Non-computability.

According to Roger Penrose, humans can perform non-computable feats, such as dealing with Gödel questions. He uses this as a foundation to claim that the human mind cannot be expressed in terms of classical processes, and as such must be party to the only other (known) game in town: Quantum Mechanics.

Now, I haven't had the patience to sit through all of his arguments yet, though I slowly make progress. My understanding is that a large part of his stance is that an algorithm cannot usefully deal with a Gödel question, or equivalently, with the halting problem, while a human can.

My objection to this is that such problems always demand a certain quality of response when asked of UTMs: failing to respond forever is not acceptable as correct, nor is providing any response other than one that yields a truth when taken in combination with the question. This much is fine, however, when it is time for the human to answer, he is permitted the liberty of rejecting the question on the grounds that it is inherently unanswerable.

Obviously I am interested in artificial intelligence, and also find his assertion to be simply a self-serving one with a contrived philosophical backdrop for foundation. If anyone knows of, or can think of, a more sophisticated argument than the one above (or expose my flaws in my assessment of it) I would like to hear it.

Apologies for bringing up a largely philosophical question, my only excuse is that I cannot trust any other board with the question.

>>25
doesn't mean it must halt in 2n steps. It could halt sooner, or it could never halt
Let M be the nonempty set of possible memory states. Let e \in M be the special state we call an end state. We call a function f: M -> M a program if f(e) = e. Let P be the set of all programs. We say that program p halts for input i, if there exists such natural number n that p^n(i) = e, where p^n means 'p iterated n times'.

Now say that our set of memory states is finite and it has q states.  Take any program p and any input i. Let S_n = p^n(i). Now, this program halts for input i if there is such index k, that S_k = e. Now let's read the sequence {S_n} from the beginning. Before reading q+1 terms, one of the following surely will happen:
1) We encounter the state e, and so our program halts.
2) We encounter a term on the position r that we encountered before on the position t - it means that for all natural i, S_r+i = S_t+i, and so our program loops forever.

Any questions?