The emergent behavior of a system, while it is determined by the elements of thesystem and the rules of interaction between them and perhaps with the environment, isnot contained explicitly in any of the rules or elements themselves, nor is the behaviorexplained by a simple summation over the components making up the system. Emergentbehavior is characterized by being “greater than the sum of the parts.” [...]The paper makes an analogy between emergent behavior as systems become complex and the classical idea of 'degrees of freedom'. I am not completely convinced about how far this analogy carries, but at least on the surface it seems like a useful one.
In sum, one should view emergence and reductionism as opposite sides of thesame coin. Dissecting complex behavior from the top down eliminates internal degreesof freedom in the course of analysis, while emergent phenomena occur when internaldegrees of freedom appear when combining component elements into more complexsystems. If individual ants are studied to determine their rules of interaction, there isnothing mysterious about the process. But given those rules, one cannot predict thebehavior of the colony because the new degrees of freedom that appear in the collectivecolony cannot be deduced from the rules of interaction—these rules are necessary but notsufficient to predict the emergent behavior. It is the unexpected consequences of the additional degrees of freedom that appear mysterious.
I've created a universal constructor based spaceship. The speed is (5120,1024)c/33699586, and it runs well in Golly's hashlife. It is larger in extent, but smaller in population than the caterpillar, and the bulk of the pattern is taken up by the instruction tapeso I think I'm just going to assume this is awesome and go eat some pie.
Ran it for 33,699,586 generations. Population census (846278) matched the initial count.It takes 34 million generations to complete. And I guess it "replicates" itself in that the final state is the same as the starting one? Isn't that just a really, really, really slow oscillator?
To make Joe in Australia's point a bit clearer: computers have a 1-dimensional memory.Computer memory has as many dimensions as you want, you can even think of each bit as dimension in a Z2 vector space if you want. In actuality they are embedded on real world 3d structures (with one very thin dimension).
I can't help but wonder if the Life geeks will eventually come up with some form of quantum communication that transcends c.Not possible.
The easiest way to show that something is a universal computer is to show that it can emulate something you already know is a universal computer, like a Turing machine. Now, it's been known since the work of Emil Post in the 1930s that something called a Post tag system (see here or here for more or less mathematical explanations) is Turing-equivalent. A New Kind of Science describes a new formal system, called a cyclic tag system (Wolfram drops "Post"), which is equivalent to a Post tag system, and so to a universal Turing machine. Finally, there is a sketch of how propagating structures ("gliders") in Rule 110 can be used to implement a cyclic tag system, assuming you had an infinite lattice to play with.posted by delmoi at 12:03 AM on June 6, 2010 [1 favorite]
This is a genuinely new result. Rule 110 is the simplest CA (in terms of the number of states and the rule radius) which is known to support universal computation. (Indeed, in his 1985 book on cellular automata, Wolfram declared that universal computation in an elementary CA was obviously impossible.) However, lots of things are capable of universal computation — there's less interest in this kind of result than there was in, say, 1970. In 1990, for instance, Cristopher Moore devised a kind of idealized pin-ball machine which is capable of universal computation. This result, like the one about rule 110, is neat for people who care about dynamical models of universal computation — on the order of a thousand scientists and mathematicians world wide. What Wolfram wants to claim is that, since one universal computer is equivalent to another, by studying the behavior of one we learn things which are true of all others (true), therefore Rule 110 is as complex as anything in the universe, and all intelligent life, including, perhaps, the gods must have much in common. This, to put it mildly, does not follow. Wolfram even goes on to refute post-modernism on this basis; I won't touch that except to say that I'd have paid a lot to see Wolfram and Jacques Derrida go one-on-one.
The real problem with this result, however, is that it is not Wolfram's. He didn't invent cyclic tag systems, and he didn't come up with the incredibly intricate construction needed to implement them in Rule 110. This was done rather by one Matthew Cook, while working in Wolfram's employ under a contract with some truly remarkable provisions about intellectual property. In short, Wolfram got to control not only when and how the result was made public, but to claim it for himself. In fact, his position was that the existence of the result was a trade secret. Cook, after a messy falling-out with Wolfram, made the result, and the proof, public at a 1998 conference on CAs. (I attended, and was lucky enough to read the paper where Cook goes through the construction, supplying the details missing from A New Kind of Science.) Wolfram, for his part, responded by suing or threatening to sue Cook (now a penniless graduate student in neuroscience), the conference organizers, the publishers of the proceedings, etc. (The threat of legal action from Wolfram that I mentioned at the beginning of this review arose because we cited Cook as the person responsible for this result.)
People who find that kind of thing interesting. I'm not sure what's confusing there. It is, to a lot of folks, fascinating and exciting stuff. You seem to be walking this weird line of saying it might, in theory, be fascinating stuff if it was just a little more fascinating in the way you preferWell, I do think Turing machines and whatnot can be interesting in and of themselves. But what I meant when I said "nothing interesting is going to happen in a 2D space" I was talking interesting in the context of creating actual self-duplicating life with evolution, competition, all that stuff. Maybe I could have explained that more but I didn't think the comment was that big of a deal.
0:d 8:b
1:d 7:b
2:d 6:b
3:b 5:d
4:s 4:sPass 1: count neighbours from the 8 adjacent cells in the same plane. Apply the usual B 3/S 2 3 ruleset.I think this should allow live cells to leak out of the existing pattern up and down into empty portions of the adjacent planes, but then run like the regular 2D rules once there is something there.
Pass 2: count neighbors from the 8 adjacent cells in the same plane plus the current cell itself. Only if this count is 0, count neighbors from the 18 cells in the 3x3 squares on the planes above and below the current plane. Apply the usual B 3/S 2 3 ruleset.
Pass 1 is run for the whole universe before pass 2, and results from pass 1 would be visible to pass 2.
Now let's say the plane immediately above this one has an identical but offset lattice (show with O's for possible cell locations):X X X X X X X X
Superimposing these in one diagram, where the X's are cells in one plane and the O's are cells in the plane above it, we get this:O O O O O O O O
If you then have the neighborhood consist of no cells on the same plane, but the 4 nearest cells on the planes above and below, you get this (with lines showing which cells are each others neighbors):O X O X X O X O O X O X X O X O
This shows each cell having 4 neighbors (even the edges if the co-ordinate system wraps around). Obviously the same thing is going on with the plane represented by X's and the plane underneath it, too, so that gives 8 neighbors.O-X-O-X | | | | X-O-X-O | | | | O-X-O-X | | | | X-O-X-O
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posted by Wolfdog at 1:17 PM on June 3, 2010 [1 favorite]