[tjradcliffe]

We find it because that's what we're looking for, or inventing. Here's a comparable question: "How is it that we can find an unfathomably small sub-set of possible symbols--a mere 26!--that are capable of encoding any idea whatsoever?"

The answer is: we are humans, doing human things within the scope of human capabilities. If there are ideas that are inexpressible by us, we can't possibly know about them. If there is physics profoundly beyond our ken (what lies behind the quantum veil, for example) we simply don't know about it.

Mathematics is a natural language (as physicists use it) to describe nature to ourselves. The fact of the knowing subject, and the activity of the knowing subject, cannot be left out without leaving a central mystery, which always amounts to "Why does the knowing subject do what they do?" (like restrict math to Smolin's four key categories of number, geometry, algebra and logic). If you imbue some mystical subject-free "mathematics" with these properties, rather than the activity of the knowing subject with them, they will remain mysterious.

This also explains why mathematics is so very, very bad at describing reality: http://www.tjradcliffe.com/?p=381

[lisper]

> How is it that we can find an unfathomably small sub-set of possible symbols--a mere 26!--that are capable of encoding any idea whatsoever?

That's not an equivalent question. Any repertoire of N distinguishable symbols for N>1 is essentially equivalent.

But there's no reason a priori to believe that the laws of physics should be modellable with mathematics at all, let alone that we should be able to figure out what those mathematics are, let alone that they should turn out to be simple enough that the model (or at least a very significant chunk of it) can fit in a single human brain.

Consider dreaming: when you are in a dream state you are living in essentially a solipsistic world where science doesn't work. There's no inherent reason why that could not be totality of your existence. It's just an accident of biology that you wake up occasionally and get to experience the "real" world, which we consider "real" because it seems to behave according to mathematical laws. The existence of such experience is not a given.