I assumed bounded memory due to the limited amount of matter and energy
available to build the computer.  For instance I've seen it said that the
total information content of this universe is about 10^90 bits.  If a
civilization gathered all the mass and energy available in their universe to
build a computer, they could only accurately simulate universes with an
information content less than or equal to that of their host universe.

I am reminded of the thread you started titled "why can't we erase
information".  Which discussed anthropic reasons for why it appears
impossible to physically delete information.  Hal Finney mentioned on that
same thread that assuming many-worlds we can't create information either.
My argument would say that if our universes is simulated in a physical
universe with similair laws to our own (impossible to create or destroy
matter and energy) that could explain why we too cannot create or destroy
information.  Creating it in an unlimited manner would eventually use up the
finite memory of the computer simulating us.  By the same measure deleting
information would eventually use up all the useful energy that computer had
to run.

Of course for any of the above to be relavent assumes that simulated
observers have a high measure, which is possible.  For example David Deutsch
belives that "a universal quantum computer, capable of rendering any
physically possible environment, actually exists near the end of spacetime
in every universe and is maintained by sentient beings with the knowledge
required to increase its memory, computing cycles, and energy supply." (
http://en.wikipedia.org/wiki/David_Deutsch#The_Turing_principle )  My
addition would be that if such sentient beings cannot continue to increase
its memory and energy supply ad infinitum, they'll have to limit themselves
to certain types of simulations.


On 1/14/07, Wei Dai <[EMAIL PROTECTED]> wrote:

Jason wrote:
> If that is true then my underlying assumptions were flawed.  My
> argument assumed that a non-reversible universe could not be simulated
> by a computer with bounded memory and using only reversible
> computations.  The way I arrived at this assumption was imagining a
> non-reversible universe, such as the John Conway's game of life.  If
> the computer that implements this simulation has limited memory then in
> order for the simulation to continue forever, prior states cannot be
> saved in memory and instead old states would have to be overwritten.
> This destruction of information which cannot be undone would be
> logically irreversible as I understand it.  However if the simulation
> were one where each state has a 1 to 1 mapping, overwritting old states
> does not destroy them forever because previous states could always be
> computed from the current state.

Ok, I understand your argument more clearly now. But, why do you assume a
computer with bounded memory? Even with a finite amount of energy, we can
(theoretically) obtain unbounded memory by spreading it over an unbounded
volume of space. I'd guess that in practice this has approximately the
level of difficulty as achieving an unbounded number of computations from
finite amount of energy.


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