Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83 based; site hou2g.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxj!houxm!hou2g!stekas From: stekas@hou2g.UUCP (J.STEKAS) Newsgroups: net.physics Subject: Re: Re: Non-linear systems. Message-ID: <386@hou2g.UUCP> Date: Fri, 11-Jan-85 10:08:29 EST Article-I.D.: hou2g.386 Posted: Fri Jan 11 10:08:29 1985 Date-Received: Sat, 12-Jan-85 05:47:02 EST References: <209@talcott.UUCP>, <328@rlgvax.UUCP> <384@hou2g.UUCP>, <1027@sunybcs.UUCP> Organization: AT&T Bell Labs, Holmdel NJ Lines: 15 Randomness and predictability are two different things. Randomness is sufficient for unpredictability but not the only source. In linear types of systems, like Newtonian orbital mechanics, one can easily show that intitial states which are infinitesimally different at t=0 will be infinitesimally different at t=T. For many non-linear systems, infinitesimally different states at t=0 can be arbitrarily "far apart" at t=T. When such things occur it becomes impossible, even in principle, for a computer to predict the future because one does not even know the precision to which the calculation must be carried. One cannot guarentee that the truncation error on even a 10^10 bit computer would not introduce unacceptable error. Jim ihnp4!hou2g!stekas