From: Matt Mahoney (matmahoney@yahoo.com)
Date: Wed Jan 23 2008 - 08:03:34 MST
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.
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).
3. Occam's Razor is observed in practice. It is predicted by AIXI if the
universe has a computable probability distribution.
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.
If any of these 4 facts did not hold, we would have proof that the universe is
not simulated by a Turing machine. (It could still be simulated by a more
powerful machine, such as a computer with real valued registers). However, we
cannot prove the opposite.
-- Matt Mahoney, matmahoney@yahoo.com
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