Quite so. There is plenty of mathematics with no relation to the physical world
Yes. Physicists find some mathematics useful in describing physical processes, while other mathematics remains just formal concepts in mathematicians' heads or scrawled in hieroglyphs on their chalkboards. W4U needs to address why that is.
So a vital thing that W4U still needs to do if he wants to turn his obsession into a plausible metaphysics, is provide some sort of account of the
actualization process necessary to hypostasize some mathematics so as to make it tangible, causally interactive and
physical.
and there are plenty of things in nature that can't be described in mathematics.
I agree again.
I haven't but it makes sense, seeing that mathematics is a highly evolved form of quantitative logic. However, there is a huge differences between a universe that is describable by mathematics and one that "is" mathematics.
One could make the same kind of assertions that W4U makes regarding
language more generally. Physical reality is describable by language. Hence (insert smoke and mirrors here) physical reality
IS language. This one is popular with a certain kind of literary theorist for whom everything becomes a 'text'.
The philosophical idealists (like George Berkeley and some of the Kantians) argued that physical reality is known through perceptions, hence physical reality
IS perceptions. (Picture 'Brains-in-vats' and Morpheus saying, "What IS reality? If reality is what you can touch, see or feel, then reality is just electrical signals interpreted by your brain.") In this version, reality is reduced to psychology instead of mathematics.
It's certainly true that mathematics is very useful (to physicists anyway, perhaps less so to biologists) in describing physical reality. So I would fully agree with W4U that there's something about physical reality that mathematics somehow captures, that mathematics is somehow isomorphic with. But that obviously doesn't imply that physical reality is nothing but mathematics. There's just something about physical reality that
some (not all) mathematics successfully models.
The book on my shelf is six inches high. That doesn't mean that my book is identical with "six inches high" or that anything six inches high is my book. There's more to my book than that.