Pascal's Wager

by James A. Connor

  Money makes the world go round, and this was also true in the seventeenth century. The aristocracy had their privileges, granted to them by birth and family history; the poor had almost nothing; the rising bourgeoisie had money, and money was slippery. The entire story of the events leading up to the French Revolution can be summed up in this truth. The seventeenth century was not merely the time in which science began to take hold, but also the time in which money began to take hold, to affect even the aristocracy in their complacent privileges. But it was the middle class, then as now, who always felt the pinch, who, unless they secured their money, could easily fall back into the nameless masses of the poor. Understandably, then, Étienne and the other investors grew disturbed over the cardinal’s decision. That March, in 1638, Étienne Pascal, the man of good breeding, the man of science and mathematics, the enlightened teacher, the socialite and intellectual, joined the other investors in a protest, which, as protests will, got out of hand. Someone made threats, and someone acted violently, and someone was openly seditious. The cardinal, in a snit, responded in kind and ordered his agents to gather them all up and throw them in prison. If Richelieu knew anything, it was how to put down protesters.

  In full flight, Étienne left his children behind to be cared for by friends and by his domestic servants. Imagine the fear of his children: they had lost their mother when they were only babies, and now their father, their only protector, had been forced to run for his life, or at least for his freedom. But the Pascals were fortunate in their friends, especially Madame Sainctot, who gathered the children around her and began to scheme for Étienne’s return and rehabilitation. The friends had one hold card. Blaise was not the only talented Pascal; his younger sister, Jacqueline, was an accomplished poet, and had been even as a child. She was a pretty child and, like Blaise, intelligent beyond her years, the kind of child who makes adults coo when they are anywhere nearby. She was also a sunny child, happy most of the time, at least according to her sister, Gilberte—though Gilberte cannot always be trusted, because she tended to idealize her family. But like her brother, Blaise, Jacqueline was also stubborn.

  Her father had once assigned Gilberte the job of teaching Jacqueline to read, and for some time the little seven-year-old seemed impervious to her sister’s instructions. Then, by accident, Gilberte read Jacqueline from a book of verse, and it changed everything, for the little girl seemed captivated by the music and rhythm of the language. From that point on, it was easy. Four years later, along with the two daughters of Madame Sainctot, Jacqueline wrote and performed in a five-act play, written entirely in verse. The play was the talk of the fashionable ladies of Paris, and the sudden notoriety started the young Pascal on a literary career of her own.

  In 1638, the king’s wife, Anne of Austria, conceived after twenty years of waiting, if not twenty years of trying. Her husband, Louis XIII, was a scrupulous man, and cold to nearly everyone, especially his wife. As was all too common in kings at that time, he didn’t like his wife very much. She had been foisted on him as a political choice, not because of any compatibility, but rather as a way of connecting the French throne to the all-powerful Hapsburgs. There is some doubt that he even consummated the marriage. No one would admit that, however, because it would have led to war. The people of Paris had begun to wonder if the king and queen would ever conceive. Mostly, they were simply frustrated with the royal pair: would they ever get around to doing their duty? At a time when producing a legitimate heir to the throne was the principal duty of any king, this was an important question. No one had forgotten the endless dynastic wars that had beggared Europe throughout the Middle Ages.

  But then, like Sarah the wife of Abraham, Anne came up pregnant just when the people were beginning to lose hope. This child would live to become Louis XIV, the Sun King, the man whose lavish lifestyle would set France solidly on the path of revolution. The court gathered around Anne to pamper her in her delicate condition and schemed to find diversions to keep her entertained. Unlike Louis, Anne was a party girl and had the reputation of someone who liked to have a good time. Just before he went fugitive, Étienne and his friends brought Jacqueline to court to read some of her sweet poetry in honor of the queen and her pregnancy. As expected, the little girl charmed both the king and queen, and both praised her and fawned over her, no doubt to the delight of her father.

  This was the arrow that Étienne’s friends used against the cardinal. Sadly, soon after her triumph with the king and queen, Jacqueline contracted smallpox, a nightmare common enough in Europe throughout the seventeenth century, one that we have nearly forgotten in our time. Hanging near death for days, she struggled against the virus, while her father sat beside her bed. Slowly, she recovered, though her perfect face was marred by the scarring the disease left in its wake. Jacqueline later claimed that it was this loss of her beauty that was God’s greatest gift, for he took her off the worldly path that she had been set upon and set her on a new road that led more directly to God.

