Pascal's Wager Read online

  When Blaise was about eight years old, he spent much of his free time lying in front of the fire in his room, drawing diagrams in charcoal and working out calculations on the stones in front of the fireplace. He knew that he was breaking his father’s rules against studying mathematics, and he tried to keep his work secret. At first, he tried to draw a perfect triangle, and then a perfect circle. As he came closer and closer to this, he began to develop his own language for his new geometry. He called a line a “bar,” and a circle a “round,” and, using his new vocabulary, he set about re-creating Euclid’s ideas. He actually managed to reconstruct several of Euclid’s theorems before his father walked in on him and found him drawing on the stones. Unseen, Étienne watched from a distance for a long time and then approached. Gilberte does not say who was more disconcerted at the discovery. Blaise had been caught disobeying his father’s orders, but for Étienne it was a happy capture, for he found his son busy working on a project much beyond his level of maturity. Suddenly he realized that Blaise was not just precocious, but a prodigy. What could he do with such a son? What should he do? Both thrilled and fearful, nearly in tears, according to Gilberte he left his son alone by the fire, to continue re-creating the work of a man he had never read. Étienne said nothing about disobedience.

  [1635]

  Blaise Among the Geometers

  For he by geometric scale,

  Could take the size of pots of ale.

  —SAMUEL BUTLER

  Philosophy is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters 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

  Fighting back tears, Étienne left Blaise to his studies and hurried to the house of his friend, another mathematician, a man named Jacques Le Pailleur. Once there, he wept openly, and Le Pailleur, concerned that some tragedy had fallen on the Pascals, fretted. What could cause his old friend to be so upset? Étienne stopped him mid-fret and told him that he was not weeping from grief, but from joy, and showed him some of the papers onto which Blaise had transferred his fireplace diagrams and calculations. After glancing at the handful of drawings, with symbols and arrows drawn in a child’s hand, Le Pailleur realized that Blaise was a gifted child. He saw that, having been denied mathematics by his father’s pedagogy, Blaise had simply invented it for himself.6 Le Pailleur advised Étienne to abandon his course of study and to introduce the boy to mathematics at once. When Étienne returned home, instead of punishing Blaise, he presented him with a copy of Euclid, and told him to study it in earnest.

  What better gift could a young intellectual have had at that time than a gift for mathematics? Mathematics was, after all, the royal science. The medieval universe was fading away, and the old divine certainties were losing ground. The scientists and philosophers of France were busy casting about for something new to bet their souls on, a new ground of order, a new way to make the universe spin properly, and for most of them, that something was mathematics. Everyone in France used it; it was the latest, hottest thing. Those in the inner circles of thought passed around treatises on geometry like junk novels at the beach, while merchants sought new ways to turn their business dealings into numbers.

  Even the philosophers and theologians turned to mathematics for insight. The great French gardens were finger exercises in geometry; the vast, ostentatious hôtels of the high aristocracy were designed and built according to mathematical principles. Metaphysics, before and after Descartes, was gradually becoming a creature of mathematical logic. The pinnacle of reality was the pinnacle of order, and mathematics was the measure of that order. In their deepest hearts, French intellectuals thought that God was the ultimate mathematician, and now Étienne Pascal’s own son had proved himself to be an adept at reading God’s mind, a mathematical prodigy, a child who was born to geometry just as Mozart, 150 years in the future, would be born to music.

