the fact that both are Turing complete means that, whatever the rules governing the interactions are, for every possible computation there is (at least) a state of the world that performs that computation
Certainly, for an infinite board. But a 3->3->3 board is infinitely smaller than that. What is in question is what portion of universe such as ours can be simulated on such a board...however:
none of these matter
I now agree—with a caveat that one allows arbitrarily long time for the simulation. My earlier remarks were based on an implicit assumption that the computation time for the 2D machine simulating a 3D machine stays constant as the 3D machine size grows.
Certainly, for an infinite board. But a 3->3->3 board is infinitely smaller than that. What is in question is what portion of universe such as ours can be simulated on such a board...however:
I now agree—with a caveat that one allows arbitrarily long time for the simulation. My earlier remarks were based on an implicit assumption that the computation time for the 2D machine simulating a 3D machine stays constant as the 3D machine size grows.