Descartes Contributions to Science

DESCARTES' CONTRIBUTIONS TO SCIENCE From what has already been said above about Descartes' Meth odology, one almost expects that his endeavour would be to reduce all science to a kind of applied mathematics. And that is what he really did attempt. "I do not accept or desire," he wrote, "any other principle in physics than in geometry or abstract mathe matics, because all the phenomena of nature may be explained by their means." Another way of expressing the same thing is to say that Descartes tried to reduce every science of natural phenomena to a branch of mechanics. But it must he remembered that for Descartes mechanics was essentially kinetics, not dynamics—a calculus of changes of position, not a calculus of "forces." The progress of the physical sciences during the i7th and i8th cen turies was due in large measure to the adoption of a mechanical interpretation of physical phenomena. This method of interpre tation was initiated by Galilei and extended by Descartes. Its merits can only be appreciated when one recalls the "substantial forms," "hypostatical principles," "real accidents," and other mystifying conceptions of the pseudo-science which preceded the Cartesian attempt to interpret all natural phenomena by means of clear and distinct mechanical concepts. It was left to a later age to discover the inadequacy of an exclusively mechanical interpre tation of natural phenomena. But this must not be allowed to detract from the merits of Descartes in the history of science. Physics and Cosmology.—Descartes, by refusing to attribute to matter any sense-qualities, which are not reducible to clear and distinct ideas, reduced matter to extension in three dimensions. Matter thus coincided for him with space. One consequence of this was that he denied the existence of a vacuum. For the same reason he also rejected the existence of "atoms" in the literal sense of the term, for any minute part of space or extension re mains theoretically divisible. But how does this apparently con tinuous extension come to assume the form of those detached material bodies with which we are familiar? Descartes explains this by reference to motion, which he regards as a separate crea tion of God, who also conserves its quantity. It is motion that leads us to distinguish separate bodies or parcels of matter. Any part of extension that moves together or simultaneously is re garded as such a body. Since, however, matter is extension and there is no vacuum, the motion of one body must be followed immediately by the motion of certain other bodies, so that the circle of extension may remain complete, without gaps. This idea of a circular motion of matter eventually suggested to him his theory of vortices. "All natural motions" (Descartes explains in Le Monde) "are in some way circular. When a body leaves its place, it enters that of another, and this enters that of yet another, and so on to the final one which occupies at the same instant the place left by the first. There is thus no vacuum between bodies when they move, any more than when they are at rest. To this end it is not at all necessary that all the moving parts should be arranged in a true circle, or be of like size or shape, for inequalities in these respects may be compensated for by other inequalities. We do not commonly observe these circular motions in the air, because we are accustomed to regard the air as an empty place. But if we observe fishes swimming in a basin we see that, if they do not approach too near it, they do not stir the surface, although they pass under it at a great speed. It is clear, therefore, that the water which they push before them does not push indifferently all the water in the basin, but only that which can best serve to complete the circle of their motion and enter the place which they have vacated." Another consequence of Descartes' identification of matter with extension or space was his insistence on the unity of physical nature, which must be a universe because space is one and con tinuous. Both in his early work The World and in his Principles of Philosophy, Descartes attempted to give an account of the genesis or formation of the physical world. The account was in tended to be purely hypothetical or speculative, not a rival theory to Genesis—just a flight of fancy based on Cartesian principles. "Give me extension and motion," he said in his earlier book, "and I will construct the world." Assuming that God has created a uni f orm matter (or extension) and endowed it with a fixed quantity of motion, which follows certain laws (namely, the laws of motion formulated by Descartes), how might a world (like the existing world) have come into being "by natural and gradual means"? Descartes answers the question somewhat as follows.