  Sometime after, Étienne brought young Blaise along when he attended the little gathering of mathematicians and scientists that met in Père Mersenne’s monastic quarters. Marin Mersenne was one of the great scientific majordomos of the age, a defender and promulgator of Galileo’s astronomy, a gatherer of mathematicians and natural philosophers, and a great opponent of those mystic fakeries alchemy and astrology. He was a priest, a member of the Order of Minims, the most humble of all religious orders. Mersenne’s little group, which would eventually become the Academy of Paris, the French equivalent of the Royal Society, would likely have met in his monastic cell sitting on hard, straight-backed chairs without much padding, in a circle or around a table. Some may have smoked tobacco in long clay pipes, since smoking was not forbidden—because, after all, better to tax it than forbid it, and because even Catherine de Médicis, the great queen of France from the century before, often took snuff as a cure for migraines. They would drink wine, not coffee (for coffee was a Calvinist drink, a Huguenot drink for the rising bourgeoisie, promoted by the Protestants as a way to awaken humanity from its Catholic alcoholic stupor to a new world of activity and industry). A bit of bread, a bit of onion, a bit of cheese, a bit of wine, and along the way they discussed matters of scientific merit, from methods of identifying prime numbers to new ways of marrying algebra with geometry to the failures and weaknesses of alchemy. Salacious, even radical, conversation they left to the libertines, those scoffers and doubters, those Deists, who were not welcome at Père Mersenne’s table. They would leave such libertine conversation to the insidious salon of Madame Sainctot, the retired courtesan with the notorious past who was another friend of Étienne Pascal’s.

  This little group gathering in Père Mersenne’s monastic cell made quite a splash. Some of the best minds in Europe were there. Descartes was a member. Mersenne himself had been the leading investigator into prime numbers. His formula n = 2p- 1 (where p is a prime number) was not perfect for identifying primes, but it came close, and it is in fact still being used to help identify large primes. As a scholar, he was so connected, through letter and personal contact, with the leading thinkers of the time that many said that telling Père Mersenne about a new idea was the same as publishing it.

  Pierre de Fermat, Blaise’s future correspondent on probability, was also a member, and it was in Mersenne’s monastic cell that Blaise first met him. Fermat is famous even today for his last theorem, and for his work on spirals and falling bodies.7 He first came to Mersenne’s group by writing to the priest and by correcting some of Galileo’s titanic mistakes in geometry. He also developed new ways of determining the maxima and minima in an equation’s curve, methods that conflicted with Descartes’ own ideas, already published in his La géométrie, where he set forth his view of algebraic geometry. Needless to say, this set off a feud. Descartes wrote, expressing his dislike for Fermat’s method for determining maxima, minima, and tangents, and Fermat fired back. Étienne Pascal entered the war on the side of Fermat, as did Gilles Roberval, a royal professor of mathematics and another of Mersenne’s group. Descartes asked Girard Desargues, yet another member, to referee, and soon after he was proved wrong. Descartes had the good grace to admit it in a letter, though grudgingly. Nevertheless, those who had sided with Fermat were from that point on in a bad odor with René Descartes.

  It was about this time that Desargues, a man known to both Pascals, published a book on conic sections that would be a strong influence on the young Blaise, leading to his first published work. Desargues’ book had the unlovely title of Brouillon projet d’une atteinte aux événements des rencontres du cône avec un plan, or Rough Draft for an Essay on the Results of Taking Plane Sections of a Cone. Inside it, however, was an entirely new type of geometry, a projective geometry, with a new way of looking at conic sections as havi
ng properties that are invariant under projection. That is, if you draw lines through points on conic sections, those lines form projections out into the space around the conic section, and those projections will act in regular ways. In this way, Desargues invented a unified theory of conic sections, something that had not been done in that way before. This was quite an achievement, one that entranced the young Pascal, who had come to believe that geometry was the path to understanding the greatest truths of all. A short time later, after his family had moved to Rouen, and while the city was on fire with revolution, Pascal would make his own contribution to this new geometry. What better way to retreat from the violence of the outside world than into your own mind?

  [1585–1642]

  Un Bâtarad Magnifique

  Deceit is the knowledge of kings.

  Qu’on me donne six lignes de la main du plus honnête homme,

  j’y trouverai de quoi le faire pendre.

  [Give me six lines written by the most honest man, and I would find some reason there to have him hanged.]

