On Thursday 04 October 2007 03:46:02 pm, Richard Loosemore wrote: > Oh, and, by the way, the widely accepted standard for what counts as a > "scientific theory" is -- as any scientist will be able to tell you -- > that it has to make its prediction without becoming larger and more > complicated than the system under study, so it goes without saying that > whatever you choose for a theory it is not allowed to simulate a massive > number of Game of Life cases and simply home in on the cyclic ones.
Wrong. Consider the amount of data, cases, and simulation involved in, say, using density functional theory to make predictions about the shape of a fairly small molecule. If physicists lived in a Life universe, they would consider finding the CA rules the "ultimate theory of everything". We don't have that for real physics, but Shrödinger's equation is similar for our purposes. DFT is a carefully tuned set of heuristics to make QM calcs tractable -- but if we had the horsepower, you can bet your bottom dollar that physicists would be using the real equations and calculating like mad. You didn't give me a formal definition of "cyclic" so I'll do it for you: cyclic S :: exists p>1,k>=0 s.t. S[i+p]=S[i] forall i>k I trust you understand lazy evaluation: lifeseries M :; M, lifeseries liferules M We're using an APL-like data semantics with implicit parallelism over vector elements: mats N = N N rho 2 baserep i for i=1..2^N^2 Then your theory is cyclic lifeseries mats 2..Whatever If you have a look at Gödel's proof, he built up to functions of about the level of Lisp from simple arithmetic. The above assumes a few more definitions, but there are 50 years of CS to draw them from. Josh ----- 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=50404151-4b1afa
