Is God a Mathematician_ - Mario Livio [35]
Entire volumes can be written (and indeed have been written) about all of Galileo’s achievements, but these lie beyond the scope of the present book. Here I only want to examine the effect that some of these astounding revelations had on Galileo’s views of the universe. In particular, what relation, if any, did he perceive between mathematics and the vast, unfolding cosmos?
The Grand Book of Nature
The philosopher of science Alexandre Koyré (1892–1964) remarked once that Galileo’s revolution in scientific thinking can be distilled to one essential element: the discovery that mathematics is the grammar of science. While the Aristotelians were happy with a qualitative description of nature, and even for that they appealed to Aristotle’s authority, Galileo insisted that scientists should listen to nature itself, and that the keys to deciphering the universe’s parlance were mathematical relations and geometrical models. The stark differences between the two approaches are exemplified by the writings of prominent members of the two camps. Here is the Aristotelian Giorgio Coresio: “Let us conclude, therefore, that he who does not want to work in darkness must consult Aristotle, the excellent interpreter of nature.” To which another Aristotelian, the Pisan philosopher Vincenzo di Grazia, adds:
Before we consider Galileo’s demonstrations, it seems necessary to prove how far from the truth are those who wish to prove natural facts by means of mathematical reasoning, among whom, if I am not mistaken, is Galileo. All the sciences and all the arts have their own principles and their own causes by means of which they demonstrate the special properties of their own object. It follows that we are not allowed to use the principles of one science to prove the properties of another [the emphasis is mine]. Therefore, anyone who thinks he can prove natural properties with mathematical argument is simply demented, for the two sciences are very different. The natural scientist studies natural bodies that have motion as their natural and proper state, but the mathematician abstracts from all motion.
This idea of hermetic compartmentalization of the branches of science was precisely the type of notion that infuriated Galileo. In the draft of his treatise on hydrostatics, Discourse on Floating Bodies, he introduced mathematics as a powerful engine that enables humans to truly unravel nature’s secrets:
I expect a terrible rebuke from one of my adversaries, and I can almost hear him shouting in my ears that it is one thing to deal with matters physically and quite another to do so mathematically, and that geometers should stick to their fantasies, and not get involved in philosophical matters where the conclusions are different from those in mathematics. As if truth could ever be more than one; as if geometry in our day was an obstacle to the acquisition of true philosophy; as if it were impossible to be a geometer as well as a philosopher, so that we must infer as a necessary consequence that anyone who knows geometry cannot know physics, and cannot reason about and deal with physical matters physically! Consequences no less foolish than that of a certain physician who, moved by a fit of spleen, said that the great doctor Acquapendente [the Italian anatomist Hieronymus Fabricius (1537–1619) of Acquapendente], being a famous anatomist and surgeon, should content himself to remain among his scalpels and ointments without trying to effect cures by medicine, as if knowledge of surgery was opposed to medicine and destroyed it.
A simple example of how these different attitudes toward observational findings could completely alter the interpretation of natural phenomena is provided by the discovery of sunspots. As I noted earlier, the Jesuit astronomer Christopher Scheiner observed these spots competently and carefully. However, he made the mistake of allowing his Aristotelian