its inclinations: All those who have written of these matters ha ve said the same thing; and even all our fountain-makers assure us sti ll today that they will make su ction pumps which will draw water to the height of sixty feet if desired. It is not that Hero, these authors, these artisa ns, and still less the philosophers, have pushed these tests very far; if they had tried to draw the water only to the height of 40 feet, they would have found it impossible; but it is only because they have seen suction pumps and siphons of six feet, of ten, of twelve, which do not fail to make their effect, and they have never seen that the water failed to ascend ther e in all the tests that they have happened to perform. In such a way that they did not imagine that there was a certain degree after which it would happen otherwise. They though t that it was a natural necessity, of which the order could not be changed; and as they believed that the wate r ascended through an invincible horror of the void, th ey were assured that it woul d continue to rise, as had occurred with no exception; and thus, drawing a consequence from what they saw to what they did not see, they gave the one and the other as equally true.99 99 Tous ceux qui ont crit de ces matieres ont dit la mesm e chose, & mesmes tous nos Fonteniers asseurent encore aujourdhuy quils feront des Pompes aspirantes qui attireront leau soixante pieds si lon veut. / Ce nest pas que ny Heron ny ces Auteurs, ny ces Artisans, & encore moins les Philosophes ayen t pouss ces preuves bien loing, car sils avoient essay dattirer leau seulement 40. pieds, ils lauroient trouv impossible; mais cest seulement quils ont veu des Pompes aspirantes & des Siphons de six pieds, de dix, de douze qui ne manquoient point de faire leur effet, & ils nont jamais vu que leau manquast dy monter dans toutes les preuves quil leur est arriv de faire; De sorte quils ne se sont pas imaginez quil y et un certain degr apres lequel il en arrivast autrement. Ils ont pens que cestoit une necessit naturelle, dont lordre ne pouvoit estre chang; & comme ils croyoient que leau montoit par une horreur invincible du vuide, ils se sont assurez quelle continuroit slever comme elle avoit commenc sans cesser jamais; & ainsi tirans une consquence de ce quils voyoient ce quils ne voyoie[n]t pas, ils ont donn lun & lautre pour galemen t veritable, ibid., 134-135. 216

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The mistake that the ancients, artisans, a nd philosophers made about suction pumps and fountains arose from their lack of mathematical rigor in the progre ssion from experiences to conclusions. The physical truth about the lim itations of water pumps is analogous to the situation of these individuals. They e xperienced some success in applying their nonmathematical reasoning to physics. However, when one seeks to ascertain a higher level of certainty, such methods lose their efficacy. They can no longer draw accurate consequences from the data of experience. Pascals Role in Continui ng the Mersenne Circle The correspondence with Ribeyre, the preface to the treatise on the void, and the two treatises on the weight of the air and its effects, express the gravitational a ttraction of the Parisian mathematical community for Pascal. He author ed all of these writings following the death of Mersenne in September 1648. During the next six years, there con tinued to be regular meetings of the groups members, but the group experienced other attrition culminating in the death of Le Pailleur in November 1654.100 The result was an increased se nse of necessity for organizing those who had become known as our geometers. Despite Pascals new interest in and even pursuit of an exercised and rigorous spirituality, the community that had nurtured him as a young man also continued to have expectations for him. It was during intermittent periods of good health between 1648 and 1654 that Pascal pursued physical and mathematic al research. When his health began to revive, Pascals work ev en more clearly followed Mersennes goals for mathematics. Setting forth new connections that multiplied consequences in a number of 100 Mydorge had died not long before Mersenne, in July 1647, tienne Pascal died in September 1651, and Desargues had returned to his native Lyon sometime in the midto late-1640s to return only sporadically up to his death in 1661. Charles Vion Dalibray died in 1653. 217

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mathematical areas, Pascal approximated to th e mathematical state of beatitude and a faithful imitation of the Creator.101 The death of Mersenne was a painful loss to the Parisian savant community. Mersenne had been the animating force behind the math ematical conferences of the 1640s. As the secretary of Europe, he also had an exte nsive correspondence network that served as a clearinghouse of ideas for the geometers of Paris to consider and as a distribution network for their own work. Ren Taton, cons idering the impact of Mersenne s death on the community that would one day become the Acadmie des Sciences states that Pierre de Carcavy made an effort to take in some of the slack in correspondence. Carcavys effo rts failed to produce as much as he probably hoped. His correspondence had partic ular personal and philosophical boundaries. Mersenne had been more inclusive.102 Jacques Le Pailleurs attempt to continue the learned conferences was more successful. Marolles Mmoires testifies that a group gathered every Saturday at Le Pailleurs home in order to speak of Mathematics.103 According to Marolles, this regular meeting attracted the members of the core group of Mersennes original acadmie : Pascal, Roberval, Desargues, and (in fulfillmen t of Mersennes prediction of 1635) Gassendi.104 The mention of other notable sa vant attendees, such as the 101 For the importance of discovering connections in math ematics as a spiritual exercise, see the chapter entitled Mathematical Liaisons in Matthew L. Jones, The Good Life in the Scientific Revolution: Pascal, Leibniz, and the Cultivation of Virtue (Chicago, 2006), 89-129. 102 Taton, Les origines 19-20. Carcavys failure to fill the gap left by Mersenne foreshadows his inability successfully to promote Pascals later wo rk on the curve known as the roulette. 103 Marolles, Mmoires 272. 104 In his original announcement of his acadmie toute mathmatique, Mersenne wrote to Peiresc that Gassendi, when he came to Paris, will see the most noble acad emy in the world part of which he will no doubt be, for it is entirely mathematical, Merse nne to Peiresc, 23 May 1635, Mersenne, Correspondance 5:209. 218

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astronomer/mathematician/correspondent Ismal Boulliau and the English philosopher and geometer Thomas Hobbes, testifies to the strong re putation of the gathering.105 It is difficult to assess the extent of Pascal s relationship with the group of savants who met at the home of Le Pailleur until the latters d eath in 1654. From the story of the visits of Descartes, it is evident that Le Pailleur was an old family friend and a regular influence in Pascals life from the time of Blaises return to Paris in 1647. More conc retely, Pascal addresses a summary of his mathematical work to the gr oup. This work, written sometime prior to 1654, refers to the groups as the learned School [erudito Lyceo ] that sustained me from my youngest years.106 An examination of this address to the Illustrious Parisian Academy of Mathematics, and of Pascals mathematical writings and correspondence of the period, demonstrates that Pascal continued his associatio n with mathematics and his appeal to colleagues in such work. In the mathematical work itself, he exhibits a continuatio n of Mersennes project to perfect mathematics through the multiplicatio n of propositions and consequences not fully uncovered by the ancients. Treatise on the Arithmetic Triang le: Continuing Mersennes Project Among the mathematical works in which Pascal engaged following his return to Paris is a series of linked treatises unified by the arithmetic triangle. This numerical pattern/figure, often called simply Pascals triangle, is made up of a set of rows and columns in which numbers are placed according to a simple rule. The upper left-h and corner of the triangle is occupied by what 105 See Marolles, Mmoires, 272. Du Verdus writes: We could also tell you something about the Porisms of the Ancients which M. de Fermat has reconstructed; about M. de Pascals magic numbers; and about the other things which we discuss on Saturday evenings at M. Le Pailleurs house in the rue S. Andr, where the geometers of this city have kindly invited me, Franois Du Verdus to Thomas Hobbes, 4 August 1654, in Hobbes, Correspondence, Vol. 1 190. Among those attending the Le Pailleur meetings, Carcavy is a relatively new face among the mathematicians of Paris. He will, like Pascal, have important ties to the Port-Royal community. 106 Celeberrimae matheseos acad emiae parisiensi, Mesnard OC 2:1032. 219

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is called the generator (u sually the number 1), and this number is duplicated in the boxes (cells) immediately to the right and below the generato r. The rest of the cells are filled by adding together the number that appear s immediately above and to the le ft of the cell (see Figure 1).107 Because another set of cells may always be genera ted from previously determined cells, there is no limit to the size of the triangle. The triangl e had been known for some time in its various applications and had a number of interesting properties that related the elements to one another.108 Pascal provides eighteen consequences or ways in which the elements of the triangle are numerically related, in his Latin treatise, Triangulus arithmeticus. The French version ( Trait du triangle arithmtique ), completed later, provides nineteen. 109 For example, Pascal shows the number in any cell of the triang le is equal to the sum of the numbers in the preceding column in the rows up to and including its own row.110 In Figure 4-1, the number in the fourth column from the left third row from the top is 10. This is equal, as Pascals consequence has stated, to the sum of the first three rows of the preceding column (1 + 3 + 6). 107 The rule for generating the elements of the arithmetic tr iangle is given as follows: In the first row: every cell contains unity [i.e., 1] . In the second row: the first cell is unity. The second cell equals the sum of th e first two cells of the preceding row . The third equals the sum of the first three cells of the preceding row . In the third row: the first cell is unity The second equals the sum of the first two cells of the preceding row. The third equals the sum of the first three cells of the preceding row . In the fourth row: the first cell is unity The second equals the sum of the first two cells of the preceding row .. The third the sum of the first three [cells] of the preceding row . Thus, the first cell of any row whatsoever is unity, and any cell equals the sum of the cells of the preceding row, from the coradical to the first incl usively, Pascal, Triangulus arithmeticus, in Mesnard OC 2:1178-1179. 108 The best exploration of the manifestations of the numerical patterns of the triangle prior to Pascal is in A. W. F. Edwards, Pascals Arithmetical Triangle (New York, 1987), 1-56. 109For the text of the Latin and French versions and the atte ndant writings considering the application of the triangle, see Mesnard OC 2: 1176-1332. The French version of the trea tise on the triangle, with the French and Latin versions of different applications of the triangle were published posthumously, in Trait du triangle arithmtique avec quelques autres petits traitez sur la mesme matire (Paris, 1665). 110 This is the second consequence in the Latin treatise and the third in the French, Mesnard OC 2: 1180, 12901291. 220

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Pascal later used the relationshi ps described in this initial tr eatise on the triangle to develop results relating to the triangles applications. 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 1 3 6 10 15 21 1 4 10 20 35 1 5 15 35 1 6 21 1 7 1 Figure 4-1. Arithmetic Triangle as presented in Pascals treatise111 Multiplication of connections In a recent study that sheds light on the motiva tions of individuals involved in what is often called the Scientific Revol ution, Matthew L. Jones provides examples of how Descartes, Pascal, and Leibniz use mathematics as a spiritual exercise. When Jones examines Pascals treatises on the arithmetic triangle, he focuses on the mathematical liaisons that Pascal uncovers. Pascals work on the triangle is, Jones argues, ultimately a matter of the multiplication of the productivity of an idea in various manifesta tions. In the first place, Jones shows, Pascal sought to explore the many prope rties of the triangle itself including the one mentioned 111 Adapted from Pascal, Trait du triangle arithmtique n. p. 221

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above.112 But the declaration of these properties wa s only the beginning of the process of what Jones calls Pascals method of varying enunciations.113 The key to the fruitfulness of the triangle was that it had applications that went far beyond a numerical pattern. Pascal showed that the triangle could be applied to figurate numbers, combinatorics, probability theory, and binomia l expansion. Two examples, figurate numbers and binomial expansion, will suffice to show these applications. The idea of figurate numbers went back to at least the time of the Pythagoreans.114 Numbers were associated with particular twoor three-dimensi onal figures based on the ability to arrange that number of dots in a regular patte rn that created that shape. For example, triangular numbers include 1, 3, 6, and 10, while pyramidal numbers include 1, 4, 10, and 20. Pascal articulated the relationship between these figurate numbers and the arithmetic triangle. The third row of the triangle lists all of the tria ngular numbers, while the fourth row shows all of the pyramidal numbers. The pattern would conti nue for higher dimensional figurate numbers as well. Secondly, Pascal showed that the arithmetic tr iangle could also be used to write out the expansion of a binomial of the form ( a + b)2. Pascal shows that the co efficients of this binomial expansion may be found in the ( n + 1)th diagonal of the arithmetic triangle. That is, for the expansion of ( a + b)5, one may find the coefficients in the sixt h diagonal of the triangle (i.e., 1 5 10 10 5 1). The production of the expansion, a5 + 5a4b + 10 a3b2 + 10a2b3 + 5ab4 + b5 provides a simple alternative to a manual method of producing the expansion. 112 Jones, The Good Life in the Scientific Revolution 97. 113 Ibid., 117. 114 Edwards, Pascals Arithmetical Triangle (Baltimore, 2002), 1. 222

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The key point that Jones argues about Pascals work with the arithmetic triangle has to do with the way the discoveries about the applications of the triangl e are related to the propositions discovered about the constitutive elements of the triangle. Relationships between the figurate numbers may be ascertained thr ough properties already discovered about the elements of the triangle. This multiplication of enunciations is important, as Pascal writes: Thus are the propositions multiplied, and not wi thout fruit; indeed different enunciations, although of the very same proposition, produce various uses. This, however, ought to be the study of geometers; indeed those enunciations furnished by this art lead to diverse and great theorems, by connecting propositions which seem entirely alien to the way the first had been understood.115 Jones argues persuasively that the mathemati cal mind that Pascal says is necessary to turn these enunciations in different ways is the same mathematical mind that Pascal describes in De lesprit gomtrique, a mind capable of holding many principles distinct.116 What is more, Jones concludes, this type of mind is useful for approachi ng ideas such as space and time that are beyond the scope of mathematical definition and fo r approaching transcendent theological ideas such as infinity.117 Jones makes an important contribution by crea ting a link between Pasc als work with the arithmetic triangle and with numbers and Christia n spirituality. Joness analysis primarily looks forward to Pascals works of spiritual a pprenticeship, which will follow his November 1654 Night of Fire. Pascals mathematical enunciations provide a sense of wonder and 115 Sic multiplicantur propositiones et non sine fructu; variae enim euntiationes, etsi ejusdem propositi, varios praebent usus. Hoc autem studium geometrarum esse debet; ill enim arte aptatae enuntiationes ad diversa et magna ducunt theoremata, connectendo quae omnino aliena videbantur ut primo concept fuerant, Pascal, Numeri figurati seu ordines numerici, Mesnard OC 2: 1202-1203; cf. a passage of Pasc als Trait des ordres numriques: ce sont ces diverses r outes qui ouvrent les cons quencces nouvelles, et qui, par des non ciations assorties au sujet, lient des propositions qui semblaient navoir aucun rapport dans les terms o elles taient conues dabord, Mesnard OC 2:1329. 116 Jones, Good Life in the Scientific Revolution 102-106. 117 Ibid., 117-124. 223

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astonishment, Jones states. The marvelous aspe ct of these connections breeds respect and prepares the reader for the elements of human existence and religion that surpass human knowledge: In his Provincial Letters and Penses, Pascal showed that reason could easily expose the paradoxes of the human condition, contradictions that no other philosophy could admit or explain, much less cure. Honest considera tion of the best human mathematical and natural-philosophical knowledge should make any reasonable person accept these contradictions, recognize the in ability of other philosophies and religions to contend with them, and search in desperation for answers elsewhere.118 According to Joness interpretation of Pascals mathematical work just prior to his Night of Fire, he was already pursuing the use of mathematics in service of a religious epistemological agenda. Joness well-presented argument provides strong evid ence for creating some kind of link between Pascals writings in mathematics an d those in religion, an important task for any Pascal scholar. But, considering the tensions and pressures Pascal experienced during the late 1640s and early 1650s about the status of mathematic s, it seems difficult to maintain an unruffled continuity between that time and the time that followed his socalled second conversion.119 Joness contributions should theref ore be considered together w ith the continuous influence of the early period of Pascals life, during which he identified himself primarily as a geometer. Furthermore, they should be evaluated in light of the possibility of geometrical exercise as a spiritual act in itself, rather than a mere preparation for spiritual truths. Relationship to Mersennien view of mathematics Pascal could plausibly view mathematics as both spiritual act a nd as preparation for spiritual revelation. His work on the arithmetic triangle is, in im portant ways, an extension of the religious view of mathematics articulated in his early mathematical community. As Chapter 118 Ibid., 132. 119 This is not to mention that the Night of Fire was a significant contributor to Pa scals self-perception, as evidenced by the discovery of his account of it on his person at death. 224

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2 argues, Mersenne, one of Pascals first me ntors, viewed mathematical work as an approximation to a state of heavenly beatitude. Mersenne especially st resses the infinity of mathematical propositions and the generativity of mathematics. In describing the circle in his La vrit des sciences contre les septiques ou Pyrrhoniens, he writes: [I]f one knew all its properties, and its uses, a nd all that one could dr aw and conclude from it, one would know more than all that had ever been writ ten in matter of sciences.120 Mersenne focuses in La vrit des sciences on the marvelous productions of mathematics in order to confound his opponent, the skeptic.121 Mersennes Christian Philosopher in La vrit des sciences seeks to impress upon his skeptical conversational partner that the utility and greatness of mathematics is the virtual uncountability inherent in combinatorial mathematic s. He calculates, for example, the possible anagrams of a name of a particular length, how many melodies are possible from a specific number of notes, and how many different ways a game of Picquet may conclude.122 The idea of multiplied enunciations is also apparent in Me rsennes interesting claim that one could represent all that is in the world, and consequently all the sciences by means of Sounds.123 Similarly, a good enough musician could explain all the propositions of Geometry through playing any instrument that he would like.124 Pascals treatises on the arithmetic triangl e also reiterate Mersennes emphasis on the generativity of mathematics. Mersenne describes the circle as a simple figure with an infinite 120 Mersenne, La vrit des sciences 764. 121 In this way, Joness observation of Pascals desire to create such astonishment is in strong continuity with Mersennes view of the importance of productivity in mathematics. 122 Mersenne, Harmonie universelle Des Chants, 145. 123 Mersenne, Harmonie universelle Livre premier, De la nature & de proprietez du Son, 43. 124 Ibid. 225

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number of marvelous propositions that may be discovered about it. The number one (unity) likewise produces all the perfect ions which are in numbers.125 It is like God in its simplicity; it is without parts. And it is li ke him in productivity, able to gene rate infinite number of integers through the act of counting. Sim ilarly, the arithmetic triangles elements are produced through a numerical gnrateur, the element at the apex of the triangle.126 The rule by which this generator creates the elements of the triangle is the ultimate source of the marvelous properties that Pascal states.127 Pascals efforts to discover the va rious interconnecting properties of the arithmetic triangle are thus in sympathy with, and even an extension of, Mersennes belief in the ability, through mathem atics, to raise yourself to the divine perfections.128 Pascal describes his work on the arithmetic tria ngle in terms that highlight the similarity between his approach as a geometer and Mersenne s spiritual view of mathematics. Pascal argues that the geometer is to work toward m ultiplied propositions in order to find diverse and great theorems.129 This articulation of the goals of the geometer is harmonious with Mersennes understanding of th e mathematician as imitating G od through the proliferation of propositions. Furthermore, Jones links the disc overy of unknown connections in geometry is to discerning relationships in Gods creation. 125 Mersenne, La vrit des sciences 669. 126 The arithmetic triangle may begin with any element, but traditionally (unity) is at its apex. Pascal only acknowledges the possibility of other generating numbers in his French treatises. However, he only uses unity in his examples and demonstrations of his propositions. He applies these to other generators in an Avertissement: Si le gnrateur ntait pas lunit, il et fallu multiplier le quotient par le gnrateur Trait du triangle arithmtique, Mesnard OC 2:1299. 127 The rule for generating the triangle is quoted above, p. 220, n. 107. 128 Mersenne, La vrit des sciences 669. 129 Pascal, Numeri figurati, Mesnard OC 2: 1203. 226

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Pascal also continues to affirm Mersennes opinion, as he did in his writings on the arithmetic machine, that geometry is a talent that requires not just natural inclination but disciplined effort. Pascal conti nues thus the passage quoted above: Whoever lacking this natural capacity for turnin g things about, the cu ltivation of geometry will be thankless; because it is not given, but is assisted, it will suffice to reveal the way through this example.130 The key difference between this passage and Pascal s writings on the arithmetic machine is its tone. Whereas his earlier work was primarily an attempt to legitimate himself as a geometer, by the time of his work on the triangle, his need to assert legitimacy had lessened. He had already gained a reputation as a mathematician. Instead, this passage depicts Pascal primarily as an instructor. With the arithmetic machine, he had blazed for himself a new route in a field entirely fraught with thorns.131 Now, he provides a means by which others, who are not as learned in geometry, may enter in to the proper study of geometer s. Pascals address to the Parisian mathematical academy under Le Pailleur also provides evidence of his transformation. He concludes the address with an appeal for others to imitate his productivity: These are the ripe fruits of our geometry: [they are] fertil e and realizing an enormous profit, if in imparting these to you, we receive back certain of yours.132 Despite assuming the attitude of instructor in geometrical wo rk, Pascals treatise on figured numbers continues to acknowledge the important influence of the mathematical community: [Y]et my efforts have surpassed my expecta tion and they allowed me this most general method which I relate, and indeed has been most pleasing even to my friends who are very learned amateurs of universal solutions, and spurred on by them, I sought to obtain a 130 Cui versatile hoc deest ingenium ingratus erit geometriae cultus; quia vero non datur sed juvatur, hoc exemplo viam aperire sufficiet, Numeri figu rati seu ordines numerici, Mesnard OC 2:1203. 131 Mesnard OC B. Pascal to Sguier, 1645, 2: 333. 132 Illi sunt geometriae nostrae maturi fructus: felices et immane lucrum facturi, si hos impertiendo quosdam ex vestris reportemus, Celeberrimae math eseos academiae parisiensi, Mesnard OC 2:1035. 227

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general solution, of the pure power s, testing it in view of the general solution of orders and happily enough it fell to my lot to discover it.133 Pascal still draws upon the praise of these savan t amateurs as a means of reiterated legitimacy; but he also recognizes that they are major factors in the choice of how Pascal applies his skills. He has felt himself pressed by them, and guided by their counsel. Clearly, the opinions of some of Pascals friends at Port-Royal about the uselessness of mere ma thematics, had not yet overcome the inertia of Pascals youthfu l connection with mathematics. Worldly Values and the Limits of Specialized Learning If tension between religious and mathematical values characterizes this period of Pascal life, so does the influence of his worldly acquaintances. One of th e uses that Pascal articulates for the arithmetic triangle is for the solution of a problem regarding games of chance. In particular, he considers how to divide the init ial stakes when players agree to cease playing before a final outcome is reached. This problem brought Pascal into close correspondence with Pierre de Fermat, and is often considered by hist orians of mathematics as the birth of modern probability theory. The worldly background of this problem reflects relationships with a circle of friends more interested in social aspects of life than in mathematics or religi on. This perspective, together with the influence of Port-Royal spirituality infl uenced Pascals questioni ng of self-identification as a motivation. According to Gilberte, Pascal began to engage in diversionary activ ities under the advice of his doctors, who believed that an excessive use of the mind was to blame for a continued illness of his body. These activities brought him under the sway of individuals outside of 133 conatus tamen expectationem superantes eam quam tradidi praebuerunt generalissimam, et quidem amicis meis, universalium solutionum amatoribus doctissimis, gratissimam; a quibus excitatus et generalem potestatum purarum resolutionem tentare, ad instar generalis ordinum resolutio nis, obtemperans quaesivi, et satis feliciter mihi contigit reperisse, ut infra videbitur, Numeri figurati, Mesnard OC 2:1214. 228

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mathematical circles and Port-Roya l. In fact, many Pascal scho lars refer to the time between approximately 1651 and 1654 as Pa scals worldly period. The shift in the focus of Pascals activities is most evident beginning with the death of his father in September 1651.134 Soon after, Pascal sent a letter to his older sister Gilberte, in which he insists that the deat h of a Christian such as his father is a happy death and that Gods ways, even in such circumstances, are as perfect as they are inscrutable. He does not mourn, he claims, as those who have no hope.135 Indeed, he states that while he could have benefited from his fathers presence for the rest of his life, he wa s in a much better position to handle the loss than prior to his association with Po rt-Royal. Despite these testim onies of pious faith, the death began a period that Mesnard claims may be characterized as a true crisis.136 He had been deprived of his first master, the one who had overseen his intellectual development and encouraged his work in mathematics and natural philosophy. To add to the loss of his father, only a year later Jacqueline, who had been living with him to that point, finally entered the Port-Royal convent. Pascals attempts to forestall that entry, as demonstrated through letters writ ten by Jacqueline, may suggest th e pain of the separation or a sense of renewed identity with his dead fa ther, who had also ente rtained objections to Jacquelines religious vocation. The upheaval of this time also included the financial pressures attached to safeguarding his fath ers succession and attempting to fi nd ways to invest his assets. Jacqueline requested her share of the estate to donate to Port-Royal upon her entry to the 134 tiennes death was recorded in a document that was copied by Rochebilire prior to the destruction of records contained in the Htel de Ville during the Paris Commune of 1871, Acte de dcs d tienne Pascal, Mesnard, OC 2:841. 135 But we would not have you ignorant, brethren, concerning those who are asleep, that you may not grieve as others do who have no hope, 1 Thess. 4.13, RSV. 136 Jean Mesnard, Pascal et les Roannez vol. 1 (Paris, 1965), 169. 229

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convent. Blaise again resiste d, only relenting in June 1653.137 Pascal also attempted to establish his income and status through his leasing of an arcade in the marketplace of the Halle au Bls, his promotion of the machine to Queen Christina of Sweden, and his involvement in the project of the draining of the marshes of Po itou undertaken by the Duke de Roannez.138 Pascals business partner, Artus Gouffier, th e Duke de Roannez, was an acquaintance of Pascal from his earliest days of living in Paris. He was in Paris when Pascal returned in the summer of 1653 from some business in Clermont, and had himself recently come to the age of majority for his fathers estate. Pascal, as Me snard states, seeking a ne w equilibrium of life since being deprived of two members of his fa mily, found a true companion in the Duke de Roannez.139 To characterize the relations hip with Roannez as worldly in character would be to ignore Mesnards fine scholarsh ip regarding the piety of th e Roannez family and their connection with the Jansenists. However, what originally sparked th eir connection was the dukes appreciation for the sciences.140 It was perhaps as the result of a trip to Poitou with Roannez that Pascal first made the acquaintance of the Chevalier de Mr.141 This chevalier named Antoine Gombaut (but almost always referred to by his title) is well-know for his characteriza tion of the seventeenth-century honnte homme The idea of the honnte homme was a development of Renaissance courtly 137 See Donation de Pascal Port-Royal, Mesnard OC 2:946-949. 138 The documents relating to the Hall au Bls are in Mesnard OC 2:1014-1020, 4:706-709. 139 Mesnard, Pascal et les Roannez 1: 170. 140 See ibid., 1: 172. All of the information presented here about the Duke de Roannez is indebted to this definitive work of Mesnard. Mesnards examinati on of the relevant documents and consideration of the issues surrounding the relationship with Pascal have been able to generate a truly nuanced portrait, not only of the duke himself, but of the entire family. 141 Pascal writes to Fermat: Jadmire bien davantage la mthode des parties que celle des ds. Javais vu plusieurs personnes trouver celle des ds, comme M. le Chevalier de Mr, qui est celui qui ma propos ces questions, et aussi M. de Roberval, Blaise Pascal to Pierre de Fermat, 29 July 1654, Mesnard OC 2:1137. 230

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manners and emerged as a key virtue of French gentlemen during the middle of the seventeenth century. The honnte homme was defined by skill in social interaction and the ability to converse on a wide range of topics in a winsome way. A notori ously difficult idea to define, honntet gradually worked its way from a primarily aris tocratic culture to that of the intellectual culture at large.142 Mrs De lesprit and the Limitations of Mathematics One of the two writings of Mr that allude to Pascal is De lesprit. This work, which does not mention Pascals name (but is almost certainly about him) contains an account of a trip that the chevalier took with the Duke de Roannez an d with a great Mathematician who is almost certainly Pascal.143 Mrs account, published for the first time only in 1677, provides an anecdote that, if taken at face va lue, would give Mr the full credit for Pascals turn from mathematics. According to the chevalier, Pascals scope of interest at this time, approximately 1653 or 1654, was strictly limited to mathematic s: he was a great Mathematician, who knew only that.144 Despite Pascals earlier cl aims to be no longer a math ematician, Mr perceives Pascal as an example of a talented individua l who did not yet demonstrate the breadth of understanding that the chevalier labeled esprit According to Mrs account of events, through a mere few days of discussion with the chev alier and two friends (including the duke de 142 On the notion of the honnte homme see Maurice Magendie, La politesse mondiale et les thories de lhonntet, en France au XVIIe sicle, de 1600 1660 (Paris, 1925); Jean Mesnard, Honnte homme et honnte femme dans la culture du XVIIe sicle, in La Culture du XVIIe sicle: enqutes et synthses (Paris, 1992): 142-159; Emmanuel Bury, Littrature et politesse: Linvention de lhonnte homme, 1580-1750 (Paris: Presses Universitaires de France, 1996). 143 Once again, the most in-depth examination of the controversy surrounding the identification of Pascal in this account, the date of the trip, and the scope of its accuracy, is in Mesnard, Pascal et les Roannez vol. 1, part 3, chs. 1-2. 144 The story was published in De lesprit: discours du Monsieur le chavelier de Mr Madame *** (Paris: Denys Thierry, 1677). The modern complete works is Chevalier de Mr, Oeuvres Compltes du Chevalier de Mr ed. Charles-Henri Boudhours, 3 vols. (Paris: Fernand Roches, 19 30). Future references to the Boudhours edition will be cited as Mr OC [vol #]:[pp. ##]. De lesprit is in Mr OC 2:57-95, and the Pascal story in ibid., 86-88. 231

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Roannez) Pascal was converted from having neith er taste, nor sentiment to one who was able to apply himself to subjects beyond the realm of his natural and develope d talents. Pascals quick conversion suggests that he was already on the edge at the time of this interaction.145 The chevaliers depiction of this episode of Pa scals life provides an interesting foil to Pascals self-legitimation of his work in mathematics and natural philosophy. It is particularly important as it regards in clination, natural talent and efforts made to develop that talent. Whereas Pascal raised his own status by pinpointi ng the limitations and restrictions of others in comparison with his own knowledge in the mathema tical sciences, Mr a pplies the language of limitation to Pascal. And while Pascal downplays the importan ce of his inclination for mathematics, Mr emphasizes the role that such inclination plays in the specialized learning that Pascal represents. He claims that natural tale nt keeps the efforts of the individual hemmed in: There are some people who do certain things by inclination, or by instinct, or by habit, and because they do well these sorts of things without knowing however by what [means] they are good, one believes that they have esprit, but when one disorients them, and one draws them away from their talent, one dismisses them immediately: for esprit and talent are not of the same nature.146 In Pascals writings on the arithmetic machine, it was the artisans who remained in a beastlike state of instinct and operate d only within the confin es of habituated learning. But for Mr, this is Pascals situation. Mrs language of the disoriented sp ecialist echoes Pascals discussion of the Rouennais clockmaker who, take n away from his mastery of turn and file, 145 Peculiarly, part of Mrs description of Pascal is that he was a man between two ages, [ un homme dentre deux ges ], ostensibly between the traditional age of youth and the age of maturity, Mr OC 2: 86. Could it be that Mr saw this episode as a defining moment for Pascal in which he moved to maturity? The hypothesis is too weak to assert more. I have, however, chosen to use this quotation as the basis of the title for this chapter, since is language embodies the position that this chapter seeks to emphasize: Pascal as suspended between devotion and learning, childlikeness and matur ity, Descartes and Roberval, etc. 146 Il y a des gens qui font de certaines choses par inclination, ou par instinct, ou par habitude, et parce quils font bien ces sortes de choses sans savoir neanmoins par o elles sont bien, on croit quils ont de lesprit, mais quannd on les dpaise, et quon les tire de leur talent, on les y renvoye aussi-tost: car lesprit et le talent ne sont pas de mesme nature, De lesprit, Mr OC 2:70. 232

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could only work gropingly. Fo r Mr, as later for Pascal, mathematics is as much a limited mtier as is clockmaking. Mr had challenged Pascal on what he considered the limitations of mathematics. For Mr, the limitation of mathematics was a limitation of scope. That is, mathematicians were so focused on abstract principles th at they could not be meaningfu lly engaged in other subjects. Mathematics is, Mr would argue, not ultimately satisfying because it is unable to communicate to a variety of people on a variety of topics. It is this limitatio n that Pascal would have in mind when he wrote in the Penses : He is a good mathematician, you will say. But I am not concerned with mathematics: he would take me for a proposition.147 Another of the limitations of mathematics is th e inability of geometry to measure up to the infallibly convincing method Pascal describes in De lesprit gomtrique. This method has two key principles: one, to use no term of which the sense has not been previous explained; the other, to never put forward any proposition not demonstrated by al ready known truths.148 According to Pascal, not even mathematics is able to adhere to these two rules, since the attempt to define all terms would lead to an infinite regress. Instead, mathematics defines all terms except those clear and understood by all men.149 Pascal makes clear, however, that mathematics employs the method that is the mo st perfect among men, and that what surpasses geometry surpasses us.150 147 Pascals narrator in this fragment goes on to st ate: What I need is an all-around good man [ honnte homme] who can adapt himself to all my needs generally, Pascal, Penses, no. 605; Brunschvicg, no. 36. 148 lune, de nemployer aucun terme dont on net auparavant expliqu nettement le sens; lautre, de navancer jamais aucune proposition quon ne dmontrt par des vr its dj connues, De lesprit gomtrique, Mesnard OC 3: 393. 149 Ibid., Mesnard OC 3: 395. 150 Ibid., Mesnard OC 3: 395, 393. 233

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There is a type of limitation to mathematics that Pascal does not sugge st. He never admits in his writing that mathematical reasoning em ployed according to its rules could yield an incorrect conclusion. The limitation s of mathematics, for Pascal, ar e limitations of scope that do nothing to undermine its basic prin ciples. Mr seems to admit th at such incorrect conclusions occur in mathematics by refusing to adm it the reasonableness of indivisibles.151 Mr, Mersenne, and Pascal on Inclination and Exercise Mr and Mersenne Despite the contrast in evaluation of mathematical endeavors, Mrs views on inclination with respect to a mtier even mathematics, are not entirely at odds with the views of Mersenne and Pascal. De lesprit resonates with the ideas of both on the necessity of the maturation of natural talent. Mersennes discussions of inclination, as Chapter 2 argues, emphasize the importance of developing and improving natural ta lents. Chapter 3 established that Pascals writings on the arithmetic machine and the void st ress development from a childlike state of natural talent to the level of established learning. The chevalier, like Mersenne, is not willing to deny the importance of inclination for success in a pa rticular art or science. For Mersenne, some individuals have a good ear and can perceive the slightest variati ons in pitch. They are thus more readily able to learn the arts of music. Mr admits the role of nature, while also downplaying it. There are gentlemen who do certain things by inc lination, instinct, or habits but, he continues, they are unlearned in a more signifi cant sense. Furthermore, he al so claims that individuals are 151 A letter, ostensibly from the chevalier de Mr to Bl aise Pascal, gives Mrs objections to Pascal about the possibility infinite divisibility of lines. This letter, probably written after Pascals death, is in Mesnard OC 3: 353359. 234

