[I will assume that Brent meant to forward this to the list, his
mailer often seems to send replies only to me.]

Brent wrote:
> >-----Original Message-----
> >From: "Hal Finney" [mailto:[EMAIL PROTECTED]
> >Sent: Tuesday, May 10, 2005 5:06 AM
> >To: everything-list@eskimo.com
> >Subject: RE: FW: Everything Physical is Based on Consciousness
> >
> >
> >Brent Meeker writes:
> >> >>From: "Hal Finney" [mailto:[EMAIL PROTECTED]
> >> >Yes, I think it is enough that I have thought of the concept!  Or more
> >> >accurately, I think it is enough that the concept is thinkable-of.
> >>
> >> Why bother with the computer at all.  Since you're just conceptualizing the
> >> computer (it is actually going to do anything) and all the computer would 
> >> do
> >> would be to produce some other bit-string, given the input
> >bit-string; why not
> >> just think of all possible bit-strings. Isn't that what Bruno's UDA does -
> >> generate all possible bit strings.
> >>
> >> But since they only have to be "thinkable-of", it seems all this talk about
> >> bit-strings and computers is otiose.  The universe is
> >"thinkable-of", therefore
> >> it exists.
> >
> >Yes, I think that is true too.  But the bit strings, interpreted as
> >programs, are crucial for the whole theory to be able to make predictions.
> >
> >The idea is that the bit string is a compressed representation of the
> >universe.  Only universes which are lawful are compressible.
> >Hence,
> >lawful universes can be represented by small bit strings, which have
> >greater measure.
> >
> >You are right that our universe exists, as its literal, expansive,
> >redundant self; but it also exists in the form of the many different
> >programs that would generate it.  Only the shortest such programs make
> >a significant contribution to the measure, so the long-form, literal
> >representation of the universe doesn't even matter.
>
> But it's the idea of "representation" that bothers me.  I think representation
> is a trinary relation, Rxyz = x represents y to z; not a binary one.
> Also, to apply Chatian's idea of algorithmic compression requires that the
> universe be infinite - all finite sequences are equally compressible.

I'm not sure how to interpret the "z" in "x represents y to z".  If a
computer generates string y from string x, is the computer the z?

And as for Chaitin's algorithmic complexity, I am afraid that you have
it backward, that it does apply to finite strings.  I'm not even sure
how to begin to apply it to infinite strings.

For example, consider all 1,000,000-bit strings.  Only about 2^1,000
of them could be represented by a 1,000-bit program, since there are
only 2^1,000 such programs.  Most million-bit strings can't be created
by programs of substantially less than a million bits in size, because
there just aren't enough short programs.


> >Without the concept of bit strings and computers, we have no basis for
> >saying that more lawful universes have greater measure than random and
> >incompressible ones.  This would eliminate one of the great potential
> >strengths of the all-universe hypothesis (AUH), that it offers an
> >explanation for why we live in a lawful universe.
>
> Why not?  In the infinite sequence of all bit-strings there are more short
> strings than long ones.

So if we had only a simple, literal equivalence between bit strings and
universes, what would that mean, there are more small universes than
big ones?  That doesn't seem to be either a very useful or accurate
prediction.

Hal Finney

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