Eric, Nobody here is actually arguing that the brain is non-computational, though. (The quote you refer to was a misunderstanding).
I was arguing that we have an understanding of noncomputational entities, and Ben was arguing (approximately) that any actual behavior could be explained equally well by an understanding of a computational entity (namely an axiomatic system describing the noncomp. entity). But, your argument *does* apply roughly to my claim that we could usefully learn that the world contained noncomputable entities... any behavior can be explained computationally, but to me this is only a little better than saying that any behavior can be explained by a hidden markov model. It is technically true, but sometimes a more sophisticated model will provide a *better* explanation. You can never know for sure that something is noncomputational as opposed to large-resource-computable, but you can similarly never know whether something is generated by a recursive definition (fractals, context-free grammers) or simply a complicated state-transition definition (regular grammars, hidden markov models). --Abram On Fri, Oct 24, 2008 at 7:01 PM, Eric Baum <[EMAIL PROTECTED]> wrote: > >>> You have not convinced me that you can do anything a computer can't do. >>> And, using language or math, you never will -- because any finite set of >>> symbols >>> you can utter, could also be uttered by some computational system. >>> -- Ben G > > I have the sense that this argument is not air tight, because I can > imagine a zero-knowledge proof that you can do something a computer > can't do. > > Any finite set of symbols you utter *could*, of course, be utterable by > some computational system, but if they are generated in response to > queries that are not known in advance, it might be arbitrarily unlikely > that they *would* be uttered by any particular computational system. > > For example, to make this concrete and airtight, I can add a time element. > Say I compute offline the answers to a large number of > problems that, if one were to solve them with a computation, > provably could only be solved by extremely long sequential > computations, each longer than any sequential computation > that a computer that could > possibly be built out of the matter in your brain could compute in an hour, > and I present you these problems and you answer 10000 of them in half > an hour. At this point, I am going, I think, to be pursuaded that you > are doing something that can not be captured by a Turing machine. > > Not that I believe, of course, that you can do anything a computer > can't do. I'm just saying, the above argument is not a proof that, > if you could, it could not be demonstrated. > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
