the natural generalization of a turing machine to infinity would be a hyper turing machine: an infinitely wide tape and infinitely many heads.

i think language of "god" is mostly expressed in terms of infinities. e.g. pi (most infinite numbers are inexpressible to us, since most infinite numbers are transcendental numbers)

2. The alphabet our math uses is pretty much all finite. What percent of the axioms and theorems that you know are infinitely long? Shouldn't the overwhelming majority of axioms and theorems be infinitely long (and in particular map onto an uncountable set?). It just seems natural given the circumstances.