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born with varying degrees of what he calls esprit [mind/wit], which is th e potential to achieve true learning.152 Mr also insists, like Mersenne and Pascal, th at there must be development, exercise, and education in order to attain true learning: It is certain that the first disposition which renders us cap able of understanding, comes to us when we come into the world, it is a present from the Heavens, it is a natural light, which cannot be acquired, but it is augmented, it is clear-sighted, it is perfected, and it is this that we call to acquire esprit For in whatever order of esprit that is met, one must not doubt that it can be acquired. If the most na turally clear-sighted is reminded with what sight he regarded the things in his childhood, and that he exam ines how they appear to him in a more advanced age, could it be put in doubt that he had acquired esprit ?153 Mr and Pascal Pascal, in his works, stressed his improvement on natural talent and on the lights of mathematics, physics, and mechanics through dilige nt application, expense, and effort. Mr praises those individuals, such as Pascal, who draw from their resources of understanding to seek the perfection of their chosen mtier. Using the language similar to Pascals regarding the overcoming of restrictions, he writes: [I]n any sort of talent and of mtier, it is an infallible mark of a little esprit that of staying always to a certain degree [of perfection]. A ll the great men, all the excellent workers, have sought means the most hidde n in order to attain to perfection; And the people who are 152 Mrs idea of esprit is intimately linked to the ideal of the honnte homme indicating the ability to interact intellectually across boundaries of particular fiel ds of knowledge. This unified understanding of esprit is in contrast with that of distinct types of mind, as articulated by Juan Huarte in Lexamen des esprits, mentioned previously. Mr seems to differentiate only between esprits that understand things in them selves and those of a lazier or more negligent nature, De lesprit, Mr OC 2:79. To be of the first type, says Mr, is to truly have esprit. In the Penses Pascal will differentiate between esprit de gom trie and esprit de finesse and again between esprit de gomtrie and esprit de justesse, Brunschvicg, nos. 1-2, Brunschvicg OC 12:9-16. See also Mesnards response to Jean Molino, Lducation vue travers Lexamen des esprits, 113. Mesnard points out the connection between Huartes distinction of esprits and Pascals. 153 Il est certain que cette premiere disposition qui nous re nds capables dentendre,, nous vient quand nous venons au monde, cest un present du Ciel, cest une lumiere naturelle, qui ne se peut acquerir, mais elle saugmente, elle sclaircit, elle se perfectionne, et cest ce que nous appello ns acquerir de lesprit. Or en quelque ordre desprit que lon se rencontre, il ne faut pas douter que lon nen puisse acquerir. Si lhomme le plus clair naturellement se resouvient de quelle veu il regardoit leschosesdans son en fance, et quil ex amine comme elles luy paroissent dans un ge plus avanc, peut-il mettre en doute qu il nait acquis de lesprit ? De lesprit, Mr OC 2:79. 235

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led by intelligence, and supported on very certain maxims, unceasingly make some progress.154 The chevaliers notion of progression toward perfection is similar to Pascals continuous, gradual attempts to create the ideal arithmetic mach ine. His insistence on not allowing room for limitations likewise expresses Pascals sentiments with respect to his machine. Mr criticizes those who merely imitate the work of human ma sters, without taking the pain themselves to give to them the derniere main .155 In Pascals writings on the arithmetic machine, he preempts the attacks of the imperfect savants against his inventions complex ity, stressing that the version that those critics see is not the first effe ct of imagination that I have had on this subject but the result of progressive improvement.156 Both Mr and Pascal agree on the linearity of progress. Pascals work required him to make extensive efforts that almost caused him to give up. The work was arduous and not for the faint of hear t. In contrast, Mr states that progress toward esprit does not come by the application of toilsom e effort. Pascals transformation on his journey with the Duke de Roannez and the ch evalier is the crowning example of one who acquires esprit through only a few days of conversati on with those who understand how to put them in good ways.157 For Mr, lengthy toil and effort are not as important as they are to Pascal. 154 [E]n toute sorte de talent de mestier, cest une marque infaillible dun petit esprit que den demeurer tojours un certain degr. Tous les grands hommes, tous les excellens ouvrier, ont cherch les moyens les plus cachez pour atteindre la perfection; Et les personnes qui se conduise nt par lintelligence, et sur des maximes bien certaines, font incessamment quelque progrez, ibid., 2:85. 155 sans se mettre en peine de leur donner la derniere main, ibid., 2: 71. 156 Avis, Mesnard OC 2:340. 157 [I]l en vienne comme par inspiration quelques-uns, qui faute dexperience ou dinstruction nen tmoignoient pas la moindre apparence, et qui neanmoins deviennent tres-i ntelligens et tres-habiles, quand on sait mettre dans les bonnes voyes, D e lesprit, Mr OC 2:79. 236

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The chevalier thus takes a differently nuanced view of restricted perfection, and he considers Pascals practice of math ematics as similar to any other mtier While he praises those who overcome the barriers of their mtiers in order to attain to perfection in those particular areas, his understanding of restri cted perfection also refers to the focus on a single discipline at the expense of general understa nding. A progression toward gene ral learning is more significant than perfection of a mtier. What is more, intellectual superi ority in one arena, he claims, is often accompanied by ignorance in other areas. Atta ining a broad perfection that escapes this disciplinary boundedness comes about through prope r exposure to other well-rounded men and their conversation.158 It is not the private act of study, but the public act of communication that makes one truly learned. Mr and Port-Royal on the limitations of mathematics Mrs desire to disabuse him [i .e., Pascal] of his mathematical mtier served to reinforce the encouragement that Pascal receiv ed from the Jansenists to renounce mathematics and the sciences for the one important duty of being entirely devoted to God and submitted to ones spiritual director. Mrs generalized learning resonated w ith the comprehensive claim of religious devotion in every aspect of life. Most likely the ch evaliers delayed account of his interactions with Pascal overestim ates his success in causing Pascal to rethink the importance of mathematics. Nevertheless, as Mesnard writ es, let us seek behind the exaggeration the suggestive and revelatory remark.159 Mr and other representati ves of worldly sociability helped to renew to him the importance of escape from the restrictive bounds of the mtier of 158 Il me semble aussi que pour acquerir de lesprit, et pour se perfectionner en toute autre chose, lexemple et le commerce des personnes rares est un moyen bien facile et bien assur, ibid., 2:79. 159 Mesnard, Pascal et les Roannez 1: 256. 237

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mathematics, within which his earliest training ha d securely situated him. [I]n his judgment on the sciences, the lessons of th e chevalier came to prepare or complete those of Port-Royal.160 On balance, Mrs influence on Pascal was limited. Another of M rs writings recounts a disagreement between the two about the infinite division of space.161 Pascal remained endowed with a respect for mathematic s. It was the finest craft [ mtier] in the world, even though only a mtier, and he was willing to accept a mathem atical reasoning that established, for example, the division to infinity, even where Mr found such ideas offensive to common sense.162 As the following chapters will show, ma thematics continued to inform the work of Pascal. It shaped the approach that he took to theological and religious reasoning, even while the childlike and mature virt ues of religious devotion provided a model for engagement with the savant world. This chapter has demonstrated the common th emes of inclination, exercise, effort, and restricted perfection during a peri od of uncertainty and turmoil in Pascals life. His experience of these tensions and upheavals helped him to forge the relationship between religious learning, mathematical proficiency, and the life of esprit as depicted by Mr. Near the end of 160 Ibid., 1: 260. Another Pascal scholar, Charles Baudouin sees the so-called worldly period as also contributing to and preparing the second conversion: it is possible, even during that period, to see a secret movement or counterstream, which continues the evolution previously begun. We should like, if it were not a little irreverent, to speak of conversion number one-and-a-half, between the first and the second. Indeed, this period appears at first like a reversal, a real conversion to worldliness but soon it became clear that it was all necessary, and that this too served as fuel to a flame which would finally burn ever ything clear, The Process of Individuation in Blaise Pascal, Journal of Analytic Psychology 5 (1960), 102. 161 The disagreement between Mr and Pascal on division to infinity is recounted in the fictive Lettre de Mr Pascal, Mesnard OC 3:348-359. 162 The quotation regarding mathematics as a mtier is in B. Pascal to Fermat, 10 August 1660, Mesnard OC 4:923. 238

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1654, the various aspects of this tumultuous period of Pascals lif e found resolution in what his sister calls a new entreprise: to be tout [Dieu].163 Redirected Efforts: New Goals and Pascals Memorial In September, as Jacqueline writes to her si ster early in 1655, Blaise came to visit her: [H]e opened himself up to me in a manner which made me pity him, vowing to me that in the middle of his occupations, which were great, and among all the things which could contribute to make him love the world, and to which one was right to believe him strongly attached, he thereby sought to leave all that, and by an extrem e aversion that he had for the follies and amusement of the world and by the continual reproach that his conscience made to him, that he found himself detached from all things in such a manner that he had never been, nor anything approaching it.164 Pascal was not content merely to heed the chev aliers encouragement to leave the restricted bounds of mathematics. He was also constricte d by the bounds of the wo rld of diversion and entertainment, which Mr embraced. The concer ns of his fathers estate, the desire for legitimacy in mathematics and natu ral philosophy, and the life of esprit advocated by Mr, ultimately did not appeal to him. Pascal sought, through Jacqueline, to identify a spiritual director to whom he might submit himself. This resumed Pascals attempts of the late 1640s to apply himself to the task of becoming spiritually learned. The most dramatic indication of the changes Pascal underwent during this time is the document that records what is known as Blaises Night of Fire.165 Dated November 23, 1654, this document was carefully conserved by him and was found on his 163 Jacqueline Pascal to Gilberte Prier, 8 December 1654, Mesnard OC 3:67-68; the passage from which the second quotation comes reads as follows: Tout ce que je vous puis di re, nayant pas de temps, cest quil [Blaise] est par la misricorde de Dieu dans un grand dsir dtre tout lui, sans nantmoins quil ait encore dtermin dans quel genre de vie. 164 Jacqueline Pascal to Blaise Pa scal, 19 January 1655, Mesnard OC 3:71. 165 This document is often called the Le Mmorial by Pascal scholars. 239

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body at the time of his death eight years later.166 The first lines following the recording of the date read: FIRE God of Abraham, God of Isaac, God of Jacob, not of the philosophers and savants167 The third line of Pascals record of transformation creates a star k break between the world (of the philosophers and savants) of the learned in which Pascal was nurtured and the world of the religious devotee that he sought to commence. It echoes the sentiments of revulsion that he felt for Saint-Ange in his attempts to discover the s ecret things of God, but goes further, suggesting the importance of Forgetfulness of th e world and everything besides GOD.168 It is a rejection of a way of life in which he had been hab ituated, a break from the restrictive bounds of memorized responses to the world. The Memorial is a classic example of mystical literature and has been studied by numerous scholars. What is most significant for the current study, however, are some lines that indicate a change in the way that Pascal expr essed the relationship between mathematics and Christian spirituality. He writes as a student of devout living rather than as a student of geometry. Near the end of the document, Pascal acknowledges a Total submission to Jesus Christ and to my director.169 This spiritual director became the tutor through whom Pascal would come to learn of the things of God, and w ho would instruct him in the disciplines he must 166 The following note in the hand of Pascals nephew, is found on the reverse side of a copy of the Memorial, and has been transcribed by Mesnard: I the undersigned, priests, canon of the church of Clermont, certify that the paper attached on the other side of this folio was written in the hand of Monsieur Pascal my uncle and was found after his death sewn into his doublet under the lining with a strip of parchment where were written the same words and in the same form as they are copied here. Performed at Paris, this 25th Septembe r 1711 / Prier, Mmorial, Mesnard OC 3:52. 167 FEU / Dieu dAbraham, Dieu dIsaac, Dieu de Jacob / non des philosophes et savant s, Mmorial, ibid., 3:51. 168 Oubli du monde et de tout hormis DIEU, ibid., 3:51. 169 Ibid., 3:51. 240

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undertake to become a religious savant.170 He emphasized the efforts and discipline needed to reach that goal. The joy of the heavenly life to come was, he wrote, ce rtainly worth a day of exercise on the earth.171 No longer were his concerted efforts to be used to perfect mathematics, in a vain attempt to attain godlik eness through imitation of his creation. Instead, the Memorial suggests a different spiritual go al: personal union with God. May I never be separated from him! he exclaims.172 The hard work of the one w ho is learned in religion is to discipline himself to seek God only by the wa ys taught in the Gospel, including Jesus command to become like little children.173 During the tumultuous period of 1646-1654 Pascal engaged in a diverse range of activities and interests. He was established as a legi timate mathematical savant through the pain and expense of the arithmetic machine and the expe riments on the void. He emphasized the exercise required to become genuinely learned in these areas and also began to explore what it would require to become savant in matters of spiritu ality. Numerous pressures bore down on Pascal during this period, including those extorted by his fathers friends, his position as his fathers heir, his illness, and his involveme nt with worldly society. Each of these pressures helped to reinforce certain ideas about the limitations of natural inclinati on, the importance of 170 Following the Night of Fire experience, Pascal sought out the direction of Antoine Singlin (1607-1664), the main spiritual director at Port-Royal from 1643-1655. Wri ting to her sister, Jacqueline discusses Pascals intention to seek out Singlin: Il est tout rendu la conduite de M. S[inglin]; et jespre que ce sera dans une soumission denfant, sil veut de son cot le recevoir, car il ne lui a pas encore accord, J. Pascal to G. Prier, 8 December 1654, Mesnard OC 3:68. In fact, the spiritual direction of Pa scal seems to have been given to Louis-Isaac Le Maistre de Sacy, perhaps because Singlin was quite ill from summer 1653-summer 1655, Antoine Singlin, Lettres dAntoine Singlin ed. Anne-Claire Josse (Paris, 2004), 111-112. The evidence for Sacys direction of Pascal is from the conversation between Sacy and Pas cal in a document by Sacys secretar y, Entretien de Pascal avec M. de Sacy, Mesnard OC 3:124-157. Jacqueline writes in a subsequent letter: Je ne sais nanmoins comment M. de Sacy saccommode dun pnitent si rjoui, J. Pascal to G. Prier, 19 January 1655. 171 un jour dexercice sur la terre, Mmorial, Mesnard OC 3:51. 172 Que je nen sois jamais spar!, ibid. 173 Ibid. 241

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242 improvement and augmentation of those efforts, and an escape from the boundaries of restricted perfection. They contributed to his decision to submit himself to the direction of Port-Royal. This apprenticeship to a religious movement, wh ich was under duress at the time, placed him in a position to carry out works for their benefit. Indeed, he engaged in works that served to legitimate the type of spirituality that he had embraced. Through the Provincial Letters and his contributions to texts intended for the Port-Royal petites coles Pascal took his place in the world as a mature individual, rea dy to teach others. He was not just as a student of Jansenist spirituality, but an educationa l consultant for Port-Royal.

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CHAPTER 5 PASCAL, PEDAGOGUE On March 30, 1656, the Port-Royal petites coles which educated children of families associated with the convent, were dispersed by official statement of the crown. The dispersion, prompted by religious conflict with the Jesuits, was only temporary and th e students returned to the schools a year later. In 1660, however, the educational wing of Port-Royal was closed decisively by royal decree and students were shuttled to various places where they could be cared for and taught.1 By several indications, Pascal was one of those to whom some of the children were entrusted. In a le tter to her brother of 6 November 1660, Jacqueline writes of the pain that I have given you and the care and in convenience, stating that M. R. will soon be in a situation to take back these children.2 Any doubt about the identifi cation of the children may be removed by Jacquelines desire for her brothe r to greet them from me, and M. du Lac also, since du Lac was one of the Port-Royal masters and Jacqueline, a nun at Port-Royal, would have been acquainted with the children as well. Likewise, the chevalier de Mr recollects a situation, quite likely overheard in 1660, in which someone sa id to Pascal: You are thus a schoolmaster, on observing him with seven or eight children in rags.3 While Pascal may not have been an official master at the petites coles his care of these children and his substantial contributions to 1 Delforge, Les petites coles de Port-Royal: 1637-1660 (Paris, 1985), 154. See also H. C. Barnard, The Little Schools of Port-Royal (Cambridge, 1913), 39-42. 2 pour vous demander pardeon en mme temps de la peine que je vous ai donne en cela; car cest moi qui vous lai procure, et jai bien peur que vous en soyez incommod.J e lai fait dans lassurance que avais que vous en auriez bien de la joie, et que le soin et lincommodit que vous en auriez ne durerait pas, parce que M. R. serait bientt en tat de reprendre ces enfants, Jacqueline Pascal to Blaise Pascal, 6 November 1660, Mesnard OC 4:963. The identity of M. R. has not been definitively determined, Mesnard OC 2:961. 3 Mr, Divers propos, Mesnard OC 1:824. Mesnard draws on Christiaan Huygenss mention of Mrs presence in Paris in December 1660 to support the chronological evid ence that this quotation refers to Pascals role as an unofficial mentor to the dispersed Port-Royal students, Mesnard OC 4: 961. 243

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the Port-Royal textbooks present Pascal in his pedagogical role as gardener of children.4 As a teacher, he had become, Jacqueline writes, fathe r of a family, in one of the ways that God himself is our Father.5 Pascals 1654 Night of Fire signals the subm ission of Pascal (as mathematical prophet and new Archimedes) to Pascal the elect of God. In the years that followed, he was transformed from a spiritual apprentice into a spiritual pedagogue, drawing at once on the imperatives of childlike faith and the necessity of growing in maturity toward perfection, both of which were encouraged by his relationship with the Port -Royal schools. While the resources of his mathematical talent continued to be used in a variety of ways, his iden tity as geometer was enveloped by his identity as a devout Christia n. Despite this profound change, the themes of Pascals post-conversion writings demonstrate si gnificant continuity with his pre-conversion works. In particular, the complex relationship between inclination a nd exercise/education, so prominent in Pascals mathematical and scientific work, is recapitulated in the relationship between the election of the believ er and the rigor of the Christia n life. Moreover, his writings against the Jesuits in the Provincial Letters undercut the members of that religious order in ways similar to those used in the mathematical/scientific writings. Importantly, Pascals natural talent and training in geometry served as resources on wh ich the Jansenists would draw as they carried out their goals of Christian education in the petites coles Children, Moral Inclinations, and Education Chapter 3 discussed two of thr ee types of inclinations listed by Cureau de la Chambre in his Lart de connoistre les hommes : bodily and intellectual. With Pascals movement toward 4 Gobry, Pascal, ou la simplicit 116. 5 [V]ous tes devenu pre de famille, en une des manires dont Dieu mme est notre pre, J. Pascal to B. Pascal, 6 November 1660, Mesnard OC 4:962. 244

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religious devotion, however, inc linations of a speci fically moral charac ter took on increased significance. Understanding chil drens moral inclinations and shaping them through habit was arguably more important to the pedagogues of the seventeenth century than was the discovery of ability in arts or sciences. Morally speaking, th e status of children was fraught with difficulty. That great authority Aristotle refers to the s elf-indulgence associated with childish faults.6 He states that children in fact live at the beck and call of appetite, and it is in them that the desire for what is pleasant is strongest.7 As a result, the moral life of child must be subject to an adult, who may temper childish nature with reason.8 The looming church father Augustine gave an account of the inheritance of sinful nature that characteri zed children as infected with sinful desires from birth. This bleak view of the child is of ten all that is highlighted in Augustine. But Augustine also provided a ce rtain place of respect for the child, which he claimed possesses innocence superior to that of adults, as Shulamith Shahar points out.9 Furthermore, Scriptural texts were clear about the virtues of childhood, with Jesus proclaiming that to such belongs the kingdom of heaven.10 Throughout the Middle Ages, that chronological period about which historians of childhood most often argue, the Christian 6 Aristotle Nicomichean Ethics 3.1119b1, in The Complete Works of Aristotle: The Revised Oxford Translation ed. and trans. Jonathan Barnes (Princeton: Princeton UP, 1984). 7 Ibid., 3.1119b5-6. 8 Ibid., 3.1119b11. 9 Shulamith Shahar, Childhood in the Middle Ages (New York, 1990), 16-17. Georges Snyders likewise recognizes in Augustine the Valeur minente de l enfant: [P]uisquil est crature de Di eu, lhomme sa naissance, et pour ainsi dire ltat brut, ne sidentifie pas simplement au pch. En ralit, lexistenc e est valeur et le pch de lenfance, cest une direction nfaste imprime une force dexister qui, en elle-mme, ne peut tre que bonne, Georges Snyders, La pdagogie en France au XVIIe et XVIIIe sicles (Paris, 1965), 183. 10 Jesus said, Let the children come to me, and do not hinder them; for to such belongs the kingdom of heaven, Matthew 19.14, RSV. Similar statements, referring instead to the kingdom of God are in Mark 10.14 and Luke 18.16. 245

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conception of the childhood was ambiguous and ambi valent. Janet Nelsons analysis of the conversion stories of saints provides further support for this ambiguity.11 During the early modern period, the ambivalent attitudes toward the morality of children continued. Huarte repeats Aristotles idea th at a child is no more than a Brute Beast, controlled by desires.12 But he also states that The Virtues of Infancy are very many and the Vices but very few. Childre n are, among other things, Doc ile, Tractible, Gentle, Charitable, Frank, Chaste, Humble Innocent, and Undesigning.13 Georges Snyders articulates a clearly negative verdict of seventeenth-century educators with respect to children, because of their focus on the childs inab ility to carry out morally responsible acts consistently.14 Educators saw these negative qualities of childhood, Snyders argues, because they were working with children on a day to day basis, while artists and writers who pr oclaim the virtues of childhood did not have to live with their unpredictable behavior.15 The question of moral natural inclinations, then, took on a de cidedly negative tone. From one educational perspective, Huarte and Bart oli argued for the strength and constancy of inclinations toward specific types of learning and the importa nce of following them. Other sources, interested in the moral formation of the child, urged the identification of such inclinations to vice in order to correct them. 11 Janet L. Nelson, Parents, Children, and th e Church in the Earlier Middle Ages, in The Church and Childhood ed. Diana Wood (Oxford: Blackwell, 1994): 81-114. 12 Huarte, Tryal of Wits (1698), 59. 13 Ibid., 81. 14 Snyders, La pdagogie en France 208ff. 15 Ibid., 208. 246

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In 1632, Pierre Bardin published Le lycee dv Sr Bardin ov en plusieurs promenades il tait des connoissances, des actions, & des plaisirs dvn honneste homme .16 In this work, Bardin argues for the importance of education and nurturan ce for the correction of inclination to vice. He claims that proper training of a child can overcome these natural inclinations: It is significant to be well born, but it is of still more advantag e to be well nurtured: Nature is strong & powerful, yet it must be confessed that Institution overcomes it. For Childhood is pliable to all sorts of hab it, & does not know what either vi ce or virtue are; it is as susceptible to the one as to the other.17 It is precisely because a child may be shaped, sa ys Bardin, that education was considered as the most important piece of a Re public in the ancient world.18 It is crucial to weigh the actions and tendencies of a child at an early age in order to draw from them some prognostications for the rest of his years.19 Bardin uses the common analogy of farm ing, as had Mersenne, to stress that natures gifts cannot preempt effort: As there is no earth, as fertile as it may be that does not demand the hand of the laborer, there is no soul that does not require cult ivating if one desires it to produce good fruit.20 Like Bardin, Cureau de la Chambres Lart de connoistre les hommes though considering qualities other than honnett also recognized the role that ed ucation plays as the modifier of 16 This is one example of an expansive seventeenth -century genre known as manuals of civility. 17 Cest beaucoup destre bien nay, mais cest encor dauant age destre bien nourry: la Na ture est forte & puissante, neantmoins il faut confesser que lInstitution la surmonte. Car lEnfance est ployable toute sorte dhabitude, & ne sachant ce que cest de vice ny de vertu, elle est au tant susceptible de lvne que de lautre, Bardin, Le lycee 1: 175. 18 Tous les Politiques ont fort racomand leducation des enfans, comme la plus importante piece dvne Republique, ibid., 1, 174. 19 [A]prs la considertion des parens de quelqvvn, on s arreste aux actions quil fait en son ge tendre, afin den tirer des prognostiques pour le reste de se s annes, ibid., 1: 166. To do so is to follow the example of Seneca in his teaching of Nero, ibid., 1: 173-174. 20 Comme il nest point de terroir pour fertile quil soit, qui ne demande la main du laboureur, il ny a point dame qui nait besoin destre cultiue, si lon desire quelle rpporte de bons fruits, ibid., 1: 380-381. Bardin goes on to say that Il est necessaie quen la composition de ceste Vertu, la Nature y apporte du sien, & que nostre raison y contribu aussi de son industrie, ibid., 1: 382. 247

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natural tendencies.21 Quality of training may affect someones virtues for good or for ill, Study being able to correct depraved Inclinations, & bad nurturance being ab le to alter good ones.22 The rigorous spirituality of the Jansenists also required overcom ing of the natural inclinations, the more so because of their strong Augustinian influences. According to Augustine and those who followed his arguments ag ainst the Pelagians, hu man beings since the fall of Adam were infected with original sin in a way that comp romised free will. Prior to the Fall, Adam could freely choose good or evil. Af terwards, the situation changed for Adam and for his posterity, the whole human race. Postlapsarian human beings, according to Augustines account, naturally and constantly tend toward evil. The only solution for this problem is Gods grace, which cannot be earned. Therefore, for those not elected by God, hard work avails nothing. However, Augustinians argued, the elect ar e not exempt from efforts toward a holy life and this is the foundation of the rigorous spirituality of Port-Royal. This attitude toward grace and works lay beneath the comments of Pascal an d his sister regarding th e necessity of pursuing unlimited perfection through un ity with Jesus Christ.23 The complex relationship between perfidious na tural inclinations and the unrelenting effort needed to overcome them is also central to Pascals first religiously-driven work, the Provincial Letters. The issues the letters consider relate to questions of natural tendencies and work. Pascals ironic dialogue brings to light the inherent w eakness of trusting natu ral inclinations in questions of human morality. In an attempt to discredit his opponents, Pascal contrasts the efforts of the Jansenists to maintain holiness with the pride that the Jesuits take in producing ease 21 The relationship of Cureau de la Chambres work to intellectual inclinations is discussed in Chapter 3 above, pp. 102-103. 22 lEstude pouvant corriger les Inclin ations vicieuses, & la mauuaise nourriture pouvant alterer les bonnes, Cureau de la Chambre, Lart de connoistre les hommes 431. 23 See above, pp. 199-205. 248

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for their penitents. Finally, the Provincial Letters provides evidence of Pascals instrumental use of the truths of geometry to accomplish sp iritual aims. Geometry cannot, by itself, provide mystical union with God and thus is not a legitimate vocation in its own right. For Pascal, geometry is, however, acceptable and helpful, since it provides insigh t and preparation for spiritual truths. Geometry, for Pascal, was a pedagogical tool.24 Resisting the science of sins: Childlikeness and Maturity in the Provincial Letters Considered one of the masterpi eces of French literature, The Provincial Letters was written by Pascal pseudonymously in response to a theolo gical controversy that had been brewing for years. At its heart were five propositions condemned by the Sorbonne and supposedly contained in Augustinus a work written by Cornelius Jansenius and published in 1640. In short, the propositions dealt with issues of human responsib ility and agency in th e question of salvation and righteous acts. According to the propositions, Gods grace trumped any human efforts to cooperate with it or re sist it, even among the justes. Antoine Arnauld defended Jansen and the Jansenists from such claims, stating that the propositions were not to be found in Augustinus Arnauld was eventually censured and ousted from the Sorbonne for his resistance to the judgments of the majority. In response to the controversy, the Jansenists sought to ga rner public support for their cause. Neither Arnauld nor Pierre Nicole seemed the right choice for the task.25 According to Nicole, Pascal the newcomer volunteered for the task of sketching the work, innocently unaware 24 On geometrys role of instructing the believer about the limitations of fallen human nature, see Matthew L. Jones, Geometry and Fallen Humanity in Pascal and Leibni z, in David Wetsel and Frdric Canovas (eds.), Pascal/New Trends in Port-Royal Studies: Actes du 33e congres annuel de la North American Soci ety for Seventeenth-Century French Literature (Tbingen: Gunter Narr, 2002): 189-202. 25 Michel Le Guern, Oeuvres compltes 1:1118-1119. 249

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of his latent literary talents.26 His capacities in mathematics had been proven, but he was still an untried novice in this type of writing. The Provincial Letters was to constitute his apprenticeship to religious writing, the test of his in clination and vocation to such work. The first few letters of the series of Provincial Letters represent an ongoing dramatic production in which the narrator, presented as neutral, disinterested, and curious, physically walks back and forth between the locations of several parties involved in a dispute about the content of the five propositions. Pascal deftly situates the narrator as one in whom childlike ignorance is combined with industr y and a desire for self-education.27 He is naive, yet obviously has a keen memory, necessary but not sufficient for facility in le arning. This literary device of naivet differs sharply from Pas cals earlier work on the arithme tic machine and the void, in which he deliberately contrasts himself with su ch ignorance. He now makes strategic use of positive aspects of childhood, combining them with an emphasis on the necessity of education. The first letters are didactic, in that both he and the reader accumulate a fuller picture of the crux of the matter. What the narrator (and read er) discover, however, is that the dispute is a mere matter of words. As such, it falls within the realm of geometrical questions of proper argument rather than theological questions of religious truth. Throughout Pascals opening salvo against the Jesuits, he aims at their ambiguous imprecise, and equivocal language. Questions regarding the consistency of language are like questions of ge ometry, arithmetic, music, physics, medicine, and architecture. These su bjects must, as the Prface to the Treatise of the Void 26 Michel Le Guern points to Pierre Nicole s preface to the Latin translation of the Provincial Letters (1658) as a significant source for the origin of Pascals choice as the one to write the defense of Jansenism, Le Guern, Oeuvres compltes 1:1119. 27 For the idea that the Provincial Letters uses what M. M. Bakhtin calls polemical stupidity, or a strategic failure to understand, see Howells, Polemical Stupidity in the Lettres provinciales 231-237. 250

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argues, be augmented in order to become perfect.28 The narrator accumulates data by collecting information from his friends arguments It is a process of educating the childlike author. As it turns out, comparing fundame ntal rules of geometrical reasoning with the arguments of the theologians demonstrates that the Jansenists opponents fall short of logical coherence. Geometry becomes the inst rument for examining spiritual error. Pascals essay De lesprit gomtrique gives the basic geometrical rules that inform his attack on the Jesuits in the Provincial Letters. In this work, he states that definitions in geometry are very free [ trs libres ], as long as they are clearly stat ed and provided also that the same definition is not given of multiple things. The solution to such confusion is to substitute mentally the definition in place of the thing defined.29 Pascal had already criticized the faulty definitions of Father Nol regarding the experiments of the void. Pascal took Nol to task for defining light ( lumire ) self-referentially as a luminary movement of luminous bodies 30 Now, likewise, the theological doctors employed defin itions that were not based on proper rules in questions of grace and obedience. Th ey were unintelligible and immature. The central concern of the first letter is the theological use of the phrase proximate power During the narrators visits to various theologi ans, it becomes apparent that the different opponents of the Jansenists (the Molinists and the Jacobins) use this to refer to quite different ways of understanding the ability that the elect have to perform a righteous action at any given time. For the Molinists, proximate power is parallel to the power possessed by a person who is not blind if that person is in a lighted place. For the Jacobins on the other hand, this individual 28 Preface sur le trait du vide Mesnard OC 2:779. 29 Mais si lon tombe dans ce vice, on peut lui opposer un remde trs sr et trs infallible: cest de substituer mentalement la dfinition la place du d fini, De lesprit g omtrique, Mesnard OC 3:394. 30 Jen sais qui ont dfini la lumire en cette sorte: La lumire est un mouvement luminaire des corps lumineux, De lesprit gomtrique, Mesnard OC 3:396. 251

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may be said to have the proximate power of seeing even if they ar e currently in the dark. However, they agree on the use of the words proximate power even if those words have no precise meaning. They have done this, at least according to the narrator s Jansenist friend, completely in order to unite themselves in opposition to the Jansenists: [T]hey have resolved to agree on this term proximate, which both parties might use indiscriminately, though they unde rstand it diversely, that thus, by a similarity of language, and an apparent conformity, they may form a large body, and get up a majority to crush him with the greater certainty.31 For both the narrator and indeed any reader, such an equivocal approach to definition violates the rules of geometri cal reasoning. And while all thos e with common sense agree to these rules, Pascals inclination for and training in geometry especially suited him to judge such matters, as he says in his De lesprit gom trique: among minds equal and with all things alike, he who has geometry wins the da y in questions of proper reasoning.32 Thus, the ignorant and childlike na rrator becomes learned in this sup posedly thorny theological question through a simple shuttling between disputants. He thereby untangles the apparent complexity of the issue by unveiling falsely subtle definitions. Th e strength of childlikeness, as it appears in the Provincial Letters, is that it is yet unsullied by schol astic logic. It matures through the accumulation of experiences. By contrast, Pascals writing portrays the critics of the Jansenists as childish. Their utterance of the words proximate power is mere babbling without proper definition. The similarity to Saint-Anges animal-like pupils, who mimicked his absurd philosophical squawking, is noteworthy. 31 Blaise Pascal, The Provincial Letters of Blaise Pascal ed. O. W. Wight, trans. Thomas MCrie (New York: Hurd and Houghton, 1864), 147, hereafter PL 32 [E]ntre esprits gaux et toutes choses pareilles, celui qui a de la gomtrie lemporte, De lesprit gomtrique, Mesnard OC 3:391. 252

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The narrator of the Provincial Letters resorts to the free and clear rules of geometrical reasoning. The Jansenists opponents, as portrayed in this work, appeal to their authority as theologians instead of taking seriously the claims of logical reasoning to validate or undermine their expertise. Thus, when the narrator has heard the basics of the argument regarding the power to obey Gods commands and claims that there appears to be no difference between the opinions, the theologian seeks to establish his special qualifications: One must be a theologian to see the point of this question. The difference between us is so subtle, that it is with some difficulty we can discern it our selvesyou will find it rather too much for your powers of comprehension.33 The implication of the passage is that only theo logians are equipped to unr avel the knot of these issues, even if in so doing they violate clear rule s of definition. And when the narrator attempts to confront such theologians with clear thinking, they dismiss him as a simpleton. Likewise, in the fifth letter one theologian reiterates the point : I have had occasion to remark, two or three times during our conversation, that you are no great scholastic.34 The theologians thus attempt to dismiss geometry as a legitimate means to undermine their arguments. In the attempt to discredit his criticisms, one of the theologians with whom the narrator interacts portrays himself as a teacher, with the narrator as his pupil. He views his conversation with this non-theologian as a pedagogical session: You have got a great deal of instruction today; and I should like, now, to s ee what proficiency you have made.35 Assuming the superior position of the theological theoretician, much as Desargues did when articulating the teacher/pupil relationship between mathematician and mason, the theologian represents himself 33 Pascal, PL 146. 34 Ibid., 209. 35 Ibid., 260. 253

