Ben, How so? Also, do you think it is nonsensical to put some probability on noncomputable models of the world?
--Abram On Sun, Oct 19, 2008 at 6:33 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > But: it seems to me that, in the same sense that AIXI is incapable of > "understanding" proofs about uncomputable numbers, **so are we humans** ... > > On Sun, Oct 19, 2008 at 6:30 PM, Abram Demski <[EMAIL PROTECTED]> wrote: >> >> Matt, >> >> Yes, that is completely true. I should have worded myself more clearly. >> >> Ben, >> >> Matt has sorted out the mistake you are referring to. What I meant was >> that AIXI is incapable of understanding the proof, not that it is >> incapable of producing it. Another way of describing it: AIXI could >> learn to accurately mimic the way humans talk about uncomputable >> entities, but it would never invent these things on its own. >> >> --Abram >> >> On Sun, Oct 19, 2008 at 4:32 PM, Matt Mahoney <[EMAIL PROTECTED]> >> wrote: >> > --- On Sat, 10/18/08, Abram Demski <[EMAIL PROTECTED]> wrote: >> > >> >> No, I do not claim that computer theorem-provers cannot >> >> prove Goedel's Theorem. It has been done. The objection applies >> >> specifically to AIXI-- AIXI cannot prove goedel's theorem. >> > >> > Yes it can. It just can't understand its own proof in the sense of >> > Tarski's undefinability theorem. >> > >> > Construct a "predictive" AIXI environment as follows: the environment >> > output symbol does not depend on anything the agent does. However, the >> > agent >> > receives a reward when its output symbol matches the next symbol input from >> > the environment. Thus, the environment can be modeled as a string that the >> > agent has the goal of compressing. >> > >> > Now encode in the environment a series of theorems followed by their >> > proofs. Since proofs can be mechanically checked, and therefore found given >> > enough time (if the proof exists), then the optimal strategy for the agent, >> > according to AIXI is to guess that the environment receives as input a >> > series of theorems and that the environment then proves them and outputs >> > the >> > proof. AIXI then replicates its guess, thus correctly predicting the proofs >> > and maximizing its reward. To prove Goedel's theorem, we simply encode it >> > into the environment after a series of other theorems and their proofs. >> > >> > -- 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/?&; >> > 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/?&; >> Powered by Listbox: http://www.listbox.com > > > > -- > Ben Goertzel, PhD > CEO, Novamente LLC and Biomind LLC > Director of Research, SIAI > [EMAIL PROTECTED] > > "Nothing will ever be attempted if all possible objections must be first > overcome " - Dr Samuel Johnson > > > ________________________________ > agi | Archives | Modify Your Subscription ------------------------------------------- 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