In a world closely packed with matter so that there is no vac uum in it the only kind of motion possible is that described above as circular motion or vortex (whirlpool) motion. Consequently when motion was imparted (by God) to matter, such vortices were set in motion—innumerable more or less circular eddies of ma terial parts of all sorts of shapes, sizes and velocities. The friction set up by this vortex motion of closely packed material bodies results in the mutual rubbing off of their corners. And so we get, to begin with, two main kinds of material particles—the original particles rendered smooth and globular by the friction which rubbed their corners off, and the finer particles composed of the rubbings or filings. These fine particles Descartes calls "first mat ter"; the larger, globular particles he calls "second matter." There is yet a "third matter," namely, the most massive and heavy of the original particles that suffer no fracture or rubbing off in the vortex motion, and such other original particles as, thanks to their peculiar shapes, combined into larger, stronger combinations that similarly resisted all damage. The first kind of matter, the finest sort, tends towards the centre of each vortex, where it forms self-luminous suns and fixed stars. The second kind of matter, consisting of globular particles, tends to move away from the centre of the vortices in straight lines towards the circum ference. It constitutes the transparent heavens, and transmits the light of the radiating stars. The third and grossest kind of matter is that of which the earth, the other planets, and the comets are composed—these are all opaque bodies.

In the Principles Descartes explains the formation of the comets and planets in this way. Sometimes as the smaller particles in a vortex pass through the interstices between the revolving globular particles, they get caught and become twisted and channelled, and when they finally reach the stellar matter at the centre of the vortex they form crusts or "sun-spots" on it. This may cause a diminution in the expansive force of the star, which is then caught up by a neighbouring vortex. If the velocity of the crusted star is greater than that of the encroaching vortex, the star will soon pass out of that vortex into another, and continue to wander from vortex to vortex. It is then known as a comet. But if the crusted star has a velocity equal to that of some part of the en croaching vortex, it will stay there and continue to revolve in that vortex. In that case it is known as a planet. The planets of the solar system are the crusted stars and their several vortices that have been swept up by the vortex of the sun.

The vortex theory enabled Descartes to reconcile Copernican with Biblical doctrine. In The W orld Descartes had embraced the Copernican theory of the earth's motion round the sun. The condemnation of Galilei, in 1633, made him drop the idea in the Copernican form. But by supposing the earth to be carried in its vortex round the sun, Descartes believed that he left the earth at rest in its vortex, and so satisfied the dogma of a stationary earth, while he also satisfied the Copernican theory inasmuch as he represented the earth's vortex as circling round the sun.

Descartes' Principles contains a detailed account of practically all the natural phenomena that had been investigated up to his time. It contains, of course, many errors. Even his fundamental laws of motion are mostly inaccurate. But it was an amazing attempt to reduce all natural phenomena to one system composed of one ultimate kind of matter and governed by the same laws of motion. One of its incidental results was the explanation of weight without recourse to gravitation. Bodies tend to fall towards the earth, according to Descartes, because the particles of the second kind of matter which move round the earth push those bodies towards the earth, and so give them what we call their weight. The popular conception of gravitation makes more or less an occult power of it. Newton's intention was merely to de scribe certain tendencies to movement without any attempt to explain them at all. Again, Descartes' rejection of the existence of a vacuum not only undermined the idea of Nature's abhorrence of a vacuum (horror vacui) which was wont to serve as an expla nation of the action of water-pumps, but prepared the way to the correct explanation, namely the pressure of the air on the surface of the water. In fact Descartes claimed that he had anticipated Torricelli (the inventor of the barometer) and that, during his visit to Paris in 1647, he had suggested to Pascal the idea of the barometric experiment which the latter carried out on the Puy-de Dome on Sept. 19, 1648. Another important consequence of Des cartes' rejection of a vacuum was that he was thereby led to give up the old corpuscular or emission theory of light, and to conceive of the transmission of light as a transmission of pressure from the luminous body through the intervening particles of secondary matter to the sensitive eye. This view prepared the way for the undulatory theory of light which was soon afterwards formulated by Christiaan Huygens, the son of Descartes' friend and corre spondent, Constantijn Huygens.

Descartes was deeply interested in optics, devoting to it not only his Dioptric (1636), but also parts 3 and 4 of his Principles (1644). He compares the transmission of light to the eye with the way in which a blind man feels his way with a stick. The resist ances or pressures of the different objects (such as stones, trees, water, etc.) are transmitted along the stick to his hand and thence to his brain, so that he can distinguish them. Similarly no cor puscles actually pass from the visible objects to the eye, only a pressure through the fine particles which constitute the transparent medium. Rays of light are the line along which the pressure is transmitted. When they pass through a transparent medium they are straight, otherwise they are deflected or even stopped just like a moving ball when it encounters some obstruction. If the obstruction is hard, the ball rebounds in another direction; if soft, its movement will be arrested. Similarly, when a ray of light impinges obliquely on certain kinds of surfaces, it is reflected, and its angle of reflection is equal to the angle of incidence. But if the medium allows the ray to pass through with diminished speed, then it is refracted. In the Dioptric the law of refraction was published for the first time. Snell had discovered it in 1621, but did not publish it ; and Descartes has sometimes been sus pected of plagiarism. Most likely, however, Descartes discovered it independently.

