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Psychohistory was designed for large groups. It wasn't designed for single creatures like butterflies
It wasn't because it couldn't. Hari tried it and failed. Applying Psychohistory to only large enough populations was his compromise. This is mentioned in Prelude to Foundation. I think Hari specifically mentions how complex predicting weather is iirc. That's why I mentioned it in the first place.
At the time Hari tried to apply it at the small scale, it was impossible. I believe by the time Gaia takes over the science could be applied to the single organism but that also feels like cheating.
The whole point of prelude and forward was that his attempts to start on the smaller scale by going backwards in time was a fools errand and impossible but starting with the relatively small scale of just Trantor was doable as it had sufficient mass to apply the generalized mathematics towards. The variables on the smaller scales were too numerous but as you abstract towards larger bodies, it reduces the complexity to the point it becomes calculable.
Well, not the whole point but still
No shade but I could not take the premise of that book seriously. The idea that any complex system could be mapped thousands of years into the future is so incredibly unrealistic to me that I was unable to suspend my disbelief.
I'm a massive Dune fan though so I have no leg to stand on. Hold on a second while I re-calibrate my metabolism and use my genetic heritage to recall events that happened 30000 years ago.
So, what Hari does is basically game theory on a massive scale. The larger the group, the less complexity because you're abstracting the different possible issues individuals would have out of the problem. Instead of making it more complex, it simplifies the whole thing because all the chaotic bits cancel each other out.
And slight spoiler warning for an old story but you find out later that the whole thing isn't just predicted ahead of time and let loose but a group of people follow along in the shadows to keep the plan on track.