I don’t remember when it was that I first heard of pi. I was home schooled, but my mum and dad said that all attempts to get me interested in maths failed, and this was one reason why they finally sent me to school aged nine. So maybe my dad explained the concept of pi while we were plodding through the Leadhills looking for dippers to ring. Or maybe it was one of a succession of long-suffering teachers and lecturers. Whoever it was, I’m grateful, because pi is a lovely number.
Now, anyone who knows anything about maths knows that pi is the circumference of a circle divided by its diameter, and that it has a value of 3.1415927 or thereabouts. If you know nothing about maths, just imagine a circular lake with a bridge right over the middle. It’ll be 3.14… times further to walk all the way round the lake than to walk over the bridge.
If you’re a real math geek, you’ll also know that pi is an irrational number, which means that it has more digits after the decimal point than anyone can ever imagine or calculate, and hence it can never be written exactly. If you’re a really serious math geek, you may even know a piem or two. And if you’re totally hardcore, you’ll object that pi could have any value you like in a non-Euclidean geometry. But I’ve never met any math geek hardcore enough that they could tell me what the meaning of pi is. Why should an everyday thing like a circle manifest itself in mathematics as a number so big and exotic that nobody can ever know it exactly?
Maybe a discussion of where circles come from would help. The circle, and its 3-D cousin the sphere, appear in nature because they are the most effective way of enclosing space. If you have to make a bag to keep stuff in, as Nature did when evolving eggs and tomatoes, then a spherical shape bags you the most “stuff” for a given amount of eggshell or tomato skin. And, since Nature abhors waste, these objects turn out spherical. Well, eggs aren’t quite spherical, but luckily for chickens, they’re not quite tetrahedrons either. So maybe pi is just a mathematical way of saying that Nature doesn’t do corners. And if it’s irrational because it’s natural, then the endless series of decimals is no more worrying than bugs in your organic lettuce.
Then again, the state of Arkansas recently redefined it to 3.0 exactly. If they’d chosen 4, maybe eggs would have turned cubical overnight and chickens would have really had something to squawk about.
Or then again, maybe pi doesn’t have any meaning whatever. I struggled with math at university because I insisted on believing that it had some kind of correspondence with reality, and looking for physical metaphors to understand it intuitively. The laws of physics can be described as mathematical equations, and the behaviour of some physical systems can be predicted by mathematics, so it’s easy to believe that the universe is somehow made out of mathematics, and learning it will unlock all the mysteries of the universe. But in the end, the universe is made out of universe, and maths is just a game that mathematicians play.
Níl i mata, a shaoi, eolaíocht nó feidhm. (“Wise one, mathematics has neither science nor use.”) – an Irish piem giving pi to 7 decimal places