From: Matt Mahoney (matmahoney@yahoo.com)
Date: Wed Jan 23 2008 - 13:52:07 MST
--- Vladimir Nesov <robotact@gmail.com> wrote:
> Matt,
>
> I'll repeat my remark about simulaion arguments in this thread then:
> what exactly does it mean for inhabitants of a world to live in a
> simulation? Simulatedness is not directly observable, only miracles
> are. Question of whether world is simulated is only relevant for
> finding out if miracles can happen.
>
> I comment on your points below.
>
> On Jan 23, 2008 6:03 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> > Evidence (not proof) that the universe is simulated by a finite state
> machine
> > or Turing machine.
> >
> > 1. The universe lacks uncomputable phenomena, such as real-valued states
> or
> > infinite memory computers such as Turing machines. We lack a non
> > probabilistic model of physics (quantum mechanics). In a finite state
> machine
> > simulation, a deterministic model would not be possible because the
> machine
> > could not simulate itself.
>
> If universe had 'uncomputable phenomena', how would you know? How
> would you test for presence of such things? Or equivalently, what does
> it mean for uncomputable phenomena to be present in reality?
An example of uncomputable phenomena would be something like classical
mechanics, in which the outcome of an experiment requires knowledge of the
position and velocity of particles with infinite precision.
> Finite state machine can perfectly well simulate itself, in any
> natural interpretation that comes to mind (you'd have to additionally
> define what it means for this formal construct to have a simulation of
> something).
A finite state machine with n states cannot model a machine with more than n
states.
> > 2. The universe has finite entropy. It has finite age T, finite size
> limited
> > by the speed of light c, finite mass limited by G, and finite resolution
> > limited by Planck's constant h. Its quantum state can be described in
> roughly
> > (c^5)(T^2)/hG ~ 2^404.6 ~ 10^122 bits. (By coincidence, if the universe
> is
> > divided into 10^122 parts, then one bit is the size of the smallest stable
> > particle, even though T, c, h, and G do not depend on the properties of
> any
> > particles).
>
> So? If anything, it supports knowability of universe, a counterpart of
> it being simulated from complex unobservable environment.
Yes, that is my point.
> > 3. Occam's Razor is observed in practice. It is predicted by AIXI if the
> > universe has a computable probability distribution.
>
> If you could please finally define what you mean by that. Occam's
> razor rule corresponds to good choice of notation/representation,
> which is usually picked to be compressible given distribution of
> described domain. What plays a role of notation in your argument, and
> why does its choice signify anything else?
Hutter proved that the optimal behavior of a reward seeking agent in an
unknown environment simulated by a pair of interacting Turing machines is to
guess at each step that the environment is simulated by the shortest program
consistent with observation so far. Occam's Razor is an example of this
strategy. The proof is valid only for the case where the environment has a
computable probability distribution. Of course this is not a proof that the
environment is simulated, but if Occam's Razor did not work in practice, it
would be strong evidence that the universe is not simulated.
> > 4. The simplest algorithm (and by AIXI, the most likely) for modeling the
> > universe is to enumerate all Turing machines until a universe supporting
> > intelligent life is found. The most efficient way to execute this
> algorithm
> > is to run each machine with complexity n for 2^n steps. We observe that
> the
> > complexity of physics (the free parameters in the Standard Model or most
> > string theories, plus general relativity) is on the order of n = a few
> > hundred bits, which is the log of its entropy.
>
> Complexity is mostly in random content, so I don't see how you move
> from simulation of universe of given complexity to complexity of
> physical laws. Physical laws make up a tiniest part of complexity of
> the world.
The fastest way to find a universe supporting intelligent life is run the k'th
universe for k steps. I claim that for our universe, k ~ 10^122.
-- Matt Mahoney, matmahoney@yahoo.com
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