This question is something I've wondered about for a while.
When people describe the P vs. NP problem, they often compare the class NP to creativity. They note that composing a Mozart-quality symphony (analogous to an NP task) seems much harder than verifying that an already-composed symphony is Mozart-quality (which is analogous to a P task).
But is NP really the "creativity class?" Aren't there plenty of other candidates? There's an old saying: "A poem is never finished, only abandoned." I'm no poet, but to me, this is reminiscent of the idea of something for which there is no definite right answer that can be verified quickly...it reminds me more of coNP and problems such as TAUTOLOGY than NP or SAT. I guess what I'm getting at is that it's easy to verify when a poem is "wrong" and needs to be improved, but difficult to verify when a poem is "correct" or "finished."
Indeed, NP reminds me more of logic and left-brained thinking than creativity. Proofs, engineering problems, Sudoku puzzles, and other stereotypically "left-brained problems" are more NP and easy to verify from a quality standpoint than than poetry or music.
So, my question is: Which complexity class most precisely captures the totality of what human beings can accomplish with their minds? I've always wondered idly (and without any scientific evidence to support my speculation) if perhaps the left-brain isn't an approximate SAT-solver, and the right-brain isn't an approximate TAUTOLOGY-solver. Perhaps the mind is set up to solve PH problems...or perhaps it can even solve PSPACE problems.
I've offered my thoughts above; I'm curious as to whether anyone can offer any better insights into this. To state my question succinctly: I am asking which complexity class should be associated with what the human mind can accomplish, and for evidence or an argument supporting your viewpoint. Or, if my qusetion is ill-posed and it doesn't make sense to compare humans and complexity classes, why is this the case?
Update: I've left everything but the title intact above, but here's the question that I really meant to ask: Which complexity class is associated with what the human mind can accomplish quickly? What is "polynomial human time," if you will? Obviously, a human can simulate a Turing machine given infinite time and resources.
I suspect that the answer is either PH or PSPACE, but I can't really articulate an intelligent, coherent argument for why this is the case.
Note also: I am mainly interested in what humans can approximate or "do most of the time." Obviously, no human can solve hard instances of SAT. If the mind is an approximate X-solver, and X is complete for class C, that's important.