Pascal's Wager Read online

  When he heard of the coming visit, Blaise, fearing that he would not have the energy to defend himself, sent word to his friend Roberval and asked him to attend the meeting. Roberval agreed. The next morning, Descartes arrived with quite a retinue: Monsieur Habert, Monsieur de Montigny, the son of Monsieur de Montigny, a cleric, and a few young boys. All of them filed into the Pascals’ parlor and greeted Blaise with massive civility and politeness, though everyone in the room knew that Descartes had not come on a mission of mercy but to debate about the void.

  Descartes asked perfunctorily about Blaise’s health, and then someone brought up the arithmetic machine, which Roberval demonstrated and which they all marveled at. Everything remained pleasant until, perhaps by prearranged signal, someone politely brought up the vacuum, and then there were flourishes and “Monsieurs” all around and everyone knew that they had stepped onto tricky ground, for they had all grown even more polite: smiles, jokes, laughter from both parties as the sides lined up. Descartes, however, had become quite serious. Roberval and the others explained Pascal’s experiments to him and asked him what he thought had entered the tube. “Subtle matter,” he said, waving off the question. Blaise did his best to respond, but his exhaustion was getting the better of him, and so Roberval tried to carry the burden of the debate himself and plunged in vigorously. A little too vigorously, as it turned out. His arguments remained civil but were too passionate for Descartes’ liking. Descartes turned away from Roberval in a huff and said he would treat with Pascal all day on the subject because at least Pascal was speaking reasonably, but he would not speak with Roberval any more. The man had too many prejudices.

  Suddenly, Descartes glanced at his watch and remembered another appointment. It was noon, and he had a dinner date arranged in the Faubourg Saint-Germain. Roberval, too, remembered another appointment, in the same part of the city, and so the debate ended, for the time being. Civility returned, and the men joked with one another, though Jacqueline noticed that the jokes smoldered behind the smiles. Descartes offered Roberval a place in his carriage, but before leaving he announced to Blaise that he was unhappy with the discussion and wished to return the next morning at eight o’clock. Presumably he had forgotten about Blaise’s early-morning difficulties, but then he turned and the men set off. After dinner with Monsieur d’Alibray, Roberval returned to the Pascal home to sort out the events of the morning, and admitted that his relationship with Monsieur Descartes had not improved on the road.

  Descartes arrived the next morning. Blaise’s friend Monsieur d’Alibray expressed a wish to come and to bring their mutual friend Monsieur Le Pailleur, but Le Pailleur didn’t show up, because, as Jacqueline put it, “he was too lazy to come over to visit.” Ostensibly, Descartes came to give Pascal some advice on his health, but in the end he said little other than to instruct Blaise to follow Descartes’ own regimen: sleep late and eat plenty of broth. At that point, Jacqueline excused herself to prepare Blaise’s first bath. Baths had given him such a headache in the past that he had stopped the practice, which was not a good idea, and Jacqueline wanted to make sure that his bath was not as hot as it had been. With that, the chief witness to the events left the room.

  As voyeurs from four hundred years in the future, we can only imagine the buzz of voices from the drawing room, rising and falling, as the debate continued. Was it a replay of the previous day’s conversation? Had they come to some kind of reckoning between the plenists and the vacuists? Likely not, for Descartes was later heard to say that Pascal had “too much vacuum in his head.” While Jacqueline was still busy with the bath, Descartes left, apparently as polite as ever, after praising Pascal’s arithmetic machine, which heartened Blaise, but Jacqueline thought it was merely a “formula of politeness.” That night, Blaise merely had night sweats and insomnia, which was an improvement.