  Then came the terrible month of March and the reversal of Étienne’s finances, the ill-conceived protest, and Étienne’s flight from the city. Étienne’s friends quickly wove the three children into their schemes. Jacqueline the charmer would be introduced to the cardinal and read a few poems to him that had been written in praise of him and his administration. The other children would look on as cherubs. It was cleverly done, for the cardinal was likely to be undone by the little poetess whose charms had only been added to by the tragedy of her illness. Could the cardinal not also see her as an orphan, now that her father had been forced to flee the city? Moreover, the cardinal had made a great enemy out of Anne of Austria, whom he never really trusted, since he reckoned that her loyalty was more strongly directed toward her brother the king of Spain than it was to her husband, the king of France. Richelieu had a cruel tongue and had made Anne squirm under it more than once, and had done so in public. So how could Cardinal Richelieu allow his enemy the queen to show more compassion for the sweet Pascal girl than he did? And of course there were plenty of courtiers present to remind him of just that. Jacqueline played her part to the hilt; after reading her poems, she sat upon the cardinal’s lap, where he kissed her cheek and praised her over and over, calling her a sweet child and a wonderful poetess. It was just at this moment that Jacqueline leaned against the cardinal’s breast and asked a favor of him. Please bring my father home, she said. He is most terribly repentant. Bring him home and you will see what a good servant you will have in him. The rest of the court smiled on benignly, including some of the king’s and queen’s closest friends. The cardinal was caught like a fish. What else could he do?

  [1639–1640]

  Conic Sections

  There is no royal road to geometry.

  —EUCLID TO PTOLEMY

  Jacqueline’s gambit had worked. According to her sister, Gilberte, “M. the Cardinal said to her: ‘Not only do I grant your request, but I heartily desire its fulfillment. Tell your father to come to see me in all confidence, and when he comes he should bring his whole family with him.’”16 Jacqueline begged her father to return home and present himself to His Eminence, which, in spite of the cardinal’s kind words, was not a completely safe thing to do. What the cardinal might say to a sweet little child, so lately the favorite of the king and queen, was one thing, and what he might say to the father, so lately the cause of civil unrest, was another. But as it turned out, the word of Richelieu was good, at least this time. Étienne Pascal appeared before him to make his apologies and to beg forgiveness, and nothing particularly dangerous happened to him. Jacqueline must have been quite the hit, even with the inventor of realpolitik, for not only was her father forgiven, but six months later he found himself with an appointment as the king’s commissioner of taxes in the city of Rouen.

  Rouen is a seaport on the river Seine in Normandy, slightly northeast of the American beachheads of World War II, and is mentioned sooner or later in nearly every movie about D-day. It was built as close to
the mouth of the river as possible and still spans the river with bridges. In its youth, Rouen was a trading center for Celtic merchants; later, it became a Roman outpost, and later still a base camp for Vikings. In the nineteenth century, its already famous cathedral was sketched and painted over and over by Monet, to capture the subtle moods of the light. It was a thriving seaport in Pascal’s day as well, and trade brings taxes, which bring tax collectors.

  In spite of all his outward kindness, Cardinal Richelieu never completely forgave the Pascals, or anyone who opposed him. What he had given to Étienne was both a reward and a punishment, for the region was aflame with a vicious tax revolt. Royal commissioners for taxes were roundly hated by the people, and France’s involvement in the Thirty Years’ War had been squeezing them into revolt or starvation. There were taxes for just about everything, and fees on the taxes. As usual, the rich understood the system and used it for their gain. The king’s creditors received the privilege of levying fees upon the people in a particular region, thus repaying the debt without much bother to the king, much as if Chase Manhattan Bank held a promissory note from the president, and in payment received the right to wring extra money out of the people of Minnesota. This saved the king the bother of trying to find the money to pay back his creditors, and if in the process he added one more tax onto the already overburdened people, what did that matter? Understandably, civil uprisings were popping up all over France, explosions of peasant and minor bourgeois fury that would brood throughout the reign of Louis XIII, then into the reigns of Louis XIV, Louis XV, and Louis XVI, and suddenly flame into the Great Revolution. But the French kings did not know that they were signing away their future just to unravel the crisis of the moment, for the easy way to solve problems is rarely the best way. In 1639, the year that Étienne Pascal brought his children to Rouen, uprisings burned across the entire region, exploding overnight and then burning on sometimes for weeks, sometimes for months.

  Such events occurred all over France. It is likely that nearly every day young Blaise overheard a report of an uprising somewhere—a riot, a brawl, a murder. Years later, in the Pensées, he wrote about kings and their use of power, about the pain they caused, about the death. Perhaps his own sympathies during those years may eventually have come to rest with the people, the common folk.

  This was a creative time for Blaise, a time when he started to build his reputation. The jury was out on his personality, however. Some said that young Blaise Pascal was a prodigy, others that he was an arrogant boy. Probably both views had some truth. Certainly, he was the overprotected son of a rich father, a father who had achieved intellectual fame and who wanted his son to do the same. He was a driven boy, and yet one can forgive much of his edge because of his lust for knowledge. He was manically curious, with an encyclopedic, roving mind that attached itself to one mathematical problem after another, a lamprey chewing through the skin of a shark until he had penetrated the problem deep to the bone. What was best about him was his openness to unfamiliar ideas and his willingness to accept the evidence of his eyes. These gifts would serve him well in the years to come.

