Kory Heath, <[EMAIL PROTECTED]>, writes: > It is very likely that even Conway's Life universe has this feature. Its > rules are absurdly simple, and we know that it can contain self-replicating > structures, which would be capable of mutation, and therefore evolution. We > can specify very simple initial conditions from which self-replicating > structures would be overwhelmingly likely to appear, as long as the lattice > is big enough. (The binary digits of many easily-computable real numbers > would work.)
Yes, I see that that is true. I think it points to a problem with some of the simple conceptualizations of measure, about which I will say more below.But let me ask if you agree that considering Conway's 2D Life world with simply-specified initial conditions as in your example, that conscious life would be extraordinarily rare? I want to say, vastly more rare than in our universe, but of course we don't know how rare life actually is in our universe, so that may be a hard claim to justify. But the point is that our universe has stable structures; it has atoms of dozens of different varieties, which can form uncountable millions of stable molecules. It has mechanisms to generate varieties of these different molecules and collect them together in environments where they can react in interesting ways. We don't have a full picture of how life and consciousness evolved, but looking around, it doesn't seem like it should have been THAT hard, which is where the Fermi paradox comes from. In many ways, our universe seems tailor made for creating observers. In contrast, in the Life world there are no equivalents to atoms or molecules, no chemical reactions. It's too chaotic; there's not enough structure. Replicators and life seem to require a balance between chaos and stasis, and Life is far too dynamic. It just looks to me like it would be almost impossible for replicators to arise naturally. Almost impossible, but not absolutely impossible, so if you tried enough initial conditions as you suggest, it would happen. I won't belabor this argument unless you disagree about the ease with which life might arise in a Life universe, and consciousness evolve. And the main point is that these are exactly the kinds of considerations which Tegmark discusses. Issues of stability of the building blocks of life, of providing the right amounts and kinds of interactions. These physics-like considerations are precisely the correct issues to consider in looking at how easily observers will arise, and that is Tegmark's point. I haven't read Tegmark's paper in detail recently, and to the extent that his arguments are based on string theory or QM then I would agree that those are too parochial. But as I recall he had a number of broad arguments that would apply even to a Life-like universe. Now I'll get back to the question above about measure. There are universes, as in your example, where life is intrinsically unlikely, but if you make the universe large enough, and provide all possible initial conditions for finite-sized regions, then in all that vastness, somewhere life will exist. The problem is, this is not too different from separately implementing alternate, smaller versions of that universe, with different initial conditions for each, so that all possible initial conditions are tried in some universe. A small fraction of those universes will have life. To specify just one of the life-containing universes will typically take a lot of information, while specifying all of the universes takes less information. This is analogous to the even broader picture of the "universal dovetailer (UD)" program, the program that runs all programs (on all initial conditions). It's a very small program, yet it creates all possible universes. Even universes with incredibly complex laws of physics and initial conditions are created by this extremely small UD program. Does this mean that all universes have the same measure, and it is large, since this small program creates them? The answer has to be no. It's not enough to find a small program which generates a desired structure, somewhere in the vastness that it creates. Otherwise all integers would have the same complexity because they are all created by a simple counting program. Wei Dai once suggested a heuristic that the measure of a structure ought to have two components: the size of the program that creates it; and the size of a program which locates it in the output of the first program. By this argument, you could have a big program which output just the structure in question, which was then located by a trivial one; or you could have a small program which output the structure among a vastness, which then required a big program to locate it. Either way, the structure has a large measure. This was the motivation for the idea I proposed a few days ago, that for applying anthropic reasoning, a universe should get a "bonus" if it had a high density of observers, rather than merely a high absolute number of them. It's too easy to create universes with low-density observers, as your example of Life suggests. But just as the existence of a counting program does not give a typical integer a low complexity, so the existence of universes that are simple but contain super-rare life forms should not give those observers a high measure. Hal Finney
