Path: utzoo!attcan!uunet!cs.utexas.edu!swrinde!zaphod.mps.ohio-state.edu!mips!apple!sun-barr!newstop!sun!amdahl!kp From: kp@uts.amdahl.com (Ken Presting) Newsgroups: comp.ai Subject: Re: Dear Roger, Summary: It's the "Observation Language" that limits paradigm shifts Keywords: Moravec, Turing machines, paradigm shifts Message-ID: <33sQ02J7889K01@amdahl.uts.amdahl.com> Date: 13 Feb 90 20:24:31 GMT References: <2206@castle.ed.ac.uk> <182@zds-ux.UUCP> Reply-To: kp@amdahl.uts.amdahl.com (Ken Presting) Organization: Amdahl Corporation, Sunnyvale CA Lines: 51 In article <182@zds-ux.UUCP> gerry@zds-ux.UUCP (Gerry Gleason) writes: >In article kp@amdahl.uts.amdahl.com (Ken Presting) writes: >> [...] So let's suppose Moravec's machine is a hypothesis- >>tester, and the signals it gets from the information source are like >>scientific observations, perhaps increasingly precise measurements of >>fundamental constants. Then, supposing that the system can make use of >>the input, it's information content can increase. But there are very >>serious problems with extending this process to full-scale science. >>If a constant coding scheme is used to represent the input measurements, >>the system would be unable to participate in major scientific conceptual >>changes, such as relativity or QM caused. > >If you are suggesting that limitations on the senses (input devices) would >keep an intellegence from making paradigm shifts, then you must be willing >to suggest that the same limitation exists for us. In this era, we have >many tools for making measurements, and presenting the information in a >form our senses can digest; much of this information in inaccessable to >out senses. An intellegent machine would have to have access to the same >instraments if you expect it to perform in the type of scientific domains >in your example. Well, I wouldn't want to imply that a computerized hypothesis-tester is necessarily incapable of making paradigm shifts. Actually, I do believe that it is possible. But Moravec's algorithm for mathematical progress is statable using a constant notation for all theorems. That is just fine for mathematics, where no assertion need ever be discarded (assuming it has been proved). But in a paradigm shift, familiar measurements get re-interpreted, and end up as descriptions of quite different phenomena, in a new notation system with new semantics. So a machine which is a lot smarter than Moravec proposes would be needed to do revolutionary science. I might add that I think the whole issue of advancing mathematics by adding true unprovable assertions is completely bogus. Every case I know of which involves an independence theorem (a proof that some assertion is unprovable on a given set of axioms) ends up generating at least two distinct theories, each of which has some interest in its own right. Take non-euclidean geometry. A lot of people were upset that the parallel postulate was unprovable, but negating it is just as interesting as accepting it! The continuum hypothesis is similar, although non-Cantorian set theory has not yet turned out to be as useful as non-euclidean geometry. It surprised me that Penrose thought that the ability to see the truth of Goedel sentences shows something important about people. Given that the incompletenes theorem is proven, I can't imagine any mathematical fact *less* interesting than a Goedel sentence. The incompleteness theorem has the information. The Goedel sentence adds nothing. In mathematics, the proofs are at least as important as the theorems, if not more so.