This one's a tough one to wrap my mind around.
Say we have a very powerful computer that can simulate (correctly) a human brain. I would assume that a Turing machine can do this if we establish the brain to be only material -- so it's just a bunch of molecules and their interactions. (This simulation is possible, since modern computers are a type of turing machine and make similar, less complicated simulations of this nature all the time. It's just a physics simulation, after all.) So, a problem can be solved by the Turing machine if and only if it can be solved by the human brain.
At this point, our implication is clear: Either humans cannot solve the halting problem, or we've botched the assumptions up. The former is hard to swallow (There's something us -- humans -- can't do?!), while the latter -- that there is something beyond the material brain -- reaches into metaphysics (which I don't think is a particularly elegant solution). In either case, there's something fishy about the answer.
Any takers?
-Brian (Thomas34 21:13, 18 November 2008 (UTC))
