Wei writes:
> If by flying-rabbit you mean any deviation from simplicity, then I agree
> with you.  Notice that our own universe is full of quantum randomness, but
> we don't see any pattern to the randomness. Similarly, an observer in a
> Conway's life universe may observe these anomolies that you described, but
> most observers would perceive them as random fluctuations rather than
> flying rabbits. 
> The universes where the deviations form patterns meaningful to their
> observers would collectively have a very small measure compared to the
> universes where the deviations are perceived as random, because in the
> former case the programs to generate the meaningful deviations would have
> to contain information about what kinds of deviations would be meaningful
> to the observers, and that would make them much longer than programs that
> simply generate random deviations.

Russell Standish sent me private mail referring to his article at
http://parallel.hpc.unsw.edu.au/rks/docs/occam/, where he made a similar
argument.  However I am not completely convinced.

Parenthetically, I don't see that the presence of quantum randomness
in our universe is relevant.  If we assume that many-worlds is the true
physics of our universe, then in fact our universe is deterministic and is
not full of quantum randomness.  Even if we do have quantum randomness,
that would not be like the situation I am describing, where you have a
universe which is almost entirely lawful and has some kind of extremely
rare exception.

I agree however that you (and Russell) are right that one would not
literally expect to see a flying rabbit or a materializing dragon.
The information content of such a manifestation would be large, and most
"miracles" which used a similar quantity of information would be random
in their effects, and probably unnoticeable.

Nevertheless I think there could be exceptions to the laws of nature which
have major, observable effects while being relatively concise to specify.
Going back to my CA example, in some CA worlds if you had a cell fixed
in the "1" state, that could have dramatic macroscopic effects.  It might
appear to be continually radiating the equivalent of energy, for example.
In such a situation, you might have conservation of energy throughout
the entire universe, except at this one location it would be violated.

The collection of all universes which have this kind of violation of the
laws of nature could, by my argument, have measure not much less than
that of a universe which had the simpler laws of physics which allowed
for no such violation.  Inhabitants of such a universe who have not yet
stumbled upon the magic location might think that their observations
give them reason to believe that the laws of physics hold everywhere.
But they are wrong.  There is a significant probability that violations
of this sort exist.  Occam's razor is not as sharp as they believe.


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