Something similar could also be done in artificial universes like Conway's "life." As is well known by now, ConwayLife allows the existence of Turing machines and also self-reproducing "universal assemblers," i.e. life. Indeed, people have actually constructed Universal Turing machines in ConwayLife in full detail, I am not sure whether anybody ever constructed the universal assembler, though. There are plenty of ConwayLife experts here who may know, and who could say what is the smallest known construction? Anyhow: one could ask what is the PROBABILITY that a random set of bits in an NxN square happens to be "alive" or "a Turing machine" or whatever. Obviously it it were a 1000x1000 square the naive probability estimate would be 2^(-1000000) for the configuration being a particular Turing machine... but a more sensible estimate would ask: "if that construction were altered by mutating K bits, what is the chance it still remains in working order?" etc. I would naively expect that most cells in any such construction are 0s, and the construction would still function if almost any 0-cell were changed to 1, because isolated 1s die out in a single generation. Therefore, the "information content" of a typical human-designed ConwayLife machine fitting in an HxW rectangle is really not at all well described by "H*W bits" and it is probably better described by lg( binomial(H*W, L) ) bits, where L is the number of live cells, but this again is a considerable overestimate. Perhaps something like 4*L is a better rough estimate. http://www.conwaylife.com/wiki/Universal_turing_machine claims that Paul Rendell in 2010 constructed a ConwayLife UTM with 252192 live cells fitting in a 12699x12652 rectangle. So it would still seem based on this that life has to be considered a "miracle" because 252192 is so damn large. Another experimental question in ConwayLife you probably already know the answer to: What is the chance that a random configuration swiftly becomes "boring" i.e. trivial to predict the whole future of? -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)