Asimov built psychohistory on a false premise he never questioned: that sufficiently large populations behave like gas molecules, statistically predictable despite individual randomness.
The math works in the book because he never shows it working — Hari Seldon makes predictions, they come true, and the reader accepts this as confirmation.
But look at what actually happens on the page. Seldon's recorded messages arrive at predetermined moments to nudge the Foundation back on track — not because the equations predicted what would occur, but because Seldon predicted what humans would choose to do when presented with specific information at specific times.
He's not predicting behavior. He's engineering it through revelation. The psychohistorical equations are a MacGuffin, and the actual mechanism is psychological manipulation disguised as mathematical inevitability.
Modern complexity science discovered exactly this: chaotic systems become more chaotic as you zoom in, not less. Asimov's psychohistory works because it operates at exactly the altitude where you can't see the chaos anymore — the moment you look closer, the whole structure collapses. The Foundation survives not because mathematics conquered human nature, but because Seldon understood that people need to believe they're following a script.
Read the four recorded Seldon Crisis scenes in Foundation back-to-back and track how each 'prediction' is actually a prompt designed to make humans choose a predetermined path—then compare this to James Holton's essay 'Chaos, Order, and Patterns' on how complex systems actually resist mathematical reduction.
Seek out Gerald Piel's 1960 essay 'Science in the Service of Man' (originally published in the Bulletin of the Atomic Scientists), where he argues that Asimov misunderstood how societies actually respond to scientific knowledge—this directly contradicts every premise of psychohistory and explains why Foundation only works as fiction.