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as having a just mastery over the Jansenist.36 But what is it that he is teaching and what is its end result? The abstruse opini ons that are supposedl y only understood by qualified doctors of theology are precisely the grounds by which they cl aim legitimacy for their learning. And yet, as the details of the censure of Arnauld come to light throughout the work and the theologians attempt to explain them to the narrator, it become s clear that the point of difference which had proved imperceptible to ordinary mortals lacks substance. The difference between truth and error is infinitesimal: Truth, we know, is so delicate, that if we make the slightest deviation from it, we fall into error; but this alleged error is so extremel y fine-spun, that, if we diverge from it in the slightest degree, we fall back upon the truth. There is positively nothing between this obnoxious proposition and the truth but an imperceptible point.37 Pascal argues in his early Provincial Letters that the truth, for the Jansenists opponents, is not discovered through hard work or the clarity of expression that charact erize the narrator and others in the world.38 Rather, their truth or falsity is attached to ones person, depending upon whether one is associated w ith a particular group or not. Furthermore, in these little theological clubs, unlike the mathematical group of Mersenne, legitimate entrance is based not upon a persons productions, but upon a mere acceptance of an incoherent doctrinal vocabulary. Pascal argues that what the Jansenists opponent s have produced is not theology, which for him should be inextricably linked to virtuous action. Instea d, it is religious nonsense. 36 See above, pp. 124-127. 37 Pascal, PL 172. This passage provides an example of how mathematical language informs the work of the Provincial Letters The notion of the hypothetical infinitesimal point for use in mathematics was up for debate in the seventeenth century, especially with the growing importance of atomism, which assumed some smallest units that could not be divided. 38 E.g., Have you forgotten, since you retired to the cloister, the meaning attached, in the world you have quitted, to the word sufficient ?dont you remember that it includes all that is necessary for acting?, ibid., 158. Subsequently, the narrator specifies all types of people, from artisans to women, who understand the word sufficient in the same general way as the narrator, ibid., 159. 254

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The narrators efforts to grasp the truth about these questions are masterfully contrasted in the Provincial Letters with the efforts of the Jesuit fathers to provide solutions for cases of conscience.39 With his ironic appeal, Pascal portr ays his antagonists as those who, under the pretense of laboring to bring sinn ers to the confessional and the alta r, actually manage to excuse their abominable acts. The examination of specific cases of moral action begins in the fifth letter, which introduces a morality having no need for recourse to spiritual discipline or industry. When the narrator strategically plays the role of an individual who has difficulty su pporting the fast, he is only cursorily instructed to do violence to my inc linations. After more in sistence, he is offered a number of possible means by which he may be excused from fasting. The Jesuit multiplies situations and possibilities, making every effo rt to be accommodating to the struggling sinner.40 This type of interaction goes on fo r several letters. The Jesuit fath er cites quotations that serve as probable opinions on which one may act, thereby excusing a number of offenses, including participation in a duel, immodesty, and even mu rder. Just as Sain t-Ange tried to win Monflaines, Auzout, and Pascal by proclaiming the astonishing nature of his philosophical viewpoints, the Jesuit seeks to excite amazement in the narrator concerning the accomplishments of a moral system that is able to excuse almost any offense. For example, the Jesuit enlarges on a case of theft in the following way: 39 The narrator also offers a praise of his Jansenist friend in the realm of his studied knowledge on a particular theological point, as compared with the Jesuit: My friend, however, who was so ready on the whole question, that I am inclined to think that he had studied it all that very morning, replied, ibid., 187. 40 This idea of stating the many possibilities is parallel to Matthew L. Joness emphasis on the importance of Pascals enunciation of mathematical propositions; see above, pp. 221-224. 255

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But only attend to this notable decision of Father Bauny, on a case which will still more astound you, and in which you would suppose th ere was a much stronger obligation to make restitution.41 In an even more obvious attempt to impress the narrator with the wit w ith which his colleagues have worked, the fictional Jesuit outlines the a pproach to solving the di fficult question of duels: Anxious to keep on good terms both with the Gospel, by doing their duty to God, and with the men of the world, by showing charity to their neighbor, they needed all the wisdom they possessed to devise expedients for so nicely adjusting matters as to permit these gentlemen to adopt the methods usually reso rted to for vindicati ng their honor, without wounding their consciences, and thus reconcile two things apparently so opposite to each other as piety and the point of honor. But, sir, in proportion to the utili ty of the design, was the difficulty of execution. You cannot fail, I should think, to realize the magnitude and arduousness of such an enterprize.42 Pascal, who had made his own appeals to the di fficulty of such tasks as the creation of the arithmetic machine and the demonstrations of the void, has here crafted a finely probing and laughably sad example of i ndustry badly placed. The Jesuits attempts to demonstrate the clev erness of moral probabilism fail. They are the source of ironic laughter with a tinge of horror and result in the undermining of the priests goals of legitimation. Indeed, rather than being st ruck by the success of the Jesuits in drawing penitents to their confessionals, the narrator elicits a different kind of surprise. He reacts with pure astonishment at finding the books of men in holy orders stu ffed with sentiments at once so horrible, so iniquitous, and so silly.43 And when confronted with more justifications and excuses, he writes that [t]his preposterous decision fairly dumb founded me with its pernicious tendencies.44 41 Pascal, PL, 255-256. 42 Ibid., 230. 43 Ibid., 259-260. 44 Ibid., 261. 256

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The Jesuits, placing much emphasis on the effort required to soothe consciences, eliminate the need for self-discipline and taming of nature Pascal suggests. According to the narrator, Their morality being entirely Pagan, nature is quite competent to its observance.45 In fact, the sin of immodest dress is excused if it is by reason of the natural in clination to vani ty. This view of human nature is distinc tly un-Augustinian and the narrator observes that while some prescribe painful austerities for healing the so ul you show that s ouls which may be thought desperately distempered are in quite good health.46 According to the portrayal of the Provincial Letters the Jesuits were concerned with making Christian life easier, in order to attr act people to their re ligious camp. But the theologians had misunderstood the purpose of their work. They were not accomplished as theologians because of their ability to handle wo rds carefully and to creat e their own definitions of sin: These are disputes of theologians, not of theology.47 The hallmark of true theology, Pascal claims, should be right liv ing and he will therefore leave the theologians to the Sorbonne and make no claims against their type of lear ning. In response to a nother excuse, this time allowing the rich to avoid giving al ms, the narrator proclaims: Why truly if that be the case I give up all pretension to skill in the science of sins.48 tienne Pascal had argued in his letter to Father Nol that his son, although young, had demonstrated virtue superior to that of the Jesuit priest. Thus Blaise had maintained in his natural philosophical work a quality that the theologians, t hose whose lives should be most in 45 Ibid., 199. 46 Ibid., 183. The use of the language of distemper may be related not only to health but also metaphorically to music. The well-tempered instrume nt is one which keeps the proper ma thematical ratios between the musical intervals. Pascal suggests that the human instrument is one that must be submitted to the professional tuner to be corrected. In this case, that tuner is the grace of God through Jesus Christ. 47 Ibid., 177. 48 Ibid., 273. 257

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keeping with the teaching of the Gospel, had ab andoned. In fact, the quip at the end of the previous paragraph suggests that at the heart of Jesuit morality is a contrast between two types of skill. The Jesuits hard work to make the penite nt more comfortable is not an innocent or even ignorant childishness that masquerades as learnin g. Instead, it is the founding of a science of sin, in which the pupils who are instructed in it become learned in how to transgress Gods laws with impunity. It is clear that Pascal believes that the mo rality endorsed by the Jesuit fathers who are cited in the Provincial Letters ultimately leaves human beings in a state of childish ignorance. They are at the whim of their natural inclinations. Th e gentleness of Jesuit morality is in accordance with their belief that humans have a natural cap acity to perform the commands of God. No instruction or transforma tion seems to be required. But for Pascal, orthodox Christian doctrine, as stated by Augustine, maintains that our natural state must be transformed to enable such obedience through charity. And indeed, it is in the famous chapter on lo ve in Pauls first letter to the Corinthians that the apostle writes: When I was a child, I spoke like a child, I thought like a child, I reasoned like a child; when I b ecame a man, I gave up childish ways.49 The critique of the Jesuits as childish in the Provincial Letters is parallel to the indictment against Pascals other adversarie s in questions of mathematics and natural philosophy, and is related to his own history as a promising boy ge nius. Pascal, who had been encouraged in his own inclinations for geometry and mathematics by his fathers friends, had to exercise those talents and give si gnificant effort in order to prove the legitimacy of those claims to natural talent. In his attempts to legitimate himself as a savant worthy of full acceptance in that community, he contrasted his own work with those who represented uncultivated inclination. 49 1 Corinthians 13.11, RSV. 258

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Pascal was born into an intellectual culture that, in rediscovering the great ancient writers, came to seek the reestablishment of a gol den age of the mind. They sought the new embodiment of those intellectual virtues that th ey saw as central to classical Greek culture.50 But Pascal was also born into a world of skeptic ism, rooted in that same classical tradition.51 He lived at the cusp of Paul Hazards brilliantly overstated Crisi s of European Consciousness.52 The intellectual trend was towa rd questioning the claim that someone might be born, one may say elected, to a position of intellectual superi ority, whether through bod ily constitution or the influence of the stars. Pascal was thus poised to fill the role of a new Archimedes. But he was also compelled to justify his posi tion as such through a gr eat deal of effort, and to show that his status as promising young savant did not remain in those terms but showed maturity and development. With the convergence of Pascals background as child prodigy and his exposure to Augustinian theology, it is hardly surp rising that Pascal should be so particularly interested in the necessity of hard work for Christian living.53 The contrast between this rigorous view of Christianity and that of th e Jesuits presented in the Provincial Letters is pronounced. For Pascal, the Jesuits attempts to make Chri stianity more palatable for its adherents are in direct opposition to historical Christianity. One of Pascals Jesuit interlocutor s admits this very point in a discussion of penance: 50 Indeed, Pascals lifetime overlaps with French Classicism, an approach to literature and art. 51 Richard H.Popkin traces these Greek source s of early modern skepticism in Popkin, The History of Scepticism: From Savonarola to Bayle (Oxford, 2003,) Chapter 2, The Revival of Greek Scepticism in the Sixteenth Century, 17-43. 52 Paul Hazard, The European Mind, the Critical Years: 1680-1715 (New Haven: Yale UP, 1953). 53 The Jansenist Augustinianism, and Pas cals ascetic tendencies, place him in si gnificant continuity with some of the prominent values of the so-called Prote stant work-ethic described in Max Weber, The Protestant Ethic and the Spirit of Capitalism (London: J. Murray, 1927). 259

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[Narrator:]But, sir, what then becomes of what Father Petau himself is obliged to own that the holy fathers, doctor s, and councils of the church agree in holding it as a settled point, that the penance preparatory to the euchar ist must be genuine, constant, resolute, and not languid and sluggish, or subject to after-thoughts and relapses? Dont you observe, replied the monk, tha t Father Petau is speaking of the ancient church ? But all that is now so little in season, to use a common saying of our doctors, that, according to Father Bauny, the reverse is the only true view of the matter.54 The Jesuits thus represented for Pascal a corr uption of the true church, controlled by the undulations of culture rather than by tradition and divine revelation. Merits and Demerits of Children: Pascals Comparaison des chrtiens Two Childhoods of Christianity and the Necessity of Christian Instruction It is in this vein of contras ting the contemporary church with the ancient church that Pascal penned a much-neglected piece that draws toge ther the duality of childhood innocence and vulnerability to emphasize the importance of educ ation for child and adult. Given the title Comparaison des chrtiens des premiers temps avec ceux daujourdhui (Comparison of Christians of the First Times with Those of Today) by later editors, Pascal demonstrates Jansenisms primitivist attraction for the firs t Christian centuries in this short work.55 The fascination for the Greek writings of mathematic s during the sixteenth an d seventeenth centuries was matched, in some circles, by enthus iasm for the early Christian church. Comparaison des chrtiens which considers the status and purpose of infant baptism, emphasizes themes of interest to this study (the importance of effort and the signific ance of education for Christians). Furthermore, it suggests a distinction between two contrasting aspects of childhood, which will inform both Pascals own understanding of the hu man condition and the interpretation of Pascal given by his later biographers. 54 Pascal, PL 290-291. 55 Philippe Sellier, Port-Royal et littrature (Paris, 1999-2000), 2: 46. 260

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The first contrast that Pascal offers between the church of the first Christian centuries and the Catholic Church of his time is the relative necessity of concerted efforts to enter into communion with the church. While Pascal recogn izes the benefit of in fant baptism (discussed below), he claims that the church of his time had, because of this practice, abandoned the kinds of rigors that were required of those who were c onverted to Christianity and baptized during the early centuries of Christianity. He states this contrast in several ways at the beginning of the piece: One then entered into the church onl y after great works and long desires. One is found there now without any pa in, without care, and without work. One was received into it then only after having denied his past life, only after having renounced the world, flesh, and the devil. One enters in it now before one is in a state that one may do these things.56 Pascal suggests that the most significant way th at hard work is manifested for the believer is through catechetical instructi on subsequent to baptism as a ne wborn. The practice of infant baptism is beneficial, he argues. The purpose of it is that those that it withdraws at such a tender age from the contagion of the world ta ke sentiments entirely opposed to the world.57 Here Pascal makes use of the positive connot ation of childhood. Th e assumption of the argument is that a child is, with respect to certain aspects of worldliness, unsullied. However, its benefit, Pascal continues, is limited, and is particularly dependent upon the faithfulness of the godfather to his duties with re spect to the child. The godfat her is given, among others an indispensible commandment to instruct th e children in the commands of God and the 56 On nentrait alors dans lglise quaprs de grands travaux et de longs dsirs. / On sy trouve maintenant sans aucune peine, sans soin et sans trava il. / On ny tait reu alors quaprs avoir abjur sa vie passe, quaprs avoir renonc au monde, et la chair, et au diable. / On y entre maintenant avant quon soit en tat de faire aucune de ces choses, Comparaison des chrestiens, Mesnard OC, 4:54. 57 Son vritable esprit est que ceux quelle retire dans un ge si tendre de la contagion du monde prennent des sentiments toutes opposs ce ux du monde, ibid., 4:56. 261

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church.58 In order to encourage such learning, it is necessary that godchildren be instructed in the history of the church and the difference in the customs which have been practiced in the church in the diversity of times.59 They must be taught, in partic ular, about how in earlier times individuals were required to be catechumens before entering th e church and that they were thoroughly instructed and examined before being accepted. Thus, Pascal states, contemporary Christians are not exempt from laboring in their faith. Although they enter the church as children, through their baptism as infants, they do not avoid their responsibility as its members because of their safeguarding from the vices into which corrupt reason leads them.60 Instead, it is necessary, as they grow older, that they receive the same education as the adult believe rs of the first centuries after Ch rist. They are obliged to be learned in questions of the faith, rather than re lying upon their status as born into the community of the church. The benefits of such a birth are not to be gainsaid, as ha s already been stated. Furthermore, it is clear that the message of Christ included the charge that the true believer is to be like a little child, that the Kingdom of Heaven belongs to little children. The danger in the baptism of infants in the Ca tholic Church, says Pascal, is that the two states of childhood will be confused rather than held distinct. In the ancient church, he writes, there was a chronological distinction between the two births taught by Ch rist and thus also the same distinction between ones physical and ones spiritual ch ildhood. Growing up in the first childhood in the world, the individual became learned in the ways of the world and progressively corrupted, while remaining as ignorant as a newb orn in the ways of the truth. In the early 58 [E]lle leur commande expressment de les garder inviolablement, et ordonne par un commandement indispensible aux parrains dinstruire les enfants de toutes ces choses, ibid., 4:57. 59 [I]l faut leur faire entendre la diffrence des coutumes qui ont t pratiques dans lglise suivant la diversit des temps, ibid., 4:58. 60 Elle prvient lusage de raison, pour prvenir les vi ces o la raison corrompue les entrainerait, ibid., 4:56. 262

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Christian church, individuals had to take pains in order to dem onstrate that they were serious about renouncing the world before being admitt ed to the second birth through the rite of baptism.61 As scholars of the Christian life, they had to first submit to a very exacting examination.62 In the church of Pascals time, however, th e two births could be confounded due to their chronological proximity: One finds oneself now be in both [the world a nd the church] at nearly the same time, and the same moment in which we are born into th e world has us reborn into the church. Thus, reason arising no long makes a dis tinction between these two worlds that are so contrary to one another. It is raised in both together. One attends the sacraments, and one enjoys the pleasures of the world.63 The danger of being born into the community of the chur ch is that instruct ion seems optional. To be baptized as an infant could carry with it a sense of chosenness that could encourage one to remain in the state of the spiritually immature child.64 The true believer must be a scholar of the commandments of God and of the ways of the renunciation of the wo rld. But instead of following in the way of the trs instruites converts of the early Chri stian church, most of the individuals born into the church in Pascals da y, he says, are now in an ignorance that provokes horror.65 Thus, for the present church, Pascal conti nues, ones birthright of election seemingly 61 [O]n quittait, on renonait, on abjurait le monde o lon avait reu sa premire naissancce pour se vouer totalement lglise o lon prenait comme sa seconde nai ssance: et ainsi on concevait un diffrence pouvantable entre lun et lautre, ibid., 4:55. 62 On ny tait admis quaprs un examen trs exact, ibid., 4:54. 63 [O]n se trouve maintenant presque au mme temps dans lun et dans lautre; et le mme moment qui nous fait natre au monde nous fait renatre dans lglise. De sorte qu e la raison survenant ne fait plus de distinction de ces deux mondes si contraires. Elle slve dans lun et dans lautre tout ensemble. On frquente les sacrements, et on jouit des plaisirs de ce monde, Comparaison, ibid., 4:55. 64 Chosenness does not, of course, always prompt such la xity. Most famously, Weber argues that for Calvinists, hard work was a way of proving that a person was, in fact, one of the elect, Max Weber, The Protestant Ethic and the Spirit of Capitalism trans. Stephen Kalberg (New York, 2009), chapters 4 and 5, 101-159. 65 [E]lles sont maintenant dans une ignorance qui fait horreur, ibid., 4:55. 263

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preempts any need for in-depth instruction: one is persuaded of the necessity of baptism, and not of the necessity of instruction.66 Pascals Comparaison and His Baptism as a Savant Pascals treatment of the question of infant baptism and catechetical instruction suggests certain parallels with the process by which he be came a legitimate part of the learned community and the writings (such as the preface to the trea tise on the void and the writings on the arithmetic machine) that articulate his status as savant. Pascals descrip tion of the presumption of those baptized into the Catholic Church is not unlik e that which is possessed by individuals who would eschew instruction of any sort in the sciences while still hoping to be considered savants. To leave intellectual inclina tions unrefined through lack of instruction was, for Pascal, to promote remaining in a childish state of ignorance. Pasc al and Huygens endured an examination, even if informal, to merit the endorsement of Mersenne and others. Pascals playroom discovery of geometry led to his baptism into the company of the learned cohort gathered together in Paris. His writing of the Essai pour les coniques was his confirmation as a mathematical catechumen. In his attempts to legitimate himself as a mathematician, the contrasts of child/adult and beast/human demonstrated his consciousness that his own natural talent would not suffice to qualify him as full-fledged mathematical savant. His mathematical training was a model for his understanding of Christian instruction. Positive and Negative Views of Childhood in the Intellectual Realm In the realms of the mind and faith in the seventeenth century, there were two distinctive dimensions of childhood; one was admirable, the other was to be left behind. There was the conception during that period of a ty pe of pristination of the mind pr ior to any type of education. 66 [O]n est persuad de la ncessit du baptme, et on ne lest pas de la ncessit de linstruction, ibid., 4:59. 264

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Although Locke had not yet presente d the modern articulation of tabula rasa, the idea had been expressed by Aristotle, Avi cenna (ibn Sina), and Aquinas.67 And many who had experienced the typical educational system in the seventeenth century, most notably Descartes, considered that this system had done more harm than good.68 Similar to Pascals expression of the sullying influence of the world on a child, the influe nce of schools was often seen as corrupting young minds. Hence, the method of self-instruction was intended to bypass the influence of the world on the genius of the child.69 Indeed, Descartes method of doubt was a chronological retrogradation of the intellect wh en he, sitting in front of hi s fire, sought to undo the various assumptions and conclusions he had previously made about the world. In spite of Descartes return to an innocent state, not ye t spoiled by false opinions, his purposeful return to childhood was not complete. According to Descartes, the childlike void of the mind had to be coupled with a mature judgmen t of the senses. The ch ilds interpretation of the world and his use of intellect were unrelia ble. Most of the errors in philosophy, argued Descartes, began in childhood.70 67 A brief summary of the historical background to the early modern tabula rasa idea is in Neal Wood, Tabula Rasa, Social Environmentalism, and the English Paradigm, Journal of the History of Ideas 53 (1992), 650-665. Avicennas theory of knowledge is in his De anima 68 In his Principles of Philosophy Descartes writes: most of those who have attempted to be Philosophers in recent centuries have blindly followed Aristotle in such a way as to often corrupt the sense of his writings by attributing to him diverse opinions which he would not recognize as his own if he returned to this world. And those who have not followed him (among whom were many of the best minds) were nevertheless immersed in his opinions in their youth (because these are the only ones taug ht in the schools), which prejudiced them to such an extent that they were unable to attain knowledge of th e true Principles, Descartes, Principles of Philosophy xx. 69 Descartes Discourse on Method has as one of its major concerns the rejection of instruction of the schools in favor of self-education, with Des cartes presenting his own biography as an example, Ren Descartes, Discourse on Method and Meditations on First Philosophy trans. Donald A. Cress (Indianapolis, 1993), 3-6. 70 Paragraph 71 of Descartess Principles of Philosophy is headed That the principal cause of errors proceeds from the prejudices of our childhood. Descar tes argues that the reason for these errors is the inability of the child to separate thought from bodily experience. As an example of childhood error, he cites the belief that the stars are no larger than the candles, since they appear only so large to the eye, Descartes, Principles of Philosophy 33. 265

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Pascal agreed with Descartes on the basic w eakness of the childs intellect. A childs thoughts, they both maintained, were formed primarily through habit and not through ratiocination. The child is hampered, they s uggested, by a quantitative lack of experiences. Pascals preface to the treatise on the void indicted the institutions of his day for revering the ancients too much, thus exalting the data-deprived childhood of humanity.71 Contemporaries, he added, had the benefit of the accumulation of experiences that leads to more perfect knowledge. Pascals view of the ancients was not unc ontested. For many during the sixteenth and seventeenth centuries the ancients typified old age because they possessed wisdom and knowledge that had survived the passage of time and had proven superior to the knowledge passed on from the Middle Ages.72 In addition, the language of renaissance as a label for the complex of intellectual developments that drew inspiration from the rediscovery of ancient writings suggests a return to a childhood, innocent of the corrupting influe nces that covered the true wisdom of earlier days of humanity. Thus, in the realm of knowledge, chil dhood had metaphorical connotations of both ignorance and innocence during the seventeenth century. Both dimensions were based on lacking something. Childhood was ignorance be cause it had not had the opportunity to accumulate the experiences that can only occur in time. It is on this state of ignorance and 71 Le respect que lon porte lantiqu ite tant aujourdhui tel point, dans les matires o il doit avoir moins de force, que lon se fait des oracles de toutes ses penses, et des mystres mme de ses obscurits, Prface sur le trait du vide, Mesnard OC 2: 777. Cependant il est trange de quelle sorte on rvre leurs [ancient authorities] sentiments. On fait un crime de les contredire et un attantat dy ajouter, comme sils navaient plus laiss de vrits connatre, ibid., 781. 72 The problem is theologically complex, considering questions of the status of the first mans knowledge before and after the Fall. Peter Harrison draw s attention to how the emergent natural philosophy of the sixteenth and seventeenth centuries was indebted in its motivations and methods to ideas about the effects of the Fall, Harrison, The Fall of Man and the Foundations of Science (New York, 2007). As one exam ple of an appeal to biblical antiquity, hermeticism drew on the notion of the perfection of Adams knowledge, emphasizing an unbroken tradition with his pristine understanding, ibid., 117-119. 266

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immaturity that Pascal focused in his preface to the treatise on the void and which is closely related to his characterization of the artisans of Rouen as like b easts trained only through habit. As a young and talented savant, he desired to make a clear claim that his successful inventions and experiments were not the result of chan ce. They were the result of hard work, determination, and training in spec ific types of knowledge. The efforts that he put forth and his training in mathematics demonstrated that though he had inclinations for such work, he became validated through his strivings toward perfection. On the other hand, the seventeenth century vi sion of childhood include d its innocence. It lacked the pollution of false teachings by author ity. In the realm of natural philosophy, many disbelieved in the void because th eir education had taught them that it was impossible. In order to explore the question, however, it was necessary to retreat to the unta ught position of the child in order to evaluate the experiences presented. This connotation of innocence was important for self-education through both books and experiences. It was the type of innocence that Desargues attempted to maintain by claiming that he had taught himself geometry through books, that he never had a master. It was also a key aspect of Pascals own education by his father, who apparently believed that mathematics had the potential to cripple the rest of his sons education. Pascals Comparaison and the Spiritual Duality of Childhood In spiritual matters the two aspects of ch ildhood were even more clearly delineated. Whereas Jesus proclaimed little children as the heirs to the Kingdom of Heaven and commended childlike faith, Paul the Apostle ta ught that Christians were supposed to grow up and be mature, no longer sustaining themselves on spiritual m ilk, but on the meat of important doctrinal issues. Pascals Comparaison des chrtiens as has been shown, includes elements of both of these aspects of childhood. In one sense, infant baptism is considered by Pascal to be a 267

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preservation of the innocence of childhood. Pascals emphasis in his Comparaison is the way that the childs reason is safeguarded from its corrupt use. Innocence, for Pascal, was also ignorance: an ignorance of the world.73 But Pascal did not stop there, for the godfather of the child was also obligated to remove that childs ignorance of spiritual thin gs, a task that, if he failed to do it, would leave the child in an ignorance that provokes horror.74 As the childs reason began to be put to use, it was to be given a full instruction in th e mysteries of religion, which is a key aspect of protecting the child from falling away from the faith.75 Childlikeness was a positive characteristic when it signified the uncorrupted use of reason (and distance from the vices of the world) but childishness in a ba ptized believer who is bereft of understanding of the grandeur of our religion is a tragic flaw.76 Childhood Innocence and the Correctio n of Inclinations: Jacquelines Rglement pour les enfants Dual Nature of Childhood in the Reglement The contrast between these two types of chil dhood is also evident in Jacqueline Pascals account of her instruction of young girls at the Port-Royal convent.77 Though technically not a part of the educational experiment of the petites coles the education of novi ces drew from the same sources of inspiration as the schools estab lished for the sons of the associates of PortRoyal. Jacquelines close relationship with her brother through the end of her life and the depth of her involvement in Port-R oyal suggest that her views on the education of the young likely 73 Comparaison, Mesnard OC 4:57. 74 Ibid., 4:55. 75 [O]n ne les y admettait quaprs une pleine instruction des mystres de la religion, ibid., 4:58. 76 [I]l arrive que la ngligence des parents laisse vieillir les chrstiens sans aucune connaissance de la grandeur de notre religion, ibid., 4:59. 77 The full text of what Jean Mesnard calls the Rglement pour les enfants is in Mesnard OC 3:1135-1198. 268

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informed those of her brother and reflected thos e of the religious community of which she was a part and with which he wa s closely associated. The Rglement pour les enfants written in 1657, is focused particularly on the shaping of thes e young girls through a correc tion of inclinations. This emphasis is understandable, since the little pi ece is about the active role that the older nuns play in the girls spiritual development. However, Jacquelines rule also gives indications of understanding childhood as synonymous with innocence. In her instruction to others who are in the position of overseeing these girls, she calls their charges these innocen t souls and sacred depo sits that he [God] has entrusted to us, and for which he will make us render an account.78 This reminder of the accountability of teachers for youngsters resonates w ith Jesus warning that it would be better to be thrown into the sea millstone-laden th an cause one of these little ones to sin.79 Furthermore, Jacqueline explains that during the past year she ha d given particular attention to teaching the girls how much Christians are ob ligated to preserve the innocence of their baptism.80 Thus, she recognizes and places importan ce on the association of childhood with preservation from sin. For Jacqueline, oversight and discipline were keys to overcoming natural fallenness. The dual nature of childhood is most clearly summed up in a piece appended to Jacquelines rule for children. Published in 1665 under the title Image dune religieuse parfaite et dune imparfaite this piece, made up of various prayers, was probably not written by Jacqueline. It reflects, howeve r, the spirit of Port-Royal a nd, as Mesnard writes, has some 78 [N]ous devons toujours regarder ces petites mes comme de sacrs dpts quil nous a confis, et dont il nous fera rendre compte, Rglement, Mesnard OC 3:1164. 79 Luke 17.2, RSV. 80 [J]e lai toute employe la pnitence, insistant particulirement sur les endroits qui font voir combien les chrtiens sont obligs de conserver linnocence de leur baptme, Rglement, Mesnard OC 3:1155. 269

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likelihood of respecting the ideas and practices of Jacqueline, even of being based on other writings that she had left behind.81 This prayer offers the c ontrast between childhood innocence and childhood ignorance succinctly: Make us, Lord, to always be children thr ough simplicity and innocen ce, as people in the world are so through ignorance and weakness. Give us a holy childhood, which the course of the years cannot remove from us, and from which we will never pass into the old age of the ancient Adam, or into the death of sin.82 In this prayer, childhood is characterized by simplicity, innocence, ignorance, and weakness. The former two are associated with the faithful believers willingness to trust and with inexperience in vice.83 The latter two refer to the lack of knowledge of the Creator and an inability to perform the works th at God requires. This piece suggests that Jacqueline and (by extension) Port-Royal, were conc erned that those within the earl iest years of th eir physical life should cultivate a holy childhood. Adulthood and old age were tied to Adam. In this case, as opposed to Pascals use of the ancients in his preface, the earliest of men was linked with old age, probably because of the introduction of deat h through his sin. This association is in line with Pauls denotation of Adam as representing the old man, and sinful nature, while Jesus Christ is the new man, the means by which be lievers experience the n ew birth and enter a second childhood of innocence. Natural Inclinations and Discipline in the Reglement With respect to childhood and natural inclinations, as has already been suggested, Jacqueline was decidedly in favor of a basic suspicion of inc linations and their correction: 81 Les addition ont cependant quelques chances de respecter le s ides et la pratique de Jacqueline, voire de reposer sur dautres crits quelle aurait laisss, Mesnard OC 3:1136. 82 Faites, Seigneur, que nous soyons tousjours enfants pa r la simplicit et linnocence, comme les personnes du monde le sont toujours par lignorance et par la faiblesse. Donnez-nous une enfance sainte, que le cours des annes ne nous puisse ter, et de laquelle nous ne passions jamais dans la vieillesse de lancien Adam ni dans la mort du pch, Rglement, Mesnard OC 3:1197. 83 Brethren, do not be children in your thinking; be babes in evil, but in thinking be mature, 1 Cor. 14.20, RSV. 270

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One tries to accustom the children to mortify themselves, and not at all to follow their inclinations, by attaching themselves to one work rather than another.84 For Jacqueline, the tendency of children to fo llow their inclinations without question is particularly pervasive and pern icious, and one of several spec ific faults of childhood that Jacqueline mentions throughout her writing. The principle of putting away ones natural bent toward a specific subject, which Jacqueline articula tes, was one of the keys to tienne Pascals original strategy for Blaises education. The elder Pascal sought to mortify his sons interest in geometry by leaving him ignorant of its content. He knew, according to Gilberte, the consuming nature of such studies and so di d not want him pursuing it at the expense of linguistic pursuits. Jacquelines emphasis on the mortification of natural inclination was more spiritual than intellectual, however. B ecause of original sin, without vigilant attention, she says, that to which one is naturally drawn inevitably leads to si nful behavior. Such vigilance requires the knowledge of the natural inc linations of the children. In Campanellas City of the Sun childrens talents were judged by their teachers to determine how they should spe nd their lives. Jacquelines Rglement pour les enfants likewise places a burden on the preceptor to be observant of their pupils: A continuous vigilance to consider them a nd recognize their humor and their inclination are necessary, in order to lear n by considering them what they do not have the power to reveal to us themselves. It is good to anticip ate them when one sees that they are ashamed to speak of their unruliness [ drglements ] and, in order to give to them more liberty to reveal them, it is good to hide from them in the beginning very many truths that we believe are too strong for their imperfect state.85 84 On tche daccoutumer les enfants se mortifier, et ne point suivre leurs inclinations, en sattachant plutt une ouvrage quun autre, Rglement, Mesnard OC 3:1143. 85 Il faut une continuelle vigilance pour les considrer, et reconnatre leur humeur et leur inclination, afin dapprendre en les considrant ce quelles nauraient pas la force de nous dcouvrir. Il est bon de les prvenir, quand on voit quelles sont honteuses de dire leurs drglements, et, pour leur donner plus de libert de les dcouvrir, il est bon de leur cacher elles-mmes dans le commencement beaucoup de vrits que nous croirions tre trop fortes pour leur tat imparfait, ibid., 3: 1172. 271

