February 2012
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Tricks of the Trade

Today, Howard Rheingold was searching for examples of clear posts in which to use as examples of online communication. One of the respondents identified a really good series set of descriptions answering the question, What is it like to have an understanding of very advanced mathematics? (Interestingly Terry Tau is referenced quite often.)

That reminded me of some things that I’ve read previously, first from Feynman:

One day he told me to stay after class.”Feynman,” he said, “you talk too much and you make too much noise. I know why. You’re bored. So I’m going to give you a book. You go up there in the back, in the corner, and study this book, and when you know everything that’s in this book, you can talk again.”

So every physics class, I paid no attention to what was going on with Pascal’s Law or whatever they were doing. I was up in the back with this book: Advanced Calculus, by Woods. [He] knew I had studied Calculus for the Practical Man a little bit, so he gave me the real works – it was for a junior or senior course in college. It had Fourier series, Bessel functions, determinants, elliptic functions – all kinds of wonderful stuff I didn’t know anything about.

That book also showed how to differentiate parameters under the integral sign – it’s a certain operation. It turns out that’s not taught much in the universities; they don’t emphasize it. But I caught on how to use that method, and I used that one damn tool again and again. So because I was self-taught using that book, I had peculiar methods of doing integrals.

The result was, when the guys at MIT or Princeton had trouble doing a certain integral, it was because they couldn’t do it with the standard methods they had learned in school. If it was contour integration, they would have found it; if it was a simple series expansion, they would have found it. Then I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me.

[Feynman, R. P. “A Different Set of Tools.” In ‘Surely You’re Joking, Mr. Feynman!’: Adventures of a Curious Character. New York: W. W. Norton, 1997]

And second about Paul Erdos, which I read in [Bruce Schechter. “My Brain is Open: The Mathematical Journeys of Paul Erdos”], but for which I don’t have an exact quote. Erdos apparently used the same few tricks to solve hundreds of problems. I think his success in publishing was likely related to his ability to encounter (and remember) many thousands of problems. Using that strategy, not only might you increase the number of tools in your box; but you’ll definitely encounter problems which your set of tools can solve (as Feynman encountered above).

Generalizing from these two examples: Most trades with some sort of detailed work, develop a large body of ‘Tricks of the Trade’. For example, Physicists/Engineers discovered that if you wish to identify whether a joint of a water carrying pipe might be leaking, it helps to wrap an alka seltzer tablet in the tape seal around the joint. That way, should water leak, the seltzer will make it noticeable. And it’s not just the Engineering/Math/Physics: I’m willing to believe that even Lawyers develop a standard set of arguments and pattern match which arguments are best for which situations.

Computer Scientists collect similar tricks, but we codify (pun!) them into terminology: virtual dispatch, multi-method, closure, trampoline, call with continuation, worklist queue. And write up books about the more general ones: Design Patterns [GoF].

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