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/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
