Pascal's Wager (10 page)

S
cience in the seventeenth century was a serious business, but it was also entertainment. Any serious researcher, if he found something of value, would sooner or later have to make a public demonstration of his experiment, either in front of the king or before a collection of interested nobility, or in a public square where the audiences alternately grumbled and were amazed. A scientist paved his reputation with such stones, because public demonstrations often led to wider controversies and therefore to larger audiences. This had a downside, however. One of the reasons Galileo had such a difficult time with the Inquisition was that he published his dialogues for a general audience and not for the hothouse world of scholars, where his ideas might generate
some heat, but not enough to explode. There is always a whiff of sedition when new ideas go public. With the lessons of the Reformation firmly in mind, the hierarchy of the Catholic Church naturally wanted to keep a watch on things, to make sure that nothing radical crept past them.

In January and February of 1647, while his father was yet healing from his broken hip, Pascal spent a great deal of money staging a series of big demonstrations of the vacuum in an open square in front of a glass factory. He had ordered a number of long glass tubes, of various lengths, up to forty-five feet long, and bound the longer ones to a ship’s mast. Then, after filling them with different kinds of liquid, he used a contraption made of ropes and pulleys to rotate the mast and inserted the bottoms of the tubes in basins of liquid. In each case, an empty space, apparently a vacuum, opened at the top of the tube as the liquid fell, but not all the way. People applauded, astounded by what they saw.

In a sense, Pascal was reworking old ground by returning to experiments done by Gasparo Berti before Torricelli made his discoveries with mercury, but for the people of Rouen it was all new. As with Galileo, the local Aristotelians buzzed with outrage. Jacques Pierius, from the University of Rouen, dashed off a pamphlet—
Can a Void Exist in Nature?
Air must have gotten into the gap at the top of the liquid, he said, air or some even more rarefied gas, unnamed
spirits
that filled the apparently empty space. Pascal, goaded by their resistance, invited any and all who were interested to come to the glassworks once again for a more dramatic demonstration. On the day, spectators collected in the yard before the mast with two forty-foot glass tubes of liquid tied to it, one full of water and the other full of wine. Naturally, the column of water would fall farther than the column of wine, since water is denser than wine, something that Pascal already knew but the spectators did not. What’s more, Pascal had already calculated the difference, and, like any good magician, he prepared his audience to be amazed.

Before rotating the mast with the two glass tubes, he staged a question period with them, asking if wine contained more spirits than water. The audience nodded, looking at one another, uncertain; a few shouted yes, of course it does. Then, Pascal said to them, once the mast is rotated,
shouldn’t they see a greater space above the wine than above the water? After all, the increased spirits in wine should push it down farther than the water. They agreed to that as well. Then Pascal rotated the mast, but the water fell farther than the wine, in spite of the spirits. The crowd was stunned to silence. A few grumbled that it was a trick. Pascal, not satisfied with their silence, went on: he exchanged the two liquids, pouring out the water from one, the wine from the other, and then reversing them. The result was the same. The Aristotelians grumbled louder, and arguments broke out.
What spirits?
some said.
I don’t see any spirits, do you?
The Aristotelians said there must be an even more subtle substance inside the glass. How, they argued, thinking of the power of suction, could such a column of liquid be supported by nothing?

One fellow took the argument to its furthest point by proposing a thought experiment: what if they built a glass flask that was long enough to lie tangent to the earth, a tube that would stretch some 8,856 kilometers, and then stuck the bottom of the flask into a canal? Could that bit of emptiness at the top hold up all that water? At this point, Pascal didn’t know, and he puzzled over it. Eventually, the question sent him down the right path. He began to wonder if the columns of water, rather than being sucked up from the top, were pushed up from below—the same thing Torricelli had realized a few years earlier, though his speculations had not yet arrived in France. So Pascal performed more experiments, and still they grumbled. No one likes a show-off.

