Frans Hals—Portret van René Descartes, Wikipedia, Public Domain
René du Perron Descartes was born on March 31, 1596, in La Haye en Touraine, Indre-et-Loire, (now called Descartes in his honor) in France, was an important philosopher and mathematician, and is dubbed the father of modern philosophy. Descartes was born into the noblesse de robe, whose members contributed considerably to intellectual life in the seventeenth century. His father, Joachim, was a conseiller to the Parlement of Brittany at Rennes [1]. From his mother, Jeanne Brochard, he received the name du Perron. He moved to the Netherlands in 1628, at the age of 32, and lived there for more than 20 years to concentrate on his work. Descartes never married, but had a daughter from a maid in the home where he was staying in the Netherlands. His daughter, Francine, was born in 1635 and died of a fever at age five [2]. Descartes’ final years were spent in Sweden where he was invited by the Queen of Sweden to organize a scientific academy in 1649. On February 1, 1650, he may have contracted pneumonia and died on 11 February in Stockholm, at the age of 54.
René was the youngest of three children. When he was one year old, his mother died. His father remarried, and René and his older brother and sister were raised by their maternal grandmother and by a family nurse for whom René retained a deep affection. As a child, he may have been often sickly since he was allowed to spend a portion of each day studying in bed. He used this time for meditation and thought. In 1606, Descartes entered La Flèche, a religious college established for the education of the sons of noblemen. He was interested in the mathematical examination of nature using ordinary things for inspiration. According to one account while he was laying in bed and examining the movements of a fly on the ceiling, he thought of a mathematical way to describe the position of the fly. He thus came up with what we now call the Cartesian three-dimensional coordinate system, which allows for precise positioning of objects and for algebraic equations to be expressed as geometric shapes. This laid the foundations for modern mathematical science.
“in the writings of the poets weightier thoughts than in those of the philosophers. The reason is that the poets wrote through enthusiasm and the power of imagination.” The seeds of knowledge in us, “as in a flint,” were brought to light by philosophers “through reason; struck out through imagination by poets they shine forth more brightly.”
After leaving college at age eighteen, Descartes earned a law degree in Poitiers, France. Then, after graduating, he volunteered as a gentleman in the army of Prince Maurice of Nassau in 1618 and met Isaac Beeckman at Breda. Beeckman aroused him to self-discovery as a scientific thinker and mathematician and introduced him to a range of problems, especially in mechanics and acoustics, the subject of his first work, the Compendium musicae of 1618, published posthumously in 1650 [4]. On March 26, 1619, he reported to Beeckman his first glimpse of “an entirely new science,” which was to become his analytical geometry. From 1618 to 1628, he traveled throughout Europe as a soldier. Living on income from inherited properties, Descartes served without pay and saw little action.
While in the duke of Bavaria’s army on the Danube, he had the experience in the famous poêle (lit. “stove” or a “well-heated room”) and claimed to have been given direction to the rest of his life. He described in the Discours de la méthode [5] how, in a day of solitary thought, he reached two radical conclusions: first that if he were to discover true knowledge, he must carry out the whole program himself, just as a perfect work of art or architecture was always the work of one master hand; second that he must begin by methodically doubting everything taught in current philosophy and look for self-evident, certain principles from which to reconstruct all the sciences.
That night, according to his seventeenth-century biographer Adrien Baillet, these resolutions were reinforced by three consecutive dreams [6]. He found himself, first, in a street swept by a fierce wind, unable to stand, as his companions were doing, because of a weakness in his right leg; second, awakened by a clap of thunder in a room full of sparks; and third, with a dictionary, then a book in which he read Quid vitae sectabor iter? (“What way of life shall I follow?”), then verses presented by an unknown man beginning Est et non; he recognized the Latin as the opening lines of two poems by Ausonius [6]. Before he finally woke up, he had interpreted the first dream as a warning against past errors, the second as the descent of the spirit of truth, and the third as the opening to him of the path to true knowledge. However, this incident may have been elaborated in the telling, and it symbolizes both the strength and the hazards of Descartes’s unshakable confidence and resolves to work alone. But he did not make his vision his life’s mission for another nine years, during which (either before or after his tour of Italy from 1623 to 1625) he met Mersenne, who was to become his lifelong correspondent and took part in scientific meetings in Paris. The next decisive incident, according to Baillet, was a public encounter in 1628 in which he demolished the unfortunate Chandoux by using his method to distinguish sharply between true scientific knowledge and mere probability.
