--- On Mon, 10/20/08, Ben Goertzel <[EMAIL PROTECTED]> wrote: > 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
That is only true in C. In U you might be able to make an infinite number of observations with infinite precision. On Mon, Oct 20, 2008 at 11:23 AM, Abram Demski <[EMAIL PROTECTED]> wrote: > As a concrete example, let's say some > physical constant turns out to be a (whole-number) multiple of > Chaitin's Omega. Omega cannot be computed, but it can be approximated > (slowly), so we could after a long time suspect that we had determined > the first 20 digits (although we would never know for sure!). If a > physical constant turned out to match (some multiple of) these, we > would strongly suspect that the rest of the digits matched as well. You are reasoning by Occam's Razor, but that only holds in a universe where AIXI holds. In an uncomputable universe there is no reason to prefer the simplest explanation for an observation. (You might also be able to compute Omega exactly). Note: I am not suggesting that our universe is not Turing computable. All of the evidence suggests that it is. -- Matt Mahoney, [EMAIL PROTECTED] ------------------------------------------- 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
