Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site topaz.ARPA Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!ihnp4!zehntel!dual!amdcad!decwrl!decvax!genrad!teddy!panda!talcott!harvard!seismo!topaz!josh From: josh@topaz.ARPA (J Storrs Hall) Newsgroups: net.physics Subject: Re: Non-linear systems. Message-ID: <214@topaz.ARPA> Date: Thu, 10-Jan-85 14:47:07 EST Article-I.D.: topaz.214 Posted: Thu Jan 10 14:47:07 1985 Date-Received: Mon, 14-Jan-85 00:38:05 EST References: <209@talcott.UUCP>, <328@rlgvax.UUCP> <384@hou2g.UUCP> <273@harvard.ARPA> Organization: Rutgers Univ., New Brunswick, N.J. Lines: 24 > > The concept of "predicable, in principle" is usefull if and only if > > it has some connection with reality. If 10^70 Cray's calculating for > > 10^10 years cannot predict next year's weather then next year's weather > > is unpredictable. ... > Sorry, you're wrong. The technical term for "predictable in principle" > is computable. This is a sensible notion of great interest and > significance in modern information science. What you're aiming at is > the notion of "computational complexity". Let's try to keep something straight here: there are lots of things that a mathemetician assumes trivially, like adding two real numbers, that are not computable--they're infinitely long, remember? So something that's computable in principle to a mathemetician or a very theoretical physicist has little to do with what we can actually compute. Predicting the motion of a perfectly deterministic Newtonian system is impossible *because you can't "know" the initial conditions: they entail an infinite number of bits*. One way to look at QM uncertainty is to say that it, or something like it, is necessary merely to avoid having to say that each particle in the universe represents an infinite amount of information. --JoSH