Good point. I was basing my argument on the backwards non-determinism, and wanted to give the easiest way for readers (who might not have known this about Life) to verify it, so I gave them a term they can look up.
Also, was it really that long before they knew about GoE patterns? Their existence is a trivial implication of multiple states mapping onto the same state. They may not have found specific GoE patters, but they surely had the concept (if not by that name).
Their existence is a trivial implication of multiple states mapping onto the same state. They may not have found specific GoE patters, but they surely had the concept (if not by that name).
I'm not entirely sure it is a trivial implication:
In a sense, you're right, in that on any finite life-field run on a computer, which has only a finite number of possible states, the existence of convergent patterns does trivially imply Garden of Eden patterns. However, most life-theorists aren't interested in finite fields, and it was considered possible that Garden ...
Many experts suspect that there is no polynomial-time solution to the so-called NP-complete problems, though no-one has yet been able to rigorously prove this and there remains the possibility that a polynomial-time algorithm will one day emerge. However unlikely this is, today I would like to invite LW to play a game I played with with some colleagues called what-would-you-do-with-a-polynomial-time-solution-to-3SAT? 3SAT is, of course, one of the most famous of the NP-complete problems and a solution to 3SAT would also constitute a solution to *all* the problems in NP. This includes lots of fun planning problems (e.g. travelling salesman) as well as the problem of performing exact inference in (general) Bayesian networks. What's the most fun you could have?