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This sensitivity to individual readiness is a hallmark of a newly developing understanding of childhood during the early modern period. The emerging consciousness of development has been explored by Philippe Aris, who gives part icular credit to Port-Royal educationalists for promoting it.86 It is this realization of stages of readiness that was also probably an aspect of tiennes pedagogical strategies.87 For Jacqueline, however, onl y recognition of a childs weakness and an awareness of his inclinations would lead to prope r spiritual oversight. For this reason, the insights of teachers in to the nature of the child we re communicated to others who watched over that child: We take some sort of confidence in these sister s who help us, in order to tell them of the inclinations of the children, especially those of the small, and those also of the great who could cause some unruliness, in order that they can better watch over them.88 Knowledge of the child was not confined to those in authority. One aspect of the educational strategy communicated by Jacqueline is that the pupils themselves should be instructed to understand th eir natural leanings, so that those may be turned, through discipline, to their proper use: One ought to strongly exhort the children to know themselves their inclinations, their vices, and their passions, and to di g to the root of their defects. It is good also that they know what their natural [self] ca rries them towards, in orde r uproot in themselves what could displease God, and change th eir natural inclinations into spiritual. To tell them, for example, that if they are of an affective humor they ought to change the love that they have 86 Aris explores this new differentiation between ages and its eventual result, th e association of particular ages with particular levels of schooling; see especially Aris, Centuries of Childhood Part 2, Chapter 4, The Pupils Age, 189-240. 87 Pier Paolo Vergerio the Elder advised parents and teachers to consider the individual differences between children that necessitated individualized curriculum. He especially advocated for teaching subjects one at a time, Benjamin G. Kohl, Humanism and Education, in Renaissance Humanism: Foundations, Forms, and Legacy ed. Albert Rabil vol. 3, Humanism and the Disciplines (Philadelphia, 1988), 12-13. 88 Nous prenons quelque sorte de confianceaux surs qui nous aident, pour leur dire les inclinations des enfants, surtout celles des petites, et celles ausi des grandes qui pour raient causer quelque drglement, afin quelles puissent mieux les veiller, Rglement, Mesnard OC 3:1162. 272

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for themselves and for creatures into loving God with all their heart, and likewise for other inclinations.89 Once they were aware of what they were, children were enjoined not to rely upon their natural inclinations to lead them in the right path Such self-centeredness was seen as the path to sin. Rather, Jacqueline contends, they must turn to God. An unquestioning and undisciplined following of inclinations, she states is antithetical to the freedom from attachment to self which was so prized in Port-Royal spirituality. Thus knowledge of the self and hard work was the means by which the natural inclinations could be controlled and put to proper use. Jacquelines emphasis of this point is clear from a le tter written about six months before the Rglement to a young girl considering becoming a nun: This, my dear Maiden, is a type of goods that the fathers of the ear th do not give, but we must hope for them from our Father who is in heaven, and we invoke him in truth in order to obtain them, not only by praying but by sincerely working to destroy little by little all the inclinations or bad habits which could be opposed to these virtues in us.90 The spiritual novice, like the appr entice mathematician had to work to gain maturity and spiritual learning. Jacquelines instruction on the education of her charges agrees with the positions of Bardin and Cureau de la Chambre, since the inclinations were seen as correctable. To simply lean on the natural inclinations was portrayed as improper. As Mersenne argues that exercice is necessary to complete what is lacking in natura l talent, so in the moral realm (as emphasized by Jacqueline, Bardin, and Cureau de la Chambre) a reliance on ones natural inclinations is the 89 On doit fort exhorter les enfants se connatre elles-mme s, leurs inclinations, leurs vices et leurs passions, et sonder jusques la racine de leurs dfauts. Il est bon ausi quelles connaissent quoi leur naturel les porte, afin de retrancher en elles ce qui peut dplaire Dieu, et changer les inclinations naturelles en spirituelles. Leur dire, par exemple, que si elles sont dune humeur affective, elle s doivent changer lamour quelles ont pour elles-mmes et pour les cratures, aimer Dieu de tout leur cur et ainsi des autres inclinations, ibid., 3:1168. 90 Voil, ma chre Demoiselle, une espce de bien[s] que les pres de la terre ne donnent point; mais il faut les esprer de notre Pre qui est au ciel, et que nous lin voquons en vrit pour les obtenir, non seulement en priant mais en travaillant sincrement dtruire peu peu toutes les inclinations ou les mauvaises habitudes qui pourraient sopposer ces vertus en nous, Jacqueline Pascal to ***, 3 October 1656, Mesnard OC 3:960. 273

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pathway of vice, which can only be overcome through effort. Therefore, Pa scals insistence that he had moved past mere habit, instinct, and natu ral inclination, was not simply an establishment of personal qualifications. It was a principle of intellectual and moral integrity. The ultimate goal of all of the instruction advocated in Jacquelines handbook was spiritual, but it reflects a trend in pedagogical innovation. She and her fellow nuns did not treat children as mere passive vessels, identical and waiting to be filled, but accounted for individual differences.91 While rejecting a path following the slope of natural inclinations, it did not ignore them completely; it sought to reshape them to what was judged to be their proper ends. From Pupil to Pedagogue: Pascals Educational Contributions and the Petites coles of Port-Royal Jacqueline was directly involve d in the education of girls at the convent, while her brother participated informally in educational endeavors. His participation demonstrates a clear shift in the understanding of his vocation. In the first place, he was th e godfather of a boy named Blaise Bardout, for whom he provided a sum of money in hi s will for apprenticeship in a trade, and with whom he may have put into practice his pleas for proper educa tion of godchildren.92 Both Jacquelines Rglement and Blaises endorsement of pr oper catechetical training in his Comparaison des chrtiens are in harmony with the concern for the spiritual nur turance that was the final goal of Port-Royals petites coles .93 91 Aris, Centuries of Childhood 27-28. 92 For the mention in the will, see Testament de Pascal, Mesnard OC 4:1509. Some scholars have mistakenly believed that he was also the godfather of his nephew, Blaise Prier. However, the baptismal record clearly indicates, as Jean Mesnard shows, that the Blaise Pascal who was Priers godfather was secrtaire du roi, and thus the first cousin of tienne Pascal, Mesnard OC 2:999. No documents have, to date, been discovered indicating the place of birth, parents, or subsequent life of Blaise Bardout. 93 Delforge reinforces the importance of the entire community of like-minded individuals would have contributed to the project of the schools: At Port-Royal education is which the masters participate, but also the Solitaires, the religious, the servants, and the friends of Port-Royal. Unde rstandably, it is not appropri ate to place these educators on the same plane; but all are united by a common vision of education and through the same desire to do what was 274

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Spiritual Work at the Petites coles Port-Royal began the project of the petites coles in 1637 with the combined intellectual and spiritual training of a handful of upper-cla ss boys at the groups c onvent in the country. 94 Soon after, the pupils moved to a second convent in Paris; there were eventually groups of teachers and students in both locatio ns. The boys, taught by the male solitaires associated with and living at Port-Royal, were sent to these schools in order to avoid the defects of other types of education, including education by pa rents and in the Jesuit colleges.95 The little schools of Port-Royal have been credited with an influenc e on educational theory and practice far beyond what their short duration and sm all number of pupils might s uggest. Port-Royal is credited, among other achievements, with inspiring education in the vernacular and with providing a number of textbooks (e.g., the Grammaire and the Logique ) that would be used for many years to come.96 Aris credited Port-Royals schools as one of the key moments in the emergence of a view of children as different, distin ct as an age-group and as individuals.97 in their power to educate correctly th e children for which they feel responsible in one way or another, Delforge, Les petites coles 173. 94 A primary source concerning the Port-Royal petite coles which I have been unable to consult, is Pierre Coustel, Les regles de lducation des enfans 2 vols. (Paris, 1687), a very rare published work that gives a retrospective view of the philosophy and operation of the schools during Pascals lifetime. Another primary source that mentions a number of informal conversations and episodes dealing with key players, including Arnauld, Nicole, and Pascal is Receuil de Choses Diverses a manuscript of which is at the Biblioth que Nationale, Paris, nouvelles acquisitions franaise, 4333. It has recently been pub lished in a critical edition, Lesaulnier, ed., Port Royal Insolite: dition Critique de Receuil Choses Diverses The definitive secondary source on the history and the significance of the petites coles is Delforge, Les petites coles See also Barnard, Little Schools of Port-Royal ; Nicholas Hammond, Fragmentary Voices: Memory and Education at Port-Royal (Tbingen: Narr, 2004). 95 Pierre Coustel mentions the possible dangers associated with educating children at home in Coustel, Rgles de lducation des enfans quoted in Delforge, Les petites coles 162. Nicholas Hammond argues that the petite coles were consciously opposed to Jesuit colleges, Hammond, Fragmentary Voices 54-55; cf., Delforge, Les petites coles, 163. 96 Through Rollin, the Port-Royalists inspired the University ; their use of the vernacular was adopted by S. JeanBaptiste De La Salle and has since become universal; thei r treatises were devoured by Rousseau; their cultivation of their mother-tongue laid the foundations of modern French prose; their school-books have been in use down to our own days, not only in France, but in several other European countries, Barnard, Little Schools of Port-Royal 4. 97 Aris, Centuries of Childhood 27-28. 275

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Jacquelines female charges would not have been a part of the petites coles, but the education of the young girls also took place under the influence of the abb of Saint-Cyran, whose writings had so affected the lives of th e Pascal family in Rouen. Port-Royals schools were envisioned by Saint-Cyran and inspired by his general inclination for all children, and the recognition that they are ve ry pure through the innocence an d the grace of baptism.98 However, innocence was accompanied by weakness a nd the possibility of being led astray by natural inclinations or bad habits.99 As such, the boys and girls of Port-Royal were treated with respect for their purity before God, understanding for their weakness, and the strong discipline that would save their souls. Ultimately, Port-Royals educational endeavors were a matter of education in Christ.100 The goal of the work was the salva tion of souls and the cultivation of lives lived entirely for God.101 Intellectual Training at the Petite coles The petites coles were to be places that primarily promoted spiritual maturity, but the formation of the intellect played a role in this process. The organizers and educators of the schools consciously ride on a current of pe dagogical innovation prope lled by the likes of 98Jean Duvergier de Hauranne to Princesse de Gumn, n.d. [January 1642], in Duvergier de Hauranne, Lettres indites 265. 99 Jean Duvergier de Hauranne to Monsieur David, n.d. [1640], in Duvergier de Hauranne, Lettres indites 56. 100 For it is indeed a matter of education in Christ. It is in Jesus Christ that the edu cators of Port-Royal find the source, the path, and the finality of education. They thin k and they live the educational work in reference to Jesus Christ. They affirm unceasingly this fundamentally Christian character of their pedagogy. For the coherent educational system that they build, they find (or aim to find, for all is not always so simple) solid biblical and patristic foundations. They want education (and moreover all that concerns human life) to be connected directly and exclusively to Jesus Christ. It is from this perspective alone that they judge the value of the masters, educational means, of the whole scien ce of education, Delforge, Les petites coles 351-352. 101 H. C. Barnard describes Port-Royals education work as a desparate attempt to save souls, Barnard, French Tradition in Education 182. Delforge writes: If the students of the Petites coles lives in a closed world, in a closely supervised universe, it is in order to better root them in the faith; this will permit them then to face, spiritually and intellectually, the most serious realities of th e world in which it is necessa ry to testify [of] the Living God, incarnate in Jesu s Christ, Delforge, Les petites coles 351. 276

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Erasmus, Ramus, and Montaigne.102 Their goal for the intellectual development of their pupils was to enable them to read and understand a variety of texts, including mathematics and physics.103 All that was needed of the tec hnical subjects was a rough understanding.104 To delve too deeply into them would be to keep from engaging with more diverse texts from nonmathematical or scientific authors. In this way, the training of the petites coles involved helping the child to develop beyond the limited scope that would ostensibly result if left to their own devices. The relationship between att itudes about natural talent pedagogical methods, and generality of education also impinged upon the growing importance of the sociability of knowledge. The petites coles were highly influenced by the confrence as were the proceedings at Mersennes academy.105 This key development with in the seventeenth century helped to reinforce the idea that following ones own whims in a particular subject was not as profitable as engaging in the give and take of discussion. There was a growing concern during the se venteenth century for the simplicity of expression in the conference, the ability to comm unicate with others, and a concern for the limits of technical jargon. Pascal s interlocutor in the Provincial Letters makes this argument with the theologians who, he claims, have resorted to a use of language that c ontradicts the way that 102 Delforge, Les petites coles 352. 103 Ibid., 314. 104 Mathematics is one of these particular sciences which it is necessary that the children have at least a slight tinge and a rough understanding, Pierre Coustel, Regles de leducation des enfans, quoted in Delforge, 315. 105 Delforge, Les petites coles 322. William Ritchey Newtons notion of a Socit de Port-Royal is dependent on the sociable interactions that would have taken place du ring spiritual and intellectual conferences. This model of social interaction is particularly important for the mingling of those who are official solitaires and those who are only friends of the convent, W. R. Newton, Sociologie de la communaut de Port-Royal: histoire, conomie (Paris, 1999), 140-141. The conference was important as an emergi ng form of sociability during the seventeenth century, Simone Mazauric, Structures et formes de la sociabilit acadmique parisienne dans la premire moiti du XVIIe sicle, Cahiers dhistoire de lInstitut de recherches marxistes 59 (1995): 27-45. 277

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words are understood by all people in le monde. Furthermore, the efficacy of the conference for the advancement of knowledge eroded the pr ivileged position of one who had a special disposition or gnie for a particular subject. It is not that such talent was thought not to exist or be efficacious, but it was considered to be subject to the necessity for improvement based on interactions with others. Thus Pascal exhibited his genius fo r geometry through his independent discovery of one of Euclids theorems. But hi s position as an Archimedes was cemented while in the company of his fathers friends in Mersennes cell. Pascals Work with the Petites coles A pedagogical turning point Pascal was indirectly involved in the proj ect of these little schools, as the opening anecdote of this chapter illustrates. His expres sion of interest in pedagogical materials and methods demonstrates that a shift was occurring in his life at this time. With his ties to PortRoyal strengthening during the mid-1650s, Pascal no longer played the part of the child prodigy seeking to legitimate himself and his work by a ppealing to his studies and efforts. Having redefined himself according to a desire for devout living in the manner of the Jansenists, he was reconsidering the various aspects of inclination and effort, ignorance and innocence. He shifted his attention, in part, to the goal of cultivati ng another generation by deploying methods that he had practiced in his career. The previous sections of this chapter suggest this pedagogical shift and Pascals reflections on childlikeness and maturity in th e context of what may be referre d to broadly as teaching. In his Provincial Letters and the little work on baptism Pas cal stressed the importance of living a life of childlike innocence, but also of escapi ng the ignorance of childhood through instruction. In the Provincial Letters he mocked the Jesuits for the so-c alled learning that would allow them to transgress against common sense, the rules of geometrical definition, and morality in their 278

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teaching of others. These Jesuits, who presented themselves as masters, were inferior to their pupils. According to Pascals reflections, the nave, child like investigator who was willing to ask intelligent questions could trump the child ish experts who babbled their equivocal words. Common-sense thinking was a means by which ab struse religious diffi culties could become clear. In his Comparaison des chrtiens Pascal also reflected on the importance of education for the Christian, now seeking to reemphasi ze the differentiation between a child like baptismal innocence and a child ish ignorance of the mysteries of th e Christian religion. In both cases intellectual maturity and childlike purity were paired together. Whereas the Comparaison des chrtiens focused on Pascals interest in specifically Christian instruction, his involveme nt in the work of Port-Royals petites coles demonstrates a more wide-ranging pedagogical engagement. The petites coles were at their high point during the time of Pascals most intimate connection to Port-Royal. Frdric Delforge, historian of these schools, has divided their development into three stages: La Cration (1636-1647); LAffermissement (1646-1655); and LAchvem ent (1656-1660). According to Delforge, the period of maturity and dynamism of th e middle years was interrupted by the short dispersion in March 1656 and then proceeded to expand and be fruitful for several years more until the 1660 dispersion.106 Pascal became a participant in certain aspects of the operations and vision of the petite coles His contributions to the project demonstrate his desire to improve upon natural ignorance through the instru ment of geometry. Alongside his Comparaison des chrtiens they also reiterate the ultimate goal of these schools: the pres ervation of baptismal innocence. 106 See above, p. 243. 279

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Pascal, contributor to textbooks The first evidence of Pascals pedagogical effort s is in a letter written from Jacqueline to her brother in October 1655, less than a year after his Night of Fir e and just months prior to the writing of the first of the Provincial Letters In her letter, Jacqueline refers to a method that her brother had apparently shared with her of teaching children how to read.107 The method advocated introducing the letters to children acco rding to the way they are pronounced rather than the formal names of those letters. Jacquelines correspondence simply suggests the basics of the method of putting the pr onunciation of letters t ogether to form words and asks several questions regarding difficulties raised by this me thod. But it does make clear that the authorities of Port-Royal were aware of Pascals ideas in this area, for she writes: Our Mothers have commanded to write to you in order that you tell me all the circumstances of your method to read by be, ce, de, etc., in which the children do not have to know the names of the letters.108 The method that Jacqueline describe s as originating with her brothe r is given in further detail in the 1660 Grammaire de Port-Royal written by Antoine Arnauld and Claude Lancelot, two of the most important masters of the petites coles .109 According to Jean Mesnard, Jacquelines letter and the excerpt from the grammar are [f]ormal pr oof of the attention given by Pascal, soon after his conversion, to questions of pedagogy raised to him by the masters of the petites coles .110 In a similar manner, Pascals discussions with Arnauld about the best way to teach geometry led Blaise to produce an lments de gomtrie for this purpose. Pascals work never 107 Jacqueline Pascal to Blaise Pascal, 26 October 1655, Mesnard OC 3:439-440. 108 Nos Mres ont command de vous crire afin que vous me mandiez toutes les circonstances de votre mthode pour apprendre lire par be ce de etc. o il ne faut point que les enfants sachent le nom des lettres, ibid., 3:439. 109 Anon, Grammaire gnrale et raisonne (Paris, 1660). The method of reading is given in Part One, Chapter VI, Dune nouvelle maniere pour apprendre lire facilement en toutes sortes des Langues. 110 J. Pascal to B. Pascal, 26 October 1655, Mesnard OC 3:438. 280

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saw the light of day, since Arnauld wrote his own Nouveaux lments de gomtrie and Pascal, considering his own inferior, burned it.111 Its introduction, however, remained, and Leibniz has preserved a fragme nt in his notes.112 The fact that this work was not officially used by Arnauld or the petites coles does not lessen its significance as a sign that Pascal was in the process, thanks to his friends at Port-Royal, of reflec ting on the means by which particular fields of knowledge were best acquired and how they were to be used in a full-fledged program of training for children. Pascal made inte llectual contributions to another textbook, La logique de Port-Royal which acknowledges Pascals De lesprit gomtrique as the source of some of its material. Arnaud sought, says one of the key tw entieth-century Pascal scholars, to make of geometry the effective instrument of a rational pedagogy.113 Pascals attempts to lay down rules, according to which proper and convincing ar guments may be constructed, assisted in this goal of Arnauld and Port-Royals schools. Publishe d just weeks before Pascals death, the first edition of La logique de Port-Royal briefly mentions the contribut ions of vn excellent esprit, while later editions, beginning in 1664, name him explicitly.114 Pascals involvement with the project of the petites coles was, finally, in the service of a goal of developing people who would be well-rounded and trained for holy living. Pascals previous experience as a mathematician resonate d with Nicoles and Arnaulds beliefs in the 111 The story, its dubious origins, and the relationship between Pascals and Arnaulds treatises are recounted in Delforge, Les petites coles 346. 112 The fragment preserved by Leibniz is in Mesnard OC 3: 435-437. The original or copy from which Leibniz copied the fragment has not been found. 113 Brunschvicg, Blaise Pascal 156. 114 On en a aussi tir quelques autres dvn petit Escrit non imprime, qui avoit est fait par vn excellent esprit, & quil avoit intitul, De lesprit Geometrique Antoine Arnauld and Pierre Nicole., La logique ou lart de penser (Paris, 1662), 18. Arnauld points to the specific portions of the text that are drawn from Pascal, ibid., 105-110; 378. Editions following Pascals death include the following wording: un petit crit, qui avait t fait par feu M. Pascal, Antoine Arnauld and Pierre Nicole, La logique ou lart de penser ed. Charles Jourdain (Paris, 1992), 15. 281

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possibility of mathematics to exercise and perfect the mind, leading to the good life, as Matthew L. Jones has argued.115 And yet, as Pascal makes clear in his De lesprit gomtrique, there are axioms and truths that transcend mathematical proof. Pascals years of practicing geometry as his mtier were over. His attention now turned to the problems of the human situation, not the least of which was the training up of young minds. His own experience as one burdened by natural talent prepared him to teach those whose temporal greatness required a special diligence in instruction. Final Contribution to Pedagogy: Pascals D iscourses on the Condition of the Great At about the same time as Pascals watchf ul care of the disp ersed students of the petites coles he expressed his pedagogical in terest through several discourse s delivered to a child of great condition.116 The content of these discourses, aided by memory and written sources, was recorded by Pierre Nicole in part of his De lducation dun Prince (1670).117 Nicoles personal interactions with Pascal allowed him to recount Bl aises passion for such a project of education: One of the things on which the late M. Pas cal had more views was the instruction of a prince that one would try to raise in the way most proportionate to th e state to which God called him, and the most appropriate to rende r him capable of fulfilling all the duties of it and of avoiding all the dangers. He was often heard to say that there was nothing to which he desired more to contribute if he was engage d in it, and that he w ould willingly sacrifice his life for such an important thing.118 115 Jones, Good Life in the Scientific Revolution 50. 116 [I]l est venu dans lesprit dune personne qui a assist trois discours assez court quil fit un enfant de grande condition, Pierre Nicole, De leducation dun Prince, divisee en trois Parties, dont la derniere contient divers Traittez utiles tout le monde (Paris: Charles Savreux, 1670), 270. Th e discourses are recorded under the title Discours de feu M. Paschal sur la condition des grands, ibid., 269-285. 117 Nicole assures the reader that although it may not be true that these are the words that Pascal himself used then these are at least his thoughts and his sentiments, ib id., 271. Nicole does not place his own name on the title page and the privilege for the book is issued to sieur de Chanteresne. Mesnard believes it possible that the Discourses are based on the expansion of some Penses dealing with those of high position, Mesnard OC 4: 10131026. 118 Vne des choses sur laquelle feu M. Paschal avoit plus de veus, estoit linstruction dun Prince que lon tcheroit dlever de la maniere le pl us proportione lestat o Dieu lappe lle, & la plus propre pour le rendre capable den remplir tous les devoirs & den viter tous les dangers. On luy a souvent ouy dire quil ny avoit rien 282

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Probably intended for the marquis dAlbert, fu ture duke de Chevreuse and son of the duke de Luynes, Pascals discourses are reminiscent of his letter written to Queen Christina some eight years earlier.119 As with the letter to Christina, Pas cal is concerned in this piece with the contrast between greatness confe rred by the circumstances of birt h, and greatness that is merited through developed qualities that ar e worthy of esteem. Pascal pr aised Christina because she not only possessed the favor of a high birth, but also had exerted the re quisite effort to be recognized as a person with a great mind. In the Discours Pascal emphasizes th at those who, like the marquis, have been favored with a privileged bi rth, must not rely upon this as a justification for respect. It is a grave error, Pascal argues, to believe being born into a particular family gives one a legitimate claim to superiority. The path by wh ich one comes to be born at a specific time and place is littered with chance meetings and marri ages. The greatness that comes from birth, he insists, is instead that of a greatness of establishment [ Grandeurs de lestablissement ].120 It is only because there has been a decision for tempor al goods and power to pass to the son that a chance birth yields wealth and influence. This decision is one that is utterly free and entirely based upon the contingencies of human government. Pascal contrasts greatnesses of establishment with what he terms natural greatnesses. These consist in true and effective qualities of the soul or of the body, which make one or the other more estimable.121 In this case, unlike the references to natural inclinations mentioned previously in this study, Pascal uses the term natural to describe pa rticular qualities, not quoy il desirt plus de contribuer, sil y estoit engag; & quil sacrifieroit volontiers sa vie pour une chose si importante, Nicole, Education dun prince 269-270. 119 This is the opinion of Lon Brunschvicg who follows that of Havet, Brunschvicg OC 9:363-364. 120 Nicole, Education dun prince 278-279. 121 Les Grandeurs naturelles, sont celles qui sont indpendantes de la fantaisie des hommes, parce quelles consistent dans des qualitez reelles & effectives de lame ou du corps, qui rendent lun ou lautre plus estimables, comme les sciences, la lumiere de lesprit, la vertu, la sant la force, ibid., 279. 283

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considering the means by which these are acqui red, but the means by which they are judged great. He argues that virtue, skill, and learne dness have a God-ordained connection with the granting of respect to those who possess them. Gods sovereign plan is that those who have these qualities should be esteemed. The most important of these natural qualities, according to Pascal, is that of being an honnte homme a man of well-rounded skills, virtue, and the ability to communicate. But also among those characteristics that merit natural rec ognition is the skill of being a geometer.122 In neither of the two particular qualities that Pascal mentions, honntet and geometry, does he make clear whether such tra its are naturally acquired. Nevertheless, it is necessary, in order to demand the esteem that is required for these natural greatnesses, that one demonstrate those qualities, whether through fine conversation or thr ough the solution of a geometrical problem.123 Some sort of exercise is necessary. The type of natural respect that is associated with these qualities may not, Pascal st ates, be accorded merely on the basis of a high birth. In this moral lesson to the young marquis, th en, Pascal attempts to make clear the limitations of what were, he believed, sometime s erroneously considered the natural possession of the highly born. Indeed, the very gift of su ch a birth has, accordi ng to Pascals analysis, specific defects to which greatness tends toward.124 A belief in an overarching superiority based only upon chance events of na tivity encourages the individual to ignore the more estimable 122 La geometrie est une grandeur naturelle, elle demande une preference destime, mais les hommes ny ont attach aucune preference exterieure, ibid., 281. 123 [J]e vous prierois de me monstrer les qualitez qui meritent mon estime, si vous le faisiez elle vous est acquise, & je ne vous la pourrois refuser avec justice; mais si vous ne le faisiez pas, vous seriez injuste de me la demander, ibid., 282. 124 Ces trois petits discours avoient pour but de remedier trois defauts ausquels la grandeur porte delle-mme, ibid., 271. This phrase is from Nicoles summary of the three discourses. 284

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qualities of virtue and intellect, so th at they do not try to acquire them.125 Pascal instructs the future duke that, if he wants to be respected, he should show me the qua lities which merit my esteem. If you do so, it will be secured by you.126 Pascal the young savant had been faced with th e similar necessity to legitimate himself as truly learned, and not a mere boy genius. While the Mersenne group could praise him to the savant world as one whose precocious talents prom ised much, his test as a true geometer came through the toil, effort, and expense of his subs equent work. Respect was not acquired through a fortuitous conjunction of stars or the makeup of ones temperament. To rely on them would be to remain as a child or as a beast. Likewise, despite the testimony that the marquis dAlberts mind was extremely advanced, already capable of the most powerful truths, and completely extraordinary in all things which depend on intell igence, it was necessary for him to take heed lest he fall prey to the temptation to rule acco rding to a mistaken belief in his superiority by birth.127 Having been so instructed, the future duk e was, in Pascals terms, saved from the brutal lives of those who are not cognizant of this difference.128 Pascal proceeds deeper in his instruction of the marquis, moving from the intellectual to the spiritual. Whereas his letter to Queen Ch ristina in 1652 stopped at co nsidering high birth and intellectual virtue, Pascal now takes the marquis into the rea lm of Christian training. He instructs the marquis to move beyond the honnte homme to be one who truly knows the difference between greatnesses of establishment and natural greatnesses. In harmony with 125 The phrase is from Nicoles summary: ils ne taschent point les acquerir, ibid., 271-272. 126 [J]e vous prierois de me monstrer les qualitez qui meritent mon estime, ibid., 282. 127 [I]l fit un enfant de grande condition; & dont les prit qui estoit extremement avanc, estoit dja capable des veritez les plus fortes, ibid., 270. The last compliment is in Arnauld and Nicole, La logique 4. 128 [I]l me suffit de vous avoir dtourn de ces vies brut ales o je voy que plusieurs personnes de vostre condition se laisser emporter, faute de bien connoistre ltat veritable de cette condition, Nicole, Education dun prince 285. 285

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286 his sentiments in the 1648 letter (cowritten with Jacqueline) and in the Comparaison des chrtiens Blaise urges that this tem poral leader aspire to this realm of charity where all the subjects breathe only charity, and desire only the goods of charity.129 The marquis should no longer claim the benefits of his fortunate birth wh en he so aspires. As Mesnard observes, he must take his place within Gods kingdo m, as the humblest of his subjects.130 Pascal shies away from taking a position of spiritual director in this realm, stating th at others than me will tell you the path of it, probably referring to those of Port-Royal.131 Yet Pascals transformation to the place of instructor, both in questions of honntet and in religion, is unmistakable. Having recognized the limitations of his own na tural bent, Pascal attempted in his three discourses and in the Penses to exercise a new role as one human teaching another about the human condition. But Pascals original talents and natural inclinations were not abandoned. The complex relationship between the mathematical work of his youth and the recognition of limitations of his late twenties and early thirties we re reflected in his fina l savant project dealing with the curve called the roulette. Through his involvement in the roulette problem, and through numerous mathematical analogies and strategies in the Penses, Pascal improved upon the gifts of his birth, moving from the mtier of geometry to a true Christian vocation. Likewise, the original tension between childhood and maturity that was evident in his early savant work was transformed by his considerations of Christian sp irituality and education. This new perspective on scholarly endeavors created an atmosphere of ambivalence toward him within the learned community in Paris and beyond. 129 Il faut mspriser la concupiscence & son royaume & aspirer a ce royaume de charit, o tous les sujets ne respirent que la charit & ne desirent que les biens de la charit, ibid., 285. 130 Il lui faut se situer dans lordre de la char it, comme le plus humble de ses sujets, Mesnard OC 4:1025. 131 Dautres que moy vous en diront le chemin, ibid., 285.

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CHAPTER 6 PASCAL AS AMOS DETTONVILLE: A RETURN TO CHILDHOOD Having sought as a young adult to distance hi mself from childhood genius, and then from the restrictions of his mathematical career, Pasc al tackled a mathematical problem in his last years that again situated him as a major figure in savant Europe. Pas cals approach to the roulette problem, however, had motivations that evoke religious issues. These motivations and Pascals approach to publicizing his soluti ons meant that his work, though considered praiseworthy, was no longer part of the mainst ream of the Parisian community of natural philosophers. Pascal, it would s eem, was not the one to fulfill Mersennes hopes for a new Archimedes. Pascals last work represents a return to a problem that exercised the geometrical group in which he was raised. The problem involved th e curve alternately known as the roulette, the cycloid, or the trochoid.1 Put simply, the roulette is the curve described by a fixed point on the circumference of a circle that is rolling along a line at a uniform velocity. The curve is the sum of two motions: on the one hand, a circular moti on; on the other, a directional motion following the trajectory of the line. In the tradition of pure geometry, Pascal discovered a means for measuring this curve.2 As Pascal demonstrated, the measur ement of the curve is a multi-faceted problem, for it includes such calcula tions as the length of the curv e, the area between the curve and the line along which the circle is rolling, and the volume of the solids created by the rotation 1 Roulette is the specifically French name which Mersenne attributed to the curve. Trochoid originally used by Roberval, is from the Greek trochodes See Pascal, Histoire de la Roulette, Mesnard OC 4:214-215. The term cycloid or Cyclode is attributed by Pascal to Jean Beaugrand,ib id., 4:216. Pascals preference for the term roulette reflects his preference for writing in French. As such, I refer to the curve by this French name. 2 The Greek literally refers to measuring the earth, an d the measurement of distances, areas, and volumes are at the heart of ancient geometry, Oxford English Dictionary, http://dictionary.oed.com/cgi/entry/50093912?single=1&query_type=word&queryword=geometry&first=1&max_to _show=10 (accessed 8 October 2008). 287

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of those curves around a vertical or horizontal axis. In addition, Pascal was particularly concerned in his work to find a method for calcula ting the centers of gravity of solids associated with the curve.3 His method for finding these dimensi ons was especially indebted to an application of the principle of a physical balance, which may be traced back to Archimedes. In order to use this technique, Pascal had to empl oy a controversial idea: geometrical indivisibles. The problem, the method, and Pascals means of publicizing it would evoke both praise and criticism from the learned. Pascal anonymously proposed a contest to the most eminent geometers of all the earth in 1658, challenging them to find a number of the di mensions of the roul ette and its solids.4 The contest was to take place during a specified ti me frame and would reward its winner with a monetary prize. While the response to the contest was limited, ther e were a handful of mathematicians from France, Holland, and Engl and who answered the ch allenge. Of these, Pascal recognized the contributions of a select few, includi ng Christopher Wren of England, Ren-Franois de Sluse of Lige, and Christi aan Huygens in Holland. In the end, however, Pascal and the panel of judges selected by Pierre de Carcavy judged that none of the solutions had truly answered the challeng e of finding a general method for the solution of the problems. Pascal presented his own solutions under th e pseudonym Amos Dettonvi lle, an anagram of Louis de Montalte, the name he used as author of the Provincial Letters.5 The response to the contest, and the subsequent publication of the Lettres de A. Dettonville was mixed. If there was 3 This includes both the solids of rotation and another solid which he calls double onglet This solid was described by Grgoire de Saint-Vincent, Mesnard OC 4:399. 4 praestantissimis tot orbe geometris, Pascal, First letter circulated to the learned geometers of Europe (June 1658) (hencefort, First circular letter), Mesnard OC 4:189. 5 In the orthography of the time, the u in the middle of words was written as a v. Hence Lovis de Montalte is a true anagram of Amos Dettonville. 288

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admiration for the subtle and ingenious methods us ed to attain to the results, there was also sharp criticism. The Englishman John Wallis, for example, strongly objected to the secretive and partial methods that, in his estimation, had characterized the contest. This chapter aims to analyze the logistics of th e contest, Pascals att itude toward it, and the responses that it received. In particular, it seeks to show how the virtues of childhood and the virtues of maturity are a part of Pascals portrayal of his role in the project. Along these lines, this chapter argues that Pascal asserted the di fficulty of the roulette problems in order to emphasize his mathematical maturity, but he emph asized ease in order to maintain the childlike immediacy and diversionary char acter of the project. This chapter will also make some suggestions about how the Parisian learned community in the middle of the seventeenth century defined itself and the virtues it considered importa nt. It will make the claim that some of the behaviors exhibited by Pascal during this late part of his life a nd some of the relationships he maintained, cultivated associations with child like behavior that al ienated him from that community. Huygens, not Pascal, would assume the role of Mersennes new Archimedes. A Mathematical Remedy As with most events of Pascals life, Gilb erte Priers biography provides an explanation for Pascals last efforts in mathematics that ma nages to highlight his admirable qualities. She describes it as an aberration from his turn toward religious questions afte r the dramatic Night of Fire, but also as a further demonstration of the power of his mind. According to her story, expanded by her daughter in a later memoir, Pas cals reflections on the roulette curve were prompted by the pain of a midnight toothache. In an attempt to disconnect his mind from the ravaging pain, Pascal applied himself to a familia r problem. By focusing on the problem, he was able to relieve his physical discomfort and arrive at a long-sought solution. 289

