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.

>>17
Dude. If you don't want to mess with the Busy Beaver, here is another program for you

def f():
    z = 0
    while True:
        z += 1
        for x in xrange(1, z):
            for y in xrange(1, x + 1):
                 if x**4 + y**4 == z**4:
                      return x, y, z

Show your "state enumerating principle" in action. What? Problems? Can't even begin?

That's because the "heuristics" you are talking are only applicable to various glorified "Hello world!" programs, a few simple loops and that's all. When people talk about nontrivial cases of halting problem, about time complexity or decidability of a typechecking/inferencing algorithm, they don't mean this kindergarten stuff.

All interesting programs have structure similar to this, even fucking fibs can be proven to terminate only by inventing and verifying a hypothesis about certain invariants in the data it operates on, not by "checking states for loops".

Pfff, what a moron.