Pascal's Wager Page 15

  Moreover, Blaise did not quite agree with her choice of Port-Royal. He had grown cool to Jansenist extremism, mainly because they did not accept him. Neither Mère Angélique nor Père Singlin had much respect for philosophers, and less for scientists. Of course, Angélique’s own brother Antoine was one of the brightest young minds of the day, but he used his mental power to defend Jansenism. Anyone who wanted to peer into the mysteries of nature, as Blaise was doing, was suspect of worldliness. Moreover, Blaise had never solved the dilemma that sat between his science and Jansenist spirituality. How could the study of nature and mathematics be as great a sin as lust—indeed, be a variant of lust? Wasn’t this a bit much? He objected to the level of surrender demanded by Angélique, especially her demand that he give up the intellectual life that his father had instilled in him, and that Jacqueline give up the one great gift that God had given her, her gift of poetry. But Jacqueline was in perfect agreement with Angélique. For Jacqueline, Blaise and all the world were on the side of the devil, while she and the sisters at Port-Royal alone were on the side of God. She was like the apostles, the martyrs, even like Christ himself, while Blaise was awash in the sin of Adam. If there was a sin that was committed at Port-Royal, it was the sin of spiritual pride and self-appointed martyrdom, and Jacqueline exhibited every ounce of it.

  Nevertheless, out of his need, Blaise visited Jacqueline often and wrote to her often, but none of these visits seemed to solve anything. Their visits became increasingly rancorous as the conflict between them deepened. During this time, Blaise’s physical condition weakened. Gilberte later described his life in this way:

  My brother, among other infirmities, could not swallow any liquids that were not warm, and even then he could only take them a drop at a time. But since he had all sorts of other maladies—dreadful headaches and severe indigestion among them—the physicians ordered that he purge himself every other day for three months. The upshot was that he had to swallow medicines, heated, drop by drop. All this resulted in a condition painful in the extreme, though my brother never uttered a word of complaint.45

  Certainly, the feud with his sister Jacqueline, who had been his closest friend and companion most of his life, did not aid his health. Nor was it easy for Jacqueline. Several times, the novice mistress, Mère Agnès Arnauld, found Jacqueline weeping in the garden, and advised her to place her family at a bit of a distance, for they were worldly people and she had separated herself from the world. The thought that Jacqueline was expected to give up her family as a pious gesture when the Arnauld family had given up nothing of the sort smacks of a certain hypocrisy, and yet the Arnauld family was so firmly entrenched in Jansenism that they could all claim to have left the world.

  Both Mère Agnès and Père Singlin tried to mediate between the Pascals but failed. It was only when Mère Angélique joined the battle that Blaise surrendered. Whenever he visited the convent he was polite, calling Angélique “ma mère,” and treating her with pious respect. But one day when Blaise was visiting Jacqueline, Mère Angélique met him in the parlor reserved for visitors and lectured him on his worldliness. She admitted that he had been faithful to what she would term “a healthy theology” and that it was he and not Jacqueline who had brought the family to the Jansenist movement. But as Blaise always knew, she had little respect for worldly intellectuals, for to her the life of the mind was an indulgence rather than a discipline. She told him that his priorities were worldly and that he should turn them toward spiritual considerations, that Port-Royal needed his sister’s dowry, and that although the community would welcome her without it, it depended upon her contribution to help support her. But if he was going to release her money, he should do so out of charity and not out of any other consideration. “You see, Monsieur, we have learned from the transcendent teaching of M. de Saint-Cyran to receive nothing for the house of God that does not come from God. Everything that is done for some other motive than charity is not a fruit of God’s Spirit, and consequently we ought to have no interest in it.”46

  That did it. Blaise surrendered, and on June 5, 1653, he formally signed Jacqueline’s money over to Mère Angélique. The very next day, Jacqueline made her solemn vows.

  [1653–1654]

  The Gambler’s Ruin

  Money is like muck, not good except it be spread.

