So the computer based solution proposed by Newton and Turing is rejected because the system is chaotic, meaning a general solution will always diverge from reality.
What I don't get is: this should still be good enough Run your solution every month or so, with updated measurements, and you'll have an ongoing "forecast" of conditions.
I'm referencing weather because that's we do. A weather forecast is a prediction of a chaotic system, but of one which changes every day or so. Prediction difficulty is dependent on local conditions and weather type, but we can still make predictions.
A gravitational system of 4 mutually interacting bodies is muuuuuch simpler than weather, and could be predicted far enough in advance to let a civilization adapt and persist!
I'm not sure what limits the sophon has. in the books, I thought it could gather all intelligence, hence the name, but physically could only interact on the extremely minute scale.
in the TV show, I don't understand why it can't just kill everyone, crash every plane, destroy all computers, and make all the main characters blind and give them hallucinations until they go insane.