| Not GP but I feel your analysis here doesn't follow. > rather than being completely unaffected by S[n]? Is n here a discretization of time or a "meta-time" that captures state progression? It would be remarkable if the "next state" of the universe did not depend or was so correlated to the "current state" that symbolically we represent it as a dependency. A ball only rolls downhill because it was once uphill, after all - one of the few things that unites various models of the universe was the existence of causality. > If the former, then you are treating time as a primitive, whereas the representation or even existence of time can be part of state and vary over state changes, so this does not work. This is interesting but I feel reductive. the "nth" state is not the state at time n, but the state that follows n-1 - it is dimensionless, but one might express it in spacetime if that is convenient. Nothing suggests it is uniformly sampled or even computable. > completely independent from each other is indistinguishable from a multiverse with inaccessible sub-universes and should be called as such No idea what this implies, but in a non-deterministic state machine there are multiple S(n + 1) for any given S(n). > you are also assuming linearity and discreteness of state changes, whereas it could be a DAG or more complex structure. GP does not suggest evolve(S) is linear or discrete (they suggest either continuous or discrete, actually). Neither of these imply anything about topology so I'm not sure what that has to do with a DAG. State transitions can encapsulate arbitrary topologies (and vice versa). They are duals. > rather than a more chaotic or unstructured universe that behaves more like a disjoint set than an orderly structure I feel GP covers this base by mentioning that state transitions may not be deterministic. Just because a system is chaotic or unpredictable does not imply we cannot formulate the nature of its chaos or unpredictability symbolically. |