From: Vladimir Nesov (robotact@gmail.com)
Date: Wed Jan 23 2008 - 09:16:58 MST
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?
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).
> 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.
> 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?
> 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.
-- Vladimir Nesov mailto:robotact@gmail.com
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