Descartes has been dubbed as the man who “tried in one bold leap to put himself at the source of everything, to make himself master of the first principles by means of certain clear and fundamental ideas, so that he could then simply descend to the phenomena of nature as to necessary consequences of these principles.” This famous characterization of Descartes as the theoretician who “set out from what he knew clearly, in order to find the cause of what he saw,” as against Newton the experimenter, who “set out from what he saw, in order to find the cause,” has tended to dominate interpretations of both these men who “saw the need to carry geometry into physics [1].”
His best-known philosophical statement is “Cogito ergo sum” (French: Je pense, donc je suis; I think, therefore I am), found in part IV of Discourse on the Method (1637—written in French but with inclusion of “Cogito ergo sum”) and in part I of Principles of Philosophy (1644—written in Latin) [5, 7].
Descartes’ influence in mathematics is equally apparent; the Cartesian coordinate system—allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system (and conversely, shapes to be described as equations)—was named after him.
19.1 Descartes’ Thoughts on Color
Descartes believed that all properties, which cannot be described in purely quantitative or geometrical terms, should be banished from science. According to some interpretations, Descartes considered colors an artifact of the mind treating them as mere sensations [8]. Another group of commentators have developed a different interpretation that attempts to reconcile his “objectivist” strand that grants colors an existence in bodies independent from the perceiver and the putative “subjectivist” strand that treats them as sensations, and thus, makes them utterly dependent on the perceiver [9]. Descartes’ mechanical theory of vision, presented in the Optics and the Meteorology [5], includes various metaphysical claims about the nature of color itself. However, it may be argued that those assertions may have referred to the external causes of visual perception [9]. He wished to demonstrate the power and superiority of the mechanistic science in explaining visual perception over scholastic Aristotelian accounts, which assumed it to be the result of the transmission of intentional forms or species from the external object to the sensing organs of the perceiver, through a medium such as air.
Regarding light and color … we must suppose our soul to be of such a nature that what makes it have the sensation of light is the force of the movements taking place in the regions of the brain where the optic nerve-fibres originate, and what makes it have the sensation of color is the manner of these movements. But in all this there need be no resemblance between the idea which the soul conceives and the movements which cause these ideas (AT VI 130; CSM 1 167).
… the properties in external objects to which we apply the terms light, color, smell, taste, sound, heat and cold, as well as the other tactile qualities … are, so far as we can see, simply various dispositions in those objects which make them able to set up various kinds of motion in our nerves (AT VIII 322: CSM I 285).
It is clear then that when we say we perceive colors in objects, it is really just the same as saying that we perceived in objects something as to whose nature we are ignorant but which produces in us a very clear and vivid sensation, what we call the sensation of color. ([3]: para. 70; see also paras 68–70)
nothing but names for something that resides exclusively in our sensitive body, so that if the perceiving creature were removed, all such qualities would be annihilated from existence [10].
Tastes, odors, colors, and so on are no more than mere names so far as the object in which we place them is concerned, and … reside only in the consciousness. Hence if the living creature were removed, all these qualities would be wiped away and annihilated. [10–13]
Experimentally, Descartes observed that rainbows occurred when water spread from a sprinkler. Using sunlight and a glassy sphere full of water and standing on foot and directing his back to the sun, he watched through a hole in the glassy sphere and shook the sphere upward and downward until he finally discovered brightness at the bottom of the sphere. As we discussed in Chap. III, Kamal al-Din al-Farisi had made similar experiments and obtained the same results as Descartes, many years before him. Using geometric construction and the law of refraction (discussed independently by Ibn Sahl (c. 940–1000 AD), rediscovered in 1602 by Thomas Harriot and in 1621 by Willebrord Snellius and 16 years later by Descartes), he showed that the angular radius of a rainbow is 42°. That is, the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow’s center is 42°. He also independently discovered the law of reflection, and his essay on optics contained the first published mention of this law.