  —FRANCIS BACON, Essays

  I’m shocked, shocked to discover that gambling is going on here!

  —LINE SPOKEN BY CLAUDE RAINS

  IN THE MOTION PICTURE Casablanca

  False as dicer’s oaths.

  —SHAKESPEARE, Hamlet

  In January 1652, Blaise Pascal was twenty-nine years old, and he was alone, more alone than he ever expected to be. After the war with Jacqueline, he fell into a deep depression. He ached with loneliness, and if that wasn’t enough, after he had handed over Jacqueline’s portion of the family’s inheritance to Port-Royal, he was riding on the edge of poverty. The Pascaline remained a toy for the wealthy and never brought in much money, and many of the debts his father owned title to were uncollectible. All the while, his dependency on Jacqueline never completely healed, for she was the last remnant of a once-supportive family. Possibly for financial reasons, or possibly out of restlessness, he moved from the family quarters on the rue de Touraine to new apartments on the rue Beaubourg. Abandoned, fidgety, empty, he quickly left the city and moved to Clermont to live with Gilberte and her family from October 1652 to May 1653, where he spent most of this time vainly trying to collect debts owed to his father’s estate.

  Somewhere in there, rumor has it, he met a young woman from a well-connected family and courted her. No one is sure whether this is anything more than a rumor, but there is just enough evidence to keep it tantalizing. Gilberte’s daughter Marguerite said that all the while he was courting, his sister Jacqueline begged him regularly to abandon his desire for marriage altogether. She may have done this for Jansenist reasons, fearing that her brother was already too deeply embedded in the world, or she may have felt that Blaise was interested in marrying the young woman only for her money, and that his love was not genuine. In either case, it is clear that it was Pascal’s intention to marry her, and this disturbed the nun of Port-Royal.

  It was around this time that Blaise befriended the duc de Roannez, a man four years younger than himself who would eventually introduce him to an entirely new circle of friends. The young duke’s original name was Arthus Gouffier, but he carried the title of the marquis de Boisy from his birth, and after the death of his grandfather he became the duc de Roannez. Coming from an old aristocratic family, a family that had won its spurs through military action, he was a war hero himself, having fought bravely in the battle that finally defeated the prince de Condé. Afterward, in 1651, a grateful queen and cardinal appointed him governor of Poitou, where he worked aggressively to increase the commercial and industrial development of the province. Apparently, he was a man of vision, who saw it as his duty to encourage new ideas in commerce and was therefore interested in Pascal’s inventions.

  It was also during this time that Pascal sent a copy of his Pascaline to Queen Christina of Sweden, who had carried on a correspondence with Galileo and had offered employment to Descartes. Unfortunately, Descartes had found that the Swedish climate did not agree with his health, and the queen’s habit of calling him to attend to her at all hours reduced his health even further, until one day in 1650 he caught a chill, which led to a fever, and he died. Pascal had been encouraged to attend to the queen of Sweden as Descartes had done, for she was widely known as a fair-minded woman with a questing mind, but Pascal wisely declined, knowing that, given his health, the climate would kill him quicker than it had Descartes.

  Instead, Blaise remained in France and satisfied his own need for companionship with the duc de Roannez and with the duke’s sister Charlotte. Blaise had met them in Paris a number of years before, because the hôtel Roannez was only a short distance from the house that the Pascals occupied before leaving for
Normandy. It was also to this house that Blaise and Jacqueline returned from Rouen to attend to Blaise’s health and to carry on the debate about the vacuum, and Blaise may have reacquainted himself with the duke. What cemented the friendship between them, however, was a mutual interest in the intellectual currents of the day. Pascal quickly became an important figure in the duke’s entourage, because he had a reputation that was all his own, earned outside the sphere of the duke’s influence. He was also fairly conservative in his politics, which would have appealed to an aristocrat who feared the disorder that arose from republican thinking. What’s more, Pascal’s frantic desire to turn his scientific endeavors into economic gain appealed to the duke’s entrepreneurial spirit, and he became ever more involved in Blaise’s projects.47

  But most of all, these two young men were attracted by a mutual desire for an authentic Christian spirituality. It was their common Catholicism, and their interest in the Catholic reform movement, that had originally drawn them together. They had encountered the spiritual wisdom of Francis de Sales, had read the books of Cardinal de Bérulle, and admired the charitable works of Vincent de Paul. As Christian gentlemen, they lived in two worlds—the world of the salon, with its witty conversations, its mildly ribald humor, and its ubiquitous gambling; and also the world of the church, where hell and damnation, salvation and eternal glory were their chief interests.

