Xref: utzoo comp.ai.philosophy:784 comp.ai.neural-nets:3127 Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!uwm.edu!ogicse!zephyr.ens.tek.com!uw-beaver!ubc-cs!scharein From: scharein@cs.ubc.ca (Robert Scharein) Newsgroups: comp.ai.philosophy,comp.ai.neural-nets Subject: Re: Continuous vs. discrete Message-ID: <1991Mar31.204818.15437@cs.ubc.ca> Date: 31 Mar 91 20:48:18 GMT References: <1991Mar26.215728.28875@watserv1.waterloo.edu> <1991Mar30.040808.1896@ddsw1.MCS.COM> Sender: usenet@cs.ubc.ca (Usenet News) Organization: University of British Columbia, Vancouver, B.C., Canada Lines: 43 In article <1991Mar30.040808.1896@ddsw1.MCS.COM> zane@ddsw1.MCS.COM (Sameer Parekh) writes: >In article <1991Mar26.215728.28875@watserv1.waterloo.edu> ssingh@watserv1.waterloo.edu (Sneaky Sanj ;-) writes: >>Time could very well be discrete as well. Something about a "chronon" >>10^-23 seconds. Space (?), anybody's guess. >> > > Space is discrete, but on a very small scale that people who don't >deal with the individual electrons don't have to worry about it. (The >electrons MUST be in one shell or another, not in between.) On >a larger scale, space then seems to be continuous, but then on >and even larger scale it is discrete again. > >-- >The Ravings of the Insane Maniac Sameer Parekh -- zane@ddsw1.MCS.COM The above is a bit misleading. While you are correct about space being discrete, it is wrong to infer this fact from regarding electron orbitals. On energy scales where electrons are in orbitals, space may be thought of as perfectly continuous, and indeed this is the assumption in classical quantum mechanics (where the theory of orbitals comes from). At very high energy scales (or at small length or time scales), where quantum gravity effects play a role, space (or more precisely space-time) is discrete. But since nobody has a completely satisfactory theory of quantum gravity, we don't know the exact nature of this quantization. As for space being discrete at very large scales, I think you mean to say that the distribution of matter in the universe appears discrete (i.e. clumpy), which is quite a different thing. There are many books which discuss these topics in great detail. I will only give two here: Quantum Mechanics, by Eugen Merzbacher (John Wiley & Sons, 1970) The Large-Scale Structure of the Universe, by P. J. E. Peebles (Princton Univ. Press, 1980) Rob Scharein Computer Science Department University of British Columbia scharein@cs.ubc.ca