After the demonstration, Pascal carried on a number of public experiments, each with the same general result, each drawing out the same arguments. But these experiments quickly exhausted him, so that after they were done he took to his bed with a migraine and a terrible weakness in his legs. Blaise’s illness had grown worse. He developed a rare form of tuberculosis, and his father sent him back to Paris, where the doctors were better. But someone had to take charge of Blaise’s care. Gilberte had married her cousin Florin Perier, and they had moved back to Clermont in June of 1641. So in order to preserve Blaise’s health, Étienne sent Jacqueline along to care for him.

Once Blaise arrived in Paris, his friends, especially Marin Mersenne and Gilles Roberval, grew anxious that he publish his findings as soon as possible. They were afraid that someone else would grab the credit if Pascal did not publish, and publish soon. But Blaise was ill throughout much of 1647, and his ability to sit at his desk and churn out copy was limited. Roberval fended off Aristotelian criticism as best he could, while Mersenne told everyone he could that Pascal would publish his work quite soon.

This galvanized Pascal, sick as he was, to climb out of bed and write up his results. His concern was a matter of ego, of course, but also of scientific honesty. Pascal had taken great care to perform his experiments correctly, and what would happen if someone who had not taken such care were to publish a paper full of quick and dirty findings? Pascal would be weighing in with too little, too late—would have to battle uphill against poor science. In his final product,
New Experiments About the Vacuum
, dedicated to his father, Blaise described a number of experiments, made with “quicksilver, water, wine, oil, air, etc.,” and explained the significance of each one. His purpose was to prove the existence of the vacuum, but then to “leave it to learned and interested persons to test what happens in such a space.”
²⁴

In the
New Experiments
, Pascal describes how he took a glass syringe with a “very exact” piston inside of it and then plunged the entire affair into water. When he pulled back the piston, it created a vacuum with very little resistance, in spite of the fact that the Aristotelians had taught that this would require an infinite force. He goes on to describe how he later used a bellows to create the same effect, and then how he took a glass tube, forty-six feet long, full of red wine, and stuck it into a tub of water, removed the plug on the bottom, and observed how the wine poured out and mixed with the water, turning it pink. The wine kept pouring out until the liquid left in the tube had reached a certain level, and then stopped a number of feet higher than the level of the wine-and-water mixture in the tub. And that was the mystery: why would the wine stop falling? Was it sucked from the top, or pushed from the bottom? He re-created Galileo’s experiment by using a piston to suck mercury up
through a glass tube, watching it rise until it reached a certain point, and then observing a space open between the top of the mercury and the bottom of the piston. Galileo had interpreted this behavior as owing to the “breaking point” of the liquid rather than to the pressure of the outside air. Pascal then calculated that the eighteen
braccia
reported by Galileo as the breaking point of water, which Pascal translated as thirty-one feet, would turn out to be two feet, three inches when done with mercury.

At the end of these experiments, he was fairly certain that the space above the wine, the water, the mercury, or the oil was not filled with air that had somehow gotten in, either through a mistake or through pores in the glass; nor had any air bubbled up from the liquid, nor was the space filled with a subtle vapor, a “spirit,” or whatnot. What he was not certain of was whether the apparent vacuum was a real one, and this was as much a methodological problem as an ontological one. Pascal was not convinced that his experiments had proved the existence of a real, actual void above the glass, only the existence of something that looked and acted like a void. The question remained: what was this empty space?

Back in Paris, Pascal’s illness nearly overwhelmed him. He suffered from constant migraines, night sweats, and such weakness that he could barely talk. He rarely bathed because this set off the headaches, and so his body stank. Still, he was able to attend church with some assistance, if nothing else. On Sunday, September 22, 1647, two men, a Monsieur Habert and a Monsieur de Montigny, came to visit the Pascal home while Blaise was off at church, and they spoke at length with Jacqueline. Both men were friends of René Descartes, and announced that Monsieur Descartes had “expressed a strong desire” to meet with Blaise and that he had “the greatest respect” for Étienne and his son because of their many accomplishments. They further announced that Descartes wished to pay a visit the next morning at nine o’clock, if it was not inconvenient, given Blaise’s illness. Not knowing what to do, Jacqueline couldn’t find a good reason to turn away the great René Descartes, so she agreed, but asked if they could come a bit later. Her brother suffered most in the early morning, she told them. They agreed to arrive at ten thirty instead.

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.