But if He exists, what substantiates the argument that He would not reach past math and physics, unless it would be an argument derived from this side of the God/math interface? Unless you believe in revelation, which I presume you don't.
If we, from this side of the god/math interface, form an argument about the probable or necessary behavior of god who is on the other side of the interface, are we not assuming that we are perceiving his signs and extrapolating into an un-perceived realm -- in other words, we percieve the marks of design. We are not formally distinct from the Psalmist, who saw in the heavens the grandeur of God.
It's the problem of god-talk. What makes language about God different from gibberish, unless it is some kind of extrapolation from here to There, or prior communication from There to here? If we extrapolate one level, like the simple peasant does, or we extrapolate three levels, like you do, we are not formally different.
And if He did "reach past" math and physics, what would He reach with ?.
If he reached past math and physics and thus left an imprint on "clay", would he not have to use an instrument susceptible to math and physical measurement to even make an imprint on matter? So how would we distinguish between an imprint made by god and an imprint made by....what? Parts of the machine which "run by themselves"?
I don't mean that it is not possible to conceive of a God who could reach past math (obviously, we both just did it) but it isn't possible to conceive of knowing the specific reaching act, unless you simultaneously posit an organ of knowledge in addition to our sense organs, or posit a physical instrument in God's hand, the epistemological question infinitely regresses from there.
BTW, I loved your response.
But surely there is just such an organ? I know, with absolute certainty, that there is an infinite number of primes. But nobody has ever seen, heard, touched &c as much as one measly prime number. That's just a reprise of Socrates' argument in the Meno, but I find it very convincing.
Hence, (a) there is a place containing the prime numbers, and it can't be this finite universe since a finite container cannot hold an infinite set. And (b) we can reason about some of the things in this funny place with - at least - a degree of confidence that cannot be obtained from our five physical senses. And finally (c) the physical universe around us obeys, systematically and totally, abstract mathematical laws.
Which strongly suggests that this universe was designed, and it tells us something about the designer. If a watch ran for ever by itself, that would be strong evidence of a perfect - and hence divine - watchmaker. To me, the very regularity of the universe - the absence of miracles, to put it plainly - is evidence of a perfect Designer.