# How do we account for the weird coincidence of math and science (e.g., physics)?

There is another question that might be worrying you: Why does the language of physics turn out to be mathematical? Why does mathematics turn out to be our best way of describing the physical world? I don't think that anyone has a good answer to this question. There may be no good answer, since it might just be a brute contingent feature of our world. One could imagine a world in which events were so disorganised that there would be no useful regularities that could be captured in a perspicious mathematical formalism. Interestingly, Putnam and Quine have used the claim that mathematical language is central to our physics as a roundabout argument for the existence of mathematical objects. One of the best reasons we have to believe in the existence of an object is if our best physical theories make ineliminable reference to them (e.g. electrons). If, as appears to be true, our best physical theories make ineliminable reference to mathematics, then by parity of reasoning, we should believe that those...

# I know a little that Galileo changed the Aristotelian world view; but would like to learn more. What is the Aristotelian world view? How did Galileo change it? Could you please give me some explanation? And it would be most appreciated if you kindly suggest me some helpful webpages. THANKS

Thomas Kuhn in Chapter 10 of The Structure of Scientific Revolutions gives a wonderfully vivid description of the contrast between the Aristotelian world-view and that which developed from Galileo. Kuhn describes how an Aristotelian and Galileo would see (apparently the same) phenomenon: a pendulum. The Aristotelian would see a pendulum as an example of constrained motion. For an Aristotelian, a heavy body always seeks to move from a higher position to a lower one; the pendulum was simply achieving this downward trajectory with tortuous difficulty. Galileo would see the pendulum, not primarily as a body falling, but an oscillator repeating the same motion over and over again ad infinitum. If the pendulum were ideal (if we discount friction), it would continue oscillating forever. Galileo's view of the pendulum as an oscillator is the seed of one of the most productive mathematical frameworks in physics: the notion of an harmonic oscillator. This framework has been successfully applied in...