Thanks for the replies, On Fri, Feb 29, 2008 at 4:44 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
> 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... > > What I'm thinking is something like this: the uncomputable 'ideal' calculus serves as a motivation for the many computable subsets. Similarly, the AIXI model is supposed to act as a motivating concept for many possible realistic implementations. It is the ideal that the computable implementations approximate. In that way, it "compresses" them; it is supposed to be the pattern behind them. (Of course, since at the moment I don't endorse Solomonoff Induction, it doesn't act as such a motivating force for me, but it could if I did endorse it.) So I think what I'm saying is that uncomputable models are useful because we can compute useful statements *about* them. But I wish I could give a more solid argument! On Fri, Feb 29, 2008 at 8:10 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote: > > There is evidence that the universe is Turing computable, as opposed to > being > computable only by a more powerful machine or uncomputable. In particular > [...] > 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] > > Accepting uncomputable models does not mean throwing out Occam's Razor, at least not the way I intend it. We can have longer or shorter differential equations. (It seems convenient to keep using calculus as the main example of an uncomputable model.) If we do discover a computable model of the universe, then the previous models will be demoted to the position of approximations. But wouldn't they still be *useful* approximations in some cases? In fact, Newtonian mechanics will probably still be what's used for everyday-scale physics. (Again, I'm trying to assert that the uncomputable can usefully abbreviate the computable.) ------------------------------------------- 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
