Descartes's Secret Notebook

by Amir D. Aczel

  The Descartes family was wealthy, and Rene would inherit even more assets directly from his grandfathers on both sides, both of whom had been successful medical doctors. His great-grandfather Jean Ferrand had been the personal physician of Queen Eleanor of Austria, the wife of Francis I of France, in the middle of the sixteenth century. He attained great wealth, which was eventually passed on to his daughter Claude, who married Pierre Descartes. Their son was Joachim Descartes, Rene's father. In 1566, when Joachim was only three years old, his father, Pierre, died of kidney stones. Pierre's father-in-law, Jean Ferrand, Queen Eleanor's personal physician, performed the autopsy on his son-in-law. In 1570 he wrote up the results of the operation and published them in a scientific paper, in Latin, about lithiasis—the formation of stony concretions in the body. His deep curiosity about nature—even to the point of dissecting the body of his own son-in-law—was passed on to his descendants. While, unlike his grandparents, Rene Descartes would not pursue medicine as a profession, late in life he would dissect many animals in search of the secret to eternal life.

  Rene Descartes would spend much time during his adult life managing his inheritance. This wealth, including significant land holdings in Poitou, would enable him to pursue his interests without concern about a livelihood. It would afford him to indulge his whim of volunteering for military campaigns as a gentleman soldier without compensation—simply for the thrill of adventure. He would be able to afford luxurious accommodations wherever he traveled, and to employ servants and a valet. His money would even allow him to look after the education of his staff, thus sharing with them some of the privilege of his family's wealth. Descartes would grow up to be a very generous employer and friend.

  Despite Adrien Baillet's statement in his very comprehensive 1691 biography of Descartes that the family belonged to the nobility, recent research indicates that, as far as Rene's life is concerned, this was not true. The renowned French historian Genevieve Rodis-Lewis explains in her 1995 biography, Descartes, that the Descartes family gained the rank of knighthood, the lowest status of nobility in France, only in 1668—eighteen years after Rene's death. According to French law, nobility was conferred on families after three successive generations had served the king in high office. Joachim Descartes certainly held such a position, and some have argued that he had originally sought to become councillor to the Parliament of Brittany in hopes of obtaining nobility status for his descendents. But Rene Descartes would choose a different direction in life, and so nobility would be conferred on the family only after another member had satisfied the three-generations requirement, years after Rene's death.

  After he remarried, Joachim Descartes spent most of his time in Rennes with his new wife and the children she bore him. He also had interests and family business farther south and west in Nantes, also in Brittany. As they grew older, Rene and his brother and sister traveled frequently to visit their father. Eventually, Rene Descartes would see all of western France as his home territory, since time in his later childhood was spent throughout the regions of Poitou, Touraine, and Brittany.

  But the frequent travel throughout the region was hard on the boy. In adulthood, Descartes described his health as a child as poor, and recounted in letters to friends that every doctor who had ever seen him as a child had said that he was in such poor health that he would most likely die at a young age. His devoted governess took such good care of him, however, that when he was eleven years old he was healthy enough to be sent away to study at the prestigious Jesuit College of La Fleche.

  Chapter 2

  Jesuit Mathematics and the Pleasures of the Capital

  IN 1603, KING HENRY IV, WHO HAD been raised a Protestant but converted to Catholicism, gave the Jesuits, as a gesture of his goodwill toward this powerful Catholic order, his chateau and vast grounds in the town of La Fleche, to be used by them as the site of a new college. The Jesuits enlarged the chateau, and the result was a series of large interconnected Renaissance buildings with spacious, square, symmetric inner courtyards. Entering the grounds, one is struck by the perfect order and symmetry of the checkerboard array of grand courtyards, and by the well-manicured gardens beyond them. This is one of the most impressive college grounds anywhere; today it is the site of a military academy, the Prytanee National Militaire.

  La Fleche was well chosen for a college. It lies in Anjou, north of Touraine, in a rich area with forests and gentle rolling hills. The town is attractive, with a river running through its center and lush meadows surrounding it. The gate of the college opens right into the spacious town square. Once students left the grounds of the college, they were in the center of the town with its many places to eat, drink, and find entertainment.

  The college was inaugurated by King Henry IV, and opened its gates in 1604 France's brightest students from the best families were encouraged to apply for acceptance. Among the students accepted to the first class to enter this elite new college was Marin Mersenne (1588-1648), who would become Descartes' most devoted and loyal friend.

  The college was run as a semimilitary school. The students had to wear a uniform, including breeches with pom-pom fastenings, a fancy blue blouse with large-puffed sleeves, and a felt hat. Each student was given a long list of items he had to bring to school. These included candles, various kinds of pencils, quills, and notebooks, and items of personal use.

