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Plasmon comments on Causal Universes - LessWrong
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I haven't yet particularly seen anyone else point out that there is in fact a way to finitely Turing-compute a discrete universe with self-consistent Time-Turners in it. (In fact I hadn't yet thought of how to do it at the time I wrote Harry's panic attack in Ch. 14 of HPMOR, though a primary literary goal of that scene was to promise my readers that Harry would not turn out to be living in a computer simulation. I think there might have been an LW comment somewhere that put me on that track or maybe even outright suggested it, but I'm not sure.)
The requisite behavior of the Time Turner is known as Stable Time Loops on the wiki that will ruin your life, and known as the Novikov self-consistency principle to physicists discussing "closed timelike curve" solutions to General Relativity. Scott Aaronson showed that time loop logic collapses PSPACE to polynomial time.
I haven't yet seen anyone else point out that space and time look like a simple generalization of discrete causal graphs to continuous metrics of relatedness and determination, with c being the generalization of locality. This strikes me as important, so any precedent for it or pointer to related work would be much appreciated.
In computational physics, the notion of self-consistent solutions is ubiquitous. For example, the behaviour of charged particles depends on the electromagnetic fields, and the electromagnetic fields depend on the behaviour of charged particles, and there is no "preferred direction" in this interaction. Not surprisingly, much research has been done on methods of obtaining (approximations of) such self-consistent solutions, notably in plasma physics and quantum chemistry. just some examples.
It is true that these examples do not involve time travel, but I expect the mathematics to be quite similar, with the exception that these physics-based examples tend to have (should have) uniquely defined solutions.
Er, I was not claiming to have invented the notion of an equilibrium but thank you for pointing this out.
I didn't think you were claiming that, I was merely pointing out that the fact that self-consistent solutions can be calculated may not be that surprising.
The Novikov self-consistency principle has already been invented; the question was whether there was precedent for "You can actually compute consistent histories for discrete universes." Discrete, not continuous.
Yes, hence, "In computational physics", a branch of physics which necessarily deals with discrete approximations of "true" continuous physics. It seems really quite similar, I can even give actual examples of (somewhat exotic) algorithms where information from the future state is used to calculate the future state, very analogous to your description of a time-travelling game of life.