Is God a Mathematician_ - Mario Livio [47]
Descartes had indeed abandoned The World (the incomplete manuscript was eventually published in 1664), but he did incorporate most of the results in his Principles of Philosophy, which appeared in 1644. In this systematic discourse, Descartes presented his laws of nature and his theory of vortices. Two of his laws closely resemble Newton’s famous first and second laws of motion, but the others were in fact incorrect. The theory of vortices assumed that the Sun was at the center of a whirlpool created in the continuous cosmic matter. The planets were supposed to be swept around by this vortex like leaves in an eddy formed in the flow of a river. In turn, the planets were assumed to form their own secondary vortices that carried the satellites around. While Descartes’ theory of vortices was spectacularly wrong (as Newton ruthlessly pointed out later), it was still interesting, being the first serious attempt to formulate a theory of the universe as a whole that was based on the same laws that apply on the Earth’s surface. In other words, to Descartes there was no difference between terrestrial and celestial phenomena—the Earth was part of a universe that obeyed uniform physical laws. Unfortunately, Descartes ignored his own principles in constructing a detailed theory that was based neither on self-consistent mathematics nor on observations. Nevertheless, Descartes’ scenario, in which the Sun and the planets somehow disturb the smooth universal matter around them, contained some elements that much later became the cornerstone of Einstein’s theory of gravity. In Einstein’s theory of general relativity, gravity is not some mysterious force that acts across the vast distances of space. Rather, massive bodies such as the Sun warp the space in their vicinity, just as a bowling ball would cause a trampoline to sag. The planets then simply follow the shortest possible paths in this warped space.
I have deliberately left out of this extremely brief description of Descartes’ ideas almost all of his seminal work in philosophy, because this would have taken us too far afield from the focus on the nature of mathematics (I shall return to some of his thoughts about God later in the chapter). I cannot refrain, however, from including the following amusing commentary that was written by the British mathematician Walter William Rouse Ball (1850–1925) in 1908:
As to his [Descartes’] philosophical theories, it will be sufficient to say that he discussed the same problems which have been debated for the last two thousand years, and probably will be debated with equal zeal two thousand years hence. It is hardly necessary to say that the problems themselves are of importance and interest, but from the nature of the case no solution ever offered is capable either of rigid proof or disproof; all that can be effected is to make one explanation more probable than another, and whenever a philosopher like Descartes believes that he has at last finally settled a question it has been possible for his successors to point out the fallacy in his assumptions. I have read somewhere that philosophy has always been chiefly engaged with the inter-relations of God, Nature, and Man. The earliest philosophers were Greeks who occupied themselves mainly with the relations between God and Nature, and dealt with Man separately. The Christian Church was so absorbed in the relation of God to Man as entirely to neglect Nature. Finally, modern philosophers concern themselves chiefly with the relations between Man and Nature. Whether this is a correct historical generalization of the views which have been successively prevalent I do not care to discuss here, but the statement as to the scope of modern philosophy marks the limitations of Descartes’ writings.
Descartes ended his book on geometry with the words: “I hope that posterity will judge me kindly, not only as to the things which I have explained,