Mathematics and the Universe

[CoxRox]

I also think it is significant that the "fundamental" physics that is elegantly expressed arose from theory instead of experimentation,

This is very interesting. I think I alluded to this in another thread. Is this the same as some mathematics being 'discovered' before they were applied to the real world? This seems to suggest these 'rules' are already out there.

I like this quote of Feynman's, when asked if he thought mathematics and hence the laws of physics had an independent existence:

"The problem of existence is a very interesting and difficult one. if you do mathematics, which is simply working out the consequences of assumptions, you'll discover for instance a curious thing if you add the cubes of integers. One cubed is one, two cubed is two times two times two, that's eight, and three cubed is three times three times three, that's twenty-seven. If you add the cubes of these, one plus eight plus twenty-seven- let's stop there - that would be thirty-six. And that's the square of of another number, six, and that number is the sum of those same integers. one plus two plus three...Now, that fact which I've just told you about might not have been known to you before. You might say "Where is it, what is it, where is it located, what kind of reality does it have?' And yet you came upon it. When you discover these things, you get the feeling that they were true before you found them. So you get the idea that somehow they existed somewhere, but there's nowhere for such things. It's just a feeling...Well, in the case of physics we have double trouble. We come upon these mathematical interrelationships but they apply to the universe, so the problem of where they are is doubly confusing...Those are philosophical questions that I don't know how to answer." (The Mind of God- Paul Davies)