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From: Lee Corbin <lcorbin.domain.name.hidden>

Date: Sat, 4 Jun 2005 17:52:26 -0700

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:

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....
*

Received on Sat Jun 04 2005 - 20:57:29 PDT

Date: Sat, 4 Jun 2005 17:52:26 -0700

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.

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.

Nothing could be truer.

Yes, but now arises my need for clarification:

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?

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

Received on Sat Jun 04 2005 - 20:57:29 PDT

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