Jesse Mazer wrote:
> As for the question of why we live in a universe that apparently has this
> property, I don't think there's an anthropic explanation for it, I'd see 
> it
> as part of the larger question of why we live in a universe whose
> fundamental laws seem to be so elegant and posess so many symmetries, one 
> of
> which is time-symmetry (or to be more accurate, CPT-symmetry, which means
> the laws of physics are unchanged if you switch particles with 
> antiparticles
> and flip the 'parity' along with reversing which direction of time is
> labeled 'the future' and which is labeled 'the past'). Some TOEs that have
> been bandied about here say that we should expect to live in a universe
> whose laws are very compressible, so maybe this would be one possible way 
> of
> answering the question.

Let me be more explicit about the point I was trying to make. Most of the 
TOEs that try to explain why our laws are so elegant (for example 
Schmidhuber's) do so by assuming that all possible computations exist, with 
our universe being in some sense a random selection among all possible 
computations. Elegant universes with simple laws have high algorithmic 
probability (i.e., high probability of being produced by a random program), 
thus explaining why we live in one.

The problem I was trying to point out with this approach is that the 
standard Turing machine we usually use to define computations is not 
reversible, meaning it includes instructions such as "set the current tape 
location to 0 (regardless of what's currently on it)" that erase 
information. Most programs that we (human beings) write use these kinds of 
instructions all the time, and thus are not reversible. A random program on 
such a machine could only avoid irreversibility by chance. But our universe 
apparently does avoid them, so this observation seems to require further 
explanation under this kind of approach.

Of course we can use a reversible Turing machine, or a quantum computer 
(which is also inherently reversible), to define algorithmic probability, in 
which case we would expect a random program to be reversible. But that seems 
like cheating...

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