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I've remembered the one time I did have call to use a lot of digits of pi.
Back when I was learning about numerical integration, in the days of very patchy net.access, I was working in a group to see how quickly different methods converged for different sorts of integrals. To do that, you have to know the right answer, which requires an analytically-tractable integral (which, of course, defeats the need for numerical integration in the first place, but you need test data somehow). You can easily invent straight-line integrals with rational integrals, but of course most numerical algorithms (apart from Monte Carlo) get the precise right answer in one or two iterations. So you need something curvy, and most of the things with curves that I can integrate analytically end up as some rational multiple of pi.
Someone had a calculator with them, which gave us about 8 digits, but we were working in doubles so wanted more like 15 or 20 or something. (Ghods, I used to know this stuff.) I was delighted, because as a teenager I'd memorised pi to 30 decimal places (because I was that sort of teenager), and for the first time in my life, it turned out to be not just a party trick (for very geeky parties) but practically useful.
I'm pretty sure that'll also be the only time.
I know it's also useful when you're testing any new suite of high-precision calculation tools, or quality-assuring new hardware. But these days you can just download as many digits as you have bandwidth and storage. I was talking to a mathematician who does that sort of thing a few years ago, and to wind him up, I asked "So what do you do when pi changes?", and the poor guy didn't clock I was joking and was literally speechless and gaping for a good few minutes.
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But I suspect that sometimes I'm just a living example of Poe's Law.
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I'm an epidemiological modeller, and I've almost never needed to actually use pi (except maybe when tutoring 1st year maths students), and I actually used pi as a variable in my thesis as a quiet protest for using tau :D
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