Descartes: Discourse on the Method

René Descartes was a French thinker who lived about 400 years ago. When he finished school, he felt that much of what he had learned was uncertain: teachers disagreed, and old books contradicted each other. Only mathematics seemed sure. So he asked: could I find a way of thinking that works as surely as arithmetic, for every subject?

He made four rules for himself. (1) Don't accept anything as true unless you clearly know it is. (2) Break a hard problem into small pieces. (3) Start with the easiest pieces and climb step by step to the hard ones. (4) Check everything at the end, so nothing is left out. These are good rules for homework, too!

Descartes used his method on science. One puzzle he solved: why is a rainbow round, and why always in the same place in the sky? He studied how sunlight bends and bounces inside a single raindrop, and found that the brightest light comes out at one special angle, about 42 degrees.

Who, when and why

René Descartes (1596–1650) was educated at the Jesuit college of La Flèche, studied law, served for a time with armies in the Netherlands and Germany, and settled in the Dutch Republic in 1628, where he lived for about twenty years. In 1637 he published, without his name, a book in French: the Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences, followed by three essays showing the method at work: the Optics, the Meteors and the Geometry. He wrote in French, not Latin, so that anyone with good sense could read it.

The Discourse is short and personal: the story of how he came to doubt what he had been taught, the rules he chose, the moral code he lived by meanwhile, the famous "I think, therefore I am" (Part IV), a sketch of his physics and of the heart (Part V), and his hopes for science (Part VI). This rung follows the science side; the Meditations rung covers his philosophy of doubt and certainty in full. Descartes's earlier, unfinished Rules for the Direction of the Mind, also in the set, spells out the method in more detail.

The problem Descartes faced

The schools taught a science built on Aristotle, with explanations in terms of forms and qualities. New discoveries (the telescope, Kepler's optics, Harvey's circulation) did not fit it well, and scholars argued without end. Descartes wanted a single, certain method that would let reason rebuild knowledge from secure foundations, the way geometers build long chains of proofs from a few simple starting points.

Idea 1: four rules

Notice what the rules leave out: they say nothing about authority, tradition or the number of people who agree. And notice their source: they are how a mathematician works. Descartes had found that algebra could solve geometry problems by breaking them into steps (see the rung on his Geometry), and he hoped the same order would work everywhere.

Idea 2: the rainbow, a test case

In the Meteors Descartes uses his method on the rainbow. He first noticed that a large glass globe filled with water, held in the sun, shines red when the line from his eye to it makes an angle of about 42° with the direction of the sun's rays (measured from the point straight opposite the sun). Then he divided the problem: one drop, one ray at a time. Using the law of refraction, he calculated the path of many rays entering the drop at different heights. Most rays come out spread over many angles, but near 42° they bunch together. Every drop at that angle from your eye sends you this extra-bright light, and the drops at that angle form a circle around the point opposite the sun. With two reflections inside the drop, the rays bunch near 51°: the fainter second bow.

Idea 3: the heart, and Harvey

In Part V Descartes describes the body as a kind of machine and gives an account of the heart. He was one of the first well-known writers to accept Harvey's circulation, only nine years after Harvey's book.

But Descartes disagreed with Harvey about how the heart moves. He thought heat in the heart made drops of blood boil and swell, pushing open the valves, like milk boiling over. Harvey was right: the heart is a muscle that squeezes.

Idea 4: science for the good of all

Descartes adds that the most important use would be health, the preservation of which is "the first and fundamental" blessing of life. He also asks for public help with experiments, which one person cannot afford alone, much as Bacon did.

Getting the history right

• Why he held back his physics. In Part VI Descartes says he was about to publish a treatise when he learned that "persons to whom I greatly defer" had condemned a doctrine in physics published by another. He meant the Roman Inquisition's condemnation of Galileo in 1633. Descartes's own book, The World, which made the Earth move, was published only after his death.
• The law of refraction was not first his. Descartes published the sine law in the Optics. Willebrord Snell had found it about 1621 without publishing, and the Persian mathematician Ibn Sahl had described an equivalent rule around AD 984. English speakers call it Snell's law; in France it is often called Descartes's law.
• The rainbow was not first his either, but the numbers were. Theodoric of Freiberg (around 1304) and Kamal al-Din al-Farisi had already traced light through a single drop with water-filled globes. Descartes was the first to calculate the 42° angle from the law of refraction. Why the colors separate had to wait for Newton's prism experiments.

What later science kept, and what it changed

Kept: the habit of breaking problems into parts and building up from the simplest; the use of mathematics in physics; the law of refraction; the rainbow angle; the dream of science serving health. Changed: Descartes hoped pure reasoning from clear ideas could reach the laws of nature, with experiments to settle details. Later science, after Newton, leaned much harder on experiment. Descartes's physics of whirlpools (vortices) in a space-filling matter was replaced by Newton's gravity, and his heat theory of the heartbeat by Harvey's muscle pump.

Method or methods? Bacon told scientists to gather many cases first; Descartes told them to start from what is certain and reason down. Galileo moved between mathematics and experiment. Most scientists today would say real discovery uses all three. Which of Descartes's four rules do you think matters most?

"Lords and possessors of nature." Descartes, like Bacon, hoped that science would bring health and comfort. Later writers have debated whether this way of speaking about nature encourages care or carelessness. People hold different views; you can weigh them yourself.

How later books answered. Newton's Principia (1687) was partly written against Descartes's physics, and its title, Mathematical Principles of Natural Philosophy, echoes Descartes's Principles of Philosophy (1644). Newton's Optics (1704) finished the rainbow by explaining its colors.

Big questions. Can any method guarantee the truth? Is it ever wise to doubt everything at once? What do we owe to the people who taught us, if we decide they were wrong?