Is God a Mathematician_ - Mario Livio [46]
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Functions are truly the bread and butter of modern scientists, statisticians, and economists. Once many repeated scientific experiments or observations produce the same functional interrelationships, those may acquire the elevated status of laws of nature—mathematical descriptions of a behavior all natural phenomena are found to obey. For instance, Newton’s law of gravitation, to which we shall return later in this chapter, states that when the distance between two point masses is doubled, the gravitational attraction between them always decreases by a factor of four. Descartes’ ideas therefore opened the door for a systematic mathematization of nearly everything—the very essence of the notion that God is a mathematician. On the purely mathematical side, by establishing the equivalence of two perspectives of mathematics (algebraic and geometric) previously considered disjoint, Descartes expanded the horizons of mathematics and paved the way to the modern arena of analysis, which allows mathematicians to comfortably cross from one mathematical subdiscipline into another. Consequently, not only did a variety of phenomena become describable by mathematics, but mathematics itself became broader, richer, and more unified. As the great mathematician Joseph-Louis Lagrange (1736–1813) put it: “As long as algebra and geometry traveled separate paths their advance was slow and their applications limited. But when these two sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection.”
As important as Descartes’ achievements in mathematics were, he himself did not limit his scientific interests to mathematics. Science, he said, was like a tree, with metaphysics being the roots, physics the trunk, and the three main branches representing mechanics, medicine, and morals. The choice of the branches may appear somewhat surprising at first, but in fact the branches symbolized beautifully the three major areas to which Descartes wanted to apply his new ideas: the universe, the human body, and the conduct of life. Descartes spent the first four years of his stay in Holland—1629 to 1633—writing his treatise on cosmology and physics, Le Monde (The World). Just as the book was ready to go to press, however, Descartes was shocked by some troubling news. In a letter to his friend and critic, the natural philosopher Marin Mersenne (1588–1648), he lamented:
I had intended to send you my World as a New Year gift, and only two weeks ago I was quite determined to send you at least a part of it, if the whole work could not be copied in time. But I have to say that in the meantime I took the trouble to inquire in Leiden and Amsterdam whether Galileo’s World System was available, for I thought I had heard that it was published in Italy last year. I was told that it had indeed been published, but that all the copies had immediately been burnt at Rome, and that Galileo had been convicted and fined. I was so astonished at this that I almost decided to burn all my papers, or at least to let no one see them. For I could not imagine that he—an Italian, and as I understand, in the good graces of the Pope—could have been made a criminal for any other reason than that he tried, as he no doubt did, to establish that the Earth moves. I know that some Cardinals had already censured this view, but I thought I had heard it said that all the same it was taught publicly in Rome. I must admit that if the view is false, so too are the entire foundations of my philosophy [my emphasis], for it can be demonstrated from them quite clearly. And it is so closely interwoven in every part of my treatise that I could not remove it without rendering the whole work defective. But for all the world I did not want to publish