I woke one morning thinking about pi. No, not the primary character in the book and movie, The Life of Pi, but the mathematical symbol, pi—representing the ratio between the diameter of a circle and its circumference.
Perhaps it had something to do with having had pecan pie for dessert the night before.
The ancient Greek mathematician Archimedes estimated pi at 22 divided by 7. Since the advent of the decimal system, it’s usually defined as approximately 3.14159. The figure has to be an approximation, always, because pi is an irrational number. That is, no matter how many decimal places you take it to, you can never get it precisely right.
That’s an act of faith, of course. Because until you actually get to a precise outcome, you can’t know that you won’t. It’s like trying to prove that life is found only on this planet. Or that God doesn’t exist. Or that global warming won’t happen.
In an attempt to prove their point, mathematicians have pushed their calculations of pi, so far, to over 13.3 trillion digits—not because anyone actually needs that level of precision.
But pi has some other interesting characteristics. As an irrational number, pi cannot be a multiple of any other numbers. That makes it unique, indivisible. It stands alone.
Wikipedia says, “The ubiquity of pi makes it one of the most widely known mathematical constants both inside and outside the scientific community.”
Mathematicians also call pi a transcendental number. I tried to understand what a transcendental number is, and failed miserably.
According to historians, approximations of pi were first used by the Egyptians and Babylonians as far back as 1600 B.C. We’ve been refining our definitions ever since. But no one actually invented pi. Rather, people discovered what was already there.
It’s like other mathematical truths. One and one always made two, long before someone noticed that predictable coincidence. Pythagoras didn’t invent the right-angled triangle; he merely identified the formula relating the lengths of its sides.
Mathematical truths operate independently of context. Pythagoras’s theorem works in any number of dimensions. So does pi. In one dimension, it defines the length of the line that forms a circle. In two dimensions, it defines the area of that circle. In three dimensions, the volume of a sphere. Presumably, it will work in all 11 dimensions required by the “string theory” of the formation of the universe—even if we have no idea what all those dimensions are.
Would pi work in zero dimensions? That is, would pi still have been valid before any dimensions existed, before the formation of the universe we know? Mathematicians would probably say yes—pi is a truth that exists independent of space and time.
In fact, they’d probably say that the universe could not have expanded as it did, if there were no such thing as pi.
The descriptions of pi bear a startling similarity to descriptions often ascribed to God: Eternal, unchanging, unique, indivisible, infinite, transcendent.
And I wonder if that’s just coincidence. Do we extrapolate mathematical truths into divinity? Or are mathematics a confirmation—an incarnation, perhaps—of our struggle to grasp otherwise ungraspable truths?
