RE: Turing vs math

From: Higgo James <>
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.


> -----Original Message-----
> From: []
> Sent: Monday, October 25, 1999 9:15 AM
> To:
> 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
> more
> > than one universe,
> Exactly.
> > but as I suggested earlier this requires an objective
> > formulation.
> There is one. The info content of a computable object such as a
> particular universe is the size of the shortest program that computes
> 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
> mean much though, because the interpreter that singles out any a single
> universe (and represents it as, say, a movie) requires additional
> information that may not be neglected. For example, the interpreter
> may identify n bits of universe U somewhere in the output. But this will
> cost additional bits beyond those in the original Pi-computing algorithm.
> To avoid such issues, bitstrings are represented by themselves; we do
> not have to worry about additional interpreter algorithms - they are
> already implicit in the original list of all possible programs.
> >Another problem is that the Kolmogorov measure is defined only up to
> >an additive constant. Given a specific, large, program which runs on
> >universal TM "T", we can construct a different UTM T' on which that
> >program is very small. (In essence we hard-wire the program into the
> >T' definition.) This means that I can create a UTM where a magical
> >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
> of almost all possible universes will have almost the same size as the
> 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
> cannot bend the rule.
> Chris:
> >....But my
> >argument still stands that the UTM is a very specific (sequence-based)
> way
> >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
> >way.)
> The point is that each UTM can simulate any other device for describing
> 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
> > it creates "everything" from zero information (or as near as dammit).
> But if you want to make predictions about the future of particular
> universes that's not enough. Bayes' rule for making predictions requires
> a prior on particular universes. "Prior" always means "prior for Bayes".
> You have observed the past of a given universe, what's the probability
> 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
> universal prior prefers complete universes "past+future" whose shortest
> algorithms are short. Since the shortest algorithm describing the past
> 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
> 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
> 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
Received on Mon Oct 25 1999 - 02:31:02 PDT

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