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Playful Problem-Solving Discovery in isolation The narrative of Blaises disc overy of a method of measuring curves suggests aspects of his continuing identification with childhood. Severa l elements of the stor y recall a similar event from Pascals childhood. Like the account of Blai ses discovery of geometry as a teenager, his solution to the problem of the roulette took place in isolation; he discovered it in a single night in his room. Both his Euclidean doodling and his work on the roulette are portrayed by Gilberte as diversionary activities, not primar y concerns. In the one case, Blai ses fathers restriction of his interaction with geometrical text s and ideas had relegated the exploration of mathematical ideas to his hours of recreation, being alone in a r oom where he was accustomed to divert himself.6 It was a playful discovery that involved a full-blown pursuit of the building blocks of geometrical reflection: line s, circles, and angles. In the case of the roulette, Pascals religious preoccupations, commitments, and pursuits were an internal barrier to a renewed pursuit of mathematical interests. This is because he had understood, at the time of his Night of Fire, that the Christian religion obliges us to live only for God and that, as such, he renounced all other [fields of] knowledge.7 Blaise remained within his father s orders by pursui ng his interests in geometry only during his playtime Likewise, Blaises sister insists that he worked on the roulette problem without design, only to divert himself from unbearable pain.8 6 [I]l se mit lui-mme rver; et, ses heures de rcra tion, tant seul dans une salle o il avait accoutum de se divertir, il prenait du charbon et faisait des figures sur les carreaux, La vie de Pascal, Mesnard OC 1:574. 7 [I]l comprit parfaitement que la religion chrtienne nous oblige ne vivre que pour Dieu . [I]l renona toutes les autres connaissances pour sappliquer uniquement lunique chose que Jsus-Christ appelle ncessaire, La vie de Pascal, ibid., 1:577-578. 8 Ce renouvellement de ses maux commena par un mal de dents qui lui tait absolument le sommeil. Dans ses grandes veilles il lui vint une nuit dans lesprit, sans desse in, quelque pense sur la proposition de la roulette, La vie de Pascal, Mesnard OC 1:585.. Bouwsma, Christian Adulthood, identifies an appreciation for play as a central aspect of the joining of adulthood and childhoo d in Christian thought: the Christian can relax, even (paradoxically) when he is most profoundly and actively confronting the sinfulness of the world. He can enjoy 290

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Effortlessness of solution The childlike aspect of Pascals geometrical explorations of the roulette, and their connection to his earlier discovery of Euclidean geometry as a teenager, is further emphasized through the supposed lack of effort necessary in order for him to solve the problem. Gilberte states that Pascals initial, unpremeditated consideration of the roulette was followed by a cascade of thoughts, apparently regarding the co nsequences of a particular proposition on the roulette.9 These thoughts uncovered to him, as if de spite himself, the demonstration of all these things, by which he was himself surprised.10 This immediacy of hi s mathematical solutions suggests the type of talent that would make great effort unnecessary for such mathematical results. It is the kind of talent that Blaise himself sought to downpl ay during his legitimacyseeking period. His sisters emphasis on it in this later case only makes clear her desire to highlight the virtues of childlikene ss in her brother. As a child, Pascal needed no adult help to attain the proof of a Euclidean proposition. He simply learned by playing. Likewise, Blaise required no assistance in Gilbertes account of the r oulette problem. playfully (which also means to delight in, for itself, not to exploit instrumentally, for himself) the goodness of the creation. His culture can be an unbounded playground for free and joyous activity. He can risk the little adventures on which play depends . Play is a natural expression of the joy of faith, which makes it possible to engage in life, even the hard work of life, as a game that has its own seriousness and that yet can be enjoyed precisely because the ultimate seriousness of exis tence lies elsewhere, with God, 92. 9 This unimpeded flow of thoughts also suggests an element of the earlier geometrical discovery story. When Pascals father questions him about his discovery of Euc lids proposition on triangles, Pascal signals the type of reasoning suggested in this account of the later event: My father asked him what had made him think to seek that: he said that it was that he had found such and such a thing; and on that having made the same question to him, he said still some other demonstration that he had made; and finally, by regressing he came from there to his definitions and his axioms, La vie de Pascal, Mesnard OC 1:574-575. 10 [E]nfin une multitude de penses qu i se succdrent les unes aux autres lu i dcouvrirent comme malgr lui la dmonstration de toutes ces choses, dont il fut lui-mme surpris, ibid., 1:586. His surprise likewise mirrors his fathers shock at finding him drawing geometrical figures on the floor. 291

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Overcoming restrictions The parallel between his teenage diversion a nd his epiphany with the roulette continues even after the isolation of the roulette discovery. His follow-up interaction with a close friend (probably the duke de Roannez) mirrors tiennes response to Blaises boyhood demonstration. After discovering him drawing on the playroom fl oor, Blaises father questioned him, ultimately giving his seal of approval to his sons study of geometry only after consulting his long-time friend Le Pailleur about how to deal with the natural talents of his son. Following Blaises surprising discovery of a number of the properties and calculations of the roulette curve many years later, his friend the duke al so questioned him about his findings. Both Pascals father and the duke were surprised at Blaise s discoveries in thei r respective cases. In the case of the teenager, tienne sought and received Le Paill eurs affirmation that it was appropriate to cultivate this talent for geometry. Hencef orth, Blaise was given permission to pursue geometrical study, with the caveat that it wa s done only during his hours of recreation.11 In the later case of the roulet te, Blaises own renunciation of mathematical work was the restriction that had to be overcom e. When he heard of the solu tions that Pascal had generated regarding the roulette, th e duke de Roannez, like tienne befo re him, envisioned the possibilities of Pascals application to mathematics. In order to overcome th e restrictions that Pascal believed had come from a heavenly father, the duke appeal ed to that same authority as the reason to pursue the problem further: M[onsieur]. de Roannez asked him what he had in mind to do with that. My uncle told him that it had served as a remedy, and that he did not ask any other thing from it. M[onsieur]. de Roannez told him that there wa s indeed another use to make of it; that, in the design in which he was engaged of comba ting atheists, it was necessary to show them 11 Cependant il nemployait cet tude de la gomtrie que ses heures de rcration, ibid., 1:575-576. 292

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that he knew more than all in what re gards geometry and what is subject to demonstration.12 Based on such arguments, at least according to the early familial biographies, Pascal became convinced that an exception to the renunciati on of mathematics might be made. But the exception could only occur under certain conditions. His teenage geometrical studies were to be pursued only in his leisure time and his pursuit of the roulette question was only allowable if it had a religious motivation and goal. The similarities between the two stories of Pa scals geometrical disc overies suggest that early biographers saw the roulette problem as a reiteration of the virtues of Pascals childhood. The links between the two stories, and the ease with which the problem seems to have been solved, serve to strengthen the theme of childliken ess. Moreover, the involvement of Pascals friend the duke de Roannez highlights another recurring biographical element that suggests Blaises characterization as a child. The duke had little problem, so it seems, convincing his friend that there was a good religious reason to make an exception to renunciation, and that the mathematical question could be pursued for reli gious ends. Once again, Pascals motivations were assimilated to others goals and purposes. His talent was deployed by others; he became a tool in their hands. Pascals compliance with such possessivene ss provides further evidence of a pattern of submissiveness to others. Pascal as sumed the position of the child, willing to be led where he was told. 12 M. de Roannez lui demanda ce quil avait dessein de faire de cela. Mon oncle lui dit quil lui avait servi de remde, et quil ne lui demandait pas autre chose. M. de Roannez lui dit quil y avait bien un meilleur usage en faire; que, dans le dessein o il tait de combattre les ath es, il fallait leur montrer quil en savait plus queux tous en ce qui regarde la gomtrie et ce qui est sujet dmonstrat ion, Mmoire sur Pascal et sa famille, Mmoire sur Pascal et sa famille, Mesnard OC 1:1104. This account is from the me moir of Marguerite Prier, Gilbertes daughter and Blaises niece. 293

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Lingering Childhood Influences The source of the roulette pr oblem shows that, even in the material choice of such problems, Pascals childhood reasserted itself. If Gilbertes biography emphasizes that his consideration of the curve was by chance, she is also clear that his original exposure to the problem was through Mersenne. Pascal wrote two separate pieces during his period of engagement with the roulette problem th at dealt with the hi story of the curve.13 The Histoire de la Roulette clearly shows that Pascal was not mere ly concerned with the accumulation of mathematical knowledge; he also sought to ensure that the mathematical community in which he had been trained received the proper credit fo r their strides in examining the curve and uncovering a number of its pr operties and dimensions. In the Histoire de la Roulette Pascal carefully credits Mers enne with defining the curve.14 Mersenne initiated the study of the curve by proposing the problem of its measurement to Roberval, Galileo, and others.15 The result was Robervals di scovery that the area under the curve was three times that of its generating circ le, which triggered responses and contributions by Pierre de Fermat and Ren Descartes, those pillars of the French mathematical community. And while Italian mathematicians claimed original ity for the results of Torricelli in this area, 13 The first is entitled Histoire de la Roulette appele autrement La Trochode, ou La Cyclode, o lon rapporte par quels degrs on est arriv la connaissance de la nature de cette ligne and is dated 10 October 1658, Mesnard OC 4:214-224; this piece is duplicated in Latin, as Historia Trochoidis, Sive cycloidis, Gallice, La Roulette; in qua narratur quibus ad intimam illius lineau naturam cognoscendam perventum sit Mesnard OC 4:225-233. The second historical writing, especially emphasizing Robervals priority, is Suite de lHistoire de la Roulette, o lon voit le procd dune personne qui stait voulu attribuer linvention des problmes proposs sur ce sujet dated 12 December 1658, Mesnard OC 4:238-245; it is duplicated in Historiae Trochoidis sive Cycloidis continuato, in qua videre est cujusdam vidi machinamenta qui se autorem problematum super hac re propositorum erat professus Mesnard OC 4:246-252. 14 Le feu P. Mersenne, Minime, fut le premier qui la remarqua environ lan 1615, en considrant le roulement des roues: ce fut pourquoi il lappela La Roulette Histoire de la roulette, Mesnard OC 4:214. 15 Il proposa donc la recherche de la nature de cette ligne tous ceux de lEurope quil en crut capables, et entre autres Galilee, Histoire de la roulette, Mesnard OC 4:214. Mersenne proposed the problem to Roberval in 1634, according to this account, ibid., 4:215. 294

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Pascal assured his readers that both he and this specifically-defined curve originated with the Parisian mathematical community. The fact that Pa scal returned to the roulette in this his last mathematical work suggests the attraction that the values and content of his early experiences continued to have for him. Living in Paris, Pa scal maintained close personal connections with members of that learned circle, as noted in previous ch apters. It is almo st as if, even though dead, Mersenne continued to exercise a powerful force on Pascals work. Pascals historical account of the curve is in some ways a reflection on his own origins. In it, he evidences a dual understanding of his pa st that reflects the ca reers of Mersenne and Roberval, two of his mentors.16 Pascal portrays Mersenne as the quintessential proposer of problems and questions. Thr ough his prodigious ability to communicate and to maintain correspondence with others, he provided the occasion for several fine discoveries, which would never perhaps have been made if he had not excited the savants to them.17 In Pascals life, Mersennes well-defined questions continue to exert their power and to determine the selection of his work. On the other hand, Roberval remain ed Pascals master and possessor in matters of the theoretical and methodological values of mathema tics. It is probably owing to Roberval that Pascal remained so opposed to algebra during his lifetime, an issue that will be considered further in the next se ction of this chapter.18 Pascals linguistic choices also reflect th e double influence of Mersenne and Roberval. Mersenne had labeled the curve with the French word roulette His use of the vernacular 16 Pascal, Histoire de la roulette, Mesnard OC 4:214-224; and Pascal, Suite de lhistoire de la roulette, Mesnard OC 4:238-245. 17 [I]l a donn loccasion de plusieurs belles dcouvertes, qui peut-tre nau raient jamais t faites sil ny et excit les savants, ibid., 4:214. Pascals opinion of Mersenne is not unmixed praise. Pascal evidences some reserve: Mais encore quil net pas un pareil bonheur les resoudre, et que ce soit proprement en ceci que consiste tout lhonneur, il est vrai nantmoins quon lui a oblig ation, et quil a donn lo ccasion de moins quon lui a obligation, ibid. 295

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highlights his role as mediator of questions and his ability to comm unicate those questions simply and effectively.19 Roberval alone, however, called it a trochoid which is based on the Greek term for wheel.20 This choice communicates the prio rity that Roberv al placed on his ancient Greek predecessors, including Archim edes, whose construction-based geometrical method became the ruling standard for Pascals own work. Pascals double exposure to Mersenne and Roberval is suggest ed in his choice to compose both French and Latin versions of some of the works on the arithmetic triangle and the roulette. On the one hand, Pascals aim was in part to make the works convenient for those whose native language was not French. On the other, this choice reflects the influences of both Mersenne the communicator and Roberval the traditional scholar. So far, this chapters account of the circumstances surrounding Pascals work on the roulette has relied mainly on bi ographies written by hi s sister and his niece. The observations above are as much about his familys interpre tation of his work as they are about his own perceptions and those of the sa vant community. These biographers were part of the same religious community with which Blaise shared many attitudes about the devout life. Moreover, they write with the full knowledge of the fragme ntary religious musings that Pascal had penned during his last few years. It is therefore important to recognize that the narrative may be shaped in a way that presents a Pas cal entirely focused on religious devotion. Such a portrayal highlights the power of Pascals mind and his lack of desire for the usual recognition associated with mathematical discovery. This virtue is in contrast with the ambiguity that would be apparent if Pascal were presented as sincerely in terested in the solution of the problem itself. 19 This is not to say, of course, that Mersenne could not communicate effectively in Latin. He had a number of correspondents (e.g., Pierre Gassendi, Galileo, Athanasius Kircher) to whom he wrote in the traditional language of learning. He also wrote several works in Latin. 20 The Greek word is Mesnard OC 4:152. 296

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The diversionary character of th is work, as presented by Gilberte signals Pascals innocent way of pursuing it and communicates to her re aders his lack of intellectual hubris. Backdrop to Diversion: The Sluse-Pascal Correspondence While many accounts of the genesis of Pascals work on the roule tte still take this essential narrative at face value, Pascal scholars recogni ze that there are signifi cant difficulties involved with it. The clearest difficulty with viewing th e work on the roulette as a single, diversionary aberration from a normal renunciation of mathematic s is the indirect and direct correspondence between Pascal and a Ligeois canon and am ateur mathematician, Ren-Franois de Sluse.21 Beginning in late 1657, Sluse began a corresponden ce with Cosimo Brunetti, an Italian who had a lively interest in mathematics and was friendly with the Port-Royalists.22 In response to a problem sent by Sluse to Brunetti, the latter sought out Pascal who apparently solved this problem before providing two others of his own.23 Brunetti presented to Sluse these two problems of geometrical construc tion proposed, as Sluse states in a letter to Huygens, by a man. most ingenious, M. Pa scal, whom perhaps you know.24 These problems, which seek 21 Sluse was born 2 July 1622 and died 19 March 1685. He was a canon in Lige and a mathematician of some significant European connections, including Henry Oldenburrg of the Royal Society, A. R. Hall and M. Boas Hall, Sluse, Oldenburg and the Royal Society, in Ren-Franois de Sluse (1622-1685): Actes du Colloque International, Amay-Lige-Vis, 20-22 mars 1985 (Lige, 1986): 49-58. He also wr ote a mathematical work of note, entitled Mesolabum seu duae mediae proportionales inter extremas datas per circulum et par infinitas hyperbolas (Lige, 1668). For biographical information, see M. C. Le Paige, Correspondance de Ren-Franois de Sluse (Rome, 1885). 22 Brunetti had represented the interests of Port-Royal in Rome during the mid-1650s and was later to take a voyage to Martinique in order to scout the possibility of the settling of the religious group in the New World; see Susan Heller Anderson, Cosimo Brunetti: Three Relations of the West Indies in 1659-1660, Transactions of the American Philosophical Society 59 (1969): 1-49. 23 The documents written by Sluse were published in 1885 in Le Paige, Correspondance Kokiti Hara has pinpointed the problem that was probably proposed to Brunetti, and was subsequently addressed by Pascal, as identical with a problem that Sluse sent to Huygens 11 July 1657, Mesnard OC 4:91-92; Kokiti Hara, Gense prsume des Lettres de A. Dettonville, in Mthodes chez Pascal: actes du colloque tenu Clermont-Ferrand, 1013 juin 1976 ed. Jean Mesnard (Paris, 1979): 101-108. 24 proponente viro ingeniosissimo, Domino Pascal, quem fortasse noveris, Sluse to Christiaan Huygens (23 October 1657), Mesnard OC 4:96. Sluses corresponden ts also included Constantin and Christiaan Huygens; Samuel Sorbire; and Henry Oldenburg, Sluse, Correspondance de Sluse esp. 21 297

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constructions meeting certain conditions, are more closely related to Pascals early works on conic sections than to his subsequent work on the roulette.25 In fact, they had already been proposed by Pascal in 1654, in the piece addresse d to the Academiae parisiensis, and prior to Pascals Night of Fire. It seems that Pascal was not averse to pa ssing along his previous geometrical thoughts, though his fa mily suggests otherwise. He did not stop with a cursory interaction with Sluse. At Sl uses urging, he and Pascal bega n an extended correspondence. The contrast between the lives a nd careers of Sluse and Pascal is stark, particularly in their exposure to learned circles. Pascal had been id entified with his past a nd the savant community that represented it. The expect ations of his father, of Mers enne, and of Roberval, largely determined the course of his mathematical work and even resulted in periodically controlling behavior, as the Roberval-Descart es verbal duel demonstrates.26 As he got older and achieved some level of renown, he also began to be pursued by those, such as Sluse, for whom mathematics held a special place of interest. For Sluse, on the other hand, the tables were turned. Pascal had been surrounded by the culture of the learned; Sluse was deprived of it. Indeed, M. C. Le Paige observes Sluses nostalgia for the years of his youth and the time during which he had been able to devote himself to his studies without interruption.27 Sluse yearned for intellectual stimulation and, in particular, an outlet for his interest in mathematics. He had such a concern to nurture an atmosphere of 25 Specifically, the problem is stated thus: Being given two circles, A, C, and a line EF, to find a circle EBDF which, being tangent to the given circles, allows on the line given an arc capable of a given angle. The second problem is: Being given five lines, AG, BF, CK, DL, EH, to find a conic section which is tangent to the five given lines, addendum to Ren-Franois de Sluse to Christiaan Huygens, 23 October 1657, Mesnard OC 4:97-98. 26 See above, pp. 163-164. 27 See Sluse, Correspondance de Sluse 18-19. 298

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intellectual learning that his house was called by one a very fa mous university where all the divine and human arts flourished.28 Sluse had never experienced the kind of engagement and excitement that came with being involved in a renowned mathemati cal group. He sought connection with such an atmosphere by establishing a correspondence network.29 Given the opportunity to exchange letters with someone like Pascal, whose name was now well-know n, Sluse made every effort to present ideas to him. His letters to Pascal indicate that he did so in the hope of recei ving feedback, in the form of acknowledgement, correction, and the reciprocal, compensatory offering of discoveries. Pascal willingly corresponded with Sluse, albeit not without a ttempting to engage the canon in discussions regarding Jansenism and th e interpretation of biblical texts.30 His responsiveness to Sluses desire for correspondence is not uncharacter istic of Pascal, given the way he yielded to the requests and nudging of friends and family. Th e intermediacy of Brunetti, a faithful friend to Port-Royal, may have added to the compulsion that Pascal felt to communicate with the canon of Lige.31 The indirect correspondence betw een Pascal and Sluse throug h Brunetti consisted in an extended consideration of the first two of Pascals problems, disc ussion of related questions, and 28 Pouvait-on voir autrefois un esprit plus illumin que celui de Monseigneur votre autre frre, chanoine de Lige et prvot dHama, la maison duquel estoit comme une universit trs fameuse o tous les arts divins et humains fleurissaient, E. Mulkeman, Nouvelle pratique darithmtique (Lige, 1698), dedication, quoted in S. Bormans, Lettres indites de Ren Sluse, Bulletin de larchologique ligeois 6 (1863), 91. 4. 29 On the important role of correspondence for those living in provincial areas and for natural philosophers and mathematicians generally during the early modern period, s ee J. L. Pearl, The Role of Personal Correspondence, 106-113. 30 Sluses letters indicate, for example, that Pascal asked for the canons interp retation of a particular Hebrew word in a passage of Isaiah, Ren-Franois de Sluse to Blaise Pascal, 6 April 1658, Mesnard OC 4: 124. Furthermore, he offered to send Sluse des pices du temps, which Mesnard identifies as those concerning the Jesuits and Jansenists, Ren-Franois de Sluse, 29 June 1658, Mesnard OC 4: 129. 31 Mesnard argues, for his part, that correspondence with Sluse was attractive to Pascal because in him [i.e., Sluse] distinction and elegance, modesty and simplicity were allied to an exceptionally brilliant intelligence, to a mind with which Pascal could feel himself de plain-pied, Mesnard OC 4:118. 299

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the appropriate methods to use in solving them. By early 1658, Sluse and Pascal were writing directly to one another. Furthermore, the mathematical problems in the ensuing letters increasingly approached the issues with which Pas cals work on the roulette would grapple. In particular, the correspondence w ith Sluse considered questions of the volume of the solids created by rotations of curves about axes and iden tification of centers of gravity of these curves and solids. The exchange of le tters continued for the several months prior to Pascals initial proposal of the roulette problem. Pascals extended correspondence with Sluse suggests that his discovery of the measurement of the roulette curve involved a longer, more involved process than Gilberte describes in her narrative of mathematical diversion.32 Gilbertes and Marg urites accounts of Pascal emphasize the diverting natu re of the work and the lack of significant mental exercise required for the solution of the pr oblem. His correspondence and the Histoire de la roulette demonstrate that this work was also the result of a long proce ss of development beginning in Pascals earliest years. But the issue is not solved simply by accepting the latter narrative of Pascals work on the roulette and rejecting the fo rmer. The Sluse-Pascal correspondence, as well as other subsequent writings and le tters from this period in Pascals life, continue to represent an uncertain relationship between immediate discov ery and gradual solution, ease and difficulty. The virtues of childhood in tersect with the virtues of maturity in the stor y of Blaises work on the roulette. The balance of this chapter will aim to anal yze the events and texts relating to Pascals work on the roulette by focusing on the issues raised that relate to childlikeness and maturity. The key theme in what follows will be the re lationship between the la nguage of ease and the 32 Mesnards position is that the unforeseen occasion [which] made me think about geometry was probably the correspondence with Sluse, Histoire de la Roulette, OC 4: 219; Mesnard OC 4: 169. 300

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language of difficulty in Pascals writings, those of the particip ants in the contest, and other contemporary works. This chapter argues that ge ometry was considered both very difficult in some ways (requiring effort to solve problems) and quite ea sy in others (immediacy of perception and of following the rule s of calculation). This chapter will also explore the reactions of the learned community to Pascals contest, especially the way those reactions compare with their reaction to Huygens (both in his works and as a person). The concluding part of the chapter will attempt to show that Pascals tendency to secrecy, his continued rejection of an algebraic approach, his association with an uncouth indivi dual such as Roberval, and his isolation all contributed to his being marginalized as a serious contributor to the savant community. Paradox of Mathematical Ease and Difficulty Contemporary Background Anyone who has spent time studying mathem atics probably knows the frustration of having someone claim that a result follows clearly from a set of statements, or that one may easily see the result, when the inference seems qu ite problematic or opaque. The description of geometrical practice in the seve nteenth century likewise indicat es a seemingly contradictory relationship between the ease of mathematics and its difficulty. In the first place, ease and difficulty are rela ted to the different mathematical domains. Geometry, for example, was often considered to be extremely simple and able to be learned by young people. Bardin, whose book consid ers the characteristics of an honnte homme follows the opinion of Aristotle when he notes the appropriateness, for young men [ jeunes gens] of studying geometry as opposed to phys ics. This attitude stems in part, Bardin states, from this subjects status as stable and st atic, a representative of that which is unch anging in the universe, 301

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whereas physics is, by definition, concerned with what is dynamic. The entities of geometry, and thus the principles of its study, ar e more evident than those of physics: Physics being attached to a material that is subject to several changes has need of experience of several singular th ings in order to establish its truth. Thus its Principles are not well known except after having made a great progress.33 Pascal highlights the simplicity of geometrys principles in his little work De lesprit gomtrique. Pascal makes clear that these principles are accessible and comprehensible by everyone. Instead of needing a long explanation, they are built on concepts such as space and time that are intuitively natural to human beings. All people, he argues, agree on what the terms space and time refer to, even if they cannot articulate definitions in unequivocal language.34 The very inability to communicate these truths cl osely links them, in a way that Pascal does not articulate, to early childhood and its pre-li nguistic character. Pascal participates in a long tradition of valuing the simplicity and clarity of geometry. These notions are at the heart of the discussi on of ease and difficulty in the correspondence between Sluse and Pascal and in the roulette c ontest. Besides the simplicity of geometrys principles and its unchanging immateriality, geomet ry was also considered accessible because of its use of figures (i.e., its visuality). This c onnection with sensory perception remained in spite of the supposed alienation that philosophers of ten suggested between the physical world of perception and the conceptual world of geometr y. Antoine Arnauld, a key figure of Port-Royal during the middle of the seventeenth century, viewed geometry as a possible remedy to 33 [L]a Physique estant attach vne matiere sujette plusieurs changemens,a besoin de lexperience de plusieurs singulieres pour establir sa verit. De sorte que ses Prin cipes mesmes ne sont pas bien connus quaprs y auoir fait vn grand progrs, Bardin, Le lycee, 1, 384. Aristotles statement of this opinion is in Metaphysics 6. 34 Elle [geometry] ne dfinit aucune de ces choses, esp ace, temps, mouvement, nombre, galit, ni les semblables qui sont en grand nombre, parce que ces termes-l dsignent si naturellement les choses quils signifient ceux qui entendent la langue que lclaircissement quon en voudrait faire apporterait plus dobscurit que dinstruction, De lesprit gomtrique, Mesnard OC 3:396. He goes on to say, specifically of time, Qui le pourra dfinir? Et pourquoi lentreprendre, puisque tous les hommes conoivent ce quon veut dire en parlant de temps, sans quon le dsigne davantage?, ibid., 3:397. 302

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childhoods attachment to sensible objects, whic h is in harmony with the distinction between the material and immaterial mentioned above.35 For Arnauld and others visuality and sensory disconnection are bridged by the intellectual faculty known as imagination. The status of the imagination in the seve nteenth century was ambiguous, with Descartes and even Mersenne assigning it little value.36 But Jean-Robert Armogathe has also shown that imagination was, in the seventeenth century as it often is today, asso ciated with childhood.37 The visuality of geometry, and thus imagina tion, were extremely important for Pascal, who began his studies in projective geometry, whic h through techniques of perspective is closely related to the visual arts.38 Scholars such as Thomas More Harrington and Pierre Humbert have concurred on the importance of visuality for Pascal.39 Specifically, this aspect of geometrical work is contrasted with the methods of algebr a that were increasingly being espoused during the seventeenth century. 35 Of childhood attachment to the senses, Arnauld writes: il faut considerer que dans les premieres annes de lenfance lame de lhomme est comm e toute plonge & toute ensevelie dans les sens, & quelle na que des perceptions obscures & confuses des objets qui font impression su r son corps, Arnauld, preface to Nouveaux elemens n.p. And of the role of geometry in removing th ese attachments, he writes: entre les exercices humains qui peuvent le plus servir la diminer, & disposer mme lesprit recevoir les veritez chrestiennes avec moins dopposition & de dgoust, il semble quil ny en ait gueres de plus propre que ltude de la Geometrie. Car rien nest plus capable de dtacher lame de cette application aux sens, quune autre application un objet qui na rien dagreable selon les sens; & cest ce qui se rencontre parfaitement dans cette science, Nouveaux Elements de Gomtrie ibid. 36 Armogathe, Limagination de Mersenne Pascal, in Phantasia-imaginatio; V Colloquio internazionale, Roma 9-11 gennaio 1986 (Rome, 1988): 259-272. 37 In particular, he offers an example of Mersennes negative assocation of the imagination with children and women, Armogathe, L imagination 267. 38 Daniel C. Fouke argues that Pascals projective geom etry, with its emphasis on the visual imagination, as structuring the rest of his thought, including his physics and his religious writings, Fouke, Pascals physics, in Cambridge Companion to Pascal 99; Fouke gives a fully developed exploration of the development of Pascals method by way of projective geometry in his dissertation. 39 Humbert writes: Pascal is above all visual, Cet effrayant gnie 166. Another exploration of Pascals visuality is in Harrington, Pascal philosophe 303

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The turn toward algebra in the practice of European mathematics is often said to take decisive form in Descartes. But it was the culm ination of a long-standing search by Renaissance and early modern mathematicians for the anci ent method of analysis. Analysis was the method that was used to originally solve the probl em and was contrasted with synthesis, which is the way that the final proof is communicated to readers. In geometry, the synthetic proof was often linked to a geometrical c onstruction. The recovery of an cient mathematical texts during the late Middle Ages and Renaissance reiterated the talent that Greek geometers had for uncovering new mathematical results. The questi on for the later mathematicians was how the ancients attained their results, for their presen tation was in the form of deductive proofs which gave no hint to how they had been invented. Thus, early modern mathematicians searched for the ancient method of analysis. During the sixteenth century, one type of an alysis that proceeded by establishing and manipulating equations containing unknown quantities began to be explored. This method drew on earlier discoveries of Arabic algebraic te xts and was also known as specious analysis.40 One of the pioneers of the use of symbols in th e method of analysis was Franois de Vite, whose admiration by Mersenne was discussed in Chapter 2.41 Algebraic methods were quite well-developed by the time of Pascal, but Descar tes is often noted as one of the key links between geometry and algebra in the seventeenth century. It is Descartes, of course, who is credited with the articulation of a coordinate sy stem that would be used to analyze curves and 40 Franois de Vite uses the term specious to describe the use of species or forms such as for example are the letters of the alphabet, thus the use of x in modern algebra, Vite, La algbre nouuelle de Mr. de Vite trans. A. Vasset (Paris, 1630), 9. This work of Vites is a French translation of Vites Latin work. 41 The historical background of Vites work and some of the key points of his accomplishment are described in a prefatory letter to Vasset s translation, Vite, La algbre nouuelle n.p. [7ff]. 304

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create equations from them.42 Pascals unwillingness to adopt Descartes algebraic approach is one important aspect of the traditional contrast that has been made between him and Descartes.43 It is also one of the reasons that some mathematic ians have seen Pascal as out of the main stream of mathematical influence.44 One of the key drawbacks to th e use of algebraic analysis wa s the difficulty in maintaining clarity despite the use of symbols for quantities. This is especially evident when contrasted with the clarity of a classical, construction-base d geometry. Jean Boulenger admitted in his La gomtrie pratique, for example, that the first part of his work was a little difficult, because the demonstrations of Algebra are used there, to which there is some pain at first to accustom oneself.45 The reason for this difficulty, especial ly for the artisans to whom Boulenger addressed it, is that in algebra, which may treat magnitude in general, one cannot use figures in 42 A recent historical work on Descartess seminal cont ribution to a transformed understanding of the place of geometrical construction in mathematics, especially as it relates to algebraic analysis, is Henk J. M. Bos, Redefining Geometrical Exactness: Descartes Transformation of the Early Modern Concept of Construction (New York, 2001). Boss work stops its chronologi cal consideration with De scartess death in 1650 and therefore does not mention the roulette contest. tienne Pascal has two listings in the index, one of which should rather be a reference to Blaise, as it deals with the latters work on the arithmetic triangle, ibid., 209. 43 Pierre Humbert states it as a contrast between the anal ytical tendency of Descartes and the geometrical tendency of Desargues, of which Pascal will choose the latter, Humbert, Cet effrayant gnie 19, adding in another place that Pascal est un gomtre, non un algbriste, ibid., 166. In offering his critique of the accepted view of Pascals genius, Koyr cites the anti-algebraism of Pascal and acc epts the contrast between Descartess geometrical mind and Descartess algebraic one, Koyr, Pascal Savant, 264, 261. For her part, Dominique Descotes believes that this contrast of Koyrs is overstated. Pascal, she ar gues nignore pas lutilit du symbolisme mathmatique. Thus, the relationship between Pascal and algebra is more complex than previously admitted, but Descotes admits that Pascal admet les expressions abstraites, condition quelles ne versent pas dans le symbolism pur, Blaise Pascal, littrature et gomtrie 67, 71. 44 C. B. Boyer, for example, believes that it was Pas cals inability to accept Descar tess new approaches to mathematics that kept Pascal from fully developing the calculus prior to Leibniz and Newton, Boyer, Pascal: The Man and the Mathematician, Scripta Mathematica 26 (1963), 284, 304. 45 Jean Boulenger, preface to La geometrie pratique des lignes des superficies et des corps, ou nouuelle methode de toiser & arpenter auec la mesure ordinaire, sans que toutes fois il soit besoin de vser de fractions, ny de reductions en petites parties (Paris, 1630), n.p. One of Boulengers subtitle s labels it a Work useful to all architects, engineers, masons, surveyors, and other geometers, 305

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order to aid the imagination.46 Newton also acknowledged th at algebraic resolution of problems is ill-suited to be taught to the masses.47 [I]ts operations are complicated and excessively susceptible to errors, and can be understood by those learned in algebra alone.48 The method of resolution was suitable for those with mathematical maturity and legitimacy, the learned not the ignorant. Synthesis, by contrast, was for Boulenger th e appropriate means of presentation, in order to make the results as transparent, cl ear, and manifest to all as possible.49 Mersennes Christian Philosopher, in La vrit des sciences contre les septiques suggests a similar relationship between the two mathematical appro aches when he writes: let us pass on to Geometry, in which you will have more contentment than in this algebra, which is too thorny and too difficult for familiar discourses.50 By articulating a standard of familiar discourses, Mersenne is arguing that those not yet trained in mathematics would find the geometry based in constructions more accessible than algebra, the analytic approach, which involves the redu ction of geometrical figures to symbolic equations.51 Mathematical pedagogy nearly always be gan with a text that took a synthetic 46 Ibid. 47 Isaac Newton, First Essays at a MultiPartite Treatise on Geometry, in The Mathematical Papers of Isaac Newton, ed. D. T. Whiteside (Cambridge, 1967-1981), 7: 307. 48 Newton, Analysis and Synthesis: Newtons Declaration of their Application in the Principia in Mathematical Papers, 8: 450. 49 Ibid. 50 [P]assons la Geometrie, dans laquelle vous aurez plus de contentement quen cette algebre, qui est trop pineuse, & trop difficile pour les discours familiers, Mersenne, La vrit des sciences 716. The language of the thorny path is also used in Pascals description of hi s hard work in the creation of the arithmetic machine, see above, pp. 130, 179, 227. 51 It is ironic, of course, that Mersennes invocation fo r new Archimedeses is articulated in the context of a discussion of the contributions of the work of Anderson and Vite. Pascals rejection of the algebraic techniques of these two mathematicians means that he could not truly continue or perfect their work. For many a historian of 306

