Cosmological Revolution V: Descartes and Newton
Descartes and the Laws of Nature
Newton on the Laws of Nature
Newton's Principles of Reasoning
Newton on the Law of Gravity
Rene Descartes (1596-1650) is best known for his philosophical thesis that "I think, therefore I exist" (in Latin: "cogito ergo sum"). But we are concerned here with Descartes' cosmological theories, along with the philosophical views that underlay his system. In 1633, having published a book on philosophical method (anonymously), Descartes was preparing two volumes on science. The first was Treatise on Man in which he analyzed the organs of the human body in a mechanistic way, comparing the heart to a pump, the lungs to a bellows, and tracing how impulses impinging upon the sensory organs became transformed into perceptions. The second book was System of the World which was based on the heliocentric Copernican system, combined with an atomistic view of matter. Descartes argued as follows:
(1) There are three elements, determined according to their sizes, motions and viscosity (hardness, liquidity): fire, air and earth. The cosmos is a plenum; there is no void.
(2) The sun and stars are formed of the first element (fire), the earth, moon and planets of the third ("earth" in the generic sense), and the intervening spaces are filled mainly with the second (air).
(3) The sun, the source of light, is at the center of the world. There are a plurality of worlds, each with a star at its center. Comets pass from one world into another, while planets revolve around the suns which are centers of each.
(4) God is the creator of the cosmos, but thereafter, the world proceeds according to fixed laws of nature. Descarte's notion of "law of nature" goes beyond the planetary laws of Kepler to include all matter and set general principles for motion of all kinds. Here is what he says:
"Know, then, first that by "nature" I do not here mean some deity or other sort of imaginary power. Rather, I use the word to signify matter itself, insofar as I consider it taken together with all the qualities that I have attributed to it, and under the condition that God continues to preserve it in the same way that He created it. For from that alone (ie that He continues thus to preserve it) it follows of necessity that there may be many changes in its parts that cannot, it seems to me, be properly attributed to the action of God (because that action does not change) and hence are to be attributed to nature. The rules according to which these changes take place I call the "laws of nature" (System of the World, ch.7)
(1) "The first is that each individual part of matter always continues to remain in the same state unless collision with others forces it to change that state. That is to say, if the part has some size, it will never become smaller unless others divide it; if it is round or square, it will never change that shape without others forcing it to do so; if it is stopped in some place it will never depart from that place unless others chase it away; and if it has once begun to move, it will always continue with an equal force until others stop or retard it."
(2). "I suppose as a second rule that, when one of these bodies pushes another, it cannot give the other any motion except by losing as much of its own at the same time; nor can it take away from the other body's motion unless its own is increased by as much."
(3) "I will add add as a third rule that, when a body is moving, even if its motions most often takes place along a curved line and (as has been said above) can never take place along any line that is not in some way circular, nevertheless, each of its individual parts tends always to continue its motion along a straight line. And thus their action, i.e., the inclinisation they have to move, is different from their motion.
For example, if a wheel is made to turn on its axle, even though its parts go round (because, being linked to one another, they cannot do otherwise), nevertheless their inclination is to go straight ahead, as appears clearly if perchance one of them is detached from the others. For, as soon as it is free, its motion ceases to be circular and continues in a straight line." [All quotes from Treatise on Light]
In 1633, his work nearly completed, Descartes wrote to Father Mersenne, a Catholic priest who acted as a sort of "clearing house" for communication among scientists, before the time of journals and societies devoted to that purpose. To his amazement, Descartes found that Galileo had been condemned for his defense of the heliocentric, Copernican cosmology -- precisely the cosmology Descartes also believed to be true. Descartes suppressed his own book, rather than have it, like the work of Galileo, condemned, or published with censorship, even if self-censorship. (System of the World was only published in 1664, after Descartes' death).
In his Principles of Philosophy, published in Latin in 1649, Descartes returned to the exposition of his cosmology, but with much care and delicacy. He states in III.15 "that various hypotheses may be used to explain the phenomena of the Planets", of which there are three. The first is Ptolemy's hypothesis which is not in conformity with the appearances (III.16), since it is contradicted by observations made by telescopes of the reflection of light on the moon and Venus.
The second is that of Copernicus, and the third that of Tycho. Descartes notes that "considered purely as hypotheses, these two explain the phenomena well, and there is not much difference between them. Nevertheless, that of Copernicus is somewhat simpler and clearer." (III.17). But having said this, he then asserts "that the Earth is at rest in its heaven which nevertheless carries it along". (III.26) This is on the face of it a somewhat contradictory statement.
How Descartes has gotten around the problem of the earth's motion is as follows: he has each planet, the earth included, moved by a vortex having the sun at its center, one eddy for each planet. Now the earth is moved, but does not move itself.
Descartes' proposal of 1649 was unsatisfactory to Newton, for Descartes' termed Copernicanism an "hypothesis" where Newton would argue for it as "fact". Moreover, he would provide an explanation, in his theory of gravity, for the revolution of the earth about the sun, and not vice-versa.
Isaac Newton (1642-1727) was born in England, and attended Trinity College, Cambridge, where he graduated, without any special distinction it is said, in 1665. Ater graduation, he returned to his home town, since the university was closed for a year and half as the result of the plague. There he formulated the basic ideas that would guide his work in mathematics, mechanics and astronomy, including his notion of fluxions that lead on to the calculus. In 1667 he returned to Cambridge, and succeeded his teacher Isaac Barrow as Lucasian professor of mathematics.
