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Understanding Nonlinear Dynamics

It is a good thing for intellectual humility — particularly in middle age into which yours truly has stepped a few years ago What constitutes “middle age” in the 2020s is a matter of some debate. Is it a matter of birth date, life style, state of mind, a combination thereof? Taking the last thing first: I have been in a middle age state of mind since I was twelve; am as much of a 2.5-child nuclear family man as a geriatric millennial can be; and am well into the third quintile of life, as foretold by the life expectancy tables for a man of my age. No red convertibles planned for purchase, though a new decked-out Mac Pro — once it comes out — would probably cost just as much and is something I would actually consider having. — to open an undergraduate textbook for a field that is just outside one’s area of expertise. A series of reviews on gene regulatory networks led me down a rabbit hole of vector fields and attractor states that was interesting-yet-unscrutable enough to get me to Understanding Nonlinear Dynamics.

It is very much a textbook, info-boxes, end-of-chapter exercise, and all. It also presupposes a grasp of mathematics which I may have had just out of high school but have long since lost. This is fine: at Mortimer Adler’s suggestion I zipped past the equations and derivations, deciding to trust the authors that they are indeed correct, and went to the meat. Which, in nonlinear dynamics, as a nice bonus, also has pretty pictures of fractals and vector fields. Alas, not as artistic as Charles Waddington’s, but nevertheless striking.

What surprised me the most was how much of the field resulted from mathematicians fiddling around with parameters to see what happens. Going to a textbook to learn this was overkill — the Wikipedia article on experimental mathematics may serve the purpose just as well — but knowing the context does make it memorable. There is a pleasing symmetry here: mathematics is usually thought of as purely theoretical, yet its most interesting aspects, Lorenz attractors to Wolfram’s (not so) “new kind of science”, have relied on experimentation. Biology has been purely experimental ever since Watson and Crick, aborted attempts at theoretical biology notwithstanding, and was even a decade ago producing more data than it can handle. Would it not be neat if the answer to this biological data overload wasn’t machine learning but instead a framework for theoretical biology? If there was one, nonlinear dynamics would play a big part.

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