Physiology.

The World, as originally planned by Descartes, was to have contained an hypothetical account of the develop ment of the universe from chaos to man. Referring to this book, in June 1633, he said : "I shall treat of man to a greater extent than I proposed; I intend to explain the principal functions of his body, and I have already given an account of some of them, such as digestion, the beating of the pulse, the distribution of nutri tious matter, the action of the five senses, etc. I have dissected the heads of various animals, in order to ascertain in what mem ory, imagination, etc., consist." The book was not published as it was then planned ; but the results of Descartes' studies in this field are contained in his L'Homme (published in 1662), the first text-book on physiology. In accordance with the whole spirit of The World, of which the treatise on Man was originally meant to be the concluding part, the human body and its functions were treated by Descartes mechanically, like "an earthly machine." In this view he was greatly encouraged by the views of Vesalius (1515-64) , the father of modern anatomy and physiology, and by Harvey's demonstration of the mechanical nature of the circula tion of the blood (his Exercitatio was published in 1628), though Descartes did not entirely agree with Harvey. Descartes explains that blood is formed in the liver from the chyle of the food. This blood flows drop by drop into the right cavity of the heart which is so hot that the blood expands and is exhaled into the lung, whence it passes into the left cavity of the heart, and is thence distributed over the whole body. He describes the valves in the arteries which secure that the blood shall flow only drop by drop. Now of the blood which flows through the direct arteries from the heart to the brain, "the most agitated and vivified parts" are called "animal spirits." They are like "a very subtle air." By dilating the brain they enable it to receive impressions of external objects, and so give rise to sensation, imagination and retentive memory; by flowing from the brain through the nerves into the muscles, they enable the nerves to function as organs of the external senses ; and by distending, and so contracting, the muscles, they effect the movements of the limbs. For Descartes the "animal spirits" were just a subtle fluid, the nerves were just tubes through which they flowed in a mechanical way.

He illustrates his strictly mechanical conception of the bodily machine as follows. "You may have seen in the grottoes and fountains which are in our royal gardens that the simple force with which the water moves when issuing from its source is enough to set in motion various machines, and to make various instru ments play or utter words, according to the different arrange ments of the tubes which convey the water. And so one may well compare the nerves of the machine which I am describing with the tubes of the machines of these fountains, the muscles and tendons with the other engines and springs which move the ma chines, and the animal spirits, the source of which is the heart and of which the cavities of the brain are the reservoirs, with the water which puts them in motion. Moreover, breathing and sim ilar acts, which are natural and usual to the machine, and which depend on the flow of the spirits, are like the movements of a [water] clock or of a mill which the ordinary flow of water keeps going continually. External objects, which by their presence act on the sense-organs of the machine and so determine it to move in different ways according to the disposition of the parts of the brain, may be compared to strangers who, entering one of the grottoes containing many fountains, themselves cause unwittingly the movements they witness. For on entering they tread on cer tain tiles or plates which are so arranged that if they approach a bathing Diana they cause her to hide in the rose bushes, and if they try to follow her they cause a Neptune to come towards them threatening them with his trident. Or if they pass in another direction they make a sea-monster spring forward and spout water in their faces, or things of a like kind according to the caprice of the engineers who constructed them.