In 1684, as the result of a question posed to him by Edmund Halley, the discoverer of the comet bearing his name, Newton showed that the orbit of a planet would be an ellipse, assuming that it were attracted to the sun with an inverse square law of force. He had thus given a reason for Kepler's elliptical orbits, which he knew about from secondary sources only. This was published in De Motu Corporum (On the Motion of Bodies), and then worked out systematically in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), published in 1687 and known popularly as Principia.
Newton was elected member of parliament for Cambridge in 1689- where his only recorded comment was a request to close the window since he was in a draft. In 1696 he was appointed warden of the mint, and master in 1699. He was elected president of the Royal Society in 1703, and held both positions till his death some quarter century later.
Newton was a solitary man who had few friends; his personality is often described as "accerbic", but his achievement in the
Principia brings the cosmological revolution to a close. In this great work, Newton then states his three axioms or laws of motion:
1. [Principle of Inertia] "Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it." By "right line", Newton simply means motion in a straight line.
2. [Principle of Momentum] "The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed."
3. [Principle of Action/Reaction] "To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."
Newton attached great importance to philosophical principles that form the basis for experimental science. In a sense, he was formalizing what would later be termed "scientific method", though this term is somewhat misleading, implying that one rule of procedure suffices. Newton identified the rules of scientific reasoning as follows:
1. [Causes as true and explanatory]:"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances." This proposition is rejects the old "saving the phenomena" theory that causes need not be "true", but merely suffice to produce the expected or observed results (as is the case for the epicycles, eccentrics, and equants of ancient and medieval astronomy).
2. [Succession of causes and effects]:"Therefore to the same natural effects we must, as far as possible, assign the same causes."
3. [Primary Qualities]:"The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever." Newton argues that only experiment and observation can teach us what these universal properties (or primary qualities) are: he mentions extension, hardness, impenetrability, mobility and inertia. This is true also of the parts, and indeed, the properties of the whole are just the result of the combination of the properties of the parts (reductionism).
4. [Hypotheses and induction]: "In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurable, or liable to exceptions." And he notes, laconically, "This rule we must follow, that the argument of induction may not be evaded by hypotheses". This is a back of the hand swipe at Descartes, who had argued for Copernicanism an "hypothesis", not as a "true system".
Newton's great innovation is the law of gravity: Fgrav = k. m1. m2/ r2 . Copernicus had suggested that each planet was a center of gravity for matter in its vicinity, but had no idea or proposal for a common law. Kepler thought there was a magnetic force emanating from the sun that kept the planets in their orbits. Descartes had his vortexes which played that role. But Newton comes up with the exact law of gravity and recognizes its universal application.
Note that Newton did not come up with the idea because of the famous apple falling on his head, though the image of Newton's apple is an enduring cultural one. He developed his law by considering the following hypothesis: could it not be that the force which acts upon the moon and changes its straight line motion into revolution about the earth, be the same as the force that attracts an object in free fall? (ie an apple). Indeed, it is, and with the aid of mathematics, he deduced that it must be a law varying directly as the product of the masses and indirectly as the square of their separation.
Newton could now explain the fundamental insight of the Copernican system: that the earth revolves about the sun and not vice-versa. This follows in part from the fact that the sun is much more massive than the earth, and so it attracts the earth more than the earth attracts it. Similarly, the moon, which is less massive, revolves around the earth; though the attraction of the earth by the moon, though the lesser of the two, can be readily observed in the tides.
Taken solely by itself, this greater force of attraction of the sun for the earth would cause the earth to collide into the sun. A second motion is at work: the tangential velocity of the earth. This is, roughly speaking the velocity with which the earth moves around the sun (approximately 30km/sec or 18mi/sec), so that it completes its journey in a year. The result of the combined action of the two motions: (i) an accelerated velocity towards the sun and (ii) a uniform velocity tangential to its orbit, results in (iii) an elliptical orbit about the sun (in conformity with Kepler's laws). Indeed, given Newton's three laws of nature and his law of gravity, Kepler's three laws can be directly deduced, indicating that Newton's are more fundamental.
To the question why did gravity work as it did, he had no ready answer. He knew its equation of operation, but not its mode of operation. Though he was able to use gravity to explain planetary motions, he could not explain gravity itself. So he introduced an hypothesis of his own: a"certain most subtle spirit which pervades and lies hid in all gross bodies", to which he gave the name "aether". This term had already been used by Aristotle for the fifth element, and was used by Newton in a different sense: it was the medium through which gravity acted, though its exact nature was unknown to him. (Later, the term "aether" would be used in yet a third sense: as the medium through which light waves travel). Newton used the aether hypothesis in a way he considered as legitimate: he introduced it as a temporary place holder to be replaced by a fuller theory at a later time, not as a subterfuge to avoid condemnation (as he held Descartes did in his later cosmology). The aether, in one form or another, would continue until Einstein simply got rid of it in his theory of special relativity. But we will return to the problem of "hypotheses" in science when we look at Karl Popper's philosophy of science in the next section.
We can now conclude very briefly on Newton:
- (1) He established the axioms or principles of physics, what we today term "laws of nature".
- (2) He established the law of gravitation as a universal law governing the action of the planets.
- (3) He left unsolved the explanation for gravitation, having no more than the hypothesis of a universal aether in which gravitation acts.