[ExI] Which direction does the arrow of time point in Conway's Game of Life?

John Clark johnkclark at gmail.com
Sat Jan 4 15:15:23 UTC 2020

You don't have to invoke Quantum Mechanics or Relativity to figure out
there are some funny things about time. In our world we, perhaps naively,
believe the past exists and is knowable but the future doesn't exist in the
same concrete way and we can only speculate what it will be like, but that
may not be true everywhere. Conway's Game of Life has just a few very
simple rules that are 100% deterministic, so given the current state it's
easy to figure out what the next generation will be, and the generation
after that and so on for as far into the future as you'd like, however it
is not reversible. Given the present state there is no way to know what the
previous state was, you can rule out some states but because more than one
state could have produced the present one there is no way to know which one
actually did.

We also know that although ridiculously simple it's more than just a toy
universe because the fundamental laws of physics in Conway's universe allow
for the construction of a Universal Turing Machine; so at least in theory a
AI could exist that lived entirely in Conways world and operated according
to his simplified physics. To such a being the future would be certain and
hold no mystery but the past could only be speculated about. To such a
being would the arrow of time point in the opposite direction from the way
we see it? I can't see why it wouldn't.

John K Clark
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