"In order to understand how the brain can be excited by ex ternal objects which affect the organs of sense, so that all the members can be moved in a thousand different ways, imagine that the delicate threads which arise from the inside of the brain and form the marrow of the nerves, are so disposed in all those parts which serve as the organs of any sense that they can be easily set in motion by the objects of the senses, and that whenever they are so set in motion, even ever so little, they pull upon the parts of the brain whence they originate, and so open certain pores on the internal surface of the brain. Through these pores the animal spirits in the ventricles pass into the nerves and then into the muscles which carry out movements like those to which we are incited when our senses are affected in that way. If, e.g., fire comes near the foot, the minute particles of the fire . . . set in motion the skin of the foot, and by thus pulling the delicate thread attached to the skin there, they open the pore against which the thread ends, just as by pulling at one end of a rope one rings a bell at the other end." In this way Descartes tried to explain physiological phenomena mechanically, and to banish from biology such conceptions as those of "vegetative" and "sensitive" souls, much in the same way as he and Boyle, and others, tried to banish from physics and chemistry such notions as those of "substantial forms," and occult qualities, etc. To this extent he rendered a service to biology in spite of his excessive proneness to follow the high a priori road, and to be satisfied with any fancies that seemed "clear and dis tinct" to him. He may be credited to some extent with the antici pation of the conception of "reflex movements," though these are not interpreted now in his purely mechanical fashion. He may also be regarded as the forerunner of modern "behaviourism," at all events as applied to the lower animals, for he would certainly have condemned a "soul-less" human psychology, as will be seen presently. His view of the lower animals as mere automata rather alarmed some people. But Descartes' main object was to vindi cate the superiority of man over animals, even over his own ani mal body, in virtue of his "rational soul" or mind.

Body and Mind.—In Descartes' philosophy, as already ex plained, the human mind is "a thinking substance" Coto coelo different from any "extended substances," including human bodies. Yet a human being seems to be an intimate association of a mind and a body, each influencing the other. How can the "extended substance" or "earthly machine" of the human body come into such intimate relation with unextended "thinking substance"? Descartes' ultimate solution of these, as of all other problems, lies in God, who graciously does all that Descartes thinks ought to be done. But as a more immediate, scientific solution of the problem, Descartes suggests that the mind comes into contact with the body in the conarion "whence it radiates through the rest of the body by means of the animal spirits, nerves and even the blood." The pineal gland "in the middle of the substance of the brain" is the primary reservoir of animal spirits, the central cavity of the brain being the secondary reservoir. Reverting to the above-mentioned comparison with the mechanical inventions in the royal gardens, Descartes likens the function of the rational soul or mind presiding at the conarion to that of "the f ountaineer who has to take his place in the reservoir whence all the different tubes of the machines proceed whenever he wants to start them, to stop them, or to change them in any way." Descartes thought he surmounted the difficulty of explaining the mutual influence of mind and body by supposing, on the one hand, that the conarion requires but a minimum of influence to incline it one way or an other, and, on the other hand, that the "animal spirits" are such a subtle kind of air that they are on the verge of ceasing to be material. But according to his own philosophy the material re mains material however fine it may be, and so remains entirely alien from the mental or spiritual.

Psychology.

The mind being, according to Descartes, a thinking substance entirely different from, and independent of, ex tended or material things, it "can work independently of the brain." This, at all events, is true of the most characteristic ac tivities of the rational soul, "for clearly there can be no use of the brain for pure intelligence," says Descartes. Ideas in which pure intelligence expresses itself are innate, not derived from without, but from the rational soul itself. For Descartes, as for Plato, experience can only be the occasion for the recall of such ideas to consciousness. These ideas are not always explicit in our con sciousness, rather they are latent in the "thinking substance," but they are not originated by experience, though experience may occa sion their explicit recall. Among such innate ideas Descartes in cludes our "clear and distinct" ideas of God, of the self as a think ing thing, the axioms of mathematics and other so-called "common notions" like those of space, time and motion. Above all, per haps, he finds the mind expressing itself most fully in acts of will, under which heading he includes all judgments and beliefs, as well as voluntary decisions. But then the mind is conjoined with a body, and they do somehow influence each other through the mediation of the conarion and the animal spirits, as already ex plained. One result of this is that in addition to the mind's own innate ideas, we have also "adventitious ideas" which come to us through the influence of external bodies, and also "factitious ideas" of merely imaginary objects which the mind puts together out of simpler "adventitious" and "innate" ideas. Descartes is not very clear or consistent in dealing with these problems. The idea of God, e.g., is treated at once as "innate," and also as pro duced in us by God Himself, and therefore, in a sense, "adventi tious." And his treatment of images is rather bewildering. Some times he treats images, in contrast with ideas, as something physi cal, and says : "no corporeal image is received in the mind ; pure thinking is carried out without corporeal images ; imagination, however, which can only arise in the case of corporeal things, needs an image, which is a truly corporeal thing; to this the mind applies itself, though the image is not received into the mind." At other times, however, he includes images, and even sensations and perceptions, under "thought," and distinguishes them from innate ideas, or pure thoughts, and volitions in so far as "imagina tion and sensation" need the brain as well as the mind; that is to say, in so far as they express not the pure activity of mind, but rather its passivity, the effect upon it of physical things, including the body with which it is mated. Hence he calls all such expe riences "passions," under which heading he includes not only the feelings and emotions, but also sensation, retention, perception, and all adventitious ideas. The feelings are passions caused by the agitation of the animal spirits, but are not referred to any objects outside the body, whereas sensations are "passions" that are re ferred to external stimuli. Descartes' account of the emotions anticipates to some extent the James-Lange theory, inasmuch as it gives primary to the physical or physiological processes. Our per ception of certain animals, e.g., causes fear and flight immediately without the mediation of reason or volition, which only come into play afterwards. Since, however, the brain is the organ of the passions and also the seat of the rational soul, the passions can be brought under the control of the reason and the will. In fact, Descartes is quite Socratic in his insistence on the competence of right reason to conduce to right feeling and action.

