[1642]
The Arithmetic Machine
I propose to consider the question—Can machines think?
—ALAN TURING
By 1642, the Pascals were well settled into the local scene in Rouen. That year, Gilberte, living in Clermont, gave birth to a son, Étienne, named for her father. Also during that year, the fearsome Cardinal Richelieu succumbed to his many diseases and died. Within a year, his master, Louis XIII, would follow. The English civil war between the Cavaliers and Roundheads began in 1642, and Galileo Galilei died of illness and old age, still under house arrest. Closer to home, the violence of the Pascal family’s first days in Normandy had subsided, and Étienne had begun his work in earnest as the chief tax collector of the region. His biggest problems had become mathematical. With the uprising, the registers had been destroyed, the office was a mess, the state of collections was disorganized, and Étienne had to spend long, laborious hours calculating, calculating, and calculating. He worked into the night every night, and soon the exhaustion that hung about this new honor was like a funeral wreath. Étienne grew snappish and complained about his health. “For four months now, I have not gone to bed more than six times before two o’clock in the morning,” he wrote to Gilberte.
Blaise, then barely nineteen, volunteered to pitch in, but he was quickly buried by the mountain of work, and since his health was ephemeral, he found himself in some distress. His head hurt. The problem was complicated by the complexity of the French currency. One French livre equaled 20 sols; one sol equaled 12 deniers, so that the steps up and down the currency were uneven and therefore not easily tabulated. One livre was therefore 240 deniers—which was unnecessarily complex. Each set of calculations, therefore, was exquisitely tedious, just the kind of work that sucks the life out of one’s soul. There had to be an easier way.
Out of pure necessity, Blaise cast about for a solution, and found it in a machine. Blaise saw fairly quickly that the kinds of calculations that his father’s work required were mechanical and could be done by a machine. But what kind of machine? The machine he came up with, the Pascaline, was the first calculating machine in the modern style. The centuries have refined the mechanism, but the basic concept underpinning the logic of Pascal’s device and the logic of an electronic computer are not that different. In essence, Pascal set up a series of gears that moved one way—forward but not backward. Inside of a long narrow box, he fixed eight cylinders, with the numbers from zero to nine printed on each one. Each cylinder had two sets of numbers, however, one descending, at the top of the cylinder, and the other ascending, at the bottom. Therefore, the top numbers were used for subtraction, while the bottom numbers were used for addition. The user would choose one operation over the other by sliding a metal bar over the unused portion of the cylinder, to highlight the calculation at hand. Underneath the row of cylinders, set horizontally across the top of the box, was a sheet of metal that hung vertically, perpendicular to the row of cylinders. On that sheet were eight wheels that turned. The wheels were attached to a set of gears inside the box with various numbers of teeth on them. In order to account for the complexity of the currency, some of the wheels had ten spokes on them, others twelve, and others twenty. A series of gears connected a series of wheels on the box lid to the drums. To calculate, the user took a metal hook and turned the wheels on the lid. In order to carry numbers past ten over to the next column, Pascal set up an escapement arm that regulated the motion of the wheel that stood for the power of ten.
