Xref: utzoo comp.ai:5275 talk.philosophy.misc:3355 sci.philosophy.tech:1815 Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!iuvax!cogsci!dave From: dave@cogsci.indiana.edu (David Chalmers) Newsgroups: comp.ai,talk.philosophy.misc,sci.philosophy.tech Subject: Re: Can Machines Think? Message-ID: <32029@iuvax.cs.indiana.edu> Date: 23 Dec 89 04:55:27 GMT References: <31821@iuvax.cs.indiana.edu> Sender: root@iuvax.cs.indiana.edu Reply-To: dave@cogsci.indiana.edu (David Chalmers) Organization: Indiana University, Bloomington Lines: 57 Ken Presting writes: >What makes the multi-body problem a counter-example is not just the fact >that the problem has no closed-form solution, but the chaotic nature of >the mechanical system. Chaos is only a problem if we need to model the behaviour of a particular system over a particular period of time exactly -- i.e., not just capture how it might go, but how it *does* go. This isn't what we're trying to do in cognitive science, so it's not a problem. We can model the system to a finite level of precision, and be confident that what we're missing is only random "noise." So while we won't capture the exact behaviour of System X at 3 p.m. on 12/22/89, we'll generate equally plausible behaviour -- in other words, how the system *might* have gone, if a few unimportant random parameters had been different. This leads to a point which is a central tenet of functionalism -- you don't need to capture a system's causal dynamics exactly, but only at a certain level of abstraction. Which level of abstraction? Well, this is usually specified teleologically, depending on what you're trying to capture. Usually, it's a level of abstraction that captures plausible input/output relationships. Anything below this, we can consider either implementational detail, or noise. Just what this level of abstraction is, of course, is a matter of some debate. The most traditional functionalists, including the practitioners of "symbolic" AI, believe that you may go to a very high level of abstraction before missing anything important. The move these days seems to be towards a much less abstract modelling of causal dynamics, in the belief that what goes on at a low level (e.g. the neural level) makes a fundamental difference. (This view is sometimes associated with the name "eliminative materialism", but it's really just another variety of functionalism. Even at the neural level, what we're trying to capture are causal patterns, not substance.) >What makes the analog causal system different from the algorithm is that >each state of the analog system encodes an infinite amount of information. Arguable. My favourite "definition" of information is due to Bateson, I think (no endorsement of Bateson's other views implied): "Information is a difference that makes a difference." An infinite number of bits may be required to descibe the state of a system, but in any real-world system, all of these after a certain point will not make any difference at all, except as random parameter settings. (The beauty of Bateson's definition is that the final "difference" depends on our purposes. If we wanted a precise simulation of the universe, these bits would indeed be "information". If we want a cognitive model, they're not.) Incidentally, you can concoct hypothetical analog systems which contain an infinite amount of information, even in this sense -- by coding up Chaitin's Omega for instance (and thus being able to solve the Halting Problem, and be better than any algorithm). In the real world, quantum mechanics makes all of this irrelevant, destroying all information beyond N bits or so. Happy Solstice. -- Dave Chalmers (dave@cogsci.indiana.edu) Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable"