On Fri, Jul 9, 2010 at 7:56 AM, Ben Goertzel <b...@goertzel.org> wrote:
If you're going to argue against a mathematical theorem, your argument must be mathematical not verbal. Please explain one of 1) which step in the proof about Solomonoff induction's effectiveness you believe is in error 2) which of the assumptions of this proof you think is inapplicable to real intelligence [apart from the assumption of infinite or massive compute resources] -------------------------------- Solomonoff Induction is not a provable Theorem, it is therefore a conjecture. It cannot be computed, it cannot be verified. There are many mathematical theorems that require the use of limits to "prove" them for example, and I accept those proofs. (Some people might not.) But there is no evidence that Solmonoff Induction would tend toward some limits. Now maybe the conjectured abstraction can be verified through some other means, but I have yet to see an adequate explanation of that in any terms. The idea that I have to answer your challenges using only the terms you specify is noise. Look at 2. What does that say about your "Theorem". I am working on 1 but I just said: "I haven't yet been able to find a way that could be used to prove that Solomonoff Induction does not do what Matt claims it does." Z What is not clear is that no one has objected to my characterization of the conjecture as I have been able to work it out for myself. It requires an infinite set of infinitely computed probabilities of each infinite "string". If this characterization is correct, then Matt has been using the term "string" ambiguously. As a primary sample space: A particular string. And as a compound sample space: All the possible individual cases of the substring compounded into one. No one has yet to tell of his "mathematical" experiments of using a Turing simulator to see what a finite iteration of all possible programs of a given length would actually look like. I will finish this later. > > > On Fri, Jul 9, 2010 at 7:49 AM, Jim Bromer <jimbro...@gmail.com> wrote: > >> Abram, >> Solomoff Induction would produce poor "predictions" if it could be used to >> compute them. >> > > Solomonoff induction is a mathematical, not verbal, construct. Based on > the most obvious mapping from the verbal terms you've used above into > mathematical definitions in terms of which Solomonoff induction is > constructed, the above statement of yours is FALSE. > > If you're going to argue against a mathematical theorem, your argument must > be mathematical not verbal. Please explain one of > > 1) which step in the proof about Solomonoff induction's effectiveness you > believe is in error > > 2) which of the assumptions of this proof you think is inapplicable to real > intelligence [apart from the assumption of infinite or massive compute > resources] > > Otherwise, your statement is in the same category as the statement by the > protagonist of Dostoesvky's "Notes from the Underground" -- > > "I admit that two times two makes four is an excellent thing, but if we are > to give everything its due, two times two makes five is sometimes a very > charming thing too." > > ;-) > > > >> Secondly, since it cannot be computed it is useless. Third, it is not the >> sort of thing that is useful for AGI in the first place. >> > > I agree with these two statements > > -- ben G > > *agi* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <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=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
