Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site rlgvax.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!bellcore!decvax!genrad!mit-eddie!godot!harvard!seismo!rlgvax!guy From: guy@rlgvax.UUCP (Guy Harris) Newsgroups: net.physics Subject: Re: Re: why FTL is illegal (wrt: free will). Message-ID: <327@rlgvax.UUCP> Date: Sat, 5-Jan-85 22:48:50 EST Article-I.D.: rlgvax.327 Posted: Sat Jan 5 22:48:50 1985 Date-Received: Tue, 8-Jan-85 03:06:09 EST References: <683@gloria.UUCP> <785@ariel.UUCP><148@lems.UUCP> <152@talcott.UUCP> <277@rlgvax.UUCP> <20@spar.UUCP> Organization: CCI Office Systems Group, Reston, VA Lines: 24 > Sorting thru back net.physics articles, I encountered this item from > Guy Harris: > > >If you assume ... and 3) enough computing ability to crank the model > >forward from that initial state, you can predict all future states > >of the universe. > > That remaining item, number (3) seems to require closer scrutiny. Correct > me if I'm mistaken, but I thought that even the simplest Newtonian models > of the universe result in intrinsically INSOLUBLE differential equations > (like the three-body problem). Note the magic word "computing ability". The fact that there is no closed-form solution to those differential equations is irrelevant. A closed-form solution is no better than numerical integration forward in time, assuming sufficient computing ability (precision, in this case) that there are no numerical problems in the integration; you can't compute the value of the closed-form expression "sin(2*pi*t/T)" to arbitrary precision. (Barring solutions which don't have nice analytical properties, so that *no* precision is "good enough"; a step function could, in principle, cause problems, but are there any real live step functions in nature?) Guy Harris {seismo,ihnp4,allegra}!rlgvax!guy