  Pascal expected his New Experiments to set off a reaction, but this happened quicker than he imagined. He was at odds with Descartes, he knew that, but this time the reaction came not directly but through Descartes’ old mentor at the Jesuit college at La Flèche, Père Étienne Noël. By this time, Noël was the rector at the College of Clermont in Paris and was a highly respected philosopher. Like Descartes and Aristotle, he believed that there was no such thing as empty space, because the entire universe was filled with matter. There is only existence and nonexistence, and nothing in between. The world for them was no dead machine but a living organism, a creature of God. If a space appeared to be empty, it was actually filled with material too subtle to be seen. Père Noël relied on the authority of Aristotle to make his point, an authority whose ideas had survived for nearly two thousand years. Pascal, on the other hand, believed that only by experimentation, by controlled seeing, and by reason, the pinnacle of which was geometry, could anyone arrive at scientific truth. He was not above appealing to authority when he needed to, but he wouldn’t rely on it to silence debate. Besides, an appeal to authority was a creature of theology and not science. But what was most important to Père Noël was that statements about the world should never conflict with sound theology, and so appealing to authority was legitimate. Pascal was himself a deeply religious man, but he did not want to take on religious questions in his physics.

  The skirmish between Pascal and Noël occurred in an exchange of letters between October and December of 1647, an exchange that grew hotter with each salvo. At first, Noël praised Pascal for the ingenuity of his experiments, but then he took issue with the entire notion of a vacuum. After all, he said, light passes through these spaces and is refracted, so there must be something there. No, Pascal responded, the refraction Noël mentions took place at the boundary of the glass tube, and not in the space above the mercury. As to the fact that light passes through empty space, the mystery may well lie in light itself, something no one in the seventeenth century had any hope of understanding. “If our knowledge of it were as great as our ignorance of it, we might perhaps know that it would exist in a vacuum with greater brilliance than in any other medium,” Blaise wrote to Noël.25

  The Aristotelians, Noël included, were as busy as ants trying to find the substance that filled the space above the mercury. Some said it was fire, others that it was the ether; some said that it was the same substance as the sky. Pascal thought that this was all in their heads, and for all he knew it was an empty space. He saw no reason to presuppose that an invisible, odorless, tasteless, undetectable something had filled the area. Why not call it empty? For there seemed to be no other reasonable alternative. Pascal then argued that empty space was not nothingness; rather, it was something between nothingness and real physical bodies, a midway point, a space devoid of material things.26 This was truly a new thought—pure extension—the first tentative step into modern physics.

  Noël received Pascal’s letter on the evening of October 31, 1647. Within a week, he fired off a second letter, this one a little nastier than the first. He turned on Pascal’s idea that empty space was somewhere between physical things and true nothingness, saying that such an idea was absurd. He returned once again to his original propositions. Empty space could not act as a medium for light, and besides, according to Aristotle, everything that existed had to be either a true substance or an accidental property of a substance. For example, a red ball is a substance because it physically exists, while the color “red” is an accidental property of the ball. Pascal waved aside the entire distinction, and even brought up a few Jesuits to back him up. He also mentioned Pierre Gassendi, another of Mersenne’s group, who argued that empty space was filled with God, and was therefore not truly empty. Before creation, God existed in an infinite, unmovable empty space, and at the moment of creation, he filled it with light. If everything in the universe disappeared, Gassendi argued, we would be left in an emptiness, an infinite space that things exist in and move in, but that itself remains unmoving.

  In his second letter, Noël tried to shift the entire argument onto theological grounds by saying that this empty space was r
eally the immensity of God. Pascal, seeing quicksand, backed away. He didn’t know what “immensity of God” meant precisely, and after what had happened to Galileo, it was better to avoid the whole question. He took a mystical position rather than a theological one, referring all such theological terms to the great mystery. The mysteries of God are “objects of adoration,” he said, not disputation, and therefore they should not be discussed in arguments about physics. Noël was nonplussed. How could Pascal not want to dispute these theological and philosophical concepts? The Jesuit was a philosopher first and last, an Aristotelian and a Cartesian. Debate, argument, disputation—these were his meat, his drink. What was experimental science compared to these things? Moreover, as a teacher he felt that it was his duty to be the gatekeeper, to guard the nation from irresponsible ideas. Like Christoph Clavius in the Galileo case, Père Noël was a natural conservative, for he was the defender of the tradition. Pascal wanted to step outside the normal course of things and to reason in a way that was utterly new.

