Yes, of course this is true ... systems need to have a certain minimum level of intelligence in order to self-improve in a goal-directed way!!
I said I didn't want to take time to formulate my point (which to me is extremely intuitively obvious) as a theorem with all conditions explicitly stated, and I still don't ;-) If some folks want to believe that self-modifying AGI is not possible, that's OK with me. Lots of folks believed human flight was not possible also, etc. etc. ... and there were even attempts at mathematical/theoretical proofs of this. Fortunately the Wright Brothers spent their time building planes rather than laboriously poking holes in the intuitively-obviously-wrong supposed-impossibility-proofs of what they were doing... ben g On Thu, Oct 16, 2008 at 11:38 AM, Tim Freeman <[EMAIL PROTECTED]> wrote: > From: "Ben Goertzel" <[EMAIL PROTECTED]> > > >On the other hand, if you insist on mathematical definitions of > >intelligence, we could talk about, say, the intelligence of a system > >as the "total prediction difficulty of the set S of sequences, with > >the property that the system can predict S during a period of time of > >length T". We can define prediction difficulty as Shane Legg does in > >his PhD thesis. We can then average this over various time-lengths T, > >using some appropriate weighting function. > ... > >Using this sort of definition, a system A2 that is twice as smart as > >system A1, if allowed to interact with an appropriate environment > >vastly more complex than either of the systems, would surely be > >capable of modifying itself into a system A3 that is twice as smart as > >A2. > > Probably not true, as stated. As you said, the dog (A2) is smarter > than than the roach (A1). If that's not true for the mathematical > definition of intelligence you give above, that's a bug in the > definition. The dog is not capable of interesting self-modification; > it will never construct an A3. > > >This seems extremely obvious and I don't want to spend time right now > >proving it formally. No doubt writing out the proof would reveal > >various mathematical conditions on the theorem statement... > > You at least need a certain minimum level of intelligence for A1 for > it to work. I don't know what that level is. In the interesting > case, it's a little less than the best humans, and in the > uninteresting case, it's orders of magnitude more and we'll never get > there. I find it hard to believe that you'll derive a specific > intelligence level from a mathematical proof, so I think you're at > best talking about an hopefully-someday empirical result rather than > something that could be proved. > > (I'm not following the larger argument that this is a part of, so I > have no opinion about it.) > -- > Tim Freeman http://www.fungible.com > [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 > -- 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: 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
