It seems the essence of your argument is: "We are Turing machines. Turing machines are completely deterministic. Our outputs are not deterministic. This is a ba

It seems the essence of your argument is: "We are Turing machines. Turing machines are completely deterministic. Our outputs are not deterministic. This is a baffling conundrum." If we are Turing machines, we are Turing machines with noise and errors. (Proof: do large mathematical calculations by hand.) This explains the lack of determinism. The remainder of your essay seems to argue that our nondeterminism is "deep", but I don't understand the distinction. You state there's a big difference between random numbers from a cryptographic PRNG (which is in fact deterministic) and generating a proof that primes are infinite. But I don't see why computers can't generate "deep" nondeterminism, whatever that is.