Infinite Powers

Steven Strogatz: Infinite Powers - too much metaphoric language and vague descriptions, a lot of political correctness, not enough substance.

cheap chapter headers like The Writhing Number of DNA and Nonlinearity Goes to War. same in the text all over.

a short section about Kovalevskaya (pg 278) says

While studying rigid-body dynamics, Kovalevskaya produced two major results. The first was an example of a spinning top whose motion could be completely analyzed and solved, in the same sense that Newton had solved the two-body problem. Two other such "integrable tops" were already known, but hers was more subtle d surprising.

More important, she proved that no other solvable tops could exist. She had found the last one. Ail others from then on would non-integrable, meaning that their dynamics would be impossible to solve with Newtonian-style formulas. It wasn't a matter of insufficient cleverness; she proved that there simply couldn't be any formulas of a certain type (in the jargon, a meromorphic function of time) that could describe the motion of the top forever. In this way, she put limits on what calculus could do. If even a spinning top could defy Laplace's demon, there was no hope — even in principle - of finding a formula for the fate of the universe.

this has to do with determinism, obviously, but i could not find any reference to Kovalevskaya findings anywhere else.

still, sections on determinism are somewhat interesting. he talks about "deterministic and still unpredictable" because of non-linearity.

at least i finally learned what integral means. just about time