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

Date: Mon, 25 Oct 1999 10:03:35 +0100

Juergen says:

"There are many complex universes that start like ours and

then become very irregular. But U predicts ours won't. And every new

day brings a new confirmation."

But 'this very universe' will indeed become very irregular in most branches

- we just dont experience them because of WAP. You 'die' billions of times

every microsecond.

James

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

*> From: juergen.domain.name.hidden [SMTP:juergen.domain.name.hidden.ch]
*

*> Sent: Monday, October 25, 1999 9:15 AM
*

*> To: everything-list.domain.name.hidden
*

*> Subject: Re: Turing vs math
*

*>
*

*>
*

*> You guys are too fast for me! Let me try to answer to earlier messages.
*

*>
*

*> Hal:
*

*>
*

*> > 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.
*

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

*> > than one universe,
*

*>
*

*> Exactly.
*

*>
*

*> > but as I suggested earlier this requires an objective
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*> > formulation.
*

*>
*

*> There is one. The info content of a computable object such as a
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*> particular universe is the size of the shortest program that computes
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*> it and nothing else.
*

*>
*

*> > Which programs count and which ones don't?
*

*>
*

*> Those that compute your universe AND NOTHING ELSE.
*

*>
*

*> > How can we know whether a program creates a single universe or more
*

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

*>
*

*> No, everything is already in place. It's basic ingredients of Kolmogorov
*

*> complexity theory. Of course there are many UTMs whose output can be
*

*> interpreted as several different universes. E.g., the infinite computation
*

*> of Pi produces all beginnings of all universes as a side-product, because
*

*> every bitstring occurs somewhere in Pi's dyadic expansion. This doesn't
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*> mean much though, because the interpreter that singles out any a single
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*> universe (and represents it as, say, a movie) requires additional
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*> information that may not be neglected. For example, the interpreter
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*> may identify n bits of universe U somewhere in the output. But this will
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*> cost additional bits beyond those in the original Pi-computing algorithm.
*

*>
*

*> To avoid such issues, bitstrings are represented by themselves; we do
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*> not have to worry about additional interpreter algorithms - they are
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*> already implicit in the original list of all possible programs.
*

*>
*

*> >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.
*

*>
*

*> Sure, you can build a UTM with millions of states (as opposed to the 10
*

*> states or so necessary for the smallest UTMs) to encode flying rabbits.
*

*> Even on the flying rabbit machine, however, the shortest algorithms
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*> of almost all possible universes will have almost the same size as the
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*> corresponding algorithms on any other UTM. That's what the invariance
*

*> theorem is about: you can create a few exceptions to the rule, but you
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*> cannot bend the rule.
*

*>
*

*>
*

*> Chris:
*

*>
*

*> >....But my
*

*> >argument still stands that the UTM is a very specific (sequence-based)
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*> way
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*> >of mapping from one n-tuple (ordered list) to another (m-tuple; m>>n),
*

*> and
*

*> >so could not be considered to provide a reliable universal measure this
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*> >way.)
*

*>
*

*> The point is that each UTM can simulate any other device for describing
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*> universes with constant costs independent of the size of the universes.
*

*>
*

*> > 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
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*> > it creates "everything" from zero information (or as near as dammit).
*

*>
*

*> But if you want to make predictions about the future of particular
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*> universes that's not enough. Bayes' rule for making predictions requires
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*> a prior on particular universes. "Prior" always means "prior for Bayes".
*

*> You have observed the past of a given universe, what's the probability
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*> distribution on the possible futures?
*

*>
*

*> P(past + future | past) =
*

*> P(past | past + future) * P(past + future) / P (past)
*

*>
*

*> The first factor is 1. P(past) is a normalizing constant. The entire thing
*

*> is proportional to P(past + future). That's where you need the prior. The
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*> universal prior prefers complete universes "past+future" whose shortest
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*> algorithms are short. Since the shortest algorithm describing the past
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*> of our own particular universe seems pretty short I can write in the 1997
*

*> paper: "...there will be less than maximal randomness in our future, and
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*> more than vanishing predictability. We may hope that our universe will
*

*> remain regular, as opposed to drifting off into irregularity."
*

*>
*

*> Note that the anthropic principle by itself is not enough to make such
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*> predictions. There are many complex universes that start like ours and
*

*> then become very irregular. But U predicts ours won't. And every new
*

*> day brings a new confirmation.
*

*>
*

*> All of this is essentially just the old theory of inductive inference
*

*> applied to the possible universes. I cannot really see major
*

*> conceptual problems here.
*

*>
*

*>
*

*> Juergen
*

*>
*

*>
*

*> Juergen Schmidhuber www.idsia.ch
*

Received on Mon Oct 25 1999 - 02:31:02 PDT

Date: Mon, 25 Oct 1999 10:03:35 +0100

Juergen says:

"There are many complex universes that start like ours and

then become very irregular. But U predicts ours won't. And every new

day brings a new confirmation."

But 'this very universe' will indeed become very irregular in most branches

- we just dont experience them because of WAP. You 'die' billions of times

every microsecond.

James

Received on Mon Oct 25 1999 - 02:31:02 PDT

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