Thus he mechanized addition and subtraction, but he failed to get his machine to multiply and divide. There was a calculating clock that had been invented in Germany back in 1624 that could do this, but it worked entirely differently. The problem was finally solved by Leibniz, who tricked up the Pascaline by adding stepped teeth that would repeat adding and subtracting over and over again to simulate multiplication and division.17
So the machine worked, and it took on much of Étienne’s burden. But Pascal the capitalist knew that he had something worth marketing, something that could make him famous throughout Europe, something beyond the work of a “clever child,” as Descartes had called him. But how to get the thing mass-produced? There were plenty of master craftsmen in Rouen. The city made some of the best glass in Europe, and there were metalsmiths and watchmakers aplenty, but none of these men understood Pascal’s science, and Pascal did not understand their craft. He had the devil’s own time of getting the workmen to produce what was in his head. In his dedicatory letter to Chancellor Séguier, he complained about his difficulties: “Knowledge of geometry, physics, and mechanics furnished me the design for it, and assured me that the employment of it would be infallible if some workmen could make the instrument whose model I had conceived. But it was at this point that I encountered difficulties as great as those I wanted to avoid, and to which I was seeking a remedy.”18
The difficulties he encountered exhausted him, and his health withered. More weakness, more headaches, more pains in his legs. Still, many people were encouraging him to continue the work—Père Mersenne, of course; Chancellor Séguier; his father; the prince de Condé and others—and so he pressed on, revision after revision, fifty revisions, until the thing was ready for market. During this process, however, a local watchmaker, obviously in league with some of Pascal’s craftsmen, came out with an inferior version of the Pascaline, and claimed credit for it. Pascal had been pirated before he even finished the work. Furious, he cancelled the entire project and fired his employees. But then his friends kept on, and even more letters of encouragement from powerful people arrived in Rouen, some with advice on dealing with craftsmen, some with advice on marketing the machine once it was done. Encouraged, Pascal worked on into 1644, when he presented the prototype Pascaline to the chancellor, along with his official letter of presentation. He included a notice along with the letter, warning people of pirated editions of his machine that were floating around and asking them to avoid them.
The one problem that Pascal had with his machine was the price. As is the case with almost all truly new inventions, the cost of producing Pascalines made them rare.19 Too often, inventions that have the potential to change the world do so only after many years. At first, they remain toys for the very rich, toys that such people buy for their obvious potential rather than for their present use. The local butcher and baker still had to count on their fingers. Nevertheless, the prince de Condé bought one, as did the queen of Poland and Louise-Marie de Gonzague. Wladyslaw VII also bought one, and asked if it could be built to accommodate Polish money.20
Even if there was little profit in it, the Pascaline was a hit. Roberval made demonstrations of the device all around Paris, and Mersenne celebrated his young protégé’s genius to all his correspondents. Pascal was suddenly the talk of the salons, the boy genius who lived up to his great promise. Throughout all of this, however, Descartes kept a grumpy silence. Sooner or later, he and the boy would go to war; he was certain of it.
[1638]
The Jansenists
The weakness of little children’s limbs is innocent, not their souls.
—ST. AUGUSTINE, Confessions
Two cities have been formed by two loves; the earthly by the love of self, even to the contempt of God; the heavenly by the love of God, even to the contempt of self.
—ST. AUGUSTINE, De civitate dei
Late in 1638, the same year that Étienne Pascal went into hiding from the cardinal’s agents, a prisoner languished in one of Richelieu’s dungeons. He was not an ordinary political prisoner, but a priest, an abbot, and one of the great religious leaders of the day. He was Jean Duvergier de Hauranne, the abbé de Saint-Cyran, one of the founders of a spiritual movement within Catholicism called Jansenism, a new form of strict Augustinianism—a Catholic version of Calvinism, at least according to the Jesuits. In happier times, he had been celebrated across France, and his name had penetrated into every corner of Europe. The destinies of these two men, one in hiding and one in priso
n, would one day cross. Étienne’s children would become the abbot’s followers, to their joy and to their sorrow.
Saint-Cyran’s movement would gather a number of great lights to itself, men like Antoine Arnauld, Jean Racine, and, of course, Blaise Pascal. Saint-Cyran also insinuated himself into several influential convents, most notably Port-Royal des Champs, an old Cistercian monastery turned fashionable center for devout young ladies, including Blaise Pascal’s sister Jacqueline. He became a strange attractor for devout young men like Blaise, who wanted to live an odd variant of monastic life, and a center for a highly ascetic and highly nationalistic brand of spirituality based on a strict interpretation of Augustine’s doctrine of original sin, according to which the vast majority of humankind, including most Christians, was doomed to hellfire. It was all fairly depressing.
