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
Received on Mon Oct 25 1999 - 02:11:47 PDT
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