Pete Carlton writes: > Imagine a Life universe that contains, among other things, two SASes > talking to each other (and showing each other pictures, and in general > having a very lucid, conscious, conversation.) Imagine that instead of > being implemented on a computer, it's implemented by a large 2d array > of coins: heads represents "live", and tails represents "dead". Each > timestep, the coins are flipped over in concordance with the Life > rules. > Does this setup implement a universe?

Let's say it does. > If you say it does, how about the next step: > Instead of doing flipping operations on one set of coins, each new > generation is laid down in the proper configuration on top of the > preceding one with a new set of coins. Does this >process< of laying > down coins also implement a universe? Yes, it would seem that laying down coins isn't conceptually different from flipping them, from the point of view of performing a calculation. > If you say it does, then what about the stack itself? (One can imagine > pointing to each layer in succession, saying "This is the current > step", "Now this is the current step", etc..) Does the stack's bare > existence suffice for the implementation of a universe? The problem with this example is that you can't create the stacks without laying them down first. So there has definitely been an implementation during the lay-down phase. What you have to be asking is, in some sense, is the implementation still going on? This assumes a certain time-bound nature to the concept of implementation which may not be valid. You are assuming that the region of our universe where the implementation occurs can be bounded in time, and asking if the boundary only encloses the active lay-down phase, or also encloses the passive stack phase. You get the same problems if you try to describe the exact physical boundaries of the implementation in space. Does the implementation encompass the spaces between the coins, for example? Assuming you also need some small calculator to compute how to flip each coin (a simple lookup table for the 512 possibilities of 9 coins in a square), is that part of the implementation? What about the space between the coins and the calculator? Or perhaps the coins themselves don't have well-defined boundaries, etc. These questions suggest that it is difficult to consider "whether a particular implementation is going on" to be a yes-or-no question that can be asked at each point-event in space-time. So it may not be meaningful to ask whether the stack is also an implementation. Having said that, I'll give two contradictory answers: > If not, then can you say what it is about the active process of > flipping or laying down that "counts" as computation but does not count > when the stack is a static block? In the philosophical literature on implementation (a good jumping-off point is David Chalmers paper at http://www.u.arizona.edu/~chalmers/papers/rock.html) it is considered that a mere "trace" of a program execution does not count as an implementation, for two reasons: first, there are no causal connections between the layers, they're just sitting there; and second, the trace does not represent counterfactuals, i.e. if you were to change a cell's value, what would happen is not clear from the trace. > If you think the static block "counts" as the implementation of a > universe, then I think you can go all the way to abstract Platonism. > Because since the stack's just sitting there, why not knock it down? > Or melt it into a big ball? Or throw it into a black hole...the two > SASes won't care (will they?) On the other hand, if I apply what I have been calling the Wei Dai heuristic (about which I wrote a few messages in the past few days; BTW Wei suggested the idea but it's not necessarily something he advocates), I'd say that the presence of the stack does increase the measure of the simulated universe, because it increases the percentage of our universe's resources which are used by the simulation. More precisely, its presence would allow a shorter program to locate the implementation among all the vastness of our universe. However, in that case, knocking down or destroying the stack would eliminate this property; the stack would no longer contain the information which would allow shortening the program which would localize the implementation. Hal Finney