**From:** Matt Mahoney (*matmahoney@yahoo.com*)

**Date:** Fri Jan 25 2008 - 08:20:58 MST

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--- Vladimir Nesov <robotact@gmail.com> wrote:

*> On Jan 24, 2008 11:56 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
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*> >
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*> > Our model of the world is one which assigns nonzero probability to all
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*> > possible observations. One could conceive of a universe where this did
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*> not
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*> > hold; that we could model certain events to occur with probability 0 or 1,
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*> in
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*> > the same sense that some mathematical statements are absolutely true or
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*> false.
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*> > If we could (correctly) model all observations with certainty, it would
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*> be
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*> > proof that the universe is not simulated by a Turing machine. In such a
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*> > universe, learning by induction would be suboptimal.
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*>
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*> But how would you know that this is the case? Even if you find a law
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*> that seemingly works all the time, you would still have finite
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*> confidence in it keeping on, although this confidence will only grow
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*> with time, to astronomically huge values.
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*>
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*> Even mathematics works only as long as computers or brains that carry
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*> it out don't fail. If they do, math also stops working. This one is a
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*> highly counterintuitive point, Eliezer tried to communicate it couple
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*> of times at Overcoming Bias, and most of commenters don't get it (I
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*> think it needs better elaboration). It took me some time since his
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*> first post to figure it out for myself independently. If you copy a
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*> file to 1000 computers, it doesn't disappear when some of them fail,
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*> but it does disappear when all of them fail.
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What I mean is, if we lived in a universe where certain things worked

perfectly, including our model of it, then that universe would not be Turing

computable. It is hard to imagine such a universe because we don't live in

one. The fact that we can't imagine it (because a perfect model is

impossible) is evidence that the universe is Turing computable.

*> > The question is whether an observer (a computer) in a universe can model
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*> > (predict) the universe (including itself) exactly. If the universe is
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*> > simulated by a Turing machine, then it is not possible. A Turing machine
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*> > state can be described by a map: N -> {0,1}. There may be more powerful
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*> > machines that can model themselves in this sense, for example, R -> {0,1},
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*> N
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*> > -> R, R -> R, (R -> R) -> R, etc. But because we lack non probabilistic
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*> > models of the universe, there is no evidence that anything more powerful
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*> than
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*> > a Turing machine is required.
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*> >
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*>
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*> You didn't describe a model. Anyway, if the goal is to simulate
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*> yourself, you can destroy the rest of the universe (so that you'll
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*> become the only object in the universe), and you'll have enough
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*> computational resources to simulate this small blob of matter. What
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*> poses a problem here?
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A whole universe simulating itself isn't really a simulation. But yes, I did

not fully describe a model, which would include operations on real numbers or

real valued functions, possibly in discrete or continuous time. There are

many such models. In some of them, it is possible for a universe to model

itself exactly. A simple example would be a fractal where each region of

space is a scaled down copy of a larger region containing it. Perfect

fractals are not Turing computable, and do not exist in our universe.

-- Matt Mahoney, matmahoney@yahoo.com

**Next message:**Matt Mahoney: "Re: Evidence that the universe is simulated"**Previous message:**Rolf Nelson: "Investing in FAI research: now vs. later"**In reply to:**Vladimir Nesov: "Re: Evidence that the universe is simulated"**Next in thread:**Vladimir Nesov: "Re: Evidence that the universe is simulated"**Reply:**Vladimir Nesov: "Re: Evidence that the universe is simulated"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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