  Pour tromper un rival l’artifice est permis; on peut tout employer

  contres ses ennemis.

  [Deception is permissible to mislead a rival; use every means against an enemy.]

  —ARMAND JEAN DU PLESSIS, CARDINAL RICHELIEU

  One must never forget that Étienne Pascal had taken his children to the Paris of Cardinal Richelieu—a fashionable place, a wealthy place, a place of power, where the Bastille glowered over all things. The Pascals had met the cardinal on several occasions, for they were themselves a fashionable family; they changed residences five times during their stay in Paris, always from one smart district to another. Their first house was on the rue de la Tissanderie, in a district where Henri IV had built two new palaces with their elaborate lawns and avenues. After a few years, Étienne brought his family across the river Seine to the Alberg-Charmaine, across from the great hôtel of the king’s cousin, the prince de Condé, the man whose son would eventually lead a revolt against the regency of Louis XIV during the Fronde of the Princes, a coup d’état by the old nobility, misnamed really, for the term fronde refers to a popular uprising.

  The cardinal was at the height of his power in those years. An odd man, diminutive, oppressed by his own conscience, sickly, he was a conservative churchman who nevertheless considered his first duty to be to his king and not to his church. He had set himself the task of welding that collection of feudal principalities that was France into one of the great nations of Europe, under an all-powerful absolute monarch, a monarch whom the cardinal controlled. Order was his abiding spiritual principle, and though he often used the rack as a finger of government, he used it no more than did any other ruler at the time.

  Richelieu worked incessantly; he was never far from his desk, a fact that showed his middle-class roots. Armand Jean du Plessis de Richelieu, the cardinal, was a breathing contradiction. He had an iron will but a weak constitution, frail and sickly, pale under his ecclesiastical robes. Though perpetually ill or suffering from the fear of illness, he terrorized the entire court.

  In spite of his frailty, once he was dressed in his cardinal’s robes, his stern, unbending appearance forced people into submission. And he even exercised this power though Louis XIII, his great protector and benefactor, did not like him very much. Everyone knew this. As he was with so many people, Louis was outwardly courteous but cool. But every time he tried to oppose the cardinal, Richelieu appeared before him and presented his case, step-by-step. Richelieu was so rigorous, so rational in his argument, that Louis could not help but agree.

  Various cabals gathered to rid the court of the little cardinal but failed. The man behind most of them was the king’s brother Gaston d’Orléans, a wastrel addicted to gambling, good times, and irresponsibility, though he was his mother’s favorite son. Time after time, in a bid for the throne he tried to unseat the cardinal in order to make his brother the king, who was chronically ill from tuberculosis, more vulnerable, for everyone knew that it was the cardinal who kept the king secure on his throne. But Gaston was not the cardinal’s only enemy. Both queens—Anne of Austria, the wife of King Louis XIII; and the Queen Mother, Marie de Médicis—detested him and wanted to be rid of him, and on at least one occasion they tried to unseat him. But he proved stronger than they, and in the end the Queen Mother, along with Gaston d’Orléans, had to flee France for their lives.

  Richelieu had some experience, and some talent, in putting down revolts. He had a world-class intelligence service, led by a Franciscan monk, Father Joseph. In 1626, the monk’s agents caught Gaston in a conspiracy. The cardinal could not imprison a member of the royal family, so he went after the other conspirators: the governor of Gaston’s territory, Marshall Dornano; and Gaston’s friend Henri de Talleyrand, the marquis de Cha-lais. Richelieu had them arrested, had the friend executed, and sent the governor to the Bastille, where he died. After that, one after another, the cardinal removed the teeth from his once-powerful opponents. The prince de Condé, the king’s cousin and the Pascals’ neighbor, a famous warrior and a lion on the battlefield, eventually held the curtains open for the cardinal to let him pass. Others did the same. Even the king was easily bullied, for Richelieu had built for himself the perfect place for any bureaucrat: he was indispensable. Louis was a weak, vacillating king, a deeply closeted homosexual susceptible to older men. Without much of a mind of his own, he left the job of running the country to his minister, Richelieu. The problem was that Louis had a conscience, an unfortunate possession for a king, and he vacillated between the realpolitik of Richelieu and the dictates of his own conscience. But Richelieu always seemed to win, even over the king’s scruples, for he set such moral issues against Louis’s own self-interests. And the fact that the cardinal’s oppressive tax policies kept the money flowing didn’t hurt, either.