The power which Descartes attributes to reason and will may seem to be little in harmony with his naturalistic, mechanical account of such large tracts of human experience. But, as already remarked, his great aim was really to vindicate the supremacy of the human mind or spirit. There was a marked tendency in his day, and long before him, to efface the sharp distinction between man and the lower animals by crediting the lower animals with human powers, including intelligence, which they were sometimes said to use more humanly than man. This tendency was mainly supported by the results of comparative anatomy, which showed essential similarity between the structures of human and animal bodies, including the central nervous system. Descartes tried to save the situation by regarding even the human body as a machine, and treating mechanically all such human experiences as might conceivably also be credited to lower animals, but claiming unique privileges for the rational soul, which he regarded as the differen tia of man, and as absolutely independent of all that is material.

Mathematics.

Descartes has been described as the first mod ern mathematician. He was certainly one of the pioneers of modern mathematics. His only treatise on mathematics is the Geometry (163 7) in which he laid the foundations of analytical or algebraic geometry. Descartes was not the first to apply alge bra to geometry, or to conceive a line as generated by a moving point, or to solve geometrical problems by regarding them as solved and analysing the result ("analytic geometry" in the older sense). These things were already known to ancient and mediae val mathematicians. But he applied these methods much more systematically and fruitfully.

He knew that a point in a plane can be fully determined if we know its distances from two given straight lines in the same plane (allowing for the sign-conventions relating to their different sides, and taking not perpendicular distances but distances parallel to given lines) . If the distances be represented by x and y re spectively, we can get an equation of the form f (x,y) = o. And although such an equation is indeterminate in the sense that it can be satisfied by an infinite number of sets of values of x and y, yet these values determine the co-ordinates of a series of points which form a curve such that the equation in question is true of every point on it. He realized, moreover, that the prop erties of a curve can be ascertained by choosing as a definition any specific geometrical property, and expressing it as an equation by means of the co-ordinates of any point on the curve. Such an equation contains by implication all the properties of that curve. And any such property can be deduced from the equation by purely algebraic processes, and without direct reference to the geometry of the curve.

Descartes was the first to attempt a systematic classification of curves. First, he distinguished between "geometric" and "mechan ical" curves, according as they could or could not be precisely expressed in equations. (These terms were subsequently displaced by Newton's terms "algebraic" and "transcendental.") Confining himself to "geometric" curves, Descartes classifies these into a series of classes of increasing complexity as follows. Class I. con sists of curves (the circle, the parabola, the hyperbola and the ellipse) whose equations contain no term of higher degree than the multiple of two unknown quantities or the square of one. Class II. includes any curve whose equation contains one or more terms of the third or fourth degree in one or both of the two un known quantities. Class III. contains curves whose equations in clude a term of the fifth or sixth degree in either or both of the unknown quantities, and so on. The curves are paired in each class in the way indicated because there are methods of reducing a curve of the fourth to one of the third degree, a curve of the sixth to one of the fifth degree, and so on. The straight line he regarded as an exceptional case of a curve of the second degree (Class I.).

