On Fri, Oct 05, 2007 at 01:39:51PM -0400, J Storrs Hall, PhD wrote: > On Friday 05 October 2007 12:13:32 pm, Richard Loosemore wrote: > > > Try walking into any physics department in the world and saying "Is it > > okay if most theories are so complicated that they dwarf the size and > > complexity of the system that they purport to explain?" > > You're conflating a theory and the mathematical mechanism necessary to apply > it to actual situations. The theory in Newtonian physics can be specified as > the equations F=ma and F=Gm1m2/r^2 (in vector form); but applying them > requires a substantial amount of calculation. > > You can't simply ignore the unusual case of chaotic motion, because the > mathematical *reason* the system doesn't have a closed analytic solution is > that chaos is possible.
To amplify: the rules for GoL are simple. The finding what they imply are not. The rues for gravity are simple. Finding what they impl are not. If I have a bunch of widely-separated GoL gliders flying along, then the analytic theory for explaining them is near-trivial: they glide along in straight lines. Kind-a like Newtonian linear motion. Ergo, I can deduce that a very common case has an analytically-trivial solution. For the few times that gliders might collide, well, that's more complicated. But this is a corner-case, it's infrequent. Like collisions between planets, it can be handled as a special case. I mean, heck, there's only so many different ways a pair of glider can collide, and essentialy all of the collisions are fatal to both gliders. So, by this reasoning, GoL must be a low-complexity system. Compare this example to, for example, taking millions randomly-sized gravitating bodies, and jamming them into a small volume, so that they're very close to one-another (i.e. "hot"). Now, the laws of gravitational motion are simple. Predicting what will happen is not. If, instead of using the solar system as an example, you used a globular cluster, and if, instead of using a high-density starting positon for GoL, you started GoL with one "sun" and nine "planet-gliders" zooming around, you could invert the argument on its head. Prediciting gliders is trivially easy, predicting globular clusters is barely computationally tractable, and is complex. I think its even proven Turing-complete, up to a rather subtle and controversial argument about grazing collisions, but perhaps I misunderstood. --linas ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=50687710-42a20d
