Mar 312019
 

Today is the birthday (1596) of René Descartes who was, and remains, extraordinarily influential in philosophy and mathematics. The adjective “Cartesian” is used to describe two of his most important contributions: Cartesian dualism, and Cartesian coordinates. I’ll hit a few high spots, and also some lesser known facts about his life, but I’ll try to keep things simple.

Descartes was born in La Haye en Touraine (now Descartes, Indre-et-Loire). His mother, Jeanne Brochard, died soon after giving birth to him, and so he was not expected to survive. Descartes’ father, Joachim, was a member of the Parlement of Brittany at Rennes. Descartes lived with his grandmother and with his great-uncle. Although the Descartes family was Roman Catholic, the Poitou region was controlled by the Protestant Huguenots. In 1607, late because of his fragile health, he entered the Jesuit Collège Royal Henry-Le-Grand at La Flèche, where he was introduced to mathematics and physics, including Galileo’s work. After graduation in 1614, he studied for two years (1615–16) at the University of Poitiers, earning a Baccalauréat and Licence in canon and civil law in 1616, in accordance with his father’s wishes that he should become a lawyer. From there he moved to Paris.

In Discourse on the Method, Descartes recalls,

I entirely abandoned the study of letters. Resolving to seek no knowledge other than that of which could be found in myself or else in the great book of the world, I spent the rest of my youth traveling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting upon whatever came my way so as to derive some profit from it.

Given his ambition to become a professional military officer, in 1618, Descartes joined, as a mercenary, the Protestant Dutch States Army in Breda under the command of Maurice of Nassau, and undertook a formal study of military engineering, as established by Simon Stevin. Descartes, therefore, received encouragement in Breda to advance his knowledge of mathematics. In this way, he became acquainted with Isaac Beeckman, the principal of a Dordrecht school, for whom he wrote the Compendium of Music (written 1618, published 1650). Together they worked on free fall, catenary, conic section, and fluid statics. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics (now a fundamental given of theoretical physics).

On the night of 10–11 November 1619 (St. Martin’s Day), while stationed in Neuburg an der Donau, Descartes shut himself in a room with an “oven” (probably a Kachelofen or masonry heater) to escape the cold. While within, he had three dreams and believed that a divine spirit revealed to him a new philosophy. However, it is likely that what Descartes considered to be his second dream was actually an episode of exploding head syndrome (an hallucinatory experience between waking and sleeping). Upon leaving, he had formulated analytical geometry and the idea of applying the mathematical method to philosophy. He concluded from these visions that the pursuit of science would prove to be, for him, the pursuit of true wisdom and a central part of his life’s work. Descartes also conceived the idea that all truths were linked with one another so that finding a fundamental truth and proceeding with logic would open the way to all science.

Not long after this experience, Descartes wrote his famous “I think, therefore I am” which links truth with reason rather than with empirical experience. People are regularly deceived by their own eyes, dreams, and imaginations. Descartes, however, realized that his argument opened a door for “radical doubt.” what was stopping people from doubting the existence of everything? The cogito ergo sum argument is his remedy. Even if you doubt the existence of everything, you cannot doubt the existence of your own mind—because doubting indicates thinking, and thinking indicates existing. Descartes argued that self-evident truths like this—and not the senses—must be the foundation of philosophical investigations.

Descartes’ desire to show that all logical truths are related led him to develop analytic geometry whereby algebra and geometry are merged. Descartes showed that you can express an algebraic function on a graph or express a line as an algebraic function. You probably know, for example, that a simple function produces a straight line graph, and a quadratic function produces a parabola (also linking conic sections). Being able to unite algebra and geometry opened up worlds – including the eventual development of calculus. Even if your eyes glaze over at this stuff, take it from me, IT’S A BIG DEAL.

In 1647, Descartes, now 51, visited the 24-year-old prodigy Blaise Pascal. Their meeting quickly devolved into a heated argument over the concept of a vacuum, specifically whether air pressure could ever be reduced to zero. Descartes said it was impossible; Pascal disagreed. Later, Descartes wrote that Pascal had too much vacuum in his head.

Descartes routinely slept 12 hours a night, from midnight until lunchtime. In fact, he worked in bed. (Sleep, he wisely wrote, was a time of “nourishment for the brain”). According to the Journal of Historical Neuroscience, he may have had a sleep disorder that helped end his life. A year before his death, Descartes had moved to Stockholm to take a job tutoring queen Christina, a devoted early-riser who forced Descartes to change his sleep schedule. Some believe the resulting sleep deprivation weakened his immune system and eventually killed him.

Descartes died in Stockholm in 1650 and was buried outside the city. Sixteen years later, his corpse was exhumed and taken to Paris. During the French Revolution, his bones were moved to an Egyptian sarcophagus at the Museum of French Monuments. Decades later, when plans were made to rebury Descartes in an abbey, officials discovered that most of his bones—including his skull—were missing. Shortly after, a Swedish scientist discovered a newspaper advertisement attempting to sell his head. Today, his head is in a collection at the Musée de l’Homme in Paris.

Blanquette de veau is a ubiquitous French recipe of venerable heritage suitable to honor Descartes. It is not difficult to make, as long as you pay attention.

Blanquette de Veau

Ingredients

800g boneless veal, neck or shoulder, cubed
3 carrots, peeled and diced
1 leek, washed and chopped
4 small yellow onions, peeled and chopped
1 bouquet garni
2 egg yolks
100 ml crème fraîche
60 gm butter
40 gm flour
200 gm mushrooms, sliced
½ lemon
salt and pepper

Instructions

Place the veal in a large pot, cover with cold water, then bring to a boil. Reduce to a simmer and skim the foam that rises. Add the cut vegetables and bouquet garni. Season with salt and pepper to taste, and cook about 90 minutes at a simmer.

Reserve the meat and vegetables, and filter 1 to 1.5 liters of broth to keep for the sauce.

Cook the mushrooms in a sauté pan with 20 grams of butter, 100 milliliters of water and the juice of half a lemon.

Prepare a white roux with 40 grams of butter and 40 grams of flour by melting the butter in a skillet, stirring in the butter and gently cooking without browning. Pour the broth in gradually and stir to make a thick sauce. Remove from the heat once the sauce has thickened. In a bowl, combine the 2 egg yolks and the cream, then stir the mixture from the bowl into the sauce.

Add the pieces of meat and mushrooms to the sauce, simmer for a few minutes and serve with plain boiled rice.