Is it very surprising that advanced mathematics describes the real world so well? We live in a world which has volume (l*w*h), rounded edges (circles), definite proportions (constants), and rates (derivatives). There is nothing logical, however, with the way that transcendental numbers exist all around us. If anything these strange numbers support the idea that our universe is nothing but a freakish accident; a product of some natural processes which happen rather than a self-conscious, purposeful Creator.
The constancy and consistency of math is frustrating to someone like me, who's always thinking that the answer must be a little more complicated than simply punching a few numbers.
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Doesn't that depend what you mean by "logical"? There's work (I know this from my one grad seminar in phil of math) done on the logic of transcendental numbers, and on their ontology and epistemology. It's far too technical for me to grasp, but it exists, and might help clarify why these things appear to crop up in nature all the time.
By logical I mean following from a previous non-mathematical premise. The world and mathematics just are.
I'm not saying anything really deep or surprising, and there's not really a whole lot behind it except my crude feeling that math is bizarre and suggests that the universe is really just bizarre, even if it does have an orderly, mathematical bizarreness.
I'm also kinda partial to the idea of the many-worlds interpretation of quantum physics. It reminds me of Spinoza, who I actually liked.
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