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approach, in the belief that a brief, logical presentation of ge ometry would create the best foundation.52 Despite apparent clarity, however, su ch a method also involves obscurity when it comes to dealing with particular problems.53 Sluses Language of Ease and Difficulty Pascals correspondence with Sluse highlight s a paradoxical relationship between method and relative difficulty in mathematics. From one side, the method of construction was portrayed as offering a relatively easy presentation of a ge ometrical result. From the other, algebra was represented as an easier, less ta xing mental process of discovery. It required less effort to produce more results. There are then two types of ease: an ease of representation and an ease of procedure. Pascal and Sluse disagreed on whether ease of procedure trumped simplicity of presentation. Pascal insisted on the necessity of a synthetic proof by construction, and in the ensuing contest concerning the roulette, would be careful to in sist on using only methods of pure geometry.54 Sluse, on the other hand, preferre d an analytic method that, in hi s eyes, sufficiently produced the mathematics, this also places Pascal ou tside the main current of mathematical thought in the second half of the seventeenth century. 52 F. W. Kokomoor surveyed a large number of seventeenth-century geometrical textbooks and found that they were generally synthetic in approach, though he believes that much of the teaching that was done may have been synthetic, Kokomoor, The Teaching of Elementa ry Geometry in the Seventeenth Century, Isis 11 (1928), 92-93. More generally, Comenius, the great educational theorist, writes: in dealing with any subject the analytical method should never be used exclusively; in fact, preponderance should rather be given to the synthetic method, John Amos Comenius, Great Didactic, in Comenius ed. and trans. M. W. Keatinge (New York, 1931), 105. 53 Kokomoor remarks this irony after having discussed the usefulness of synthesis for reasons of format and concision: On the other hand, there is very often an obscurity of explanation in connection with the brief and beautiful synthetic proof which leaves with the learner a sense of helplessness. The method of attack is missing, Kokomoor, Teaching of Elem entary Geometry, 93. 54 Lettre de A. Dettonville a Monsieur de Carcavy, in Lettres de A. Dettonville 12; Mesnard OC 4:426. 307

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results sought without th e great expenditure of time that was required to create a visually compelling general proof.55 Sluse himself recognized the deep divide that existed between himself and Pascal in his letter to Brunetti of December 1657: It is quite true that it displeases me first that I am not of the sentiment of M. Pascal regarding Analyse speciose of which I make a greater case than he.56 It is unfortunate that Brunettis letter to Sluse regarding Pascals views on the analytic method has not survived, since Pascal never gives a clear statement of his objections to it in his extant writings.57 On the other hand, Sluses justification of its usefulness and ease in solving problems is made clear in his letter to Brunetti. He continues: I daresay that the proofs that I have through it [analysis] are so great that not only do they persuade me, but they oblige me to make a ve ry great estimation of it. I avow that the return from it is very often difficult; but, because, when I have made exactly the analysis, I am as sure of the solution of the problem as if I had demonstrated it by synthesis, I do not care sometime to seek the easiest [ le plus aise] construction, being persuaded of what M. Pascal said on another occasion: non esse par labori prmium .58 Sluse was prepared to concede that a proof by construction was le plus aise; it was the easiest, the most convenient, or the most accessible to the reader. It was the ease of presentation, 55 Mesnard emphasizes this difference between Pascal and Sl use, claiming that Sluses use of the methods of pure geometry were in deference to his correspondent. In commenting on one letter from Sluse to Pascal, he writes: This piece shows that Sluse spontaneously retreats to analysis. If he makes discreet use of it in his letters destined for Pascal, it is in order to submit himself to the preferences of his correspondent, Mesnard OC 4:114, n. 1. 56 Il est bien vrai quil me dplat que dabord je ne suis pas du sentiment de M. Pascal touchant l Analyse speciose, de laquelle je fais plus grand cas que lui, Ren-Fran ois de Sluse to Cosimo Brunetti, December 1657, Mesnard OC 4:103. 57 Pascal mentions the method of analysis in his De lesprit gomtrique: La gomtrie, qui excelle en ces trois genres, a expliqu lart de dcouvrir les vrits inconnus; et cest ce quelle appelle analyse, et dont il serait inutile de discourir aprs tant dexcellents ouvrages qui ont t faits, De lesprit gomtrique, Mesnard OC 3:390. 58 [J]ose dire que les preuves que jen ai sont si grandes que non seulement elles me persuadent, mais elles mobligent den faire une estime bien grande. Javoue que le retour en est bien souvent difficile; mais, parce que, quand jai fait exactement lanal yse, je suis aussi sr de la solution du problme comme si je leusse dmontr par synthse, je ne me soucie pas quelquefois den chercher la construction la plus aise, me persuadant ce quen une autre occasion M. Pascal dit: non esse par labori prmium Sluse to Brunetti, December 1657, Mesnard OC :103. 308

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not of procedure. In contrast to this ease was the great difficu lty of producing such a proof. Sluse used Pascals Latin phrase (it is not the re sult of a first attempt) to emphasize that he did not have the time for a proof by construction. The proofs of analysis, Sluse argued, have a persuasive power that would be sufficient for the dismissal of the need for the geometrical proofs that pure geometricians like Pa scal would require. Furthermor e, he was convinced that a creation of a construction from his analytical so lution (le retour) would be possible because of his belief in the efficacy of analytic met hod. Translating his solutions into synthetic constructions was but a matter of time and effort. In his correspondence with Brune tti and Huygens, Sluse also ma de use of the language of difficulty and ease. In a letter to Huygens, upon the reception of Pascals problems, he writes of the first that its solution posed no difficult y, although it presents a construction a little complicated,59 an opinion echoed in a letter to Brunetti, where Sluse writes: Having made a little rough sketch of analysis, I recognized th at the problem was plane, and that the resolution of it was not difficult, but that the constr uction of it would be a little long and muddled.60 In the first place, then, Sluse attempts to legitimate himself as a mathematician by professing the simplicity of the solution of the problem. The imp lication of his letters is that this kind of solution is the most interesting and important and that his ease in perceiving it adequately demonstrated his mathematical accomplishment. Secondly, and concomitantly, Sluse implied that the difficulty of le retour after the little rough sketch of analysis was basically a matter 59 nec difficilis solutionis, licet ostendat paulo intricatiorem, Ren-Franois de Sluse to Christiaan Huygens, 23 October 1657, Mesnard OC 4:96. Sluse also puns on the Latin word planum : thus when he describes the solution as planum (reperi planum esse), he is stating that the locus of the points is a plane and that it is clear or obvious, ibid. 60 [A]yant fait un petit griffonnement danalyse, je reconnus que le problme tait plan, et que la resolution nen tait pas difficile, mais que la construction en serait un peu longue et embrouille, Ren-Franois de Sluse to Cosimo Brunetti, October 1657, Mesnard, OC 4:100 309

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of overcoming technical complications. The time and effort would result in a proof that was easiest [ le plus aise ] but not one that was substantially mo re convincing. Sluse suggested that it was not geometrical inferiority that has prevented him from giving thes e synthetic proofs, but because I do not at this time have the leisure due to the multitude of affairs which overwhelm me.61 Sluse blamed not his lack of skill, but Brunettis lack of timeliness in supplying the problems, for his lack of thoroughness. He writes scoldingly to Brunetti: If they had been sent to me when I had asked for them, I would have tried to give satisfa ction to him [Pascal].62 As it is, he claims, he only had time to consider one case, and to give a brief construction based upon this one example.63 Nevertheless, he claims that based on this simplification all intelligent persons will easily see th at I have the universal construction.64 The matter of generalizing from this single cas e to the universal, Sluse sugges ts, is not the essence of the problem. It is permissible, on this view, to mi nimize its importance, esp ecially in light of his many duties as a canon, which do not permit me to apply my mind to such niceties [ gentillesses ].65 61 Sluse to Brunetti, December 1657, Mesnard OC 4:106; Sluse to Brunetti, October 1657, Mesnard OC 1: 100. This is reiterated later in the same letter: lembarras continuel des affaires qui se sont prsentes et multiplies au triple depuis que vous navez t ici ne me donne pas le temps dy penser pour le prsent, Sluse to Brunetti, October 1657, Mesnard OC 4:100. For another example of Sluses decrying of the lack of leisure time, see Sluse to Brunetti, December 1657, Mesnard OC 4:108: Le porisme des anciens la description des sections coniques me semble trs joli, mais je nai pas le loisir de les examiner pour cette heure. 62 [S]ils meussent t envoys quand je les ai demand s, jaurais tch de lui donner satisfaction, Sluse to Brunetti, October 1657, Mesnard OC 4:100. 63 [J]ai choisi un cas seulement entre plusieurs qui sont dans le problme; et pour trouver une construction plus brve, je lai appliqu aux nombres, ibid. 64 [T]outes les personnes intelligentes verront aisment que jai la construction universelle, ibid. 65 ne me permettent pas dappliquer mon esprit semblables gentillesses, ibid. 310

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The characterization of particular geometrical efforts as mere gentillesses would have probably been quite amenable to Pascal. It is in agreement with hi s general evaluation of application to non-religious matters during the post-Night of Fire period as diversionary. Within the context of a deliberate applic ation to geometry, even if it were primarily a leisure pursuit, Pascal insisted in his articulat ion of problems that the synthetic solution was not simply an appendix to an algebraic solution; it constitute d the solutions substance. Sluse acknowledged this insistence of the Parisian mathematician when he wrote that Pascal does not simply want the analytic solution, but also a nice [ gentille ] and easy [ facile ] construction.66 Sluses portrayal of Pascals attitude toward synthesis and specious analysis makes clear the dual nature of synthesis as both difficult ( difficile embrouille ) and easy ( facile aise ). But this duality also points to the more general a nd widespread double-portr ayal of savant work, particularly in mathematics. On the one hand, Slus e, Pascal, and others wa nted to highlight, just as did Pascals earliest biographers, the im mediacy, simplicity, and ease of his solution to problems. Based on such portrayals, the prob lems could be associated with a leisurely, recreational, and hence childlike activity. On the other hand, just as Pascal claims that his arithmetic machine is not the first effect of the imagination that I have had on this subject, 67 and that his experiments in physics cost him much expense, pa in, and time, it was important that the problems be recognized as suffici ently demanding in order to highlight the accomplishment that their solution represented.68 66 [L]e susdit Monsieur ne veut pas la solution simplement analytique, mais quil veut aussi une construction gentille et facile, laquelle je nai pas pour cette heure le loisir de la chercher, Slus e to Brunetti, December 1657, Mesnard OC 4:106. 67 [L]a forme de linstrument, en ltat o il est present, nest pas le premier effet de limagination que jai eue sur ce sujet, Avis, Mesnard OC 2:340. 68 Pascal, Experiences nouvelles Au lecteur, n.p. [5]. 311

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It is already clear that, in his correspondence with Brunetti and Huygens, Sluse desired to communicate the immediacy of his own comprehens ion, especially of Pascals first problem. This is true, Sluse claims, even if he does not have the time to find the full, geometrical demonstration. Likewise, regardi ng a second problem, he writes: The resolution of it is long, but I do not believe it so difficult.69 In this he is echoed by Huyge ns, who says that it is not difficult to show how to reveal the equation; but the calculation is entirely too much work.70 Sometimes, both Sluse and Huygens suggest the work is not worth the reward. As a provincial amateur, Sluse stressed how easily he had percei ved the crux of the geometrical matter, probably because of his desi re to legitimate himself in the eyes of the mathematicians whose correspondence he craves. It was his way of expressing the kind of mathematical aptitude that tienne Pascal di scovered through his young sons playful acquisition of a Euclidean geometrical theorem. If he were able to show, despite the limitations on his time, that he had been able to penetrate deeply in to the problems supplied him, he might gain the respect of savant geometers such as Pascal and Huygens.71 To be sure, Sluse was also not overly bold. Despite his previous statement to Brunetti that the solution of Pascals problem of the five lines is not so difficult, Sluse writes just two months later: For that which concerns the other problem of the five given lines, I do not know who has told him that I judge it easy. I do not believe to have written you any such thing, since I 69 La rsolution en est longue, mais pourtant je ne la crois pas si difficile, Sluse to Brunetti, October 1657, Mesnard OC 4:100. 70 At neque in altero illo de coni sectione quinque da tas positione lineas contingente, difficile est ostendere quomodo ad aequationem perveniatur, sed calculus nimii profecto laboris, Christiaan Huygens toRen-Franois de Sluse, 2 November 1657, Mesnard OC 4:99. 71 He seems to have found a place of respect with Huygens, who corres ponded with him until 1668, Sluse, Correspondance de Ren-Franois de Sluse 455. He also communicated with Samuel Sorbire, Henry Oldenburg, and John Wallis. 312

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perceived then that one could come with diffi culty to the equation and that after one will have found it, the construction of it would be very involved.72 Sluses about-face in his perspective on the ease of the problem was likely prompted by a response from Pascal, who had read or heard about Sluses words. Not wanting to alienate the renowned Pascal, Sluse backpedale d and took a conciliatory tone. The canons cautious approach to statements of ease continued with the initiati on of the direct correspondence between Pascal and Sluse. But he was encouraged and emboldened by a number of observations and methods that he was achieving, including a means by which to draw tangents to a number of different types of curves Sluse was thus ready, in a letter of June 1658, to question Pascals evaluation of the difficulty of a particular problem. He writes with a combination of confidence and deference: The other [problem], that you perhaps believe mo re difficult, has seemed to me very easy in the manner in which it is proposed, if however I have indeed understood it, for which I ask you to enlighten me through yours.73 As the correspondence continued, and with the proposal of the contes t of the roulette anonymously drawn up by Pascal, Sluse asserted th e effortlessness of solution of one of the problems proposed. Likely unaware that he addressed the problem s author, Sluse confidently asserted to Pascal in a letter wr itten 6 July 1658, that the thing is very easy. Considered in the way that he proposed, Sluse continues, one will not meet more di fficulties in their measures and their parts than in that of a triangle.74 72 Pour ce qui est de lautre problme de cinq lignes donnes, je ne sais pas qui lui a dit que je lestime facile. Je ne crois pas de vous avoir crit une telle chose, puisque je maperus alors quon pouvait venir difficilement lquationet quaprs quon laurait trouve, la constructi on en serait beaucoup embrouille, Sluse to Brunetti, December 1657, Mesnard OC 4:106. 73 Lautre, que vous croyez peut-tre plus difficile, ma se mbl trs facile en la ma nire quil est propos, si toutefois je lai bien compris, de quoi je vous prie mclaircir par les vtres, Sluse to B. Pascal, 29 June 1658, Mesnard OC 4:128. 74 Et la chose est trs facile; il faut seulement considrer lorigine des cyclodes dautre faon que lon ne fait, car alors on ne rencontrera pas plus de difficults leurs mesures et de leurs parties qu celle dun triangle, Ren313

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Sluses use of the language of ease and difficulty in hi s correspondence with Pascal suggests that it was a rhetorical attempt to highlight the clarity and penetration of his mind that would class him among the learned. Because he c onsidered himself limited with respect to the time and effort he was able to give to these ma thematical problems, he tried to emphasize his childlike virtues and natural talents associated with mathematics, such as immediacy of perception. He repeatedly states the ease with which problems may be solved, particularly as they relate to other questions that he had pr eviously considered. But he also continually considered himself as under the control of his offi cial activities as canon. In this way, Sluse may be seen as a foil for Pascal, whos e own notions of relative and absolute difficulty in his writings on the roulette are in significant conflict with the opinions of the Ligeois mathematician. The following section shows that the dialogue betwee n the virtues of child like simplicity and the virtues of maturity, wisdom, and hard work conti nued in the work of the roulette. It will argue that by expressing the language of simplicity and co mplexity, Pascals language in the contest of the roulette drew on ideas that were linked with early modern notions of childlikeness and maturity. In particular, the sensory immediacy of construction -based geometry that Pascal preferred and Pascals portrayal of the diversionary status of his discoveries were set alongside his insistence on ultimate diffi culty of the problems that coul d only be solved by the truly learned. Pascals Language of Ease and Difficulty and the Roulette Pascals anonymous announcement of the roulette contest opened by affirming the difficulty of problems whose solution woul d merit reward: we come upon propositions Franois de Sluse to Blaise Pascal, 6 July 1658, Mesnard OC 4:267. Sluse seeks to justify this assertion in a later letter to Pascal: Ce nest pas sans raison que vous avez t surpris de ce queje vous ai c rit davoir trouv la mesure des cyclodeset de leurs parties avec la mme facilit que celle dun triangle, car mtant peut-tre fort mal expliqu, je vous ai donn sujet de croire quil y et du mystre o il ny en a point, comme vous allez voir par cette figure, Ren Franois de Sluse to Blaise Pascal, 2 August 1658, Mesnard OC 4:269. 314

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sufficiently strenuous and difficult, as it seems to us.75 That he would even think of proposing a contest would already suggest the challenge of sk ill, since it is supposed that not all those who dabbled in geometry could solve them. The early biography by Pascals niece, Margurite Prier, suggests that the duke de Roannez encouraged the contest to demonstrate that a devout mind could successfully deal with complex and diffi cult problems as well as any other savant. It was important that it required significant aptitude and effort to accomplish this goal. Other evidence also suggests that the very difficulty of the problem prompted Pascals decision to initiate the contest. In his Histoire de la Roulette Pascal writes that he had devised a method for finding centers of grav ities of curves, surfaces, and so lids, from which few things could escape.76 He firmly believed that he had developed a powerful, gene ralized tool; but it remained to test this tool in order to know whether it delivered as promised. From the memories of his own experien ces and his knowledge of the Parisian mathematical community, Pascals mind lit on a curve that had exercised the mind and skill of Roberval and others. It was pr ecisely in order to make the te st of it [his new method] on a subject more difficult that Pascal began to consider the unsolved measurements of the roulette.77 Using his method on this curve, he obtained the results for which he had hoped, results which appeared to me so difficult by any other way.78 But was this problem of the roulette of such difficulty that it would prove the power of his method? Pascals contest was 75 in propositiones satis arduas ac difficiles, ut nobis visu m est, incidimus, Pascal, First circular letter, Mesnard OC 4:189. 76 [J]e me formai des mthodes pour la dimension et les centres de gravit des solides, des surfaces planes et courbes, et des lignes courbes, auxquelles il me sembla que peu de choses pourraient chapper, Histoire de la roulette, Mesnard OC 4:219. 77 [P]our en faire lessai sur un sujet des plus difficiles, je me proposai ce qui restait connatre de la nature de cette ligne, ibid. 78 Ibid. 315

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specifically designed to determine i f they [the roulette problems] we re in fact as [difficult] as I had imagined, and therefore to test the extent of his methodological accomplishment.79 Pascal ostensibly chose the roulette curv e as the basis for the contest because he remembered the difficulty that it had posed for th ose with whom he had his first mathematical apprenticeship. In his Histoire de la roulette Pascal traces the at tempts by a number of mathematical savants to discover the measurements of the curve. In so doing, he implicitly and explicitly asserts its challenges. Implicitly, the long years of research that Europes greatest mathematical minds had expended on its explorat ion show its full arduousness. It had become a classic geometrical puzzler of the seventeenth century and had been pursued by Roberval, Galileo, Fermat, Desargues, and Beaugrand, all re nowned mathematicians. Even for these, the work was not easy. When, for example, Mersenne initially described the curve and proposed its research to the savants of Europe, including Ga lileo, none could succeed in it, and [they] despaired of it.80 Only Roberval, that great professor of mathematics, succeeded in finding the measurement of the area under the curve. Furthe r on in the history, Pascal again clearly states the quality of the problems associated with th is curve when he describes Torricellis failed attempt to find the volume of the solid engendered by the roulette rotate d around its base: it is there that he found well the diffi culty; for it is a problem of a high, long, and painful research.81 Pascals description of the difficulty of th e roulette problems was another way of saying that its solution required penetrating vision a nd force that comes from a natural talent, as 79 Je commenai par les centres des gravit des solides et des demi-solides, que je trouvai par ma mthode, et qui me parurent si difficiles par toute autre voie que, pour savoir sils ltaient en effet autant que je me ltais imagin, je me rsolus den proposer la recherche tous les gomtres, et mme avec des prix, ibid. 80 Mais aucun ny put russir, et tous en dsesprrent, ibid., 4:214. 81 Mais ce fut l quil trouva bien la difficult; car cest un problmdune haute, longue et pnible recherche, ibid., 4:218. Cf. Pascals language regarding the experiments on the void, above, pp. 179, 211-212. 316

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well as masterful expertise.82 Pascal made the claim, in his Numeri figurati seu ordines numerici that the key skill of the geometer was the multiplication of propositions and putting them to different uses. For those who cannot do th is, he continues, the cultivation of geometry will be thankless.83 What is more, whereas natural tale nts may seem to be the key to the qualities of mind, Pascal reiterates in Numeri figurati that the skill of geometry is not given, but is assisted.84 In other words, Pascal suggested that his own ability to uncover new methods of finding the measurements of curves was due to th e hard work of the mature mathematician, not the immediate perceptions of the child. In the roulette problem, Pascal made a cl ear distinction between the kind of arduousness involved in finding a method, like hi s, and difficulties that are merely time-consuming. Lesser minds, those trained in the habits of calculation, could tackle the latter challenge; only the truly learned could achieve the former. Pascals correspondence with Sluse provided him with a good example of one whose self-proclaimed main obstacle was his duty-la den position as canon.85 The design of Pascals roulette contest, however, sought to clearly distinguish successful results 82 Pascal suggests in his second circulated letter that it was his desire to reward a particular application of mind: that he characterizes as perspicacitate ingenii and viribus ingenii, Second letter circulated by Pascal to the learned geometers of Europe (July 1658) (henceforth Second circular letter), Mesnard OC 4: 196. The date for this letter is inferred by Mesnard from Boulliaus transm ittal of it to Huygens on 19 July 1658, Mesnard OC 4: 255. In Pascals first circular letter, he had suggested a similar characterization by highlighting that neither vis ingenii nor peritia artificis were necessary for pe rforming the technical calculations, as op posed to the difficult work of setting forth a method, First circular letter, Mesnard OC 4:191. 83 Cui versatile hoc deest ingenium ingratus erit geom etriae cultus, Numeri figurati seu ordines numerici, Mesnard OC 2:1203. M. L. Jones uses the notion of multiplying enunciation as the key to viewing Pascals thought on geometry as a spiritual exercise. See above, pp. 221-224, and Jones, The Good Life in the Scientific Revolution For the importance of geometry as a way of teaching one to think in the work of the Abb Fleury, see Frederick B. Artz, The Development of Technical Education in France, 1500-1800 (Cambridge, MA, 1966), 16. 84 non datur sed juvatur, Numeri figurati seu ordines numerici, Mesnard OC 2:1203. 85 By contrast, some have suggested that Copernicus had plenty of time for mathematical and astronomical work precisely because of his position as a canon. A brief description of the duties of a canon in Copernicuss situation is in Hermann Kesten, Copernicus and His World (New York, 1945), 72. Kesten sugg ests that, as a canon, Copernicus would not even have been expected to be in residence for more than half of the year. 317

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of method from the finishing work of calculation. He did not want to discriminate against those who, like Sluse, did not have a great deal of leisure time. Pascals first circular letter for the contest thus allows for an abbreviated solution to the problem. As the anonymous proposer of the contest, Pascal requests: 1) a demonstration, in the manner of the ancients [i.e., synthe sis/construction] or through the theory of indivisibles, that the given pieces of data that the problems suppose are sufficient for the calculation; or, 2) a full calculation of two specified cases.86 These options were slightly modified in the second circular letter, with Pascal specifying one particular case whose proper calculation was necessary to lay claim to the prize.87 What does not change from one ci rcular letter to the other is that Pascal expects that, whatever abbreviations of demonstration or re duction to a single calc ulation are made, they would be followed, in time, by a full demonstrat ion. The contestant must make a claim to Carcavy, the administrator of the contest, that he possesses the demonstration of the questions posed and, if only a calculation is given, that the person must be ready to demonstrate in their entirety all these things at the signal of M. de Carcavy.88 Pascal explains that the sending of a calculation simply signals a persons eligibility for the prize within the time set for the contest, as Pascal further clarifies in the th ird circular letter. He no doubt be lieved that such a calculation could only be accomplished by someone who was in possession of a perfect and geometrical 86 vel more antiquorum, vel certe per doctrinam indivisibilium, First circular letter, Mesnard OC 4:190. 87 Pascal, Second circular letter, Mesnard OC 4:197. 88 The Latin full text reads: Qui publico instrumento, intra praestitutum tempus, illustrissimo domino de Carcavi significaverit eorum quae quaesita sunt demonstratione m penes se habere; et aut ipsammet demonstrationem quantumvis compendiosam ad ipsum miserit; aut si cartae mandare nondum per o tium licuerit, saltem ad confirmandam suae assertionis veritatem, casus quem m ox designabimus calculum dederit; seque paratum esse professus fuerit omnia omnino demonstrare ad ipsius D. de Carcavi nutum, hunc nobis satisfecisse declaramus, First circular letter, Mesnard OC 4:196. Mesnard writes: Ds lorigine, Pascal entendait certainement rserver les prix ceux qui apporteraient une solution complte, ou, comme il le prcisait trs clairement, les principes de cette solution. Rpondre aux seules premires questions ne pouvait ouvrir droit la rcompense, Mesnard OC 4:174. 318

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demonstration.89 The Jesuit Father Lalouvre, however, se nt a faulty calculat ion for the contest but still expected to claim the pr ize, saying that he had simply made a mistake. But for Pascal, the difficulty of the calculation was not the centra l problem to be solved. There was no backing down from the truly difficult work, which was a generalized construc tion that would make accurate calculations possible. The importance of the difficulty of the probl em to the purpose and effectiveness of the contest became even more tran sparent with the pseudonymous publication of Pascals results in his Lettres de A. Dettonville.90 The very first article in the book is a letter from Carcavy to Monsieur Dettonville, requesting the mathematical results that are then articulated in the remainder of the book.91 In the letter, which sets th e significance of the work, Carcavy specifically pinpoints a particular set of problems (i.e., th e determination of th e centers of gravity of the surfaces of the solids produced by ro tation around the axis and the base) as most important, precisely because they are difficult ra ther than easy. For Carcavy, they appear so difficult by their mere enunciation.92 But he goes further: [W]hen I had in fact considered them a little it seemed to me, accord ing to the little light that I had concerning it, that the least that one could say of it was that there is nothing more 89 une dmonstration parfaite et gomtrique, Pascal, Third letter circulated to the learned geometers of Europe (7 October 1658), Mesnard OC 4:202. 90 Lettres de A. Dettonville contenant Quelques-vnes de ses Inuentions de Geometrie (Paris: Guillaume Desprez, 1659; reprint London, 1966). This publication is included in Mesnard OC 4:407-565. 91 The letter prefaces Pascals Lettres de A. Dettonville which is a set of four letters with accompanying treatises. The parts of the work include Lettre de A. Dettonville a Monsieur de Carcavy (Paris, 1658); Lettre de A. Dettonville a Monsieur de Sluze Chanoine de la Cathedrale du Liege (Paris, 1658); Lettre de A. Dettonville a Monsieur A. D. D. S. (Paris, 1658); and Lettre de A. Dettonville a Monsieur Hugguens de Zulichem (Paris, 1659). 92 ils paraissent si difficiles par la seule nonciation, Lettre de Monsieur de Carcavy a Monsieur Dettonville, in Lettres de A. Dettonville n.p. [1]; Mesnard OC 4:410. 319

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hidden that has been solved in all of geometry, either by the ancients, or by the moderns, and I was not alone in this sentiment.93 The declaration is extreme! According to Car cavy, Dettonville is consider ing something that is so geometrically obscure that even the discoveries of the ancients could not match it. It is an astonishing statement for one of the missionaries of Mersennes group of geometers, which so valued what was received from Greek mathematics. When Carcavy expands on these thoughts, he vaguely suggests Dettonv illes kinship to Archimedes, and even the way in which he surpasses the great ancient geometer: For even though, for greatness of genius, none of the ancients has perhaps surpassed Archimedes, it is certain nonetheless that, for th e difficulty of the prob lems, those of today surpass his by a great deal, as is seen by the comparison of the entirely uniform figures that he has considered to those that one consider s now, and especially the roulette and its solids, the escalier the cylindrical triangles, and othe r surfaces and solids of which you have discovered the properties.94 The above passage, with its suggestion of the way in which moderns surpass the ancients, hearkens back to Pascals statements regarding the status of moderns as adults in comparison with the childhood associated with the ancients. It suggests that although it may be difficult to claim that anyone has as much penetration of mind as the anci ent mathematicians and natural philosophers, contemporary mathematicians coul d build upon their accomplishments. The child (i.e., the ancients) naturally had first to tackle the less comple x, more obvious, and more regular problems. This is the case even if the talent of the child is extremely evident (and seventeenthcentury geometers certainly believed in the brilli ance of the ancients). The modern geometer, 93 [Q]uand je les eus un peu considrs en effet, il me sembla, selon le peu de lumire que jen ai, que le moins quon en pouvait dire tait quil navait t resolu rien de plus cach dans toute la gomtrie, soit par les anciens, soit par les modernes, et je ne fus pas seul dans ce sentiment, ibid. 94 Car, encore que, pour la grandeur du gnie, aucun de s anciens nait peut-tre surpa ss Archimde, il est certain nanmoins que,pour la difficult des problmes, ceux daujourdhui surpassent de beaucoup les siens, comme il se voit par la comparaison des figures toutes uniformes qu il a consideres celles que lon considre maintenant, et surtout la roulette et ses solides, lescalier, aux tr iangles cylindriques, et aux au tres surfaces et solides dont vous avez dcouvert les proprits, ibid., 4:411. 320

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having benefited from the maturation begun by the ancients, explores (as a full-fledged adult) problems that are even more hidden and have co mplex irregular characteristics. These are produced by multiple motions: e.g., the roule tte, which is defined by two simultaneous movements; and the escalier which is a type of spiral that in cludes both a circular and a vertical component. Insofar as Dettonville solved a more difficult (or at least more hidden) problem than any of those considered by the great Archimedes, he had pr oven himself to have achieved greater things than the mathematician from Syracuse. For Carcavy, the difficulty of the roulette problem was further attested by the ultimate failure of others to find the solutions. Dettonville had implied that he was more mature in learning than other mathematicians of his time, exploring the obscure reac hes of the geometrical unknown. Carcavy, as the previous passage showed, believed that Dettonville bore characteristics as impressive as the ancients. Perhaps he would have concurred in giving Pascal the label of a new Archimedes who w ill bring mathematics to its last perfection.95 Pascals reasons for proposing the contest, then, are closely rela ted to the perceived difficulty of the problems, as recognized by Pa scal, Carcavy, and others Frans van Schooten (1615-1660), Huygenss teacher and me ntor, wrote to his pupil that in order to find the solutions sought by the anonymous author of the contest one would have to be a man thoroughly at leisure, as well as unrestrained, in order to solve them within the determined time.96 Moreover, 95 Mersenne, La verit des sciences 750. See above, p. 67. 96 homini penitus ocioso atque libero competat, ut illa intra praestitutum tempus solvat, Frans van Schooten to Christiaan Huygens, 22 July 1658, Mesnard OC 4:257. Van Schooten was himself the son of an illustrious father, taking over his fathers chair in mathematics at Leiden. He is perhaps most well-known for his popularization of the work of Descartes. It was in his capacity as professor of mathematics that van Schooten met Christiaan and his brother. Van Schooten was to remain one of Huygenss key correspondents, Edwin van Meerkerk, The Correspondence Network of Christiaan Huygens (1629-1695), in Les grands intermdiaires culturels de la Rpublique des Lettres: tudes de rseaux de correspondances du XVIe au XVIIIe sicles ed. Christiane BerkvensStevelinck, Hans Bots, and Jens Hseler (Paris, 2005), 214, 216, 220, 223. On the relationship between Schooten and Huygens, see Frankfourt and Frenk, Christiaan Huygens 35-36. 321

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he argues that the slight chance of winning the prize is not worth th e effort that is necessary, an echo of Sluses earlier comments to Brunetti ab out the difficulty of the constructions Pascal sought.97 Huygens communicates similar thoughts to Boulliau, who had ostensibly avoided considering the roulette because of time constraints. This young Archimedes questions the very possibility of the solutions that are sought by the anonymous mathematician: They seem to me so difficult for the most pa rt that I strongly doubt if even he who has proposed them could solve them all, and we w ould like to know that he has assured us of it in this publication.98 A month and a half later, Huygens wrote lett ers to Sluse and to Wallis, in which he once again communicated questions concerning the possi bility of solution of solving all of the problems.99 The reply from Wallis suggests that both he and Christopher Wren agreed: in any case, we have solved most of them. [W]e dou bt, however, that all of th ese things are able to be solved in a way other than through geometrical approximation.100 It was precisely the sort of reaction, as Mesnard points out for which Pascal was hoping.101 Pascal had portrayed the process of discovery of the means of solution to the problems as especially difficult. He believed, however, that the proper presentation of the solutions would 97 [L]auteur se glorifiant mme de produire de plus grandes choses encore, il ny a pas de raison, mis part un lger et douteux espoir de rcompense, de se charger la lgre (du moins mon jugement) du travail que cela requiert, Schooten to Christ. Huygens, 22 July 1658, Mesnard OC 4:257. 98 Ils me semblent si difficiles pour la pluspart que je doubte fort si celuy mesme qui les a proposez les pourroit tous resoudre, et voudrois bien quil nous en eust assur dans ce mesme imprim, Draft of letter from Christiaan Huygens to Ismal Boulliau, 25 July 1658, Huygens OC 2:200. Huygens goes on to ask of Boulliau si vous me pouuez que assurer de sa part que ce quil nous propose est chose qui soit desia trouue, ou du moins trouuable, ibid., 201. Mesnard states that Huygenss doubt about the solvability of the problems is a measure of le science du temps and suggests that, because of his little enthusiasm for the use of indivisibles in mathematics, Huygens se trouvait mal arm devant de tels problmes, Mesnard OC 4:255. 99 Draft, Christiaan Huygens to Ren-Franois de Sluse, 6 September 1658, Mesnard OC 4:282; draft, Christiaan Huygens to John Wallis, 6 September 1658, Mesnard OC 4:316. 100 pleraque saltem solvimus ; an omnia tamen possint aliter quam per approximationem geometrice solvi dubitavimus, Wallis to Christ. Huygens, 1 January 1659, Mesnard, OC 4:316. 101 Mesnard OC 4:255. 322