  Pascal did not respond to Noël’s second letter, which puzzled many of his friends. Was Pascal abandoning the field to Descartes? In a letter to his friend Jacques Le Pailleur, Pascal explained that he had heard through other sources that Père Noël had been concerned about Pascal’s health and had begged him not to bother with a second letter, that the Jesuit had intended the letters to be a private conversation and not a public debate. In other words, he had offered Pascal a truce. Pascal admitted that if the offer had not come from one of the good fathers, he would have been suspicious.

  Perhaps Pascal should have been. In January 1648, Père Noël published a book, The Fullness of the Void, where he quoted parts of his own letters to Pascal. Understandably, Pascal was furious. Because of the supposed truce, he had kept silent, and many people thought that Noël had won the day, that Pascal had retreated, full of shame. Pascal intended his letter to Le Pailleur to be widely circulated, so he added that he intended to answer the Jesuit’s book in a treatise of his own and to conclude “that this space is empty until someone has shown that a matter fills it.” The debate moved on to its next chapter.

  [1647–1652]

  Jacqueline’s Vocation

  It is true that I am free now to make my own commitments.

  It has pleased God, who chastises by granting favors and

  who favors us by chastising us, to take away the last

  legitimate obstacle that could prevent my making the

  commitment I want to make.

  —JACQUELINE PASCAL TO BLAISE, MAY 7–9, 1652

  While Blaise was rocking the scientific world with his experiments on the vacuum, his sister Jacqueline remained with him in Paris. She was his primary caretaker, seeing to his bath and his diet, sending for the doctor when his health declined, and she was not happy. Jacqueline was arguably her brother’s equal in intelligence, and she too had enjoyed her touch of fame. But at this point, her life had become something out of a Victorian novel—an invalid brother, little freedom, no life of her own, few options. All she needed was a dark and creepy moor. The fact that she lived in Paris, a green, promenading city, did not satisfy her; she had ideas of her own about how her life should be. Ever since her brother had become interested in Jansenism, he had carried her along with him, and although his zeal had cooled after they returned to Paris, Jacqueline’s had not. While her brother had been out proving the existence of the vacuum, the empty place in Jacqueline’s heart had been growing, and she longed for the convent, for the life of a holy sister. She kept these feelings to herself for a very long time, but eventually they came to the surface.

  Much of what Jacqueline was feeling was true piety. She had been, bit by bit, experiencing the second and, for the Jansenists, the true conversion, whereby the mere churchgoer becomes the fervent daughter of Christ. The rest was a desire to break out and make a life for herself. Gilberte had been a happy wife and mother for years, but Jacqueline never wanted that life. She had already refused several likely young men, but that left her with few options. By default, she was the spinster sister of the great man, the great but sickly man, and the daughter of another great man, and, by convention, she was swamped by family obligations. There were really only two paths available for a single woman from a bourgeois family: she could stay home and take care of her sickly brother, or she could enter a convent and be free. It is hard for contemporary people to see the life of a nun as a symbol of freedom, but that is what it was for many women, from the earliest days of Christianity. The path of the holy virgin, or the consecrated widow, was the only way a strong-willed young woman could free herself from the control of her family. Jacqueline had been growing in her commitment to the Jansenist vision of Catholicism for years, and desired the freedom to pursue it. Just before she and Blaise left Rouen, Jacqueline had received the sacrament of Confirmation, which she prepared herself for by reading a number of tracts by Saint-Cyran, after which she was never the same. Gilbert attributed the change to the Holy Spirit.

