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From: Higgo James <james.higgo.domain.name.hidden>

Date: Mon, 25 Oct 1999 09:24:00 +0100

You are being a dualist when you talk of a turing machine and a program. The

difference is in our minds only. It is silly to talk of 'hard wireing'

aspects of the universe as opposed to having them in the software. This is

not a 'hole'.

*> -----Original Message-----
*

*> From: Christopher Maloney [SMTP:dude.domain.name.hidden]
*

*> Sent: Saturday, October 23, 1999 4:17 AM
*

*> To: everything-list
*

*> Subject: Re: Turing vs math
*

*>
*

*> 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
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*> > 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).
*

*>
*

*> This, combined with Bruno's computational indeterminism (thanks for
*

*> quoting your previous post Bruno -- I hadn't read that) provides the
*

*> basis for predictions of our future observations.
*

*>
*

*>
*

*> > You can try to say that this program doesn't count because it creates
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*> more
*

*> > than one universe, but as I suggested earlier this requires an objective
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*> > formulation. Which programs count and which ones don't? How can we
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*> > know whether a program creates a single universe or more than one?
*

*> > We need something more in the theory to solve this problem.
*

*>
*

*> I would be inclined to reject any theory that threw ad hoc
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*> rationalizations
*

*> for rejecting some universes and accepting others. The whole appeal of
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*> "everything exists" is its zero information.
*

*>
*

*>
*

*> > Another problem is that the Kolmogorov measure is defined only up to
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*> > an additive constant. Given a specific, large, program which runs on
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*> > universal TM "T", we can construct a different UTM T' on which that
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*> > program is very small. (In essence we hard-wire the program into the
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*> > T' definition.) This means that I can create a UTM where a magical
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*> > flying-rabbit universe is more probable than the one we live in.
*

*>
*

*> I agree that this is a hole, and it has bothered me (sort of in the
*

*> back of my mind) for some time. In Juergen's paper, he says
*

*>
*

*> Under different universal priors (based on different universal
*

*> machines), probabilities of a given string differ by no more
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*> than a constant factor independent of the string size, due to the
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*> compiler theorem (the constant factor corresponds to the
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*> probability of guessing a compiler). This justifies the name
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*> ``universal prior,'' also known as Solomonoff-Levin distribution.
*

*>
*

*> I don't know what this means exactly. It worries me that the
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*> probabilities are not completely well defined. It seems to me that
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*> Hal is correct that certain UTM's can be contrived to make certain
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*> bit strings very likely.
*

*>
*

*> We could borrow the section from Tegmark's paper on making
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*> predicitions, and apply it to this discussion.
*

*> I'll assume Bruno's computational indeterminism, and restrict the
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*> discussion to just two consecutive time steps in the computation.
*

*> We want to predict the probability of our seeing Y at time t1,
*

*> given that we now see X at time t0. As Bruno often points out, we
*

*> have no way of knowing exactly who we are or what bit strings we
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*> are represented by, but we do know that at time t0, we see X.
*

*>
*

*> Let Si be a bit string within a single time snapshot of a universe
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*> history. Let's also assume that it's possible, in principle, to
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*> evaluate Si to see if it qualifies as an observer, and if it observes
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*> X or Y.
*

*>
*

*> Then,
*

*>
*

*> P(Y,t1|X,t0) =
*

*> Sum j { Sum i { P(Y|Sj) P(Sj,t1|Si,t0) P(X|Si) } }
*

*>
*

*> In words, the probability that I'll see Y at t1, given that I see X
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*> at t0, equals the sum of all probabilities that Sj sees Y, that Sj is
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*> a computational continuation of Si, and that Si sees X.
*

*>
*

*> Now, being able to determine what a "bit string observes" depends,
*

*> of course, on the TM. The TM "breathes life" into the bit strings.
*

*> Also, the determination of the middle term depends on the TM.
*

*> I'm just thinking out loud, here, really, but it seems to me that
*

*> even a "constant" factor will throw this equation out of whack. We
*

*> should be able to show that this probability is independent of the
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*> TM.
*

*>
*

*>
*

*> > A related problem is the uncomputability of the Kolmogorov measure.
*

*> > There is no way in general to know what is the shortest program to
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*> > construct a given string or a given universe. Yet probabilities are
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*> > real and so apparently someone/something is in effect computing them.
*

*> > In other words, our observations of probability imply that uncomputable
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*> > values are being computed. This is at least a bit paradoxical.
*

*>
*

*> I don't see this as a problem, on the other hand. Just because
*

*> probabilities exist doesn't mean that anyone or anything is computing
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*> them.
*

*>
*

*>
*

*> >
*

*> > Hal
*

*>
*

*> --
*

*> Chris Maloney
*

*> http://www.chrismaloney.com
*

*>
*

*> "Donuts are so sweet and tasty."
*

*> -- Homer Simpson
*

Received on Mon Oct 25 1999 - 02:02:22 PDT

Date: Mon, 25 Oct 1999 09:24:00 +0100

You are being a dualist when you talk of a turing machine and a program. The

difference is in our minds only. It is silly to talk of 'hard wireing'

aspects of the universe as opposed to having them in the software. This is

not a 'hole'.

Received on Mon Oct 25 1999 - 02:02:22 PDT

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