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involve an ease of procedure. Dettonville claims this for his own work in the final sentence of a section of the Lettres de A. Dettonville written to Carcavy: It will be easy based on that for everyone to find the calculations of all these cases, by mean s of these methods.102 By thoroughly detailing his me thod he was able to avoid the diffi culty that reader s often had with the ancient Greek mathematicians, who have left only their solutions without instructing us in the ways by which they had arrived there.103 Through explanation, he believed, he had created a way that others could calculate the dimens ions sought without the same expenditure of effort.104 Through his concerted applicati on to the problem of the arithmetic machine Pascal had reduced the inconveniences and di fficulties of arithmetic to a simple movement of the hand. Similarly, he had now uncovered th e hidden aspects of the roul ette, allowing unfettered access to its dimensions. Thus, Pascals work on the roul ette suggests a dual status of geometry. It is both difficult and easy and invol ves both maturity and childlikeness. The problems posed an incredible challenge even to th e learned. Through his efforts and the disciplined application of method, however, Pascal/Dettonville fathomed its d eepest mysteries. Howeve r, his insistence on 102 Il sera sur cela facile tout le monde de trouver les calculs de tous ces cas, par le moyen de ces mthodes, Traitt General de la Roulette, in Lettres de A. Dettonville 10. 103 [J]e vous ai souvent ou plaindre de ce que les anciens nen ont pas us de mme, ne nous ayant laiss que leurs seules solutions sans nous instruire des voies par lesquelles ils y taient arrivs, comme sils nous eussent envi cette connaissance, Lettre de A. Dettonv ille a Monsieur de Carcavy, in Lettres de A. Dettonville 1. 104 Dettonville recognizes, in fact, that this method might present problem s to some, because of its use of indivisibles. He asserts, however, th at their use provides no difficulty: I have wanted to write this notice in order to show that all that is demonstrated by the true rules of indivisibles is demonstrated also in the rigor and manner of the ancients; and that thus one of the these methods does not differ from the ot her except in the manner of speaking; which cannot wound reasonable people when one has once warned them of what one understands by that. / And this is why I will have no difficulty in what follows of using this language of indivisibles : the sum of lines, or the sum of planes; and thus when I will consider the diameter of a semicircle divided into an indefinite number of equal parts . I will not have any difficulty using this expression : the sum of the ordinates, which seems not geometrical to those who do not understand the doctrine of indivisibles, and who imagine that it is to sin against geometry to express a plan by an indefinite number of lines; which comes only from their failure of intelligence ibid., 10. 323

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the use of construction and the numerous diagrams highlight the visual immediacy of Pascals solutions to the roulette problems. A Game for the Learned The previous section has sought to show that Pascals procedure of sharing his new method of calculating areas and volumes in the form of a contest was based primarily upon the desire to emphasize the difficulty of the problems of the roulette The idea of a mathematical contest did not originate with Pa scal. University chairs of mathematics were often awarded based on the solving of significant problems.105 The contest was an established way for mathematicians to legitimate their abilities. By proposing a contest, Pascal likely hoped that many of the geometers of Europe would be drawn to attempt the solution, in order to gain, as Sluse expressed it, the glory that will accompany you if you accomplish it.106 When Pascal anonymously proposed the contest, he did so to the most eminent geometers of all the earth.107 In addition, he offered the legi timation that the one who solved the problem within the time allotted will be our great Apollo.108 Through such a challenge, Pascal appealed to individuals who would like to prove their prowess in geometry. Pascals rhetoric in the first circular letter was clearly an attempt to engage the curiosity and the desire for achievement of the savant geometers of Europe. The anonymity of the challenge created further intrigue that would draw attention and conversat ion to the question of 105 In fact, this is one of the reasons for Robervals notorious tendency to keep his mathematical results secret. Probably the most famous of the early modern mathematical contests was devised by Tartaglia (1500-1557) regarding cubic equations. Tartaglias challenge is descri bed in Martin A. Nordegaard, Sidelights on the CardanTartaglia Controversy, National Mathematics Magazine 12 (1938): 327-346. 106 Non illud intelligo quod infra te esse scio; sed gloriam quae te sequetur si rem, uti spero confeceris, Ren-Franois de Sluse to Christiaan Huygens, 5 July 1658, Mesnard OC 4:279. 107 Pascal, First circular letter, Mesnard OC 4:189. 108 Quisquis superius proposita, intra primum diem mensis octobris anni 1658, solverit et demonstraverit, magnus erit nobis Apollo, ibid., 4:192. 324

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their origin. The problems of the roulette did indeed become f odder for conversation within the learned correspondence networks, and the identity of the anonymous author of the problems excited interest.109 The consideration of the roulette by way of a contest suggests childhood connotations of gaming. Pascal had done a good deal of reflectio n on the diversions of gambling, both in the circles of the Chevalier de Mr and in his correspondence with Fermat regarding the geometry of chance.110 The connection with these considerations of games of chance is even stronger given the monetary award associated with the ro ulette contest, which was one of its unique features. Pascal recognized that the offer of money could seem a particularly vulgar motivation for solving the problems. Sluse affirmed this when he wrote to Huygens of this material prize: I know that it is below you.111 Pascal justified the reward by its symbolism: not for the lure of reward (far be it from us!), but as a public proof of our consideration, or rather of the merit of those who would have solved it.112 The monetary prize was a tangible wreath of vict ory in the contest, a token that the winner had emerged as superior to other contestants. Pascals observations about diversion and 109 The question of the authorship of the contest arises in correspondence between Huygens and Boulliau: je vous priai de me faire savoir le nom de lauteur des problme s de la cyclode, draft, Ch ristiaan Huygens to Ismal Boulliau, 19 September 1658, Mesnard OC 4:260; Huygens and Sluse: De Pascalio autem, in suspicionem incidi eum esse qui problemata proposuerit, Ren-Franois de Sluse to Christiaan Huygens, 10 January, 1659, Mesnard OC 4:284; Huygens and Wallis: Si autem (quod suspicor) Pascalius sit qui haec proposuit, Wallis to Christ. Huygens, 1 January 1659, Mesnard OC 4:317; Sluse and Pascal: Il me semble aussi de pouvoir tirer de la mme histoire par consquence assure que cet excellent anonyme qui nous a propos les probl mes, cest M. Pascal, et que ce sera aussi lui seul qui les rsoudra, Ren-Franois de Sluse to Blaise Pascal, 16 November 1658, Mesnard OC 4:274. 110 Pascals initial interest in probability theory is said to have come from his interactions with the Chevalier de Mr, which contributes to interpretations of Pascal that stress the importance of friendships and their influence on his work, Humbert, Cet effrayant gnie 11; Le Guern OC 1:xiii. The terminology of geometry of chance (original Latin: aleae geometria) originates in Pascals address to the Parisian Academy, Celeberrimae matheseos academiae parisiensi, Mesnard OC 2:1035. 111 infra te esse scio, Sluse to Christ. Huygens, 5 July 1658, Mesnard OC 4:279. 112 quarem solutionem a praestantissimis toto orbe geometris supplices postulamus, proposito ipsis praemio, non mercedis gratia (quod absit!) sed in obsequii nostri, aut potius meriti eorum qui haec invenerint, publicum argumentum, First circular letter, Mesnard OC 4:189. 325

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gambling, which appear in the Penses highlight that the material gain is not the primary goal that most have in doing it. The player of a game may have no need of the monetary prize, but the game offers the diversion of risk as well as so that he can boast tomorrow to his friends that he played better than someone else.113 Pascal directly implicated mathematics in this same attitude of competition: Likewise others sweat away in their studie s to prove to scholars that th ey have solved some hitherto insoluble problem in algebra. 114 In the passages above, the fierce competition and pride involved in the games is seen for the absurdity that it is, and the supposedly important adult activities such as huntin g, gambling, and algebra become associated instead with childishness. To take such significant pains, si mply in order to be the first to solve a problem, is to mistake a diversionary activity for a serious occupation. It is to be just lik e children taking fright at a face they have daubed themselves.115 In his Lettres de A. Dettonville Pascal describes an indivi dual who seems to represent a mature view of mathematics. He addresses the la st of Dettonvilles letters to A. D. D. S., who embodies the ease of geometrical thought, for t hat which is a study for others is only a diversion for you.116 The initials, following Mesnard, ar e almost certainly those of Antoine Arnauld (Arnauld Docteur de Sorbonne) and this identification hearkens back to what Pascals earliest biographers claim was th e purpose of the roule tte contest: a design which regarded only 113 Pascal, Penses, trans. Krailsheimere, no. 136, 40. In the roule tte contest, there was both risk and the possibility of award, as in a gaming situation. The risk was one of time lost and pride shattered. With respect to the first, Sluse writes: One of those who have wasted their effort is, I th ink, Wallis, or another English geometer, Sluse to Christ. Huygens, 27 Decemb er 1658, Mesnard OC 4:283-284. For pride lost, one may consider the negative reception given to Lalouvres entry. 114 Pascal, Penses, trans. Krailsheimer, no. 136, 40. 115 Ibid., no. 136, 41. 116 ce qui est un tude pour le s autres nest quun diverti ssement pour vous, Lettre de A. Dettonville a Monsieur A. D. D. S., in Lettres de A. Dettonville 1. 326

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the glory of God.117 Convinced by the duke de Roannez, Pascal tackled the project to combat the belief of certain skeptics and unbelievers that those w ho are devout have weak minds.118 The roulette contest represents a serious and concerted intell ectual effort by Pascal, with the attempt to earn a favorable place among poster ity by providing the means of progressing still further.119 Paradoxically, this mature effort was expended in an activity that could be characterized as a game, as childlike. Furthermore, within the game that was the roulette contest, there was another game, the puzzle of Pas cals pseudonymous identity. The use of the pseudonym Amos Dettonville forged a link between the ironic religious writer (under the pseudonym Louis de Montalte) and the ingenious ge ometer. Both characters demonstrated how the virtues of childhood and superior learning could go hand in hand. Dettonville combined a playful, diversionary approach to geometry with the intellectual probity respected by geometrical savants. Louis de Mont alte, the author of the Provincial Letters, represented the innocence and ignorance that was able to disarm critics of the Jansenists.120 Limitations of a Mathematical Mtier The link between the pursuit of mathematics as a game/diversion/child like activity, and the intellectual maturity Pascal pursued during the fina l period of his life, became even more explicit after the roulette contest. In 1660, Pascal articulated his view that the meaningfulness of mathematics as a personal pursuit was limited. The letter to Fermat that expresses this was a 117 un dessein qui ne regardait que la gloire de Dieu, La vie de Pascal, Mesnard OC 1:586. For an explanation of Mesnards identification of Arna uld as the addressee, see Mesnard OC 4:391-392. Other possibilities that have been suggested are Augustin (i.e. Antoine) de Singlin and Alphonse-Antoine de Sarasa, Brunschvicg OC 8:249. 118 argument puissant contre lidentit souvent pos e entre croyance et faiblesse desprit, Mesnard OC 4:168. 119 Mesnard OC 4:193. 120 To these we may add that Pascals planned apology for the Christian religion was to be written under the pseudonym of Salomon de Tvltie, another anagram of these two names; Pascal, Penses, trans. Krailsheimer, no. 745, 229 and note 1. 327

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response to a request by the provincial mathema tician to meet somewhere between Toulouse and Clermont-Ferrand, the location to which Pascal ha d retired when he had once again lapsed into ill-health: For, to speak to you frankly of geometry, I fi nd it the highest exercise of the mind, but at the same time I understand it to be so useless that I draw no distinct ion between a man who is only a geometer and an able artisa n. I also call it the finest craft [ mtier ] in the world, but in the end it is only a craft [ mtier ], and I have often said that it is good for the testing, but not the employment of our forces: in such a way that I would not take two steps for geometry, and I am very much assured that you are of the same disposition.121 In this passage, the limitations of the geometer are portrayed as similar to those of any manual laborer, an idea that conjures Pascals belittli ng spirit toward artisa nal knowledge that was manifest during his early career. But the artisan that he now considered was the geometer, and the mtier was the one to which he himself had been apprenticed in the Mersenne group. When Pascal began his mathematical and scie ntific career, as Chapter 3 has argued, he differentiated himself from the limited place of the child genius, from talent due to inclination, and from the habitual training of artisans. Du ring the roulette contest, he maintained the importance of the hard work that he believe d would earn him the recognition of posterity.122 At the same time he stressed the ease and immediacy that his method contributed to the solution of the problem and, based on his letter to Fermat and Gilbertes story of the toothache, he considered this last work in mathema tics as little more than a diversion. The labeling of mathematics as a mtier and the link between childlike diversion and the roulette contest suggests a pa rticular way of understanding Pascals childhood. Pascals 121 Car pour vous parler franchement de la gomtrie, je la trouve le plus haut exercice de lesprit; mais en mme temps je la connais pour si inutile que je fais peu de di ffrence entre un homme qui nest que gomtre et un habile artisan. Aussi je lappelle le plus beau mtier du monde; mais enfin ce nest quun mtier; et jai dit souvent quelle est bonne pour faire lessai, mais non pas lemploi de notre force: de sorte que je ne ferais pas deux pas pour la gomtrie, et je massure fort que vo us tes fort de mon humeur, B. Pasc al to Fermat, 10 August 1660, Mesnard OC 4:923. 122 Pascal, First circular letter, Mesnard OC 4:193. 328

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discovery of geometry was made in the cont ext of diversion. It was shaped into a mtier through the influence of his fathers friends. In the Penses, Pascal describes the process by which people choose careers: The most important thing in all of life is the choice of a craft [ mtier], chance disposes us to it. Custom makes masons, soldiers, roofers. Tha t is an excellent roofer, says one, and in speaking of soldiers, They are indeed fools, says one, and others on the contrary: There is nothing greater than war, the rest of me n are rascals. Through the force of hearing praised in childhood these crafts [ mtiers] and scorning all the ot hers, one makes ones choice. For naturally one loves virtue and ha tes folly, these words then end up deciding it, and one sins only in the application.123 It is for this reason, Pascal goes on, that some countries produce more people of one mtier and others contain more of another. It is not a question of temperam ent, the matrix of the hot/cold and wet/dry of the body that had often been used to explain differences in custom based upon climate.124 For Pascal, being raised by a father whose friends often gathered at their home to discuss geometry and had particular philosophical and religious reasons for praising it may have served as an important accustomization to the mtier of mathematics. For Pascal, early in his life, geometry became the model for virtue. With time, according to Pascals own autobiographical musings, he had begun to see limitations in the study of mathematics: 123 Custom makes masons, soldiers, roofers. He is an excellent roofer, they say, and speaking of soldiers: They are quite mad, while others on the contrary say: There is nothing as great as war, while everyone else is worthless. From hearing people praise these trades in our childhood and running down all the others we make our choice. For we naturally love virtue and hate folly; the very words w ill decide, we only go wrong in applying them. Pascal, Penses trans. Krailsheimer, no. 634, 209. 124 Huartes use of the four qualities as determinate for different esprits is in agreement with this perspective: Whence it clearly appears that from Cold pro ceeds the greatest difference of Wit in Man, viz the Understanding. Aristotle therefore enquiring, why the Men inhabiting hotter countries (as gypt is) are more Subtile and Ingenious than those who live in colder Clim ates, makes Answer, That the Ambient Heat being excessive, draws forth and consumes the Natural Heat of th e Brain, leaving it cold, which makes Men more sharp, Huarte, Tryal of Wits (1698), 135-136. 329

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I had passed a long time in the study of the ab stract sciences and th e little communication that one could have with others about them disgusted me. When I began the study of man, I saw that these abstract sc iences are not proper to man.125 Pascal explains in this excerpt from the Penses that he was repulsed from geometrical study because of the limited ability to effectively talk about those disc overies with others.126 It was a limitation of scope, made clear through the failu re of interpersonal communication. When he was working with the artisans of Rouen on the cons truction of the arithmetic machine, Pascals inventiveness collided with the incommunicability of the mathemati cal theory of the device. In that case, the habituated learning that a cl ockmaker received during his apprenticeship was considered incompatible with a full understanding of the details of the mechanism of the machine. In the above passage, there is a transformation of the significance of incommunicability. The difficulty is not on the side of those, such as artisans, untrained in mathematical thinking. Instead, it is a characteristic of geometry itself. Pascal had earli er suggested that artisans, who learn through habit, are not at th e highest level of human enterprise In this passage, on the other hand, geometry is also considered to be not proper to man.127 Pascal insist s that by giving himself to the study of geometry he was s traying further from my true condition.128 The limitation of scope was so severe that it was not just a minor liability of mathematics, but a justification for abandonment. 125 I had spent a long time studying abstract sciences, and I was put off them by seeing how little one could communicate about them. When I began th e study of man I saw that these abstr act sciences are not proper to man, Pascal, Penses, trans. Krailsheimer, no. 687, 217. 126 That Pascal is referring to geometry when he speaks of these abstract sciences [ sciences abstraites ] is made explicit later in the fragment, ibid. 127 Ibid. 128 Ibid. 330

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In the roulette problem, Pascal tried to avoid the problems a ssociated with taking geometry too seriously by keeping the conclu sions strictly differentiated fr om practical application. The most basic reason for pursuing the answer to a difficult problem was to find out whether his mind was as strong as was believed. Pascal expr esses this approach when he writes to Fermat that geometry is good to make a te st, but not the use of our force.129 In addition, Pascals solution to the problem of the roulette uses a process whereby figures are divided into an indefinitely small size in order to calculate their area. Pascal then had to deal with the question of the existen ce of indivisibles that was then current. Although this does not seem to be geometrical to those do not understand the doctrine of indivisibl es, Pascal shows that it is equivalent to ac cepted ancient practices.130 These troublesome aspects of mathematical method, he states in his De lesprit gomtrique, are what make it worthwh ile: they are able to produce reflections which are of better worth than all the rest of geometry.131 The insights to which such mathematical con cepts lead the mathematician deal with the nature of humanity, as situated between infinite greatness and infinite smallness.132 And these are fundamentally linked to Christian teachings about childlikeness and maturity. On the one hand, humanitys smallness suggests the position of the child, thrown into an immense universe 129 B. Pascal to Fermat, 10 August 1660, Mesnard OC 4:923. 130 Et cest pourquoi je ne ferai aucune difficult dans la su ite duser de ce langage des indivisibles qui semble ntre pas gomtrique ceux qui nentendent pas la doctrine des indivisibles, Lettres de A. Dettonville, Mesnard OC 4:424 131 Sur quoi on peut apprendre sestimer son juste prix, et former des rflexions qui valent mieux que tout le reste de la gomtrie, De lesprit gomtrique, Mesnard OC, 3:411. 132 For, after all, what is man in nature? A nothing compared to the infinite, a whol e compared to the nothing, a middle point between all and nothing, infinitely remote from an understanding of the extremes; the end of things and their principles are unattainably hidden fr om him in impenetrable secrecy, Pascal, Penses, trans. Krailsheimer, no. 199, 61. 331

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and humbly dependent upon the Creator.133 On the other hand, the grea tness of human beings is the capacity for what might be achieved and understood through thought.134 The practice of geometry is the exercise of that adult-like capacit y for reason. But because of the shortness of its grasp, limited in that it considers only very simp le lines, it is also related to childhood; it is extremely clear but also extremely limited. For Pascal, then, the roulette contest was proof that the geometrical strength of a Dettonville and the spiritual devotion of a Mont alte or a Salomon de Tultie (an authorial pseudonym used in the Penses ) may legitimately coexist and, in fact, mutually support one another. The glory of si gnificant contributions to the mtier of mathematics should be balanced by the recognition that these ab stract sciences are not proper to man.135 This section has shown that Pascals last majo r mathematical endeavor was indeed a return to childhood. It was a return to the type of geometrical work he had done in Mersennes group and to a problem that had been of special concer n for the members of that group. In the exercise of the contest, he was dependent upon the indivi duals associated with that group: Roberval, for his prior knowledge of the curve; Carcavy, for the administration of the contest. In content and mathematical approach, Pascals return to ch ildhood involved the search for an easy method that would reduce the difficulty of the mathemati cal problem and make it possible to solve other types of curves. The childlike immediacy of ge ometry and its status as diversion was matched by a deep sense of accomplishment in the face of a difficult problem. 133 I see the terrifying spaces of the universe hemming me in, an d I find myself attached to one corner of this vast expanse without knowing why the brief span of life allotted to me should be assigned to one moment rather than another, ibid., no. 427, 130. This helplessness is reflect ed in Pascals famous statement: The eternal silences of these infiinite spaces fills me w ith dread, ibid., no. 201, 66. 134 Through space the universe grasps me and swallows me up like a speck; through thought I grasp it, ibid., no. 113, 29. 135 Pascal, Penses, trans. Krailsheimer, no. 687, 217. 332

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For many of the members of the European savant community at large, however, the roulette contest hardly represen ted the heights of virtue. A br ief exploration of some of the negative reactions to the contest w ill provide insight into the deep gulf that separated Pascal from those who would become the key players in the la te-seventeenth-century scientific community. His gaming approach to mathematics did not resp ect the adult virtues of civility so important to that community. Moreover, while Pascal expr essed the limited scope of geometry by referring to it as merely a mtier the childlike, synthetic approach to geometry was in the process of being rejected as obscure and without utility. Criticisms of the Contest: Between Childhood and Sociability Pascals efforts in the roulette contest were criticized by members of the savant community in ways that directly undermined his attempts to combine childlike and adult virtues in his pursuit of mathematics. The mathematicians invo lved in the contest did not always agree with Pascals evaluations concerning th e ease or difficulty of the problem s or with the clarity of the solutions offered. Furthermore, they called th e administration of the contest into question, reacting negatively to Pascals game of identity and the peculiarity of the contest rules. This section will explore some of these criticisms and their contrast with Pascals claims for the contest. It will conclude with a comparis on of Pascal with Huygens regarding the two mathematicians involvement with the roulette problem. This comparison will suggest reasons why Pascal was marginalized by the Parisian savant community near the end of his life. This chapter has stressed the importance that Pascal accords to the difficulty of solving the set of roulette problems. Signi ficant references to the question of the problems difficulty by those who became involved in trying to solve them suggest this as a central theme of the roulette contest. The Lettres de A. Dettonville opens dramatically with a letter written to the author by Carcavy, in which he asks Dett onville to reveal his solutions. In it, Carcavy distinguishes 333

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between the problems that you have proposed as easy and those that you have proposed as difficult.136 When he first received word of the proposed problems, Christiaan Huygens questioned the possibility of a solution.137 Expanding upon this questi on, he inverts the issue, contrasting the effort required for resoluti on of arduous mathematical problems with the simplicity of proposing them. Objections to the Characterizati on of the Problems as Easy The response to the contest by Antoine Lalouv re, himself a Jesuit from Toulouse, further demonstrates the centrality of questions of relative ease to the contest. Lalouvre sent solutions to the problem, but these were minimized by Pascal in documents circulated later.138 Lalouvre had sent the calculation of a sp ecific instance of the problems, but the calculation contained an error. Having been taken to task in writing, La louvre continued to justify his responses and criticized the contest. A key aspect of his argument against the contest was his rejection of Carcavys claim, mentioned above, that the probl ems of the roulette surpassed the problems of the ancients, including Archimedes. Though the problems of the roulette were astonishingly difficult, Lalouvre admits, their solution was proportionally less significant in comparison to the progress made by the ancients. The differe nce between the roulette problems and the common diligence of the Geometers of the seve nteenth century was not, Lalouvre argues, as 136 Et il soffre encore un soulagement votre travail, en ce quil ne sera pas ncessaire de vous tendre sur les problmes que vous avez proposs comme faciles ; de sorte que vous naurez pres que qu donner ceux que vous avez proposs comme difficiles, Lettre de Monsieur de Carcavy a Monsieur Dettonville in Lettres de A. Dettonville n.p. [1]. 137 See above, note 98. 138 The third circular letter about thecontest (7 October 1658) appears, as Mesnard suggests, to refer to Lalouvre, when it states: je ne puis assez admire r la vaine imagination de quelques autres, qui ont cru quil leur suffirait denvoyer un calcul faux et fabriqu au hasard pour prendre date du jour quils lauraient donn, sans avoir produit autre marque qui fasse connatre sils ont rsolu les problmes, Third circular letter, Mesnard OC 4:201. A similar judgment is given in Pascals announcement of the results of the contest (25 November 1 658), Rcit de lexamen et du jugement, Mesnard OC 4:234. 334

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great as the difference in difficulty between th e work of Archimedes and the state of accepted geometry during the time that he lived.139 In a gesture of self-deprecation, Lalouvre argues that the fact that he, an amat eur geometer, a man of so little mind, was quickly able to find some of the calculations provides evidence that the problems are less difficult than the anonymous had suggested.140 The original proposal labeled th e problems in their entirety as being an arduous challenge and was addressed to the most outstanding geometers in all the world. The contest did not make distinction be tween what was required of apprentices and of these masters, of these consummate men of science.141 This inability clearly to state the requirements for demonstrating learnedness in geom etry proved to Lalouvre that the author of the contest determined which pr oblems he would consider easy and which he would consider difficult based on what the contestants were able to solve successfully.142 The Jesuit father calls into question the adult mathematical virtue an d exercise necessary in order to solve such problems, arguing that their difficulty was merely relative and not absolute. Conversely, Lalouvre questions Pa scals claim that the calculations that would result from his method of using indivisibles would be eas y. He does not believe that Pascals work simplifies the issue to the extent that its author claims. Pascal had written of the ease of finding 139 Thirdly, I do not deny that the thought of the cycloid en tirely pertains to our present age, and that the problems proposed regarding it are remarkable in their difficulty, even if they are attempted by he who is well-instructed in the uncommon principles of the balance; but in bringing forth their solution, could you surpass the common diligence of the Geometers by as great distance as Archimedes su rpassed the accepted geometry of his time? There is rightly reason to doubt it, Antoine Lalouvre, Veterum geometria promota in se ptem de cycloide libris et in duabus adjectis Appendicibus (Toulouse, 1660), excerpted in Mesnard OC 4:903. 140 However, what a man of meager mind has so quickly discovered, who could say that this is impenetrable and hidden as much as possible, in such a great light of the geometers of ours age, ibid. 141 [T]he Anonymous once he had without distinction proposed all the problems to the most outstanding geometers in all the world, and had made no distinction between what he required of novices and what of Masters (those consummately learned men), whispered to us through his friends that what we had been the first to give was without difficulty, ibid. 142 Ibid. 335

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the calculations using his methods.143 But Lalouvre states that F or my part, I have never found it easy since this book came into my hands.144 Pascal suggested that the work of calculation was childs play, a matter for an apprentice of the mathematical mtier Lalouvre disagreed: Do not suppose, Learned Reader, that this calculation is of the number of commonplace ones and, as the Anonymous says, is of those that do not depend on the power of innate genius, and which is able to be committed to whatever novice comes along; clearly it is most intricate, and it requires a complete geometer, and often the Father of the very demonstration.145 Lalouvre counters both of Pas cals suggestions regarding child likeness and maturity. He dismisses Pascals claims to being geometrically mature in a way that rivals the ancients; and he rejects the assertions of the ease and simplicity of the resultant calculations. While Lalouvre questioned Pascals evaluati on of the various asp ects of the roulette problem, Huygens, for the most part agreed with Pascal regarding the difficulty of the problems, to the point that he believed them impossible. However, he did not share the anonymous writers belief that what was most important about the contest was how challenging it was: Not indeed that I value geometrical discoveries only for their difficulty (which nevertheless in this case was actually quite gr eat), but also if around them would turn things that may be pleasing to learn.146 One of the results that impressed Huygens the most was discovered by Christopher Wren. Wren made the discovery of the length of the roulette curve, which Huygens says is admirable and has pleased me marvelously. I ndeed, [t]his is the best of wh at has been found concerning this 143 See above, note 102. 144 Ego certe id facile non reperi unquam ex quo ille liber venit in manus meas, Lalouvre, Veterum geometria excerpted in Mesnard OC 4:905. 145 Neque existimes, Erudite Lector, istum calculum esse de numero vulgarium et a viribus ingenii, ut dixit Anonymus, non pendentium, qui Tyroni cuilibet demandari queunt; intricatissimus quippe est, et totum Geometram, atque saepe ipsius demonstrationis Parentem desiderat, ibid., 4:888. 146 Non enim sola difficultate (quae tamen in his etiam satis magna erat) reperta goemetrica estimo, sed ex eo quoque si circa ea versentur, quae cognoscere jucundum sit, Draft, Christiaan Huygens to Ren-Franois de Sluse, 1659, Mesnard OC 4:639-640. 336

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line.147 Wrens result prompted Huygens to write, in opposition to Pascals stress on difficulty, that [i]t would please me to di stinguish difficulty from elegance.148 Without doubt, the problems concerning the centers of gravity of so lids associated with the curve were very arduous, Huygens makes clear, but Wrens so lution was more pleasing and thus more important.149 Huygens thus questioned Pascals privileging of difficulty as of the utmost importance, but he also stressed how the work of Dettonville faile d the test for the childlike virtue of clarity. Pascal, Huygens maintained, forfeited his cl aim through his unwillingness to engage in calculation or examples, instead sustaining a general discussion of his method using purely geometrical terms. Dettonvilles solution, Huygens argues, was neither as easy nor as rigorous as he claimed: This method is indeed, in my opinion, sometimes obscure, sometimes a little too bold and too distant from geometrical exactness.150 He did not perceive restriction to pure geometrical demonstration as an advantage, as Pascal did, but argued instead that it prevented complete clarity: 147 [J]ai compris linventin de Wren, qui est admirable et qui ma plu merveilleusement. Cest le meilleur de ce qui a t trouv sur cette ligne, Draft, Christiaan Huygens to John Wallis, 31 January 1659, excerpted and translated into French from Dutch in Mesnard OC 4:318. On Christopher Wrens contribution to the roulette contest and his other mathematical work, see D. T. Whiteside, Wren the Mathematician, Notes and Records of the Royal Society of London 15 (1960): 107-111; James Arthur Bennett, The Mathematical Science of Christopher Wren (Cambridge, 1982). 148 Il me plat de distinguer la difficult de llgance Draft, Christ. Huygens to Wallis, 31 January 1659, excerpted and translated into French from Dutch in Mesnard OC 4:318. 149 In a letter to Wallis, Huygens writes: As to this whic h regards me, the writings addressed to Carcavy fill me with admiration and wonder for their extreme subtlety. Th e difficulty was extreme; but there are other questions on which we can exercise our subtlety and our intelligence, holdi ng on matters that there is more pleasure to know. On the comparison of cycloid lines with ellipses, one remark s for their elegance of reasonings to which however the illustrrious Wren has given occasion th rough his invention, Christiaan Hu ygens to John Wallis, 6 June 1659, excerpted and translated into French from Dutch in Mesnard OC 4:658-659. 150 Est enim methodus kista, ut mihi quidem videtur, tum obscura, tum audacior paulo atque a geometrica Draft, Christ. Huygens to Sluse, 1659, Mesnard OC 4:639. In his response to Huygens, Sluse generously writes: It seems that he deviated in places in his demonstration from precisi on and from clarity, but he has wanted, in my opinion, to follow the highest summits of matters, content to have indicated his method, RenFranois de Sluse to Christiaan Huygens, 13 June 1659, Mesnard OC 4:642. 337

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I admire more and more the subtlety of the writings of Monsieur Dettonville, but it is necessary to avow that it is a labyrinth when one wants to make the construction of some problem, and for that I would like that he ha d everywhere taken only the easiest case in order to give the calculation of it at length or indeed an example for each theorem.151 Huygens believed that Dettonv illes approach to his problem s would alienate readers. Pascal himself recognized that th e approach of pure geometry was difficult for some individuals because its principles are distant from everyday life.152 A perfected geometrical procedure in matters outside of geometry, Pa scal claimed, is not only diffi cult but totally impossible. Nevertheless, within the mtier of geometry, Pascal insisted th at such purity of demonstration was a model for perfect reasoning and should not be forfeited. The perfect geometer, he believed, was absolutely clear because supremely rigorous. The procedural aspects of the contest, like the issues of c ontent considered above, drew questions and criticism from savants. John Wa llis, an English mathematician who submitted solutions to some of the problems, upbraided Pas cal for unfair treatment of all but the French participants, since the time given to solve the problems was, in his opinion, absolutely prohibitive.153 Moreover, when Wallis began to suspect that Pascal was not only the author of the problems but had taken Carcavys place as th e recipient of the solutions while Carcavy was out of town, he wrote to Huygens: 151 Jadmire de plus en plus la subtilt des escrits de Monsieur Dettonuille, mais il faut auouer que cest un labyrinthe lors que lon veut faire la construction de quelque problme, et pour cela je voudrois quil eust partout pris seulement un cas le plus facile pour en donner le calcul tout du long, ou bien un exemple a chaque Theoreme, draft, Christiaan Huygens to Pierre de Carcavy, 22 May 1659, Huygens OC 2:411. 152 The principles of geometry, Pascal states in the Penses are ones that esprits de finesse have never seen in practice and are quite outside ordinary experience, Pascal, Penses trans. Krailsheimer, no. 512, 183. 153 John Wallis preface to Tractatus duo, prior de cycloide et corporibus inde genitis (Oxford, 1659), n.p., exerpted in Mesnard OC 4:727-728. 338

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I am unaware of how candidly it may be a sserted to be done, seeing that it may by no means be free from every suspicion of being able to pick out from there [i.e., others submissions] either solutions or at least opportunities for solutions.154 Some commentators have joined Walliss critique of Pascals contest, claiming that the winner had been predetermined and that Pascals critical remarks of c ontestants were unfair.155 This was not necessarily an uncommon strategy in the seventeenth century. Mersenne, for example, had concocted a contest for musical composition that seems to have been merely a demonstration of the superiority of French composition.156 Rejection of Detonvilles Anti-Social Behavior with Robervals Rusticity In England and France, savants were becomi ng ever more concerned with sociability. Pascals use of a pseudonym undermined community values. It exposed him to accusations of plagiarism and conflict of interest, diminishing the sense of fair play. Parisian geometers already had a reputation for being inwardly focused a nd boastful about great accomplishments and this contest only served to reinforce those beliefs.157 Its pseudonymous presentation also implicated the contest in the anti-social behavior of secr ecy. The delay in publication of the contests results was, for Wallis, a symptom of the French geometers tendency to hoard their results, thus denying the importance of sociability.158 Walliss objections show that the roulette contest, with its lack of clarity and openness, chafed agains t the desire for the transparent, forthright development of knowledge with in the learned community. 154 nescio quam id candide fieri dicatur, cum non omni suspicione vacet se vel inde solutiones aliquas vel solutionum saltem ansas desumpsisse posse, Wallis to Christ. Huygens, 1 January 1659, Mesnard OC 4:317. 155 Condorcet, Pascal (Paris, n.d.), 21-22. 156 D. P. Walker, Joan Albert Ban and Mersennes Musical Competition of 1640, Music and Letters 57 (1976), 234, 244-245. 157 This tendency of the Parisians to forget others contributions is suggested in Walliss criticism of the Histoire de la roulette for minimizing the contributions that the Ita lians had made with respect to the curve. 158 Wallis especially objects to Robervals choice to maintain secrecy of the solutions: he and his friends keep them private, [and] have not publicly divulged them, Wallis to Christ. Huygens, 1 January 1659, Mesnard OC 4:317. 339

