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He's not arguing chaos- far from it. He's saying that the system is impossible to derive algorithmically but possible to model computationally. That's the argument he's making with that whole three body problem thing: we've been using computation to attempt to derive the underlying algorithms at play when it probably isn't possible. However, integrating by parts might not only give you enough of a prediction to profit off of, it might give you better answers than the system can absorb without massive change. Primarily he's arguing that we're trying to algorithmically model something that can't be modeled, and that the way forward is to look at the problem in a completely different way.