Hal, the simple counter to what you just said is that when we speak of
"white-rabbit" universes, we don't actually mean just the universe
that has a flying white rabbit, we mean the whole host of other
universes that are indistinguishable from our own, except in one
observable facet - eg flying white rabbit, or a dragon, or
whatever. It takes a more subtle argument (based on finiteness of the
set of mental concepts) to show that this latter set of universes
still do not dominate the lawlike ones.
Have your read Alistair Malcolm's web page? I thought he explained it
quite well.
Cheers
-
>
> The most fundamental point in this discussion, which you seem to be
> overlooking, is that a flying rabbit is infinitely more complex than an
> infinite ensemble of all possible universes. Re-read Tegmark. Obviously the
> UD creates ALL multiple universes, hence Kolmogorov complexity is mimimised,
> perhaps to one bit of information. A flying-rabbit-only-universe requires a
> long program, as you will dicover if you try to simulate one on your PC.
>
> > -----Original Message-----
> > From: hal.domain.name.hidden [SMTP:hal.domain.name.hidden.org]
> > Sent: Monday, October 25, 1999 2:42 AM
> > To: dude.domain.name.hidden; everything-list.domain.name.hidden.com
> > Subject: Re: Turing vs math
> >
> > Christopher Maloney, <dude.domain.name.hidden>, writes:
> > > hal.domain.name.hidden wrote:
> > > >
> > > > Juergen Schmidhuber, juergen.domain.name.hidden, writes, quoting Hal:
> > > > > > I do think that this argument has some problems, but it is
> > appealing and
> > > > > > if the holes can be filled it seems to offer an answer to the
> > question.
> > > > > > What do you think?
> > > > >
> > > > > Where exactly are the holes?
> > > >
> > > > One is what I mentioned earlier, that a trivial program which
> > enumerates
> > > > and executes (in dovetailing, interleaved form) all possible programs
> > > > will create every mind in every possible situation. This is a very
> > > > short program and hence is the most likely universe for us to live in.
> > >
> > > I don't see this as a hole at all. Maybe I'm missing something, but I
> > > thought the whole point of postulating a universal dovetailer was that
> > > it creates "everything" from zero information (or as near as dammit).
> >
> > To see that it is a hole, you have to know what the argument is that it
> > is a hole in!
> >
> > The argument attempts to explain why we don't see flying rabbits or
> > other magical exceptions to the natural and simple laws of physics.
> > The reason, according to this argument, is that universes with simple
> > laws of physics can be described (simulated) with a shorter program
> > than universes which have complicated laws of physics with all kinds of
> > exceptions like magical flying rabbits. The argument further assumes that
> > universes exist with greater probability the shorter their program is.
> > Since flying-rabbit universes have larger programs than non-flying-rabbit
> > ones, they are therefore of lower probability. Hence we are unlikely
> > to be living in a flying-rabbit universe.
> >
> > That is the argument. The hole is that it does not work if we consider
> > one of the shortest possible universe programs, the universal dovetailer
> > (UD). This simple program creates, as part of its output, flying rabbits.
> > Yet it is an incredibly simple program, hence it is very high probability.
> > In fact, it is very likely that we do live in the universe created by
> > this program, and since that universe has flying rabbits in it we have
> > failed to explain why we don't see flying rabbits.
> >
> > To resolve this, we have to do one of two things, as I see it. We can
> > disallow the UD as a legal "universe" simulator, by saying that it doesn't
> > really create one universe, it creates multiple ones. And if we do that,
> > we can then restrict our attention to programs which create only single
> > universes, and then indeed we find that flying-rabbit universes are less
> > probable than others.
> >
> > However to take this step we need an objective basis for doing so.
> > We could say that "one universe" is identified with a single spacetime
> > manifold, or is some kind of structure that has a certain amount of
> > connectivity and continuity. Since the UD creates multiple independent
> > structures with no connection to each other, we could argue that it
> > objectively creates multiple universes. However this adds considerable
> > baggage to the theory.
> >
> > The other possibility, which was proposed by Wei Dai and is the one
> > which makes sense to me, is to state that the probability of an event
> > or structure is not just a matter of how probable the universe is which
> > creates it.
> >
> > Rather, you have to look at how easy it is to localize that particular
> > structure within the universe. A simple program which outputs an enormous
> > universe which has, buried in one tiny place, a copy of my mind, should
> > not count for much. A more complex program which outputs a smaller
> > universe in which my mind is a proportionately bigger piece might actually
> > contribute more, even though the program to create the universe is larger.
> >
> > Hence, the solution is to say that the contribution to the probability of
> > structure A in universe X is the size of the program to create universe X,
> > plus the size of the program which, given universe X, outputs structure A.
> >
> > There is a very strong precedent for this in Kolmogorov complexity.
> > We say that the complexity of a string is the size of the smallest program
> > which outputs (only) that string. We could write a trivial counting
> > program to output all strings, but that doesn't mean each such string
> > has a small complexity. If you have two programs, one which outputs many
> > strings, and the other which takes that output and selects some particular
> > substring for output, then the sum of the sizes of those two programs
> > represents the total size of the program to output that substring. It
> > is this total size which is used to calculate K. complexity.
> >
> > This is exactly what Wei proposes to do for measuring probabilites in
> > the context of the multiple universes. It is not enough to know the
> > probability of a universe which includes the desired structure (my mind,
> > say) somewhere; you also need to add in a measure of how hard it is to
> > localize that structure within that universe.
> >
> > This plugs the hole in the argument above, because even though the UD
> > outputs a flying-rabbit universe, localizing that universe within the UD
> > output is going to take at least as large a program as one which creates
> > it in the first place. Hence the net contribution of the UD to the
> > probability of any given structure is no larger than for a straightforward
> > program which implements that structure. The hole is thereby plugged.
> >
> > Hal
>
>
----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Mon Oct 25 1999 - 17:30:45 PDT