My statement was *** 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 *** This seems to incorporate the assumption of a "finite period of time" because a finite set of sentences or observations must occur during a finite period of time. -- Ben G On Mon, Oct 20, 2008 at 4:19 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > 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/?&; > Powered by Listbox: http://www.listbox.com > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "Nothing will ever be attempted if all possible objections must be first overcome " - Dr Samuel Johnson ------------------------------------------- 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