In

algebra Descartes' systematic application of it to geometri cal measurement involved important consequences. It involved the geometric interpretation of negative quantities. It also led to the idea of continuity, which in its turn led to the theory of function and to the theory of limits. Descartes, moreover, made impor tant contributions to the theory of equations, to which the third and last book of his Geometry is devoted, and to which he appears to have been led by his (successful) efforts to solve the problems tf doubling the cube and of trisecting an angle. It is also worth noting that we are indebted to Descartes for the convention of using the first letters of the alphabet to represent known quan tities, and the last letters for unknown quantities. He also in troduced our system of indices (although he frequently used xx instead of On the other hand, he used the sign co instead of = which Recorde had already introduced with its present meaning.

Descartes' general rule for solving equations is this. Write the equation in the zero form, and try to factorize the L.H.S. so as to reduce the equation to two or more equations of lower degree. If this is impossible, higher methods must be used. If the equation is of the third or fourth degree, the solution depends on the inter section of a circle with a conic. To solve equations of still higher degree, Descartes proposes the use of intersections of circles with the successive classes of geometric curves—conics being used to generate curves of Class II. and these again to generate curves of Class III., and so on. He thought that equations of any order could be solved in this way; but he was mistaken.

What is still known as Descartes' Rule of Signs is to the effect that an equation can have no more "true" (i.e., positive) roots than its coefficients have changes of sign from + to —, and no more "false" (i.e., negative) roots than the number of times two plus or two minus signs occur in succession.

BIBLIOGRAPHY.

Oeuvres de Descartes, ed. by C. Adam and P. Bibliography. Oeuvres de Descartes, ed. by C. Adam and P. Tannery (13 vols., 4to, Paris, 1897-1911) . This edition supersedes all other editions of Descartes' works. Since then some hitherto unpublished letters have been edited by L. Roth in Correspondence of Descartes and Constantyn Huygens, 16.35-47 (Oxford, 1926) . The most reliable biography of Descartes is that by C. Adam, forming vol. xii. of the above-mentioned Oeuvres de Descartes. Of books for English readers the following are the most important: The Philo sophical Works of Descartes rendered into English by E. S. Haldane and G. R. T. Ross (2 vols., 1911, 1912) ; Kuno Fischer, Descartes and his School, translated by N. Porter (1887) ; J. P. Mahaffy, Descartes (1902) ; E. S. Haldane, Descartes, His Life and Times (1905) ; N. Smith, Studies in Cartesian Philosophy (1902) ; L. Roth, Spinoza, Descartes and Maimonides (1924) ; The Cambridge Modern History, vol. iv., chap. 27, contains an account of "Descartes and Cartesianism" by E. Boutroux ; Science Progress (No. 83, 1927) contains an account of "The Physical Work of Descartes" by F. Wootton; The Geometry of Rene Descartes, translated by D. E. Smith and M. L. Latham (1925) ; M. Foster's History of Physiology (1924) deals with Descartes' Physiology; and G. S. Brett's History of Psychology (vol. ii., 1921) , treats of Descartes' Psychology. See also the Histories of Philosophy by J. E. Erdmann, H. Hoffding and W.

Windelband ; and articles CARTESIANS ; PHILOSOPHY ; PSYCHOLOGY, HISTORY OF. The best German translation is that by A. Buchenau, Descartes' Philosophische Werke (Leipzig, 19o5—I I) . Of German books on Descartes the following are the most important: A. Hoffmann, Rene Descartes (Frommann's Klassiker der Phil., Stuttgart, 1922) ; K. Jungmann, R. Descartes (Leipzig, 1908) ; A. Kastil, Descartes (Halle, 1909) ; E. v. Aster, Ein f iihrung in die Phil. Descartes (Munchen, 1921) ; C. v. Brockdorff, Descartes (Munchen, 1923) ; E. Cassirer, Descartes' Kritik der mathem. u. naturw. Erkenntnis (Marburg, 1899), and Das Erkenntnisproblem (vol. i., book III. Berlin, 191I) ; P. Natorp, Descartes' Erkenntnistheorie (Marburg, 1882) . Of recent French books the following may be mentioned: O. Hamelin, Le Systeme de Descartes 0910 ; G. Milhaud, Descartes Savant (1921) ; E. Gilson, La Liberte chez Descartes et la Theologie (1913) ; H. Gouhier, La Pensee Religieuse de Descartes (1924)• (A. Wo.)