Mathematical Notes: p is the link between finite and infinite

David Blatner
Sunday 23 October 2011 07:47

EVERY BOOK-LOVER knows that there's nothing like a good mystery. We're fascinated by the slow accumulation of clues that unfold into patterns, inevitably leading us to a solution and satisfying denouement. In fact, the idea that a mystery might not be solvable is deeply troubling to most people.

Of course, it wasn't always that way. For most of our history, everyone simply assumed that a mystery was something esoteric, unknowable, and certainly without solution. But now, as we approach the millennium, we seem simultaneously anxious and fascinated by the thought that perhaps there really are old-style mysteries after all.

It's not surprising, then, that people are increasingly looking to mathematics and the sciences to find a bridge between what is knowable and what is not. Nor is it surprising that the symbol most able to represent this bridge is the 16th letter of the Greek alphabet: p.

Truly, no other mathematical constant is more widely known. Or, to be more exact: more widely known of. Almost anyone who has studied basic geometry knows that the number has "something to do with circles," and many may even remember the truncated value 3.14. But p is an iceberg, and these sea-level descriptions only barely touch the depth of this curious constant.

First, some basics: if you measure how far a piece of string wraps around a can of soup and divide that by the can's diameter, you'll find an approximation for p which is probably as close as you'll ever need. If you're an engineer, you'd be better off knowing two or three more digits (3.14159 perhaps), and a physicist will never need more than 10 or 15 more. But, by means of advanced mathematics, computer scientists have now calculated over 51 billion digits of p. Why?

Reseachers tell us that the human mind is optimised for memorising seven or eight numbers at a time, but one man recently memorised and recited 42,000 digits of the number. Why? The number that most often plays a supporting role in science fiction (such as Carl Sagan's novel Contact) and the arts (such as Alfred Hitchcock's Torn Curtain or the film The Net) is, of course, p. Why?

One glance at the symbol evokes the whole of mathematics, and for good reason. The number appears in the answers to a host of equations, most of which curiously have nothing to do with circles (including the puzzler, "What is 1/12 + 1/22 + 1/32 + so on"). It appears in probability theory and statistics, as well as studies of waves, from those at the ocean to those within sound. As a crowning glory, the number is integral in the most famous of mathematical oddities: ei - 1=0.

But p symbolises more than just maths. p is an irrational and transcend- ental number, which means that there is no end to and no repeating pattern within its digits. p reels off endlessly toward infinity, where each additional digit signals an approximation 10 times more precise than the last.

Because we can never truly know p, we can never truly measure circles, or any curve at all. We can only approximate our measurements, which is why the phrase "squaring the circle" has become synonymous with a futile task.

In this way, p is the link between the finite and the infinite, what can be known or measured and what cannot. So while the number appears in legal battles (Judge Ito wrestled with p during the infamous O.J. Simpson trial), in comedians' routines, and even the world of fashion (Givenchy perfumes will reportedly soon release a fragrance called . . . well, you know), ultimately it is the mystery of p that truly captures our imaginations and our hearts.

David Blatner is the author of `The Joy of Pi' (Penguin, pounds 6.99)

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