Hal Finney has provided some intriguing notions and possibly some very useful explanations. But I would like help in clarifying even the first several paragraphs, in order to maximize my investment in the remainder.

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But first a few comments; these may be premature, but if so, the comments should be ignored. > Some time back Lee Corbin posed the question of which was more > fundamental: observer-moments or universes? I would say, with more > thought, that observer-moments are more fundamental in terms of explaining > the subjective appearance of what we see, and what we can expect. But in general, what do observer-moments explain? Or what does the hypothesis concerning them explain? I just don't get a good feel that there are any "higher level" phenomena which might be reduced to observer-moments (I am still very skeptical that all of physics or math or something could be reduced to them---but if that is what is meant, I stand corrected). Rather, it always seems like a number of (other) people are trying to explain observer-moments as arising from the activity of a Universal Dovetailer, or a Platonic ensemble of bit strings, or something. > An observer-moment is really all we have as our primary experience of > the world. The world around us may be fake; we may be in the Matrix or > a brain in a vat. Even our memories may be fake. But the fact that we > are having particular experiences at a particular moment cannot be faked. Nothing could be truer. > But the universe is fundamental, in my view, in terms of the ontology, > the physical reality of the world. Universes create and contain observers > who experience observer-moments. This is the Schmidhuber/Tegmark model... Yes, but now arises my need for clarification: > In terms of measure, Schmidhuber (and possibly Tegmark) provides a means > to estimate the measure of a universe. Consider the fraction of all bit > strings that create that universe as its measure. I think that perhaps I know exactly what is meant; but I'm unwilling to take the chance. Let's say that we have a universe U, and now we want to find its measure (its share of the mega-multi-Everything resources). So, as you write, we consider all the bit strings that create U. Let's say for concreteness that only five bit strings "really exist" in some deep sense: 010101110100101010011101010110001010110101... 101101110100010101111111001011010110100101... 001010100111010100111010001001000010101111... 11011101000100100001010l110110000101010011... 110010111010101110100010000101001010011111... and then it just so happens that only 2 out of these five actually make the universe U manifest. That is, in the innards of 2 of these, one finds all the structures that U contains. Am I following so far? > In practice this is roughly 1/2^n where n is the size of the > shortest program that outputs that universe. So each of these universes (each of the five, in my toy example) has a certain Kolmogorov complexity? Each of the five can be output by some program? But is that program infinite or finite? Argument for finite: normally we want to speak of *short* programs and so that seems to indicate the program has a limited size. Argument for infinite: dramatically *few* bit strings that are infinite in length have just a finite amount of information. Our infinite level-one Tegmark universe, for example, probably is tiled by Hubble volumes in a non-repeating irregular way so that no program could output it. Thanks, Lee > The Tegmark model may allow for similar reasoning, > applied to mathematical structures rather than computer programs. > > Now, how to get from universe measure to observer-moment (OM) measure? > This is what I want to write about....