  According to new research, Rene Descartes entered the College of La Fleche right after Easter 1607. A college such as La Fleche was an educational institution at which young boys studied before going to a university. As such, it was akin to a modern preparatory school rather than what we call a college today. Descartes' admission to the college was delayed because his health wasn't good enough when he was younger; and until then, he was educated at home by a tutor. Rene was eleven years old when he started his studies at La Fleche, and he stayed there until his graduation eight years later, in 1615. The tuition at the college was free, but students' families had to pay for room and board and other expenses. At the time Descartes studied there, the college had about fourteen hundred students, who came from all over France. Fortunately, the college was a day's journey from Descartes' home in La Haye, so he could easily visit his grandmother and governess.

  Since Descartes was still frail, the family made a special request to the college, asking that its administration take exceptionally good care of his health. The rector, Pere Charlet, who was a relative of the Descartes family and whom Rene would later describe as “almost a father to me,” was eager to comply, and gave Rene unprecedented privileges so that the boy would not feel any stress, in hopes that his health would improve. He thus allowed Rene to sleep late in the mornings and stay in bed until he felt well enough to join the others in the classroom. This unique arrangement started Descartes on a lifelong routine of waking up late in the mornings and staying in bed, thinking and working, until he was ready to get up and face the day. Most of his life until his last few months in Sweden, with the exception of periods in which he was in an army involved in heavy fighting, Descartes never had a forced wake-up in the morning, but rather arose whenever his body was sufficiently rested.

  Life at the college, for everyone else, began at 5:00 A.M. From 5:00 until 5:45, the students said their morning prayers, washed and dressed, and got ready for work. Personal hygiene was very important: students were made to wash well, and if they were sick they were confined to the infirmary. The time from 5:45 to 7:15 was spent on individual work, followed by breakfast. The first classes were held from 7:30 until 10:00. Rene Descartes was exempt from having to sit through these early classes. At 10:00 A.M., mass was held, followed by dinner, which was the first substantial meal of the day. There followed a period set aside for recreation. Afternoon classes began at 1:30 and lasted until either 4:30 or 5:30, depending on the season. The students spent the remainder of the day—until 9:00 P.M., when they went to bed—having their evening meal and playing games, mostly ball games that were popular in France during this period (
including the famous jeu de paume). They were also allowed to play cards, a popular pastime, but the involvement of money in any kind of game was strictly prohibited. Just before they retired at 9:00 P.M., they attended a spiritual lecture. On special days, equestrian skills were taught, as well as swordsmanship.

  Rene Descartes joined his fellow students after the morning classes had ended. His special arrangement, allowing him to stay in bed late, made him learn how to study on his own. This was especially useful in mathematics, where he could derive ideas by himself, without having to sit through the material slowly with an entire class. This habit of intellectual independence enabled him to forge ahead swiftly and—a little later in life—to create new mathematical and scientific knowledge on his own without being held back by conventional beliefs.

  Students were taught grammar, which meant Latin and Greek. They also studied humanities, rhetoric, and philosophy. Both humanities and rhetoric were centered on the classics. Humanities included the works of the Roman poets Virgil, Horace, and Ovid, while rhetoric was mostly a study of Cicero and the Platonic method of argumentation. The philosophy taught at La Fleche consisted of the works of Aristotle, in the medieval scholastic tradition, as well as logic, physics, and metaphysics.

  The Jesuits taught their students the essentials of Greek mathematics: the works of Euclid, Pythagoras, and Archimedes. The Greeks, with their clear, abstract view of nature and its elements, simplified all construction in geometry to figures that could be drawn with only two tools—the simplest tools they could conceive and ones that they believed should suffice to construct any geometrical figure one could imagine or need. These two elementary tools were an unmarked straightedge and a compass.

  A straightedge

  A compass

  The straightedge made angles and straight lines, while the compass was used for making circles and marking off distances. By combining the operations of both instruments, anything that was of importance to Greek mathematicians could be drawn.

  Figures drawn with straightedge and compass

  Descartes was fascinated by the simplicity of thought and the power of abstraction the ancient Greeks had demonstrated with their geometry, an entire science based on the use of two instruments. The priests who taught this ancient knowledge at the college outlined the entire theory of Euclidean geometry, and explained to the students how to prove a variety of theorems in geometry. Mathematics courses at La Fleche also included arithmetic, in which the rules of computation were studied, as well as algebra, in which methods of solution of equations were explained—as much as these equations were understood at that time.

  Interestingly, the grounds and buildings of the College of La Fleche, perfectly symmetrical and square in their design, seemed constructed as if by straightedge and compass. Descartes' writings later in life—particularly his Discourse on the Method of 1637—make it clear that he was impressed by symmetry and straight lines in the design of buildings and towns:

  Thus old cities, which were at their beginnings nothing but small towns, and have become in time large cities, are generally not well designed as by compass [ordinairement si mal com-passees], at the cost of the regularity of their squares that an engineer traced following his fantasy on the plane…. Seeing how the buildings are arranged, here a large one, there a small one, and how they make the streets curved and unequal, one would conclude that it was chance, rather than the will of men using reason, that has thus laid them out.

  What the young boy saw on the grounds of his college and learned from his study of Greek geometry using straightedge and compass became important elements in shaping his philosophy and his mathematics. With enough imagination, one can trace the origins of the Cartesian coordinate system to the perfectly symmetric design of the grounds of Descartes' College of La Fleche.

