J Storrs Hall, PhD wrote:
On Thursday 04 October 2007 11:06:11 am, Richard Loosemore wrote:
As far as we can tell, GoL is an example of that class of system in
which we simply never will be able to produce a "theory" in which we
plug in the RULES of GoL, and get out a list of all the patterns in GoL
that are interesting.
What do you exclude from your notion of a "theory"? If it can require
evaluating a recursive function, or solving a Diophantine equation, or any of
the other (provably) Turing equivalent constructs we often use to express
scientific theories, then I can readily give you a theory that will take the
rules, run huge numbers of experiments, do clustering and maxent type
analyses, and so forth, using any definition of "interesting" you can
formally specify.
Do it then. You can start with interesting=cyclic.
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.
Since you say you can "readily" do this, I'm sure everyone here will be
waiting with baited breath -- can we expect to see the result by Monday
morning?
Richard Loosemore
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