  It is tempting here to think that Pascal, in his worldly period, had succumbed to the temptations of the flesh, but this is unlikely. The term “worldly” is a relative one. What would seem worldly to the people in and around Port-Royal would seem the height of religious austerity to most modern Americans. Pascal, like the young duke, was surrounded by the Augustinian God of wrath, and they strove to serve him, even love him. Like Étienne, even in his most worldly moments young Blaise was a deeply committed Catholic Christian, and it is likely that he never once had a sexual encounter in his life. Not that his health could have survived it anyway. Nevertheless, Jacqueline looked on her brother’s flight into the world with increasing dismay. How much of her own responsibility for that flight she was willing to admit to remains uncertain.

  In September 1653, Pascal accompanied the duke on a trip to Poitou. As governor of the region, the duke needed to oversee his estates and manage the affairs of the duchy. The region is a lush farmland, with vineyards and orchards, apple trees in long rows over the hills, and sheep sweeping white across the green, grassy knolls. Shepherds follow behind the flocks, with dogs circling around, driving strays toward the center. Once, Cardinal Richelieu had been a young bishop there. The Calvinists had once bombarded the city of Poitiers. Their commander had been Admiral de Coligny, the man whose murder had sparked the massacre of St. Bartholomew’s Day.

  Pascal was ill through much of the time, though he remained with the duke until early in 1654. By now, he was thirty years old, a slight man with a high forehead and a thin, almost adolescent mustache. His eyes were dark, and his nose was aquiline; his hair was long, nearly to his shoulders. His skin was pale from his constant illness; he had almost no eyebrows, and had a languor about him that belied the force of his spirit, for he was a man with a white-hot intensity, tempered by a puckish, sometimes even mean-spirited sense of humor.

  But Pascal was not the only man in the duke’s retinue on this visit to the country. Antoine Gombaud, the chevalier de Méré, was also along, to visit some property that he owned in the region. He had once been a knight, busy about war, but as he passed from his youth into his early forties, he tried to re-create himself as one of the new intellectuals, a man of poetry and fashion. He was fairly good at the latter but less than mediocre at the former. One of his attempted accomplishments was to try to master mathematics, something he succeeded in doing only nominally. Like some aging aristocrat out of a B movie, he had an ingratiating charm mixed with an irritating air of superiority. His one great love, however, was gambling, an aristocrat’s pastime. Along with the chevalier was a younger man named Damien Mitton, a man who had arisen out of the middle classes and a fellow traveler with the libertins érudits. He had maintained a cool religious skepticism until his marriage, when his wife converted him into a lukewarm Catholic.

  In modern language, de Méré and Mitton were the cool kids and Pascal was the nerd. Neither of them liked Pascal much—he bored them to tears—for mathematics and religion were all he talked about, and all the two of them wanted to talk about was gambling. During the long months in the duke’s company, the cool kids managed to tolerate Pascal with only an occasional sneer. Meanwhile, Pascal’s two sisters fretted about him from a distance. Many years later, Gilberte wrote about his journey into the world in a way that only an overbearing big sister could. Her one concern was his connection with bad companions, most notably de Méré and Mitton, and their gambling fetish. Whether or not she and her sister understood that their brother’s interest in the subject was largely mathematical is uncertain.