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Pascals close association with Roberval and his defense of Roberval s originality in the Histoire de la roulette further undermined the acceptability of the community represented by the contest. Roberval was notorious for keeping his results secret and for being suspicious of others discoveries. For those who valued sociability, he represented the ep itome of what they wanted to avoid in their learned conversations. He also symbolized the inability of geometry to communicate with those who were non-mathem atical. Though Pascal recognized these limitations, he remained willing to associate hims elf with the work of Roberval, who was the clearest example of the artisangeometer to which the 1660 letter to Fermat refers. Robervals reputation and actions, however, helped to undermine Pascals attempts to portray the mathematical community as at the nexus of simplicity and maturity. During the middle of the contes t, Robervals reputation suffered even further from a famous outburst that occurred at the Montmor Acad emy, the center of Parisian savant sociability in the late 1650s and early 1660s: Monsieur de Roberval has done a stupid thi ng at the home of Monsieur de Montmor, who is as you know a man of honor and of quality; he ha s been so uncivil as to say to him in his house, being piqued about one of the opinions of Monsieur Descartes that Monsieur de Montmor approved, that he had more wit [ esprit] than him and that he had nothing less than him except the goods and the charge of Mast er of Requests, and that if he was Master of Requests, that he would be worth one hundred times more than him. Monsieur de Montmor who is very wise told him that he c ould and ought to behave more civilly, than to quarrel with him and to treat him with contem pt in his house. All the company found very strange the rusticity and the peda ntry of Monsieur de Roberval.159 159 Pour Monsieur de Roberual il a faict un sottise chez Monsieur de Montmor, qui est comme vous scauez homme dhonneur & de qualit, il a est si inciuil que de luy dire dans sa maison, sestant picquez sur vne des opinions de Monsieur desCartes que Monsieur de Montmor approuuoient, quil auoit plus desprit que luy & quil nauoit rien de moins que luy que le bien & la charge de Maitre de s requestes, & que sil estoit Maitre des Requestes, quil vaudroit cent fois plus que luy. Monsieur de Montmor qui est tressage luy dist, quil en pourroit & deuoit vser plus ciuillement, que de le quereler & le traicter de mespris dans sa maison. Toute la compagnie trouua fort estrange la rusticit & pedanterie de Monsieur de Roberual, Is mal Boulliau to Christiaan Huygens, 6 December 1658, Huygens OC 2: 287. This episode has taken on a particular importance for scholars who have focused on the importance of etiquette and sociability and especially to emerging state-sponsored academies of science in London and Paris. Mario Biagioli argues that Robervals outburst against Montmor exemplifies the tensions between different types of social no rms and points to a connection between Roberv al the rustic (practitioner of the craft [ mtier ] of mathematics) and Robert Hooke, who had an artisans social style, Biagioli, Etiquette Interdependence, 340

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Robervals behavior at Mont mors home provided the savant community with evidence that the geometers represented not childlike simplicity and clarity, but childish argumentativeness. Furthermore, it reinforced the restricted nature of mathematics as a mtier. The account above shows that Robervals similarity to unsophisticated ar tisans did not begin and end with a tendency to focus upon mere mathema tics. In his outburst against Montmor, he behaved, writes Boulliau, like one of the lower social cl asses of rural areas (a rustic) who, like artisans, were not a part of the cultured society of the truly learned.160 The restrictedness of the artisan was matched by the immaturity and the outburst of a child. The learned community at large admired the re sults that Pascal publis hed, but the virtues of the community of geometers and the ulti mate value of the published results were compromised by the social drawbacks of the contest and the obscurity of the subject. Pascal had emphasized the fine balance between the virtue s of maturity (e.g., concerted application to difficult problems) and those of childhood (e.g., clar ity and ease of application); instead, the contest was shrouded in complexity and pollu ted by the perception of childish behavior. Two Archimedeses: Pascal and Huygens in the Roulette Contest Pascals failure to acquire untarnished praise from the evolving savant community coincided with the rise of Chri stiaan Huygens, Mersennes other Archimedes. It is with the roulette contest that their liv es converged (and diverged) most decisively. Through the mid1650s, contact between the young mathematicians was sporadic and indirect. In 1656, Huygens corresponded with Mylon and Carcavy about the work of Pascal and Fermat in probability and Sociability in Seventeenth-Century Science, Critical Inquiry 22:2 (Winter 1996), 198, 200 n. 23. For Steven Shapin, the disruptive nature of the Roberval episode was what the Royal Society wanted to avoid with its standards of sociability, Shapin, The House of Experiment in Seventeenth-Century England, Isis 79 (1988), 397-398. On this episode, also see Harcourt Brown, Scientific Organizations in Seventeenth Century France, 82-89. 160 Boulliaus description of Robervals rusticity may be a reference to Robervals origins inter multos see above, p. 88. 341

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theory.161 And when on his voyage to Paris in 1655, Huygens did not meet Pascal and did not make significant attempts to do so, having been to ld that his counterpart had entirely abandoned the study of mathematics.162 Huygens later regretted not ma king more of an effort at an acquaintance, and it was probably only during the roulette contest that the two first directly corresponded. Their interaction provoked a growing mutual admira tion. Pascal, as Dettonville, addressed one of the parts of his publication to Huygens, praisi ng his incomparable clock and his geometrical reflections, which are a s ubject of admiration to all our geometers.163 Reflecting a similar pairing of practical a nd theoretical accomplishments, in 1659 Huygens expressed his admiration of Pascal to Chapelain: I esteem Pascal in finitely both for [the arithmetic machine] and for his knowledge in geometry, of which he has given the proof.164 Huygens and Pascal mutually praised the two el ements that qualified th em to bear the name Archimedes: technical mathematical skill and the practical application of that skill. The involvement of Pascal and Huygens in the roulette contest and their respective approaches to the curve show their comparable talents and accomplishments. However, the 161 Huygens had learned about this work during his 1655 visit to Paris and had undertaken some solutions of his own. The series of letters includes especially, Pierre de Carcavy to Chri stiaan Huygens, 20 May 1656, Huygens OC 1:418-419; draft, Christiaan Huygens to Claude Mylon, 1 June 1656, Huygens OC 1:426-427; Pierre de Carcavy to Christiaan Huygens, 20 May 1656, Huygens OC 1:431-433; Christiaan Huygens to Pierre de Carcavy, 6 July 1656, Huygens OC 1:442-446; Christiaan Huygens toClaude Mylon, 6 July 1656, Huygens OC 1:448-449; Pierre de Carcavy to Christiaan Huygens, 28 September 1656, Huygens OC 1:492-494; draf, Christiaan Huygens to Pierre de Carcavy, 12 October 1656, Huygens OC 1:505-506; draft, Christiaan Huygens to Claude Mylon, 8 December 1656, Huygens OC 1:524-525; Claude Mylon to Christiaan Huygens, 2 March 1657, Huygens OC 2:8-9. 162 Si lon ne meust asseur lors que jestois Paris que ce dernier avoit entierement abandonn lestude de mathematiques jaurois tasch par touts moyens de faire connoissance avec luy, Christiaan Huygens to Claude Mylon, 1 Feb 1657, Huygens OC 2:7. 163 cet horloge incomparable; ces merveilleuses dimensio ns des surfaces courbes des conodes, que vous venez de produire, et qui sont un sujet dadmiration tous nos gom tres, Lettre de A. Dettonville a Monsieur Hugguens de Zulichem, in Lettres de A. Dettonville 1. 164 Jestime Pascal infiniment et pour ceci et pour son savo ir dans la gomtrie, dont il a donn la preuve, et quil ma ddie, Christiaan Huygens to Jean Chapelain, 11 September 1659, translated in to French from Dutch in Mesnard OC 4:691. 342

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contest also represents an occasion during whic h the Archimedeses are sifted by circumstances and by the savant community, with Huygens em erging as the mathematician who embodied the ideals of the learned community that would become the Acadmie Royale des Sciences. Pascal, despite his efforts to play the broad-minded ho nnte homme gomtre, was alienated from the Montmor Academy, which defines the French learned scene of that time.165 By contrast, the learned group of Paris increasi ngly recognized and admired Huygens as a rising star. There are two reasons why Huygens became the central young celebrity of the Parisian learned community while Pascal was marginalized. Both of thes e reasons highlight the Parisian communitys preference for adult virtues to the childlikeness that plays such an important role in Pascals work. First, Huygens was preferred to Pascal becau se of his loyalty and commitment to the community of learning. He was sociable a nd communicative, corres ponding regularly with individuals from the Low Count ries (e.g., Sluse), England (e .g., Wallis), and Paris (e.g., Boulliau). Through these individuals, he maintain ed a steady contact with the work of others.166 Correspondence was an important element of early modern scientific endeavor, as recent research makes abundantly clear.167 Although living at a geographica l distance from the Parisian savant community, by writing and receiving letters he maintained close personal and scientific contact. He also established face-to-face relationships with Pari sian savants during his visit to the capital of France during 1655. His interpersona l aptitude is furthe r attested by his busy 165 Dominique Descotes uses this label and the term mathematical honntet to describe Pascals work as Dettonville in the roulette contest. It is necessary to the honnte savant to unite competence, universality, and utility to others, Descotes, Blaise Pascal: littrature et gomtrie 34-35. 166 Van Meerkerk, Correspondence Network of Christian Huygens, 211-228. 167 See, for example, Robert A. Hatch, Peiresc as Co rrespondent: The Republic of Letters and the Geography of Ideas, Science Unbound: Geography, Space, Discipline (Stockholm, 1998); also, L. T. Sarasohn, Peiresc and the Patronage of the New Science; and Les grands intermdiaires culturels ed. Christiane Berkvens-Stevelinck et al. 343

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schedule and interaction within the social and le arned circles of Paris during his visit there in 1660-1661.168 During this visit, he cemented his pl ace within the lear ned community through the polite and polished communication of his work on the pendulum clock and his observation of the rings of Saturn. Aided by the reputation an d social standing of his father, Christiaans favorable interactions with the Montmor group in Paris generally increased the respect its members had for him.169 By contrast, Pascal did not display the same sensitivity to sociability during the roulette contest. Besides the issues of secrecy discu ssed above, the limitation of access to the contests key figures promoted isolation, not conversation. Both Pascal and Carcavy were at times entirely cut off from the savants of Europe, and ev en from those in Paris. Despite having issued a challenge to submit solutions by 1 October 1658, the administrator of the contest, Carcavy, was absent from Paris during the month of September.170 What is more, Pascal withdrew from Paris, for health and religious reasons, being, as B oulliau writes confined I know not where in a Jansenist phrontistery.171 He was effectively detached fr om the learned community at a time when the work that he had produced suggested th e most possibility for the type of conversation so valued by this community. 168 Huygens maintained a detailed journal of his Voyage en France de 1655. Huygens OC 22:473-492; The journal for the 1660-1661 journal is in Huygens OC 22:525-576; 169 On technical aspects of Huygens, especially the centrality of mathematics to his work, see Joella Yoder, Unrolling Time: Christiaan Huygens and the Mathematization of Time (Cambridge, 1988). 170 This is attested by Boulliau to Christ. Huygens, 27 September 1658, Mesnard OC 4:261 Boulliau excuses himself for not responding the questions made by Huygens concerning the contest becaus e of this absence, ibid. 171 Monsieur Paschal sest confin je ne scay ou dans vn phrontistere de Jansenistes, que jignore encores, ainsi je ne pus la faire voir, Ismal Boulliau to Christiaan Huygens, 7 March 1659, Huygens OC 2:366. 344

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As Huygenss correspondence with him shows, Wallis believe d that the Dutch mathematician possessed the quality of fair-minde dness that the author of the contest did not.172 Wallis questioned Pascals civility in having ex travagantly offered a prize for the solution, for not giving adequate time to non-French mathema ticians to solve the problem, and for the deception of the hidden identity of the initiator of the c ontest. Huygens demonstrated great tact in these letters, repeatedly pr aising the subtlety of Pascals work on the roulette, while recognizing the possible negativ e aspects of the contest.173 Huygenss ability to build bridges marked him as a skilled social diplomat. Huygenss sociability was more conduciv e to his ongoing acceptance by the savant community than was Pascals secrecy and isolati on, but the practical applications of his work were also in harmony with the Montmor groups goa ls. In a letter from Sorbire to Hobbes outlining the constitution of Montmors group, the first rule of the gathering emphasizes the importance of practical benefits in those arts and sciences wh ich are best suited to achieve them.174 The same rule contrasts the importance of such utility in contrast with useless subtleties.175 It is not insignificant that the word subtle is used by some contemporaries to describe Pascal and his on the roulette.176 172 Judicium vero quod de me meisque feceris, quanto candidius sit quam quod tulerint Galli, posteriores quas misisti litterae notum faciunt, John Wallis to Christiaan Huygens, 10 September 1660, Huygens OC 3:126. 173 For example, Huygens himself questions the motivations fo r the offering of a prize, Draft, Christ. Huygens to Wallis, 6 September 1658, Mesnard OC 4:316. 174 Samuel Sorbire to Thomas Hobbes, 1 February 1658, in Hobbes, Correspondence Vol. 1 495. 175 Ibid. 176 Answering Huygenss inquiries about the roulette contest, Boulliau states his belief that Pascal was its originator. He then gives a brief descripion of Pascal: Il est vrai quil a lesprit trespr ofond & tres-subtil, Ismal Boulliau to Christiaan Huygens, 3 January 1659, Huygens OC 2:309. Huygens writes in a letter to Carcavy, 16 January 1659: Je crois les choses de Pascal encore plus subtiles [than those that he and Wren had done], Christiaan Huygens to Pierre de Carcavy, 16 January 1659, translated into French from Dutch in Mesnard OC 4:349. In describing his own work, Huygens writes of the Horologium that Il y a beaucoup dhasard a rencontrer des inventions semblables 345

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The preference of Sorbire and the Montmor groups for utility over subtlety does not suggest a complete dismissal of mathematics. In another letter, So rbire characterizes mathematics as godlike, showing the greatness of the human soul. However, its usefulness is limited: I do not discover there the grea t advantage which has resulted from it, for the perfection of our reasoning on other matters.177 The contest was, for Pascal, a purely geometrical one; little thought wa s given to application. The goal, suggested above, was to demonstrate the overpowering intelligence of the one who solved these difficult problems. Huygens, on the other hand, contributed to the geometrical conversation on the roulette, but he also made practical use of the roulette curve in the design of his pendulum clock. The curve used for a piece of metal to regulate the movement of th e pendulum clock was the roulette (or the cycloid, as he refers to it).178 Huygenss other major discovery of this period, the rings of Saturn, though not practical in itself, was closely linked to the technology of telescopes and lenses and was associated with observation rather than subtle reasoning. Huygens thus had the impressive ability to communicate mathematically with the likes of Pascal while maintaining a fruitful discussion with others w hose interests were less abstract. Huygenss fruitful work with the pendulum clock, much more successful than Pascals arithmetic machine, also suggests a more comfortable relationship with the artisa nal epistemology that informed the continued hands-on element of early modern natural philosophy. et fort peu de science ou de subtilit, Christiaan Huyg ens to Amos Dettonville [Blaise Pascal], 5 February 1659, Huygens OC 2:340. 177 Je ne descouure pas le grand aduantage qui a en reussi, pour la perfection de Nostre raisonnement sur les autres matires,Samuel Sorbire to Abb Tallemant (1 June 1659), BN, Paris, f. fr. 20612, folio 220 recto. 178 Horologium Oscilatorium (1673), Huygens OC 18:102-104. 346

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347 Huygens was convinced of the importance of ge ometrical study and believed that Pascals talents in mathematics would have proven of great worth to the lear ned community. After hearing of Pascals death, Huygens wrote to his brother Louis: I had always hoped that he would be given remittance from his weakness and that he would take up again some day this study in which he has so greatly excelled.179 Perhaps, had Pascal lived longer, Huygens might have urged him to publish more of his findings in mathematics; Chapelain had suggested the possibility that Pascals friends could convince him to do so: Retired from the world as he is, I do not believe that any similar ma terial could be drawn from him. He has a great number of other Tr eatises ready to give some curious Problems, but he keeps them most cruelly suppressed. Little by little one will win over him as he allows them to appear.180 Pascal and Huygens both believed in the power of mathematics, but in his final analysis the power was, for Pascal, only indirect. Scientif ic inquiry could not offe r spiritual consolation, the most important of goals.181 By bringing together childlike and adult virtues, mathematical practice mirrored the Christian lif e. Having known a career of math ematics from an early age, Pascal drew on the resources of that experien ce, and the virtues and vices of childhood as displayed in geometry, to encourage him to a lif e of Christian submission that pressed on toward spiritual perfection. 179 Javois tousjours esper quil se remettroit de sa foiblesse et quil reprendroit quelque jour cette estude ou il a si fort excell, Christiaan Huygens to Louis Huygens, 31 August 1662, Huygens OC 4:213. 180 Retir du monde comme il est je ne croyois pas quon pust rien tirer de luy de semblable matiere. Il a vne grande quantit dautres Traitts prests a donner de Problemes curieux, mais quil tient supprim auec asss de cruaut. Peu a peu lon gaignera sur luy quil les souffr e paroistre, Jean Chapelain to Christiaan Huygens, 15 October 1659, Huygens OC 2:496. 181 Pascal writes in the Penses : Knowledge of physical science will not console me for ignorance of morality in time of affliction, but knowledge of morality will always console me for ignorance of physical science, Pascal, Penses trans. Krailsheimer, no. 23, 6.

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CHAPTER 7 CONCLUSION Pascals life has been descri bed as a struggle between his religious devotion and his work in mathematics and science. This conflict has be en a legitimate and central concern of scholarly accounts of Pascals life and wor k, though in diverse ways. Some scholars have been content to lament Pascals waste of intellectual talent on superstitions and mysticism.1 But arguably, Pascal has proven attractive as a cultural icon precisely because of his complexity, that diverse mix of motivations and ideas so characteris tic of the perennial pursuit of knowledge, transcendence, and salvation. For nearly four centuries, scholars have sought to analyze Pascals writings and behaviors to unders tand how he navigated between reason, faith, science, and religion. The primary goal of this study has been to s how that the relationship between Pascals religious devotion and his scientific pursuits is closer and less adve rsarial than is often assumed. A guiding concern has been to show that these two types of pursuits represent a common tension between childlikeness and adult maturity. This study has shown that religious and scientific communities in seventeenth-century France shared many of the same concerns: the necessity of proper training and the mature exercise of disc ipline, as well as the continued innocence and receptivity of childhood. This study of Pascal is not a biography. It has not recounted all of the events of Pascals life (or even all of the important ones, some ma y argue) and all of his wr itings. It has instead sought to highlight the role of childlike and matu re virtue in Pascals life and work. More 1 Carl Boyer expressed the sentiments of many when wrote: As mathematicians, many of us undoubtedly would prefer that he had continued as a creator of mathematics rath er than as the tormentor of the Jesuits, Carl B. Boyer, Pascal: The Man and the Mathematician, Scripta Mathematica 26 (1963), 296. 348

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broadly, it has suggested what this tension might mean for the re lationship between a devout life and a learned life in seve nteenth century Paris. Pascals navigation of these waters is unique and this study has attempted to make these peculiarities clear, suggesting how they relate to the broader sevent eenth-century milieu. Pascals childhood talent, it has been shown, was a ppropriated by the Mersenne Circle, as he was pinpointed early as a possible candi date to contribute to the com pletion or perfection of mathematics. This study has linked Mersennes ma thematical goals with Pascals early talent to an extent that previous studies have not. It ha s done so, in part, by highl ighting the close parallel that Mersenne draws between Pascal and Huygens. This parallel, which is reiterated and analyzed further in Chapter 6, has also extended beyond the contributions of previous scholars. In addition, this study has emphasized the educational role of the Mersenne Circle in Pascals life and has attempted a consolidation of the pedagog ical associations of the term acadmie. This studys investigation of the tension between childlikeness and maturity in Pascal has uncovered instances of his appeal to the contrast between his ow n work and childish, instinctual behaviors. When taken together, these examples suggest Pascals attempt to distance himself from the associations that his early ment ors had made between his young age and his mathematical accomplishments. Along these lines, this study has located a previously unidentified connective thread be tween Pascals work on the arit hmetic machine and his work on the void. It has shown the signifi cant childlike/mature parallels between Pascals self-defense against the counterfeit work of the artisans of Rouen and the justifi cation of novelty in his preface to the treatise on the void. It has thus suggested how the artisan/theorist distinction (and its relationship to a burgeoning scientific method) is given fu rther nuance and complexity through emphasizing its connection with both childlike receptivity and mature mastery. 349

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Underscoring the geometrical origins of Pas cals religious pursuits and the role that mathematics plays in his broader views of knowledge, this study has reflected key epistemological shifts during the early modern period. It has argued that the Jansenist questioning of the sufficiency of mathematical re asoning combined with the chevalier de Mrs suggestions that mathematics was of dubious value disturbed Pascals confidence in geometrical supremacy. This study has linked Pascals uncertain ty about the role of rh etorically useful but restricted mathematics with his religious reflecti ons concerning the need of believers to submit to the limitations of their createdness while also s eeking the self-transcendence of perfection. The present study has maintained that the combin ation of these ideological concerns and the circumstances of Pascals position between devout and learned communities created an atmosphere in which religion and scie nce mutually informed one another. This studys examination of the period of Pas cals life following his 1654 Night of Fire has reiterated what other scholars have also recognized: Pascals life did not follow a linear trajectory away from mathematics and toward a more devout religious commitment. Focusing on the duality of childlikeness and maturity has demonstrated that Pascals expression of these traits in his religious works has underlying connections with th e language of his mathematical and natural philosophical writings. Pascals back-and-forth movement between mathematical and religious work shows that he continued to explore this troubles ome relationship throughout his life. This study has attempted to show how reflections on childhood virtue and the necessity for mature application of talent appear as str ong and consistent elements in Pascals life and work. Reflecting these ongoing concerns, Pascals ro ulette contest, this study has argued, was a quasi-return to the mathematics that he had prac ticed as a child and as a young man. While he 350

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351 attempted to prove through his discovery of new results that his mathemati cal talent had been put to good use and that such work had a kind of ut ility, he also reverted to an attitude of mathematics as a diversion. In the end, Pas cals ambivalence about mathematics and the contingencies of his ill health helped to fr ame his separation from the community of savants during the late 1650s and early 1660s. Pascals life was not tidy and neat, it did not march toward a clear and simple conclusion. When Pascal died at the age of 39, he left many questions unanswered. Biographers and historians are left to conjecture about what might have happened, and what legacy Pascal might have left had he lived longer. If he had returned to full healt h, it seems likely that Pascal would have made another attempt to es tablish the quality of his mind and his legitimacy in the learned community of Paris. Given the opportunity, the evidence suggests that Huygens would have been keen to develop a deep er relationship with Pascal.2 The interaction between the Catholic Archimedes and the Protestant Archimedes woul d certainly have benefited both. As this study has suggested, a detailed comparison of Pascal and Huygens would be fruitful and telling, it would shed light on their stat us as childhood mathematicians, the role and influence of Mersenne, and respective experiences and relationships with artisans. Pascals legacy is unique. Because of his variegated identity translated through more than three hundred years of works about him, he is a rich source of insight regarding the cultural values of the seventeenth century and the assump tions of those that have written about him. Pascals complexity, refracted through so many lenses, may sometimes appear aberrant. But when viewed from the intersection of childlikene ss and maturity, many faces of Pascal come to focus, sometimes with a fresh shock of recognition. 2 See above, p. 347.

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APPENDIX CHRONOLOGY1 19 June 1623 Birth of Blai se Pascal in Clermont 1625 Publication of Mersennes La vrit des sciences contre les septiques in which Mersenne invokes some new Archimedeses 1626 Death of Antoinette Bgon, Pascals mother 14 April 1629 Birth of Christiaan Huygens at The Hague November 1631 The Pascal family relocates from Clermont to Paris 6 February 1635 Richelieu appoints a commission of five individuals to investigate JeanBaptiste Morins supposed inventio n of a method for determining longitude. The commission includes tienne Pascal, the abb Chambon, Claude Mydorge, Jean Boul enger, and Pierre Hrigone 23 May 1635 In a letter to Nicolas-Claude Fa bri de Peiresc, Mari n Mersenne announces the existence of the Parisian mathematical academy September 1635 Mersenne lists by name the me mbers of the group he had previously announced: tienne Pascal, Mydorge, Cl aude Hardy, Gilles-Personne de Roberval, Girard Desargues, abb Chambon, and some others. 1635-1636 According to the familial legend, Bl aise discovers geometry during his leisure time. Shortly thereafter Blaise is introduced to Mersennes circle of friends 24 March 1638 tienne Pascal goe s into hiding after an uprising of those who received Hotl de Ville rents, which went unpaid due to French war debts February 1639 Publication of Desargues Brouillon Projet November 1639 After having return ed to favor in late spring, t ienne Pascal is appointed as Deputy Commissary of Norman dy. The Pascal children remain in Paris under the care of Louise Delfault 1640 Pascals Essai pour les coniques is printed in Paris. The Essai is distributed to a number of Mersennes correspondents, including Ren Descartes 1 Much of this appendix is indebted to the detailed chronological work of Jean Mesnard in Blaise Pascal, Oeuvres compltes vols. 2-4. 352

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Spring 1640 The Pascal children return to the care of their father, living in Rouen 1642-1643 According to his sisters biography, Blaise begins work on his arithmetic machine 14 May 1643 Death of Louis XIII 26 February 1643 Letter from Pierre Bourdelot to Pascal indicates that Pascal had an arithmetic machine ready to demonstrate 1645 Pascal writes his two major account s of his invention of the arithmetic machine: his Lettre ddicatoire a Mo nseigneur le Chancelier and his Avis ncessaire ceux qui auront curiosit de voir la machine arithmtique, et de sen servir January 1646 tienne Pascal falls on some ice and breaks his leg, bringing him into contact with the Jansenist brothers Adrian and Jean Deschamps. The brothers introduce the family to the writings of Saint-Cyran September 1646 Pierre Petit describes the experi ment of mercury in tubes of glass to tienne and Blaise Pascal 12 September 1646 Constantin Huygens introduces Chri stiaans work to Mersenne in a letter. This begins a correspondence be tween Mersenne and Christiaan October 1646 Pierre Petit and tienne a nd Blaise Pascal perform the mercury experiments together in Rouen January 1647 In letters to Constantin and Christiaan H uygens, Mersenne favorably compares Christiaan to Archimedes 1, 5 February 1647 Interview between Pascal, Hall de Monflaines, Adrien Auzout, and the priest Jacques Forton, sieur de Saint-Ange, recorded in the Rcit de deux confrences Summer 1647 Pascal and J acqueline return to Paris 20 August 1647 Death of Claude Mydorge 23-24 September Meetings between Descartes and Pascal. The September 23 meeting is in 1647 the presence of Roberval, and ends in a heated argument between the two older mathematicians. The Septembe r 25 meeting is attended by Dalibray October 1647 Publication of Pascals Expriences nouvelles touchant le vide 353

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October-November Exchange of letters between Pascal and Father tie nne Nol, concerning 1647 the question of the void 26 January 1648 Letter from Blaise to Gilberte in which he recounts the meeting between him and Monsieur de Rebours of Port -Royal. Rebours, suspicious of Pascals background in mathematical st udies, reproves Pascal for his claim to be able to defeat Port-Royals enemies through reason January 1648 tienne Nol publishes his work Le plein du vide Winter 1648 Letter from Pascal to Jacques Le Pailleur, explaini ng his non-response to Nols claims regarding the void April 1648 Letter from tienne Pascal to Father Nol 1 April 1648 Letter to Gilberte Prier from Bl aise and Jacqueline Pascal, in which they articulate the need for recognition of limitations and a striving toward Christian perfection Summer 1648 Jacqueline desire s entry to the convent of Port-Royal, but is opposed by her father 1 September 1648 Death of Mersenne 19 September 1648 Under the advice of Pascal, Flor in Prier performs the mercury experiment on Puy-de-Dme in Auvergne May 1649 tienne, Blaise, and Jacqueline Pasc al escape difficult conditions in Paris due to the Fronde. They live in Clermont until November 1650 22 May 1649 Privilege issued for Pascals arithmetic machine 11 February 1650 Death of Descartes in Stockholm November 1650 tienne, Blaise, and Ja cqueline Pascal return to Paris 7 September 1651 Louis XIV assumes his throne 24 September 1651 Death of tienne Pascal 1654 Date of Pascals address to Pari ss mathematical circle, Celleberrim matheseos academi parisiensi. In it, Pascal gives an outline of his completed works and his works-in-progress 5 June 1653 Despite Blaises opposition to the plan following tiennes death, Jacqueline becomes a nun at the co nvent of Port-Royal de Paris. 354

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1653 or 1654 Journey with the Duke de Roann ez and the Chevalier de Mr, described in Mrs De lesprit July-October 1654 Correspondence be tween Pierre de Fermat and Pascal, marking the beginning of modern probability theory September 1654 Pascal visits Jacqueline and confides in her his movements toward spiritual renewal 4 November 1654 Death of Jacques Le Pailleur 23 November 1654 Pascals Night of Fire. Summer/Fall 1655 Christiaan Huyge nss first visits to Paris 26 October 1655 Letter from Jacqueline to Blaise in which she mentions Blaises method for teaching children to read 23 January 1656 Date of first of the Provincial Letters. The letters would continue to be written and published quickly, with th e eighteenth lette r dated 24 March 1657 30 March 1656 Temporary dispersion of Port-Royals petites coles Children would return to the schools a year later 15 or 17 April 1657 Jacqueline Pascal writes her R glement pour les enfant s in a letter to Antoine Singlin, regarding her procedures for teaching and overseeing the young girls in her care Fall 1657 Ren-Franois de Sluse begins indirect correspondence with Pascal through Cosimo Brunetti Spring 1658 Beginning of the direct co rrespondence between Sluse and Pascal JuneJuly 1658 Pascals anonymous first circular letter concerning the contest of the roulette is distributed to sava nt mathematicians across Europe July 1658 Second letter on the roulette contest is printe d and circulated September 1658 Carcavy, responsible for receiving solutions to the roul ette problems, is absent from Paris 1 October 1658 Date at which the first circular letter requires solutions to the problems of anonymous to be attested as complete 355

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356 7 October 1658 Date of third circul ar letter on the roulette contest 10 October 1658 Date of the Histoire de la Roulette written anonymously in both French and Latin December 1658 Printing of the first of Pascals Lettres de A. Dettonville 6 December 1658 Letter from Boullia u to Huygens describing Roberv als disruptive outburst at Montmors home 12 December 1658 Date of Suite de lhistoire de la roulette February 1659 First publication of the full form of Pascals Lettres de A. Dettonville 12 March 1660 Final closing of Port-Royals petites coles 28 October 1660 Christiaan Huygens returns to Paris. He remains there until 19 March 1661 6 November 1660 Letter from Jacqueline to Blaise which refers to Pasc als temporary care of students displaced by the closing of Port-Royals petite coles 4 October 1661 Death of Jacqueline Pascal June 1662 Pascals last illness begins 3 August 1662 Date of Pascals Last Will and Testament 19 August 1662 Death of Blaise Pascal

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Huygens, Christiaan. Oeuvres compltes de Christiaan Huygens 22 vols. The Hague: Martinus Nijhoff, 1888-1950. Le Gallois, Pierre. Conversations acadmiques tires de lAcadmie de M. labb Bourdelot 2 vols. Paris: Claude Barbin, 1674. Lesaulnier, Jean, ed. Port-Royal Insolite: Ed ition Critique de Recue il de Choses Diverses Paris: Klincksieck, 1992. Magni, Valerian. Principia et specimen philosophiae. Cologne, 1652. Marolles, Michel de. Les memoires de Michel de Marolles. Paris: Antoine de Sommaville, 1656. Mr, Chevalier de. De lesprit: discours du Monsieur le chavelier de Mr Madame *** Paris: Denys Thierry, 1677. Oeuvres Compltes du Chevalier de Mr 3 vols. Paris: Fernand Roches, 1930. Mersenne, Marin. Cogitata Physico Mathematica Paris: Antonio Bertier, 1644. Correspondance du Pre Marin Mersenne Edited by Cornlis De Waard. 17 vols. Paris: G. Beauchesne, 1933-1985. Harmonie vniverselle conte nant la theorie et la pratiqve de la mvsiqve Paris: Cramoisy, 1636. La vrit des science contre les septiques ou Pyrrhoniens Paris: Toussainct Du Bray, 1625. Limpiet des deistes, athees, et libertins de ce temps combatu, & renuersee de point en point par raisons tirees de la philosophie, & de la theologie Paris: P. Bilaine, 1624. Lusage de la raison. 2002 edition. Paris: Adrien Taupinart, 1623. Novarum Observationvm physico-mathematicarvm, tomus III Paris: Antonio Bertier, 1647. Questions inouyes; Questions harmoniques; Qu estions thologiques; Les machniques de Galile; Les prludes de lHarmonie Universelle, corpus des oeuvres de philosophie en langue franaise Paris: Fayard, 1985. Trait de lharmonie universelle Paris: Guillaume Baudry, 1627. Universae geometriae mixtaeque mathematicae synopsis Paris: Antonio Bertier, 1644. 360

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BIOGRAPHICAL SKETCH Daniel Timothy Julich was born in 1974 in Baton Rouge, Louisian, the seventh of nine children. He grew up in Indialan tic, Florida and graduated from Melbourne High School (FL) in 1992. After receiving an Associate of Arts degree from Brevard Community College in 1994, he majored in mathematics, with a minor in secondary education, at Palm Beach Atlantic College, graduating with a Bachelor of Science degree in December 1996. He enrolled in the Wheaton College (IL) graduate school in 1998 and received a Master of Arts in Biblical and theological studies in 2000. His mast ers thesis was titled Certainty and Transcendence: An Interpretation of the Interaction betw een Mathematics and Theology in the Life and Works of Blaise Pascal Daniel entered the doctoral program in histor y at the University of Florida in 2003 and completed his Ph.D. in the history of science in May 2009.