[sgt101]

I think one question here is to ask where are the machines in the universe that are not equivalent to a (near) Turing machine? As far as I know all physical processes that are understood are equivalent to a UTM, the ones that aren't understood may or may not turn out to be, but I don't know of any examples.

Another question is to ask what calculations / inferences are intractable when implemented on a UTM and yet can be performed by humans - I mean exact calculations, not guesses that are mostly right (I'm happy that humans are allowed to make errors, but the process must be transparently able to produce exact correct results). Some people claim that mathematicians can create insights that could not be done on a machine, but I have never heard of a specific example and I think that things are running backwards here. Now machines are creating proofs that humans don't understand.