Jim, I think you are using a different definition of "well-defined" :). I am saying Solomonoff induction is totally well-defined as a mathematical concept. You are saying it isn't well-defined as a computational entity. These are both essentially true.
Why you might insist that program-space is not well-defined, on the other hand, I do not know. --Abram On Sun, Jul 18, 2010 at 8:02 AM, Jim Bromer <[email protected]> wrote: > Solomonoff Induction is not well-defined because it is either incomputable > and/or absurdly irrelevant. This is where the communication breaks down. I > have no idea why you would make a remark like that. It is interesting that > you are an incremental-progress guy. > > > > On Sat, Jul 17, 2010 at 10:59 PM, Abram Demski <[email protected]>wrote: > >> Jim, >> >> >> Saying that something "approximates Solomonoff Induction" doesn't have any >>> meaning since we don't know what Solomonoff Induction actually >>> represents. And does talk about the "full program space," merit mentioning? >>> >> >> I'm not sure what you mean here; Solomonoff induction and the full program >> space both seem like well-defined concepts to me. >> >> >> I think we both believe that there must be some major breakthrough in >>> computational theory waiting to be discovered, but I don't see how >>> that could be based on anything other than Boolean Satisfiability. >> >> >> A polynom SAT would certainly be a major breakthrough for AI and >> computation generally; and if the brain utilizes something like such an >> algorithm, then AGI could almost certainly never get off the ground without >> it. >> >> However, I'm far from saying there must be a breakthrough coming in this >> area, and I don't have any other areas in mind. I'm more of an >> incremental-progress type guy. :) IMHO, what the field needs to advance is >> for more people to recognize the importance of relational methods (as you >> put it I think, the importance of structure). >> >> --Abram >> >> On Sat, Jul 17, 2010 at 10:28 PM, Jim Bromer <[email protected]>wrote: >> >>> Well I guess I misunderstood what you said. >>> But, you did say, >>> "The question of whether the function would be useful for the "sorts of >>> things we keep talking about" ... well, I think the best argument that I can >>> give is that MDL is strongly supported by both theory and practice for many >>> *subsets* of the full program space. The concern might be that, so far, it >>> is only supported by *theory* for the full program space-- and since >>> approximations have very bad error-bound properties, it may never be >>> supported in practice. My reply to this would be that it still appears >>> useful to approximate Solomonoff induction, since most successful predictors >>> can be viewed as approximations to Solomonoff induction. "It approximates >>> solomonoff induction" appears to be a good _explanation_ for the success of >>> many systems." >>> >>> Saying that something "approximates Solomonoff Induction" doesn't have >>> any meaning since we don't know what Solomonoff Induction actually >>> represents. And does talk about the "full program space," merit mentioning? >>> >>> I can see how some of the kinds of things that you have talked about (to >>> use my own phrase in order to avoid having to list all the kinds of claims >>> that I think have been made about this subject) could be produced from >>> finite sets, but I don't understand why you think they are important. >>> >>> I think we both believe that there must be some major breakthrough in >>> computational theory waiting to be discovered, but I don't see how >>> that could be based on anything other than Boolean Satisfiability. >>> >>> Can you give me a simple example and explanation of the kind of thing you >>> have in mind, and why you think it is important? >>> >>> Jim Bromer >>> >>> >>> On Fri, Jul 16, 2010 at 12:40 AM, Abram Demski >>> <[email protected]>wrote: >>> >>>> Jim, >>>> >>>> The statements about bounds are mathematically provable... furthermore, >>>> I was just agreeing with what you said, and pointing out that the statement >>>> could be proven. So what is your issue? I am confused at your response. Is >>>> it because I didn't include the proofs in my email? >>>> >>>> --Abram >>>> >>> *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> >> <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
