Ben, I agree that these issues don't need to have much to do with implementation... William Pearson convinced me of that, since his framework is about as general as general can get. His idea is to search the space of *internal* programs rather than *external* ones, so that we aren't assuming that the universe is computable, we are just assuming that *we* are. This is like the "Goedel Machine", except Will's doesn't need to prove the correctness of its next version, so it wouldn't run into the incompleteness of its logic. So, one can say, "If there is an AGI program that can be implemented on this hardware, then we can find it if we set up a good enough search."
Of course, "good enough search" is highly nontrivial. The point is, it circumvents all the foundational logical issues by saying that if logic X really does work better than logic Y, the machine should eventually notice and switch, assuming it has time/resources to try both. (Again, if I could formalize this for the limit of infinite computational resources, I'd be happy...) But, on to those philosophical issues. Generally, all I'm arguing is that an AGI should be able to admit the possibility of an uncomputable reality, like you just did. I am not sure about your statements 1 and 2. Generally responding, I'll point out that uncomputable models may compress the data better than computable ones. (A practical example would be fractal compression of images. Decompression is not exactly a computation because it never halts, we just cut it off at a point at which the approximation to the fractal is good.) But more specifically, I am not sure your statements are true... can you explain how they would apply to Wei Dai's example of a black box that outputs solutions to the halting problem? Are you assuming a universe that ends in finite time, so that the box always has only a finite number of queries? Otherwise, it is consistent to assume that for any program P, the box is eventually queried about its halting. Then, the universal statement "The box is always right" couldn't hold in any computable version of U. --Abram On Mon, Oct 20, 2008 at 3:01 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > Yes, if we live in a universe that has Turing-uncomputable physics, then > obviously AIXI is not necessarily going to be capable of adequately dealing > with that universe ... and nor is AGI based on digital computer programs > necessarily going to be able to equal human intelligence. > > In that case, we might need to articulate new computational models > reflecting the actual properties of the universe (i.e. new models that > relate to the newly-understood universe, the same way that AIXI relates to > an assumed-computable universe). And we might need to build new kinds of > computer hardware that make appropriate use of this Turing-uncomputable > physics. > > I agree this is possible. I also see no evidence for it. This is > essentially the same hypothesis that Penrose has put forth in his books The > Emperor's New Mind, and Shadows of the Mind; and I found his arguments there > completely unconvincing. Ultimately his argument comes down to: > > A) mathematical thinking doesn't feel computable to me, therefore it > probably isn't > > B) we don't have a unified theory of physics, so when we do find one it > might imply the universe is Turing-uncomputable > > Neither of those points constitutes remotely convincing evidence to me, nor > is either one easily refutable. > > I do have a limited argument against these ideas, which has to do with > language. My point is that, if you take any uncomputable universe U, there > necessarily exists some computable universe C so that > > 1) there is no way to distinguish U from C based on any finite set of > finite-precision observations > > 2) there is no finite set of sentences in any natural or formal language > (where by language, I mean a series of symbols chosen from some discrete > alphabet) that can applies to U but does not apply also to C > > To me, this takes a bit of the bite out of the idea of an uncomputable > universe. > > Another way to frame this is: I think the notion of a computable universe is > effectively equivalent to the notion of a universe that is describable in > language or comprehensible via finite-precision observations. > > And the deeper these discussions get, the more I think they belong on an > agi-phil list rather than an AGI list ;-) ... I like these sorts of ideas, > but they really have little to do with creating AGI ... > > -- Ben G > ------------------------------------------- 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