  During his time at La Fleche, Descartes and the other students at the college took part in a most unusual ceremony. King Henry IV was considered the founder of the college, and the gate to the college bore (and still does today) the letter H on each side, in honor of the king, as did most buildings on the campus. In his will, the king had specified that his heart, that of his queen, and those of their heirs were to be buried at the Church of Saint Thomas on the grounds of the college, his former Chateau of La Fleche.

  Henry IV, whom history would remember as one of France's most benevolent monarchs (he's the king who promised a “chicken in every pot” in his realm for Sunday meals), had difficulties throughout his rule with tensions between Protestants and Catholics, the latter never quite trusting him completely even though he was nominally a Catholic. Things became more dangerous for the king when in 1610 he allied himself with several German Protestant princes against Catholic Spain. On May 14 of that year, the king's carriage was passing through a particularly busy street in Paris, the rue de la Ferronerie. As traffic on the street momentarily came to a halt, a Catholic fanatic named Ravaillac rushed onto the royal carriage and stabbed the king in the chest. He died almost instantly.

  After the king's assassination, the ritual prescribed in the king's will began. It started with prayers for the soul of the dead king held on May 15 at the church of the College of La Fleche. The king's body was embalmed in the Louvre palace, and the heart was carefully removed. The heart was kept for three days in the Jesuit chapel in Paris, and then transferred to the care of Pere Provincial Armand, who gathered a group of twenty leading Jesuits and a larger number of the king's knights to accompany the heart to its final resting place in La Fleche.

  The college chose a group of twenty-four of its most distinguished students to join the procession as the party carrying the king's heart arrived in town. Among these twenty-four students was Rene Descartes. The procession came to order at the central square in town, and now included also archers and royal guards, who had joined it. From the town of La Fleche, the entire assemblage marched to an open field and stopped. Torches were lit, and in a solemn ceremony, the heart was transferred from Pere Armand to the duke of Montbazon. The procession then continued on to college grounds and into the Church of Saint Thomas. Inside the church, the duke raised the heart for all to see, and in a communal prayer, it was placed in an urn forever to remain in the church. This ceremony was deeply etched into Rene Descartes' memory.

  After his graduation in 1615, Descartes moved to Poitiers to study law at the university. He spent an uneventful year there, since he was not interested in the law. Much of his spare time was devoted to practicing his swordsmanship skills learned at La Fleche. He received his doctor of law degree in 1616, and after spending a pleasant summer with his family in Rennes, riding horses and enjoying the outdoors, he moved to Paris. (In 1985, Descartes' thesis for his law degree was discovered at the University of Poitiers. The date of acceptance of the thesis was November 10, 1616. When they found the thesis, scholars were struck by its date. This day—November 10, and sometimes the night of November 10-11, or November 11—reappears as if by magic as the date of many key events in the life of Descartes.)

  Descartes' family did not take well to his expressed wish to move to Paris after his graduation. Even though Rene's health was now much better than it had been in his childhood, the family was concerned about the prospect of his living alone so far away. Joachim Descartes was especially worried about his son moving to the big city, but Rene assured him that this was what he wanted to do and that it was an important step toward his future. At twenty, he argued, he was old enough to live on his own and find his way in the world. The father finally agreed to let him go—but only on the condition that he move to Paris with servants and a valet to assist him. Throughout his life, Descartes would never be without a valet. He chose them well—his valets were always extremely loyal to him and would literally risk their lives for his safety and well-being.

  The city of Paris has always been the center of life for the French, who have been flocking there for centuries from small towns and villages throughout the land. They come to seek a better life, economic rewa
rds, and culture. But many come to Paris for the sheer excitement it offers. In the days of Descartes, this impulse was no different than it is today.

  Descartes lived during the time of d'Artagnan and the swashbuckling adventures depicted in Alexandre Dumas' Three Musketeers. Looking at seventeenth-century French paintings and engravings gives us a good idea about the styles of the time of Descartes: richly colored flowing silk garments with voluptuous folds, plumed velvet hats, shoes with ornate silver buckles. Descartes loved to dress in style, and he carried his polished sword with him wherever he went, as did many young gentlemen of his time. He was intent on learning as much as he could from “the great book of the world,” as he called it. He was on a search for truth about life and the human experience. And what better place to explore life than the city of Paris ?

  By the time he finally moved to Paris, Descartes' health was excellent. He had lost the paleness of his youth, and he no longer suffered from whatever ailments had plagued him in childhood. Feeling well for the first time in his life, and finally having finished his education, he was eager to experience life. In Paris he met up with many of his old friends from La Fleche, who had congregated in the capital, and he also made some new ones.

  Descartes' early days in Paris were a carnival of drinking, gambling, and merrymaking. He learned very quickly that he had a knack for card games and other games of chance—now, unlike at college, played for money. He was very successful at these games, winning significant amounts of money, which made him even more popular with his old and new friends alike. Descartes was constantly surrounded by people, and life for him was a continuous, endless party. These young men paraded down the streets of Paris, pursuing beautiful women.