Pascal's Wager (4 page)

M
an is but a reed,” wrote Blaise Pascal in his last work, the
Pensées
, “the most feeble thing in nature, but he is a thinking reed. The entire universe need not arm itself to crush him. A vapor, a drop of water suffices to kill him. But, if the universe were to crush him, man would still be nobler than that which killed him, because he knows that he dies and the advantage which the universe has over him, the universe knows nothing of this. All our dignity then, consists in thought. By it we must elevate ourselves, and not by space and time which we cannot fill. Let us endeavor then, to think well; this is the principle of morality.”
⁵

Certainly it was a risk, an act of belief, perhaps even faith, for Étienne Pascal to cart his children all the way to Paris, so far from their family and friends. Likely, his main reason for doing so was to introduce them to the more cultured life of Paris, to the circle of great intellectuals, and possibly to a new life at court, where the intellectual world of a provincial
tax judge could expand beyond expectations. There is some evidence that Étienne, seeing some intellectual promise in his son, Blaise, had developed a master plan to turn the boy into one of the great minds of the day. He succeeded in this, even though Blaise himself later rejected that life and embraced the rigors of Jansenism. Blaise was by Gilberte’s account a precocious little boy who asked questions far beyond his years and held conversations that would seem appropriate to an adult. This, of course, may be more mythology than fact, for it was common in seventeenth-century France to describe saints in their youth in biblical terms, like Jesus sitting among the doctors of the law in the Temple of Jerusalem, astounding them by the acuity of his questions. Thus, sanctity and genius were intertwined. In Gilberte’s way of thinking, if Blaise had already become a great man by the time of the writing of her biography of him, then, like the saints who as toddlers wanted to listen only to the wisdom of old men, he would certainly have shown that same kind of supernatural promise, that divine gift, early in his life.

Étienne set about the task of educating his children, and along the way created an innovative regimen of homeschooling. He proved to be quite a capable teacher, a man who was ahead of his time in understanding the psychology of education. It was his maxim, according to Gilberte, that he would always keep his lessons at a level just above the level of the work his students were capable of. Thus his children had to strive to understand that which was in sight but which was just beyond their grasp. In this way, Étienne built up the confidence of his children by giving them problems that they could solve, but only with sweat. Each solution then became another triumph and allowed their minds to grow, leaving them secure in the knowledge that they could solve whatever puzzles were laid before them.

Homeschooling, however, had its drawbacks, for Blaise was never allowed to attend school and thus never learned the art of fine negotiation that most children learn on the playground. Thus he remained ignorant, at least experientially, of many of the subtleties of human life. He never attended school or matriculated at a university. He never married or even seriously courted. Although Étienne introduced his children to the intel
lectual life in a profound way, he failed to give them the kind of emotional training one needs to live a fully human life. Had Antoinette been alive, that might have been different.

One source of Étienne’s pedagogical method was his own experience of mathematics—how it could become an all-consuming fascination that could distract the mathematician from other kinds of study. He was also concerned that, given Blaise’s fragility, he not tax his son’s strength. He therefore refused to allow Blaise to study mathematics until he was sixteen. He did not want him to be caught by this great passion too early, until he had been firmly grounded in grammar and in languages, especially the classics and classical literature. Instead, he presented his children with little problems in natural science. At the dinner table one evening someone struck a porcelain plate with a fork, and Blaise asked why the plate hummed. What was the cause of the sound? Why did the sound stop when you put your hand to the plate? After dinner, Blaise went about the house striking dishes with various kinds of silverware and found that different plates made different sounds, each with its individual pitch and timbre. In this one moment, Étienne introduced his son to experimental science, and encouraged him at each step. The problem, however, was that Blaise was in fact as precocious a child as Gilberte indicated. He was curious and, when given a boundary by his father, could not help but try to jump over it.

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.

F
ighting 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
= 2
^p
- 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 having 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?