Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/3/84; site talcott.UUCP Path: utzoo!watmath!clyde!burl!ulysses!allegra!bellcore!decvax!genrad!mit-eddie!godot!harvard!talcott!gjk From: gjk@talcott.UUCP (Greg Kuperberg) Newsgroups: net.physics Subject: Non-linear systems. Message-ID: <209@talcott.UUCP> Date: Fri, 4-Jan-85 23:34:45 EST Article-I.D.: talcott.209 Posted: Fri Jan 4 23:34:45 1985 Date-Received: Mon, 7-Jan-85 03:14:14 EST Distribution: net Organization: Harvard Lines: 45 There seems to be considerable skepticism about my proposition that a non-linear system is a sufficient condition. Well, here is a simple model of a non-linear system in which there is exactly *zero* predictability. In this "universe", time goes in discrete jumps, as in Conway's Game of Life. In fact, one could easily picture this universe as a cellular automaton. Anyway, the universe at any point in time consists of a non-terminating sequence of 0's and 1's. After each time unit, the sequence has its first binary digit (bit, I guess) removed. Thus, the whole sequence shifts right by one. The evolution of the universe would progress like this: Time 0: 1101110011... Time 1: 1011100111... Time 2: 0111001110... Time 3: 1110011101... Time 4: 1100111010... And now, the twist. The *observable* universe is only the first bit of the sequence at each point in time. So what is the state of the observable universe as it progresses with time? Simply any sequence of 0's and 1's. Utterly unpredictable, even though the entire state of the universe "existed" at the beginning of time! Well, someone might object, "but it's only because of QM that we are limited in our measurements, so we still need QM." But I say that QM is not our only limitation. Even without QM, the thickness of the doping on our silicon chips is limited to the size of the atom, the speed that the signal in them propagates is limited to the speed of light, and the size of our computers is limited to the size of the universe (and probably the size of our galaxy). These restrictions probably apply to *any* computing device in our universe. So, if we're lucky, we may get 10^200 megaflops tops. By the (exponentional) nature of non-linear systems, this would give a predictive power of, say, 200 days of weather. Less than one year of weather predicted, even with a computer as big as the universe! Furthermore, it would necessarily disrupt the weather patterns if we were to take 10^200 data samples. Thus, the exact weather for next year is forever beyond our reach, without all those theories that the Nobel Laureates have cooked up. --- Greg Kuperberg harvard!talcott!gjk " " -Charlie Chaplin, for IBM