# Re: why can't we erase information?

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Le 11-avr.-06, à 01:11, Wei Dai a écrit :```
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>
> 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
>
> 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.

Except that I done understand what you mean by "our universe", due to
the 1/3 person pov distinction. Adding that ourselves are the result of
a long (deep) computations could help here (cf Bennett's work on
computational depth), but will be enough only if you allow the result
of the deep computation to remains stable on some dovetailing on the
reals, to explain away the first person rabbits!

>
> 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.

To my knowledge, Hao Wang (a expert on Godel) has been the first to
program a universal turing machine which never erase its tape. Much
work has been done (cf Toffoli). Abramski has written a compiler
transforming irreversible programs into reversible one.
In term of combinators, a quantum world lacks Kestrels (capable of
eliminating information) and Warbler or Starling or any combinators
capable of duplicating information. I explain this in my last paper
(the one which is not yet on my web page).

> 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...

Certainly. Note that a kripke multiverse with a symmetric accessibility
relation (good for reversibility), needs to obey to the modal law LASE:
p -> BDp. I got it with the interview of the lobian machine but only
for the atomic p. This means that true irreversibility is still an open
problem with comp, but there is some evidence at the bottom.

Apparently information, at the bottom, cannot be created, cannot be
erased, and cannot in general be duplicated. Quite unlike classical
bits. But with comp this is just due to our ignorance about the
infinite set of computations which emulate us. I think it is the same
with Everett, information is never lost at the bottom, but when we
measure bottom states, we entangle ourselves with all possible
alternative results and the information "dissipates" through parallel
histories. The increase of entropy could be a local and a first person
(plural) phenomenon.

Bruno

http://iridia.ulb.ac.be/~marchal/

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