  Gilberte was then twenty years old and Blaise nearly seventeen. Rouen was an old city, with winding, narrow streets and tall half-beam houses. The Pascal house was in a compact neighborhood near the monastery of Saint-Ouen, what would have passed for a suburb in that time, on the northwest edge of the city, an area mainly occupied by bureaucrats and their families. Their friends and neighbors were mostly government employees at one level or another. Churches were all around them, with shops sprinkled here and there. Nearby was the rue du Gros-Horloge, where St. Joan of Arc had been burned as a heretic. The gothic spires of the church of Saint-Ouen dominated the skyline, with the building’s stained-glass windows depicting biblical stories and moments in the lives of the saints. When the sun shone through them, the interior of the church was cast with rose- and gold-colored light. In the summertime, flowers peered blue and red and white above the lips of planter boxes, while off in the distance the sea boiled up hillocks of vapor that marched onshore as the day waned.

  Blaise was now in the coils of adolescence. He was not a handsome boy, small for his age, thin and frail looking, snappish one moment, sentimental and pious the next, slouching between insecurity of body and arrogance of mind. His sister Gilberte had maintained her dark beauty, dark eyes, dark hair, white skin, and elegant figure, and she was surrounded by young men. Jacqueline, though her face had been spoiled by smallpox, was lovely enough to have her share of suitors. Étienne tried to find a husband for her several times, but it never quite happened. Jacqueline showed little interest. Outwardly, however, the Pascals were the perfect provincial family—middle-class, comfortable, acceptable, with hints of great expectation sprinkled through. Inwardly, they were hyperintelligent, given to emotional extremes, and not a little eccentric. Though Blaise had shown the first signs of great promise, it was Jacqueline who kept winning prizes for her poetry, and it was this rather than romance that consumed her life. Blaise had yearned for celebrity since childhood, and Jacqueline’s early success must have galled him in his private room, though he would have smiled and applauded her in public. Moreover, while Blaise was utterly under his father’s thumb, following out his father’s program, Jacqueline showed an alarming independence, something that was simply not done among their kind.

  While in Rouen, the family had met Pierre Corneille, the Norman tragedian, who quickly befriended them and encouraged Jacqueline to pursue the life of a poet and playwright. It seemed at first that she was on the verge of doing so. Meanwhile, Blaise received a copy of Desargues’ book on conic sections and, egged on by his father and by Mersenne, set out to make his own contributions. Living in Rouen at the time, he was off in the provinces, like Fermat in Toulouse, and had to rely on letters and gossip for news of the intellectual tides of Mersenne’s academy. But the monk, the great communicator, kept everyone apprised of the latest, and made sure that the right books ended up in the right hands.

  While Blaise scribbled his notes on conic sections, crowds gathered in the street below and shouted angry insults at the government employees in the neighborhood. Richelieu’s gluttonous taxes, the very thing that the Pascal family had come to Rouen to administer, had crushed the common people into rebellion. Brush fires of plague had also erupted in parts of the city and throughout Normandy. In the summer of 1639, just as the Pascal family had taken up residence, the city exploded with riots. Gangs of looters roamed the streets, singing bawdy songs and throwing curses. For the first year of the Pascal family’s stay in Rouen, they must have felt as if the people’s vengeance would swallow them whole.

  Finally, Blaise sent his first work of serious mathematics off to Père Mersenne. It was a short piece, a pamphlet entitled Essai pour les co-niques, or Essay on Conics. In it, Blaise outlined his proof for what has been called the Mystic Hexagram. Here is a short description of the concept:

  1. Take a cone:

  2. Take a simple plane, and slice the cone in two.

  3. If the plane is straight across, the section cut out will be a circle. This is the specialized case:

  4. If the plane is at an angle, the section cut out will be an ellipse. This is the more general case, because ellipses can be squat or long, thin or nearly round:

  Because Pascal wanted to prove a general theorem, he took the case of an ellipse:

  5. Draw a hexagram, a six-sided figure, inside the ellipse. The hexagram does not have to be regular.

  6. Now, take a pencil and make big dots on the vertices of the hexagram, and draw lines between the vertices. Then, extend the lines out to where they cross.

  7. The three points of intersection where the lines cross will always form a straight line, for any conic section and any hexagram.

  Mersenne was deeply impressed when he received a copy of Blaise’s pamphlet. Everyday geniuses like Descartes are one thing, but a child prodigy is another. There is something divine about a child, even a teenager, w
ho shows promise beyond his years. Blaise was thirteen years old when he first began attending Mersenne’s seminar, and everyone thought that he showed great promise. But unfulfilled promise is only air until the prodigy actually does something, and Blaise’s pamphlet was not only the first sign of that fulfillment but also the vindication that Mersenne had been waiting for. He had been telling everyone about the bright young son of Étienne Pascal for years, and if that boy had done nothing with his talent, it would have been sad for Blaise and embarrassing for Père Mersenne.

  At once, Mersenne sent word about the younger Pascal’s success to his contacts throughout Europe. Scientists and intellectuals as far away as Poland heard about the young geometer. Meanwhile, Descartes, too, heard about the pamphlet, and on a visit to Mersenne, the monk showed him a copy. Descartes, who was then forty-four and still angry about Étienne’s criticism of his own geometry, was not impressed, and instead grumped like a grandfather with a bad tooth. “I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients,” he said, “but other matters related to this subject can be proposed that would scarcely occur to a sixteen-year-old child.”