Question
Is psychohistory possible? Is it possible and useful to mathematically formalize human behavior on large scales to probabilistically predict the future?
Answer
I very strongly doubt it. The math involved in long-range predictive models simply doesn't work that way.
Asimov wrote the books before the chaos theory field took off and the full nature of sensitive dependence on initial conditions was properly understood (this stuff was sort of vaguely known all the way back to Poincare, but until the chaos-theory people started simulating such systems with computers in the 70s, nobody really had really thought through the implications and understood the full extent of the unpredictability of things like the weather or even simple things like a coupled set of pendulums, let alone all of human history).
Asimov himself appeared to have vaguely intuited why the model is unrealistic. The character of the Mule in Foundation and Empire was, in many ways, basically the classic butterfly flapping in one part of the world causing hurricanes in another (a chaos theory trope).
Another reason to doubt the possibility is complexity theory. Chances are, a full-blown prediction algorithm for a sufficiently large and highly thermodynamically isolated subset of the universe would be NP-complete.
In general, long-range prediction follows a longer-is-coarser scaling. The further out you want to predict, the more coarse your prediction. But there are times in history when the future becomes unreasonably clear and smart people can make interesting anticipatory moves. But that's still far short of psychohistory.
Adding probability theory/Bayesian math to the picture doesn't change things much. Probabilistic prediction is philosophically different in certain key ways, but faces the same modeling/information-theoretic limits.
That said, I'll leave one loophole open. There appear to be very interesting scaling laws and weird symmetries and constants in the mathematics of long-term predictive models. So perhaps some future math innovations could get to uncanny predictions.
Asimov wrote the books before the chaos theory field took off and the full nature of sensitive dependence on initial conditions was properly understood (this stuff was sort of vaguely known all the way back to Poincare, but until the chaos-theory people started simulating such systems with computers in the 70s, nobody really had really thought through the implications and understood the full extent of the unpredictability of things like the weather or even simple things like a coupled set of pendulums, let alone all of human history).
Asimov himself appeared to have vaguely intuited why the model is unrealistic. The character of the Mule in Foundation and Empire was, in many ways, basically the classic butterfly flapping in one part of the world causing hurricanes in another (a chaos theory trope).
Another reason to doubt the possibility is complexity theory. Chances are, a full-blown prediction algorithm for a sufficiently large and highly thermodynamically isolated subset of the universe would be NP-complete.
In general, long-range prediction follows a longer-is-coarser scaling. The further out you want to predict, the more coarse your prediction. But there are times in history when the future becomes unreasonably clear and smart people can make interesting anticipatory moves. But that's still far short of psychohistory.
Adding probability theory/Bayesian math to the picture doesn't change things much. Probabilistic prediction is philosophically different in certain key ways, but faces the same modeling/information-theoretic limits.
That said, I'll leave one loophole open. There appear to be very interesting scaling laws and weird symmetries and constants in the mathematics of long-term predictive models. So perhaps some future math innovations could get to uncanny predictions.