(February 15, 2010 at 5:01 pm)Purple Rabbit Wrote: I agree it could all be a ridiculous coincidence.
But I propose the following alternative explanation for the observed coherence between nature and (parts of) math. It's just my hypothesis but I can give you a few qualitative arguments for it. And maybe it's just a matter of rephrasing your words: math and nature match so well because they are both necessarily founded on symmetries. The more we discover about nature the more it becomes manifest that symmetry is what fuels our models of nature. Symmetry is everywhere in physics. In the structure of the atom, in the standard model of fundamental particles, in the way forces act, in the relativeness of viewpoints, in the immunity for spatial translation, in rotation of objects, in the spin of particles, in the particle wave duality, in the creation of matter-antimatter. Symmetry was what Einstein drove to general relativity. Hell the LHC is rigged to find supersymmetry! We seem to finally get it: symmetry, symmetry, symmetry! Like in circles, like in the building blocks of algebra, like in the mathematical equivalents of translation, transformation, rotations. Like in balance on both sides of the equation. Like in the order of natural numbers. Like in projections from one set of co-ordinates to another one. Mathematics is imagination restricted to consistency and symmetry. And why is symmetry a necessary essence of reality? Because only symmetry can ensure some sort of stability.
I'm fascinated by your idea. This is an old topic now, but was any consensus formed on this matter? Like Vaeolet Lilly Blossom I'm not entirely sure how necessary stability is, nor was I aware of how wide-spread symmetry is.
(a related quote: )
"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." - Eugene Wigner
