PI versus TAU

In 1854 Henry David Thoreau published his best known work, Walden. It’s an account of two years of his life spent in a hut near Walden Pond in eastern Massachusetts. Thoreau, a proficient amateur naturalist, spent much of his time observing, and writing about, the daily minutia of the rural woodland and lakeshore where he was living.

Among his writings is the description of a titanic battle in microcosm, an account of a mortal conflict between two species of ants that he watched close up, on his very doorstep. He reports on the fighting much like a war correspondent, describing the fury and devastation with which the tiny combatants attacked one another and the death and destruction that ensued. And all of it hidden among the weedy stems and leafy grasses around his hut.

One notion that he imparts from that experience was that such hidden conflicts are always around us, but only the careful observer will discover them.

I have discovered such a conflict.

Camouflaged by symbols and formulae, obscured by operands and integers, disguised in chalk dust and flat-screen graphics, a gruesome battle is being engaged in the arcane world of mathematics.

On one side are the Pi (π) loyalists, a group dedicated to the preservation of 3.14159… as the primary definition of the linear and spatial relationships in circles. In opposition are the Tau (τ) revolutionaries, equally motivated number fanatics who insist that 6.28318… is the complex integer that would better serve geometricians, trigonometricians and all-round mathematicians throughout the known universe.

I was raised in the Pi camp. The abridged version of Pi, 3.1416, was a mantra taught early and repeated often in the pre-PC primary, secondary and advanced educational forums through which I progressed. There were no circles without Pi. With due reverence I learned that Pi times the diameter (π x d = c) equals the circumference. I was drilled in reciting that Pi times the radius squared (π x r² = A) equals a circle’s near-mystical Area. Even now, “Pi-r-squared” floats unbidden into my mind whenever I encounter circles or circular objects. It resonates in my near-sub-conscious along with other embedded phrases, like “please-and-thank-you” and “green-eggs-and-ham.”

But in the late 19^th century, some French (wouldn’t you know) mathematician suggested that Tau, which is twice Pi (as the brighter among you may have noticed) is actually the more utilitarian number. As if any numbers that have been calculated out more than a hundred million decimal places—and still counting—could be considered utilitarian. That’s why we round off these numbers: because they appear to be infinitely complex and are, technically, irrational numbers. Really, how handy is that?

Still, it is much more common, among the professional mathematicians, even the mercenaries, to use twice the radius rather than the diameter in doing calculations. Diameter is out, radius is in.

Okay, I admit the distinction escapes me, but for some reason it’s significantly more convenient for advanced mathematics, perhaps comparable to flush toilets versus outhouses. Or maybe not. Chopsticks versus forks? Cans versus long necks? Whatever.

The Tauists (pronounced TOW-ists, and not to be confused with philosophical Tauists, pronounced DOW-ists) insist that Pi is imprecise, since it is used to describe other math properties besides circular ones. Piists (pronounced…oh, never mind) rightly point out that Tau is used in physics to describe certain elementary sub-atomic particles of the lepton family, having a mass about 3,490 times that of the electron, and a mean lifetime of 3×10-13 seconds. (A word to the wise: this may be on Friday's quiz.)

Adding to the fog of war is the trend in current mathematics to parse circles not in portions of their circumference, but in portions based on angular sections of the entire circle, called radial arcs, which apparently confuses some students. I call it collateral damage.

It may not seem important, but consider what is at stake: wedding rings and golf cart tires, trash can lids and shirt neck sizing, clothes dryers and piston rings, geo-stationary TV satellites and icing-filled chocolate cookies, shower drain strainers and wristwatch gears, particle accelerating supercolliders and toddlers teething rings, inner tubes and sliced baloney. Circles reach into every part of our lives—and a battle of covert forces will determine who controls them all.

Eh.

It’s still just arithmetic to me. But, as Thoreau said, “…he must be a great calculator indeed who succeeds.” No problemo—my computer came with a great calculator.

Nevertheless, I hope you celebrated, as I did, this past Monday, March 14^th, marking the 22^nd annual Pi Day (3/14, get it?). Here at the RV park the festivities were somewhat subdued. This was just as well. Because, for me, the whole idea of Pi is a personal experience. I opted to observe the Pi holiday in my usual quiet fashion—with a generous radial arc of a bakery-fresh deep-dish pecan beauty that I nuked to medium hot perfection and then topped with a big scoop of some French (wouldn’t you know) vanilla ice cream.

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