Wei writes: > If you think about it more, I think you'll realize that the greater number > of observer-moments observing flying rabbits or similar happenings can't > make up for the much smaller measure of each such observer-moment. > Unfortunately right now I can't find a way to easily articulate the > reasoning behind that conclusion.
Here is an example. Suppose we had a universe which was a CA system like Conway's Life game, but more complex. It still has a fairly simple program to represent its functions and so will have generally high measure. Now suppose we modify that program to be, "follow the normal rules except at position X, always set the cell to 0". This represents a "flying rabbit" universe, one which has relatively simple laws of physics but where there is an exception. If the universe is very large, then to specify X will take a large number of bits. Hence the flying rabbit universe program is much larger than the simple universe program, and its measure is much less. This is the explanation I accepted for why we are not in a flying rabbit universe. (I am assuming the universal distribution as a measure, where the measure of an n-bit minimal program is 2^(-n).) However if you consider all possible universes of this type, that is, all possible values of X, then there are 2^n of these if X is n bits long, exactly countering the loss in measure due to the size of X. The collection of this kind of flying rabbit universes has only modestly less measure than the simple universe. The only decrease is due to the size of the "except at position" and "set to 0" clauses, which might be only a few bits long. And this is only one possible kind of exceptional universe. If we consider the various other special-case exceptions to the normal rule then the collective measure of all of these will come even closer to the simple case. This suggests that the simplicity explanation against flying-rabbit universes is not strong, because the total collection of flying-rabbit universes is close in measure to the simple universe to which they rerpesent exceptions. That's the problem as I see it. Hal