Edward Lorenz, meteorologist and founder of chaos theory, passed away today at the age of 90. He discovered the chaotic properties of nonlinear systems as a result of an unexpected result while running numerical weather simulations in 1961, and changed the way we think about complex systems.

For those of you with a mathematical background, I recommend taking a look at his 1963 paper “Deterministic Nonperiodic Flow,” in which he proves one of the most basic results of chaotic dynamics (that nonperiodic flows are unstable against small perturbations), applies it to a simple problem in fluid dynamics, demonstrates vividly and in pictures the way that the system becomes unpredictable, and reflects on its significance for weather prediction. It seems a fitting way to mark his passing, and the paper is *great*; very straightforward^{1} and well-written, and full of the best pictures that 1963-era computing could produce.

^{1} By comparison to most technical papers in mathematics, that is, and especially to most papers on differential equations. I realize that this is not the best definition of “straightforward.”

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Thanks for that link! It’s amazing how the basic result (I knew about, but never studied its proof) turns out to be trivial — in the good sense of being foundational: not requiring lots of machinery (any machinery, in fact), but just following by reflection on some illuminating definitions. I really had no idea.

Thanks for that link! It’s amazing how the basic result (I knew about, but never studied its proof) turns out to be trivial — in the good sense of being foundational: not requiring lots of machinery (any machinery, in fact), but just following by reflection on some illuminating definitions. I really had no idea.

just like einstein’s 1905 electrodynamics paper. 🙂

just like einstein’s 1905 electrodynamics paper. 🙂

I feel like I ought to put together a stack of papers like that, ones that are very fundamental and explain a novel idea in a way that makes it seem entirely obvious in retrospect.

I feel like I ought to put together a stack of papers like that, ones that are very fundamental and explain a novel idea in a way that makes it seem entirely obvious in retrospect.

that’d be really valuable for inductions on the nature of creativity.

elegant mathematical results (and proofs) would be good, too. euler alone is probably a bottomless well – how can you improve on euler’s identity? then there’s the otherworldliness of ramanujan.

that’d be really valuable for inductions on the nature of creativity.

elegant mathematical results (and proofs) would be good, too. euler alone is probably a bottomless well – how can you improve on euler’s identity? then there’s the otherworldliness of ramanujan.

Suck. 😦 Truth be told, though, I didn’t know he had been still alive.

Suck. 😦 Truth be told, though, I didn’t know he had been still alive.

Yeah, I saw that last night. Very sad.

Mandelbrot, on the other hand… is very much alive, at least according to Jonathan Coulton. 🙂

Yeah, I saw that last night. Very sad.

Mandelbrot, on the other hand… is very much alive, at least according to Jonathan Coulton. 🙂