I am not so sure that humans use uncomputable models in any useful sense, when doing calculus. Rather, it seems that in practice we use computable subsets of an in-principle-uncomputable theory...
Oddly enough, one can make statements *about* uncomputability and uncomputable entities, using only computable operations within a formal system... For instance, one can prove that even if x is an uncomputable real number x - x = 0 But that doesn't mean one has to be able to hold *any* uncomputable number x in one's brain... thus is the power of abstraction, and I don't see why AGIs can't have it just like humans do... Ben On Fri, Feb 29, 2008 at 4:37 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > I'm an undergrad who's been lurking here for about a year. It seems to me > that many people on this list take Solomonoff Induction to be the ideal > learning technique (for unrestricted computational resources). I'm wondering > what justification there is for the restriction to turing-machine models of > the universe that Solomonoff Induction uses. Restricting an AI to computable > models will obviously make it more realistically manageable. However, > Solomonoff induction needs infinite computational resources, so this clearly > isn't a justification. > > My concern is that humans make models of the world that are not computable; > in particular, I'm thinking of the way physicists use differential > equations. Even if physics itself is computable, the fact that humans use > incomputable models of it remains. Solomonoff Induction itself is an > incomputable model of intelligence, so an AI that used Solomonoff Induction > (even if we could get the infinite computational resources needed) could > never understand its own learning algorithm. This is an odd position for a > supposedly universal model of intelligence IMHO. > > My thinking is that a more-universal theoretical prior would be a prior over > logically definable models, some of which will be incomputable. > > Any thoughts? > > ________________________________ > > agi | Archives | Modify Your Subscription -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC Director of Research, SIAI [EMAIL PROTECTED] "If men cease to believe that they will one day become gods then they will surely become worms." -- Henry Miller ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=95818715-a78a9b Powered by Listbox: http://www.listbox.com
