Interesting. I really enjoyed the books by Penrose and Cohen.
A human certainly cannot solve a non-computable problem by "playing" computer. However the insight that is created by trying to solve (or invent, in Post's case) something like the PCP, and then the ability to intuit and then prove there cannot be a solution by a non-human, is still an open question. Penrose has his quantic processes inside microtubules explanation which seems a very up your sleeve answer. I don't know if that would be too different to a massively parallel machine with true stochastic non-determinism.
In any case attempting to compare the brain to a computer and calculating the maximum number of states in terms of bits for me is not fair. There are certainly hard physical limits but that pertains the question of consciousness tangentially.
A human certainly cannot solve a non-computable problem by "playing" computer. However the insight that is created by trying to solve (or invent, in Post's case) something like the PCP, and then the ability to intuit and then prove there cannot be a solution by a non-human, is still an open question. Penrose has his quantic processes inside microtubules explanation which seems a very up your sleeve answer. I don't know if that would be too different to a massively parallel machine with true stochastic non-determinism.
In any case attempting to compare the brain to a computer and calculating the maximum number of states in terms of bits for me is not fair. There are certainly hard physical limits but that pertains the question of consciousness tangentially.