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.
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:
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.
> 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....