Wednesday, March 14, 2012

happy pi day!

So I got to say on the radio for pi day that pi is the circumference divided by the diameter of a circle. And  short story shorter, this got me thinking about why people like pi so much in the first place. I think it comes down to a combination of three things:

First, pi shows up everywhere in science. From the time you learn basic geometry in elementary school, pi is popping up in your school notebooks. Then you move on to trigonometry, calculus, Fourier analysis, and on up as complicated as you want to get, and that pi is carried along for the whole ride. Anything oscillatory turns out to be described with sine and cosine functions, which boil down to geometry of circles, so waves, pendulums, light, sound, planets, optics, electrical currents, et cetera et cetera, all involve pi. Then it turns out that that other famous constant, e, is also related to pi, so population growth, electric charge, compound interest, probability distributions, and anything else exponential in nature, also all contain pis lurking quietly in the background. And somehow, even when you get into the domains of pure mathematics that seem superficially disconnected from all of that other real-world stuff, pi keeps showing up. The sum of the reciprocal of each natural number squared? There's a pi in that. Is it any wonder that pi begins to feel like a familiar friend?

But that's not all, of course. Lots of numbers appear all over the place. 10. 2. Physicists have the speed of light. Chemists have Avogadro's number. Why don't these constants have the same appeal as pi? Unlike these other boring old numbers, pi is shrouded in mystery as a result of being irrational and transcendental. Its irrationality means that you can't write it down as a fraction, and that if you try to write down its digits, the sequence will continue forever without repeating. Transcendence is like turbo-charged irrationality. Not only can you not write it down as a fraction, you can't calculate it with any combination of whole numbers and algebraic operations like division and exponents and roots. You can get closer and closer the longer you try, but you can never quite get there. There's nothing to do but symbolize it with a Greek letter and forget about the fact that you can never be exactly sure what it represents.

But that's still not the whole story. e is also transcendental. The square root of 2 is irrational. i is certainly mysterious in its own way. There are plenty of other loved constants, but still none approach the popularity of pi. And that comes down to pure nostalgia. For many of us, learning about pi is the first time we catch a glimpse of the immense mystery of the universe and realize we can't hold on to it, put it in a box, and study it in all thoroughness. We have to content ourselves with squinting at it from many angles and then try our hardest to put together a coherent abstract picture in our minds. The mystery never ends, and for us mystery-junkies, the scientists, that first glimpse into the infinite abyss is an unforgettable moment that continues to drive us throughout our lives. And even after we come to terms with all our numerical friend implies, each time we casually say hello, a tiny part of our subconscious mind is reminded of that deliciousness of discovery.