France was undergoing a major Catholic revival in the seventeenth century. There were two lines of thought generating it, turning on the question of whether human beings were truly free and whether human nature was capable of goodness after the Fall. Each of these two lines of thought had a political dimension as well. The first was a Gallican line that wanted to promote the local French church as a separate culture distinct from Roman oversight. Included in this camp was Pierre de Bérulle, the founder of the Oratorian order, and later Cornelis Jansen and the abbé de Saint-Cyran, the founders of the Jansenist movement. Characteristic of this group was a deep pessimism about human nature—a belief that, left on their own, human beings were incapable of choosing the good and that human nature needed to be disciplined to the point of annihilation. This was straight Augustine, and those who followed this line of thought were proud to trumpet that fact. Bérulle, who was in many ways the spiritual father of the entire French revival, was close to a number of the great spiritual leaders of the day—St. Vincent de Paul, St. Francis de Sales, and St. Jeanne-Françoise de Chantal. His own spiritual thinking, which was Neoplatonic in origin, called for the annihilation of all of the natural powers of the individual and their replacement with a strict adherence to Jesus in the Eucharist. The purpose of life for Bérulle could be found in the conforming of the individual to God’s will, which would require self-immolation, burning out all instances of self-love.
Bérulle likened this to a Copernican revolution:
An excellent mind of this century wishes to hold that the sun is at the center of the world and not the earth; that it is immovable, and that the earth, in proportion to its round shape moves in reference to the sun…. This new opinion, scarcely followed in the science of the stars, is useful and ought to be followed in the science of salvation. Because Jesus is the sun, immovable in his grandeur and moving all things…Jesus is the true center of the world and the world ought to be in continual movement toward him.21
One of Bérulle’s disciples was the man who would eventually become the prisoner at Vincennes, the abbé de Saint-Cyran, who took Bérulle’s spiritual teaching and, with the help of his friend Cornelis Jansen, ran with it, formulating a strict construction of the Augustinian theory of grace and free will. It was their extremism that cast light on the other line of thought during the revival, which was spearheaded by Francis de Sales and the Jesuits. Francis de Sales eventually wrote his greatest work, An Introduction to a Devout Life, with the idea that people had a natural inclination toward God—that concupiscence, the propensity for evil, was not the only player in the human soul, but that the primary movement of the human heart was for its Creator. This mirrored the Jesuit idea, which came directly out of the personal experience of St. Ignatius of Loyola that every human being had the possibility, the duty even, to make a choice for God or against God—to march under the standard of God or under the standard of the devil. Therefore, the Jesuits opposed Augustine’s limitations on human freedom. And their liberality, I would argue, was the wellspring from which the modern idea of liberty flowed.
For Saint-Cyran, these milquetoast spiritualities were just too soft on sin. A Christian should be made of sterner stuff. His official portrait shows a man dressed in cassock and surplice, nearly bald and with a full beard, his lips pressed tightly, his eyes sliding away, as if with an irreparable sadness. The painting does not do him justice, however, for he was one of the most successful religious salesmen of the century. Vincent de Paul and Francis de Sales had both fallen under his influence for a time, but after suffering through painful crises of faith that involved serious anxiety over whether they were included in the elect, they both broke with him, saying that they were horrified by his religious paranoia. Nevertheless, he was able to convince others—those more attuned to his brand of religion, even powerful women like Mère Angélique, the abbess of Port-Royal, the dowager empress of religious women in France, and others. He taught them that only a life of extreme self-punishment could lead to salvation, an annihilation of all attachments and worldly associations, an extreme discipline of the body, to the point that the nuns of Port-Royal encouraged the growth of body lice and other vermin as an act of mortification.
Richelieu had thrown Saint-Cyran into prison on the exaggerated charge that he had criticized the king’s prayer to the Blessed Virgin, where he asked for her special protection for France. This was rude at best and unpatriotic at worst. But this charge was only a convenience, for Richelieu had been cultivating his disappointment with Saint-Cyran for some time. They had once been acquaintances, and had met regularly to discuss things theological. But Richelieu did not care for the penitential way of life, and he eventually broke with the entire movement and sided with the Jesuits, who were the liberal modernists of the time, for they were men who understood politics and did not shy from engagement with the world.
