Feels like I may have brought a spoon to a gun fight, but I would have considered psychohistory to be the ultimate extrapolation of determinism, and the fact that the prime radiant is able to predict _which_ version of events will happen is because it (somehow) knows the state of the system.

Of course, to argue against myself, it would surely be based on layers of probabilities, and they say several times in the series that it can't predict low-level specific things, just high-level things. And perhaps the whole underlying question posed by the series is whether the universe really is deterministic. But anyway I don't think it's all off-base.

Did you intend to link to https://en.wikipedia.org/wiki/Deterministic_algorithm?

No, it is a reference to https://en.wikipedia.org/wiki/Laplace%27s_demon - Pierre Simon Laplace, A Philosophical Essay on Probabilities

(if you know the state of a system + all the rules then you can know the next state)

and determinism actually applies way beyond just algorithms.