Wei Dai wrote:
Jason, I think there may be some incorrect assumptions behind your argument.
Let me state the facts as I understand them and you can check them against
your assumptions or correct me if I'm wrong.
The only reason we need reversible computation to do an infinite number of
computations is that physics is reversible. If we had irreversible physics,
then we would be able to do an infinite number of computations with
irreversible computations.Also, "reversible" and "irreversible" computation
refers to the method of implementing the computation, not the content of the
computation. Reversible computation can be used to simulate an irreversible
universe, and vice versa.
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.
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