From: Matt Mahoney (matmahoney@yahoo.com)
Date: Thu Jan 24 2008 - 13:56:39 MST
--- Vladimir Nesov <robotact@gmail.com> wrote:
> On Jan 24, 2008 7:57 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> > We could have laws of physics that allow us to make exact predictions.
> The
> > existence of any such law would prove that the universe is not simulated.
> >
>
> By problem of induction you can't have absolute certainty even if you
> have such law, so again it doesn't make a test. If degree of certainty
> that your computer won't suddenly turn into a fire-breathing dragon
> isn't good enough, what is?
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.
> > I mean that if there is a program on A that can simulate any program on B,
> > then there is no program on B that could simulate this program on A. I
> could
> > make a similar argument about Turing machines, replacing the number of
> states
> > with algorithmic complexity. In either case, it means you cannot build a
> > computer that could run an exact simulation of the universe (including
> your
> > computer), unless the universe is not computable by a Turing machine.
>
> Okay. But you say that question is if machine can simulate itself, so
> it's not an arbitrary machine already.
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.
-- Matt Mahoney, matmahoney@yahoo.com
This archive was generated by hypermail 2.1.5 : Wed Jul 17 2013 - 04:01:01 MDT