--- 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?
There is evidence that the universe is Turing computable, as opposed to being computable only by a more powerful machine or uncomputable. In particular, it has a finite age T, its size is limited by the speed of light c, its mass by G, and the number of quantum states by Planck's constant h. (The entropy is on the order of c^5 T^2/hG ~ 10^122 bits, which coincidentally makes a bit about the size of a proton even though the constants don't depend on the properties of any particles). Likewise, all other conserved properties are quantized, such as electric charge, baryon number, etc. We also observe that Occam's Razor works in practice, which is predicted by AIXI if the universe and our brains are both Turing computable. -- Matt Mahoney, [EMAIL PROTECTED] ------------------------------------------- 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