  Somewhere in there, de Méré discovered that Pascal, the “mere mathematician,” had a talent that they could make use of. The chevalier had a problem. He and Mitton had been gambling nearly every night, and he had been losing money by the bucketful. At first, the chevalier had tried to bet that he could roll one six in four throws, and he had won more than he lost, but then started to lose. So he changed games and bet he could throw two sixes in twenty-four throws, but then he started to lose in a big way. One throw after another went sour, and with each bad throw he grew more philosophical. He noticed that there was an odd pattern in his luck, that he had had a slight advantage whenever he tried to roll a six in four tosses of a single die, but when he tried to roll two sixes—a “double-six”—in twenty-four tosses of two dice, he was at a slight disadvantage.48 Why that should be so puzzled him, and worse, it was costing him money. Was he unlucky, or merely imprudent?

  Then he noticed Blaise the “mere” mathematician standing nearby and put the problem to him. The question, as he put it, was how the odds would change during a series of throws. Two players agree on a game that would include a certain number of rolls of the dice. Where in this series should a player bet on getting a six? Note that the question had subtly shifted from an oracular question to a probabilistic one. In other words, the chevalier did not ask what the next throw of the dice would be, which would be something no mathematician could answer. Rather, he asked what the likelihood was of a certain outcome occurring. With that question, the idea of the future mutated, and something new was born. Pascal, who had been around gamblers and gambling most of his life, felt a vague uneasiness over the morality of the entire business, but he was intrigued by the mathematics of the question, and commenced calculating. He quickly showed the chevalier that his original observations were correct—that if he tried to bet on rolling a single six in four tosses of a single die, he was more likely to win than if he tried to go for the double-six.

  Then de Méré posed Blaise a second question: two men are playing a game, whereby they agree that each man will roll the dice, and if one of them wins the roll three times in a row, he will win the bet. Each man wagers thirty-two francs, but while they are in the middle of the game something happens and they are forced to retire, after only three throws. The first man, Jean, has won twice, while his friend Jacques has won only once. How, then, should they divide the money?

  Pascal answered that Jean should say, “I am certain of winning thirty-two francs even if I lose the fourth throw. Since the chance of winning the fourth throw is equal between me and Jacques, I should receive the forty-eight francs and he sixteen.” But that wasn’t the complete answer. What Pascal needed to do at that point was to explain how this would change if the number of throws changed. What if, for example, the game stopped after only two rolls of the dice? According to Pascal, Jean should say, “If I would have won the next toss, all sixty-four francs would have been mine. But even if I were to lose it, my share of the stake would have been forty-eight francs, as in the previous case. Therefore only sixteen fr
ancs remain to be divided by chance—eight for me and eight for Jacques—allotting me a total of fifty-six.”49

  In autumn 1653, as the golden fall leaves turned brown and fell away, the science of probability was born. The world changed utterly. In a series of letters he exchanged with his friend Pierre Fermat in Lisieux, Blaise formulated the laws of chance. From that day on, the world would no longer turn to oracles to cast a dim light on the future, for the gods had been replaced by mathematics, and risk was no longer something people suffered, but something they managed.

  [1654]

  Letters to Fermat

  As for a future life, every man must judge for himself between conflicting vague probabilities.

  —CHARLES DARWIN, Life and Letters of Charles Darwin (1887)

  The Theory of Probabilities is at bottom nothing but common sense reduced to calculus.

  —PIERRE-SIMON DE LAPLACE (1749–1827)

  The right of the people to be secure…against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause.

  —FOURTH AMENDMENT TO THE

  CONSTITUTION OF THE UNITED STAKES

  The science of probability began with a series of letters Pascal wrote to and received from his friend Pierre Fermat. Some of these letters, including the first letter that Pascal wrote, raising the question, have been lost, so we don’t really know how the idea was introduced. What we do have is Fermat’s reply, and this letter seems to indicate that Pascal had said something like this:

  In a game of dice, a gambler bets that he will throw a six with a single die in eight tosses. The gambler throws three times and loses every time, but then for some reason the game is called off. What proportion of the stake does the gambler have the right to take with him?