Matt, The "currently known laws of physics" is a *description* of the universe at a certain level, which is fundamentally different from the universe itself. Also, "All human knowledge can be reduced into physics" is not a view point accepted by everyone.
Furthermore, "computable" is a property of a mathematical function. It takes a bunch of assumptions to be applied to a statement, and some additional ones to be applied to an object --- Is the Earth "computable"? Does the previous question ever make sense? Whenever someone "prove" something outside mathematics, it is always based on certain assumptions. If the assumptions are not well justified, there is no strong reason for people to accept the conclusion, even though the proof process is correct. Pei On Tue, Oct 28, 2008 at 5:23 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote: > 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/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- 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