  Richelieu was an amateur at finance, but his policies, though not very successful in growing the economy, managed to wring enough money out of the people to keep the royal family in palaces. Everyone at court knew this and gnashed their teeth in frustration. Meanwhile, powerful men ended their lives in the Bastille or swinging at the end of a rope. “Give me six lines written by the most honest man, and I would find some reason there to have him hanged,” Richelieu once said. Everyone knew this to be true.

  Historians have been hard on Cardinal Richelieu, and perhaps unfairly. The Enlightenment pundits loathed him; their novelists and playwrights made fun of him, because he was the architect of the Old Order. Nevertheless, it would have been a disaster for France had the cardinal fallen. Gaston was too self-involved to be a good king, and he owed too many favors to the old feudal princes to be his own man. The same can be said of the prince de Condé, for he was the man in charge of the old baronial party. Had either of these men dethroned Louis and his first minister, France would have shattered into a hundred feudal pieces and fallen back into medieval disarray, to be nibbled to death by the surrounding Hapsburg powers. It was probably best for France that the Magnificent Bastard crushed all his opponents at court, though you couldn’t have told them that.8

  The fact that Étienne Pascal had chosen to live in such fashionable surroundings, so close to the seats of power, suggests that he had more than one reason for moving his children to Paris. Like the cardinal, he was a consummate bureaucrat, a man whose fortunes lay with the administration of the nation. To grow in power and influence would mean to find ways of being close to princes—but, as he would find out, the power of princes can be a force of nature, shifting with the winds of policy. And the man who drove those winds was Cardinal Richelieu.

  If Étienne had wished for the life of an intellectual, with an intellectual’s reputation, he soon got it. Jean-Baptiste Morin had developed a new technique for calculating longitude, a vital problem for any nation that had dreams of maritime trade, the solution of which meant life or death for sailors. In 1634, Cardinal Richelieu appointed Étienne to a special seven-member committee of scientists and ma
thematicians called together to evaluate Morin’s technique. Richelieu wanted a quick solution to the longitude problem but had little idea of what that involved. After all their long discussions, the committee was not able to declare a solution, though Étienne’s gamble had paid off. He had left his hometown for the great city, and the cardinal had favored him—at least for the moment. That would change.

  [1631–1638]

  Madame Sainctot’s Salon

  A gentleman should be able to play the flute, but not too expertly.

  —ATTRIBUTED TO ARISTOTLE

  A gentleman knows how to play the accordion—but doesn’t.

  —AL COHN

  Fortune favors the brave.

  —TERENCE

  Père Mersenne’s little group was not Étienne’s only circle of friends in Paris. Another was the group of pundits, poets, and satirists who gathered around Madame Sainctot, a woman of the court, well known to the queen. Madame Sainctot, like so many court women, was a great beauty with an infamous past. A women of influence, she was a member of the lower nobility who had cultivated the virtues of the courtesan—timing, beauty, cheek, brilliance, joie de vivre, grace, and charm.9 And she had l’esprit aplenty. She was a mistress of the art of conversation, surrounding herself with witty and often outrageous companions, so that her soirees were like her own private court, filled with glittering people who told ribald stories and preached mildly radical ideas. She was also pious in her own way, and sprinkled among the literati was a pinch of clergy. The literati knew their part, as did the clergy, so the conversation was often radical, but not too radical—that could get one a ticket to the Bastille—just radical enough to titillate.