To make this discussion more concrete, please look at http://www.vetta.org/documents/disSol.pdf
Section 2.5 gives a simple version of the proof that Solomonoff induction is a powerful learning algorithm in principle, and Section 2.6 explains why it is not practically useful. What part of that paper do you think is wrong? thx ben On Fri, Jul 9, 2010 at 9:54 AM, Jim Bromer <[email protected]> wrote: > On Fri, Jul 9, 2010 at 7:56 AM, Ben Goertzel <[email protected]> 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 <[email protected]> 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> > <https://www.listbox.com/member/archive/rss/303/> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Ben Goertzel, PhD CEO, Novamente LLC and Biomind LLC CTO, Genescient Corp Vice Chairman, Humanity+ Advisor, Singularity University and Singularity Institute External Research Professor, Xiamen University, China [email protected] " “When nothing seems to help, I go look at a stonecutter hammering away at his rock, perhaps a hundred times without as much as a crack showing in it. Yet at the hundred and first blow it will split in two, and I know it was not that blow that did it, but all that had gone before.” ------------------------------------------- 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