  After Jacqueline and Blaise returned to Paris, they visited Port-Royal as often as they could. Blaise’s health improved through the year because of the treatment he was receiving from the doctors in Paris, and so he was able to publish his treatise on conics and continue his work on the vacuum. In between sick days and work days, they attended Mass at the convent and listened to the sermons of Père Singlin, Saint-Cyran’s successor at Port Royal, and Jacqueline’s certainty about her vocation grew. One day, she pulled Blaise aside and told him about her desire to become a nun at Port-Royal, and he supported her at once.

  So it was puzzling for him that while Jacqueline had been so easily accepted at Port-Royal, his own conversations with Père Singlin and Mère Angélique did not go well. He and Jacqueline spent time talking about spiritual matters with them after Mass, and when they asked, he explained his own religious experience to them, but they reacted with doubt and suspicion. Blaise was a scientist, a mathematician, and they did not trust him. His interest in science was all too worldly, a taint on his piety, an attachment that came between him and his jealous God. They both recognized Jacqueline’s devotion as pure, as an unspoiled piety, for she did not try to understand God in her mind, but accepted him in all his divine irrationality. The truth of God was beyond human reason, and Blaise had not freed himself from that terrible habit of thought that wanted to know the world as it stood to the senses, apart from God. But Blaise could not see this. He was cheerfully ignorant of the source of their concern, and would have sunk into a depression if he had known. Never once forgetting what Jansen had written about scientific study, he felt torn between his desire for a rational understanding of the world and his desire for God. He would not abandon reason so blithely, so he strove to use it to bolster his faith. Reason itself, he told them, shows the truth of Saint-Cyran’s principles, and the foolishness of his opponents. Père Singlin and Mère Angélique squinted back at him in silence. Here was Blaise the intellectual with all his power of argument arrayed on their side, and yet those very powers were suspicious. The fact that Mère Angélique’s own brother Antoine was as intellectual as the young Pascal, as trusting in reason as he was, did not seem to matter. The sisters of Port-Royal took Jacqueline to their hearts at once, but to Blaise they remained cool.

  In 1648, the year after she and Blaise returned to Paris, Jacqueline wrote a long letter to her father, still in Rouen, asking for his permission to enter Port-Royal. Blaise ardently supported her desire, at least at this point, even though he would have been the one most affected by her departure. In her letter, Jacqueline said she was willing to abide by her father’s decision but that she was also determined to have her own life. “Since ingratitude is the blackest of vices, everything that comes close to it is horrifying,” she wrote. Denying her father’s will would have been a sin of ingratitude, waving off the fact that he had given her life and raised her into adulthood. Paternalism was the norm among the bourgeoisie in the seventeenth century, and children owed their father mo
re than just respect; they owed him obedience. Much of the first part of the letter was filled with protestations of her profound obedience, how she had always obeyed him and how she believed that it was God’s will, “whom we must consider in all matters,” not only that she obey her father but that she follow her heart. She had done her duty by Étienne, and now she wanted out. “After all this, Father, I can no longer doubt that you wouldn’t do me the honor of agreeing with me and granting me my request.”27

  Jacqueline was asking her father if she could make a retreat to Port-Royal and there test her desires to enter that convent, to see if she indeed had been called by God to that life. She must have already known what her father’s reaction would be, for even at this point she puts the decision back into his hands. “On the other hand, if God leads me to understand that I am right for this place, I promise you that I will put all my energy into waiting serenely for the moment you would like to choose for his glory.”28 She must have known that Étienne, the possessive father who sacrificed much for his children and then gathered them around him like chicks in a thunderstorm, who even when he was on the run from Richelieu’s police kept control of their lives, would resist any thought of her entering Port-Royal. Marriage was one thing; it brought new children into the family. For her to enter the convent meant a kind of death; it would be a parting that would take her outside his influence. His daughter would pass beyond him into the cloister and be lost to him forever. Toward the end of that year, Étienne finished his term of office in Rouen and returned to Paris, where he gave Jacqueline his answer. Deeply upset, tearful, he told her that at sixty-one he was an old man and that he needed his children about him in his last years. He could not part with his youngest daughter, and would not.