Yes, Andy, that makes more sense. Thank you. I've been thinking about this today and I eventually figured out that's what it must be. So the question is about a finite pattern which, if run long enough, will eventually contain every other "eligible" finite pattern. Each eligible finite pattern could be found somewhere within a portion of some future generation of the "Adam and Eve"'s evolution. Eligible patterns are, as described before, those which have ancestors going back arbitrarily (or "infinitely") many generations. (Of course, if you allowed the "Adam and Eve" configuration to be infinite, then it can contain all finite patterns, so clearly that wasn't the question.) My glider collision idea isn't too important, and I think it restricts the thought too much. I think the universal computer with a "printer" idea has a lot of promise. Perhaps someone can prove that the universal computer with a "printer" is necessary, then someone else can prove that a "universal printer" is impossible. It also invites a philosophical approach referencing the brain-in-a-vat argument [1]. If the Life pattern exists in a representation inside the Turing machine, who's to say it is any "less real" than the actual Life pattern that would be produced by the "printer"? Perhaps we don't need to print out the patterns to say we have generated them. In that case, a suitable binary counter[2] is our "Adam and Eve" configuration. [1] http://en.wikipedia.org/wiki/Simulation_hypothesis [2] http://www.conwaylife.com/forums/viewtopic.php?f=2&t=337#p1884 On Tue, Dec 6, 2011 at 12:51, Andy Latto <andy.latto@pobox.com> wrote:
Robert, I think that you are taking "pattern" to mean "configuration of the entire 2-d grid", while in what Dan was asking about, "pattern" means "finite rectangle with a given configuration". [...]
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