> 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.

>From the viewpoint of my paper "Occam's Razor" paper, QM is not the
"true physics" of the universe. It is just that any observer is
unlikely to be able to distinguish the behaviour of er world from one
described by QM. That is the result of the last section of that paper. 

> 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.

I hadn't noticed until now that Wei Dai agrees with my argument in
Occam's razor...

> 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.

A rather poor choice of example - our universe appears to have a
violation of exactly this sort at its origin. But then, that is
required of the Anthropic Principle, otherwise we would be here to
argue about it :)

More seriously, any undergraduate will be able to demonstrate the
failure of conservation of energy. I did it several times - even at
high school. However, the reason this is not worthy of a Nobel prize
is that experimental error is a more likely explanation for the
experimental results, than that the conservation law broke down. It
would require a really massive violation of the magnitude of the
afore-mentioned dragon to convince the Nobel Prize committee...

Now of course, with more sophisticated experimental and statistical
techniques one can increase the sensitivity of the test by many
orders of magnitude (ie reduce the amount of extra information
required for a "magical" universe). Of course this can be done so far,
that the violating universe is no longer considered "magical". For
example, if some experimenter should show that mass/energy was violated on
the scale of 10^{-20} (lets say), then it is unlikely that people
would say the universe was not regular, and that science failed. The
researcher might get the Nobel prize, but that would probably be the
limit of the discovery's impact on the methodology of science.

Incidently, experiments were conducted in the 1980s to detect
violations of the baryon conservation no, which were expected to be of
the order of 10^{-32}/year. In the event, the violations were not
detected, ruling a particular class of GUT.

> 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.
> Hal

I would agree with you. Occam's razor is probabilistic in nature,
rather like the second law of thermodynamics. There is always the
possibility of violation.

Dr. Russell Standish                     Director
High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile)
UNSW SYDNEY 2052                         Fax   9385 6965, 0425 253119 (")
Australia                                [EMAIL PROTECTED]             
Room 2075, Red Centre                    http://parallel.hpc.unsw.edu.au/rks
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