Jim, Aha! So you *are* a constructivist or intuitionist or finitist of some variety? This would explain the miscommunication... you appear to hold the belief that a structure needs to be computable in order to be well-defined. Is that right?
If that's the case, then you're not really just arguing against Solomonoff induction in particular, you're arguing against the entrenched framework of thinking which allows it to be defined-- the so-called "classical mathematics". If this is the case, then you aren't alone. --Abram On Thu, Jul 22, 2010 at 5:06 PM, Jim Bromer <jimbro...@gmail.com> wrote: > On Wed, Jul 21, 2010 at 8:47 PM, Matt Mahoney <matmaho...@yahoo.com>wrote: > The fundamental method is that the probability of a string x is > proportional to the sum of all programs M that output x weighted by 2^-|M|. > That probability is dominated by the shortest program, but it is equally > uncomputable either way. > Also, please point me to this mathematical community that you claim rejects > Solomonoff induction. Can you find even one paper that refutes it? > > You give a precise statement of the probability in general terms, but then > say that it is uncomputable. Then you ask if there is a paper that refutes > it. Well, why would any serious mathematician bother to refute it since you > yourself acknowledge that it is uncomputable and therefore unverifiable and > therefore not a mathematical theorem that can be proven true or false? It > isn't like you claimed that the mathematical statement is verifiable. It is > as if you are making a statement and then ducking any responsibility for it > by denying that it is even an evaluation. You honestly don't see the > irregularity? > > My point is that the general mathematical community doesn't accept > Solomonoff Induction, not that I have a paper that *"refutes it,"*whatever > that would mean. > > Please give me a little more explanation why you say the fundamental method > is that the probability of a string x is proportional to the sum of all > programs M that output x weighted by 2^-|M|. Why is the M in a bracket? > > > On Wed, Jul 21, 2010 at 8:47 PM, Matt Mahoney <matmaho...@yahoo.com>wrote: > >> Jim Bromer wrote: >> > The fundamental method of Solmonoff Induction is trans-infinite. >> >> The fundamental method is that the probability of a string x is >> proportional to the sum of all programs M that output x weighted by 2^-|M|. >> That probability is dominated by the shortest program, but it is equally >> uncomputable either way. How does this approximation invalidate Solomonoff >> induction? >> >> Also, please point me to this mathematical community that you claim >> rejects Solomonoff induction. Can you find even one paper that refutes it? >> >> >> -- Matt Mahoney, matmaho...@yahoo.com >> >> >> ------------------------------ >> *From:* Jim Bromer <jimbro...@gmail.com> >> *To:* agi <agi@v2.listbox.com> >> *Sent:* Wed, July 21, 2010 3:08:13 PM >> >> *Subject:* Re: [agi] Comments On My Skepticism of Solomonoff Induction >> >> I should have said, It would be unwise to claim that this method could >> stand as an "ideal" for some valid and feasible application of probability. >> Jim Bromer >> >> On Wed, Jul 21, 2010 at 2:47 PM, Jim Bromer <jimbro...@gmail.com> wrote: >> >>> The fundamental method of Solmonoff Induction is trans-infinite. Suppose >>> you iterate through all possible programs, combining different programs as >>> you go. Then you have an infinite number of possible programs which have a >>> trans-infinite number of combinations, because each tier of combinations can >>> then be recombined to produce a second, third, fourth,... tier of >>> recombinations. >>> >>> Anyone who claims that this method is the "ideal" for a method of applied >>> probability is unwise. >>> >>> Jim Bromer >>> >> >> *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/> >> > > *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> > -- Abram Demski http://lo-tho.blogspot.com/ http://groups.google.com/group/one-logic ------------------------------------------- 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
