From: Vladimir Nesov (robotact@gmail.com)
Date: Thu Jan 24 2008 - 15:00:43 MST
On Jan 24, 2008 11:56 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
>
> Our model of the world is one which assigns nonzero probability to all
> possible observations. One could conceive of a universe where this did not
> hold; that we could model certain events to occur with probability 0 or 1, in
> the same sense that some mathematical statements are absolutely true or false.
> If we could (correctly) model all observations with certainty, it would be
> proof that the universe is not simulated by a Turing machine. In such a
> universe, learning by induction would be suboptimal.
But how would you know that this is the case? Even if you find a law
that seemingly works all the time, you would still have finite
confidence in it keeping on, although this confidence will only grow
with time, to astronomically huge values.
Even mathematics works only as long as computers or brains that carry
it out don't fail. If they do, math also stops working. This one is a
highly counterintuitive point, Eliezer tried to communicate it couple
of times at Overcoming Bias, and most of commenters don't get it (I
think it needs better elaboration). It took me some time since his
first post to figure it out for myself independently. If you copy a
file to 1000 computers, it doesn't disappear when some of them fail,
but it does disappear when all of them fail.
> The question is whether an observer (a computer) in a universe can model
> (predict) the universe (including itself) exactly. If the universe is
> simulated by a Turing machine, then it is not possible. A Turing machine
> state can be described by a map: N -> {0,1}. There may be more powerful
> machines that can model themselves in this sense, for example, R -> {0,1}, N
> -> R, R -> R, (R -> R) -> R, etc. But because we lack non probabilistic
> models of the universe, there is no evidence that anything more powerful than
> a Turing machine is required.
>
You didn't describe a model. Anyway, if the goal is to simulate
yourself, you can destroy the rest of the universe (so that you'll
become the only object in the universe), and you'll have enough
computational resources to simulate this small blob of matter. What
poses a problem here?
-- Vladimir Nesov mailto:robotact@gmail.com
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