>From: "Wei Dai" <[EMAIL PROTECTED]>
>Reply-To: everything-list@googlegroups.com
>To: <everything-list@googlegroups.com>
>Subject: Re: why can't we erase information?
>Date: Mon, 10 Apr 2006 16:11:28 -0700
>
>
>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...

I have a vague memory that there was some result showing the algorithmic 
complexity of a string shouldn't depend too strongly on the details of the 
Turing machine--that it would only differ by some constant amount for any 
two different machines, maybe? Does this ring a bell with anyone?

Jesse



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