May 30, 2002
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Nonlinear, again

June Lester isn't convinced by my nonlinear arguments. She observes, correctly, that how we think has very little to do with how we transfer ideas. (It's even worse: how we experience thought may have nothing to do with how we actually think. I may be convinced that my mind is nonlinear, or funny, or purple, but neither you nor I really know)

But the notion that scientific arguments are inherently linear is simply wrong. Long chains of argument are the mark of textbooks that have simplified and decontextualized old arguments. Look at any real scientific argument (the synthesis of adamantane, the Woodward-Hoffman rules, the Michelson-Morley experiment) and you'll find complex web of interdependent observation and argument.

Scientific argument is not what you find in textbooks.

Exception: look at Misner, Wheeler, and Thorne, Gravitation. It's a textbook intended to take the reader all the way from the end of sophomore physics to the research frontier circa 1975, and it's probably the best paper hypertext yet published. Of particular note, look at how the authors acknowledge that not all physics students are equally comfortable with mathematics, although (naturally) they're fairly good. Each argument is made three ways; in exposition, in equations, and in pictures.

It works: I actually did some slightly interesting research in the class where this was assigned, even though I never mastered tensors. A couple of years later, I completely fouled up my graduate E&M course because I got stalled on a particular DiffEQ issue for a couple of weeks and, having gotten myself tangled up, never could get back on track. Nonlinear presentation can be easier both for the writer and the reader.

Mathematical argument, on the other hand, can be linear by construction. That, however, is a special case.