Hutter proved Occam's Razor (AIXI) for the case of any environment with a computable probability distribution. It applies to us because the observable universe is Turing computable according to currently known laws of physics. Specifically, the observable universe has a finite description length (approximately 2.91 x 10^122 bits, the Bekenstein bound of the Hubble radius).
AIXI has nothing to do with insufficiency of resources. Given unlimited resources we would still prefer the (algorithmically) simplest explanation because it is the most likely under a Solomonoff distribution of possible environments. Also, AIXI does not state "the simplest answer is the best answer". It says that the simplest answer consistent with observation so far is the best answer. When we are short on resources (and we always are because AIXI is not computable), then we may choose a different explanation than the simplest one. However this does not make the alternative correct. -- Matt Mahoney, [EMAIL PROTECTED] --- On Tue, 10/28/08, Pei Wang <[EMAIL PROTECTED]> wrote: > From: Pei Wang <[EMAIL PROTECTED]> > Subject: [agi] Occam's Razor and its abuse > To: [email protected] > Date: Tuesday, October 28, 2008, 11:58 AM > Triggered by several recent discussions, I'd like to > make the > following position statement, though won't commit > myself to long > debate on it. ;-) > > Occam's Razor, in its original form, goes like > "entities must not be > multiplied beyond necessity", and it is often stated > as "All other > things being equal, the simplest solution is the best" > or "when > multiple competing theories are equal in other respects, > the principle > recommends selecting the theory that introduces the fewest > assumptions > and postulates the fewest entities" --- all from > http://en.wikipedia.org/wiki/Occam's_razor > > I fully agree with all of the above statements. > > However, to me, there are two common misunderstandings > associated with > it in the context of AGI and philosophy of science. > > (1) To take this statement as self-evident or a stand-alone > postulate > > To me, it is derived or implied by the insufficiency of > resources. If > a system has sufficient resources, it has no good reason to > prefer a > simpler theory. > > (2) To take it to mean "The simplest answer is usually > the correct answer." > > This is a very different statement, which cannot be > justified either > analytically or empirically. When theory A is an > approximation of > theory B, usually the former is simpler than the latter, > but less > "correct" or "accurate", in terms of > its relation with all available > evidence. When we are short in resources and have a low > demand on > accuracy, we often prefer A over B, but it does not mean > that by doing > so we judge A as more correct than B. > > In summary, in choosing among alternative theories or > conclusions, the > preference for simplicity comes from shortage of resources, > though > simplicity and correctness are logically independent of > each other. > > Pei ------------------------------------------- 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