Nor did it help that Saint-Cyran had inadvertently become tangled in one of the king’s fits of conscience. Absolute monarchs of the period lived in a strange world. On the one hand, from the time they were children they were told that God himself had blessed them with royalty and that the exercise of power was not only their privilege but their responsibility. The king had to rule, and by that very fact he lived in an alternate moral universe. Not even his spiritual director complained too much about his lovers, which, in the case of Louis XIII, were generally older men; nevertheless, his conscience, if he had one, could be a source of political leverage. Unfortunately, Louis XIII had a conscience, and a touchy one at that. He was an extraordinarily complicated man, who could ruthlessly order the storming of a castle or the execution of an enemy one day and then wring his hands over his failure to achieve perfect contrition the next.
Louis XIII had a spiritual director named Père Caussin, a Jesuit who was secretly involved with the Spanish faction and who also tried to use his influence with the king to awaken Louis to the desperate condition of his people. Ironically, it was Cardinal Richelieu who had first introduced Caussin to the king and had appointed him his spiritual director. Caussin’s politics were decidedly anti-Richelieu, however. He opposed the cardinal’s attempts to reach out to the Protestants, and conspired with the Spanish faction to influence the king to reverse Richelieu’s policy of siding with the Protestants against the Hapsburgs during the Thirty Years’ War.
Caussin reminded Louis how sinful it was for him to be living in luxury while his own mother, Marie de Médicis, was living in relative poverty in exile after the Day of Dupes. He reminded him again about how sinful it was that his people should suffer through another war of religion. Finally, Louis spent three nights in sleepless agony after Caussin told him that he could not be forgiven unless he performed acts of spiritual love that were completely selfless, without any self-interest, without even the desire to go to heaven. How one can have such control over his own psyche and be assured of his own motivations to that degree remains a mystery, even today. Actually, Caussin had overstepped his bounds, for his doctrine was not something that the Jesuits taught, and they would have been angry to learn what he had been doing. Its origin was traced along the twisting path back to the abbé de Saint-Cyran, who, surprisingly e
nough, never taught it.
On the feast of the Immaculate Conception, December 8, 1638, Caussin preached to the king on his sinful behavior toward his mother and on the terrible deeds committed in his name during the war. Once again, during Communion as the king knelt at the altar rail, Caussin argued with him, telling him how sinful he had been and how he needed to redeem himself through acts of perfect love. Upset, Louis invited Caussin to argue his case before Richelieu during supper. Even though Caussin arrived early, the cardinal had gotten wind of what the king’s spiritual director had been doing and ordered him to sit in a waiting room while he discussed these issues with the king. Richelieu was nothing if not rational, and he argued each point that Caussin had made until the king’s conscience was salved. After that, the cardinal had Caussin banished from the court. Saint-Cyran’s name came up in the aftermath of the Caussin affair, which only contributed to Richelieu’s decision to imprison Saint-Cyran.
Richelieu’s final reasons for having Saint-Cyran imprisoned, however, were complex and subtle, as was typical of the cardinal. First and foremost, Richelieu did not trust the convent at Port-Royal and suspected them of heretical leanings, so that the abbot’s association with the good sisters was suspect immediately. Port-Royal had taken too many bright young servants of the king, like Antoine Lemaître, a brilliant young lawyer who was a blood relative of the Arnaulds, into its penitential bosom. Moreover, at the abbot’s encouragement, one of the Arnaulds—Antoine the younger, later nicknamed the Great Arnauld—like some rabbit-and-hat magician, wrote a treatise arguing that the Eucharist was so sacred that ordinary sinners dare not approach it without undergoing a process of purification and penance. This galled Richelieu, because his own conscience was so touchy, mainly because of his ruthless exercise of power, that regular confession and Communion were essential parts of his psychological maintenance. Then, Saint-Cyran’s old friend and collaborator Cornelis Jansen wrote a book attacking Richelieu’s looming war against the Spanish Hapsburgs. But what did the trick was that Richelieu tried to buy Saint-Cyran off with a bishopric, that of the abbot’s hometown of Bayonne, but Saint-Cyran turned him down. The fact that the abbot had been ready to accept the same offer from Richelieu’s enemies was a personal insult to the cardinal, and the cardinal did not brook personal insults.
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