Pi Day and Universal Numbers

(Photo by Stuart Caie)

Pi Day is coming up next week, on the 14th. Of course, that Greek letter represents the ratio between any circle’s diameter and its circumference, which is roughly 3.14. You probably know number freaks who have memorized the number to 100 decimal places. I’m one of them. I must confess, though, that knowing so many digits is not only useless, also but probably indicates mental problems. But having never seen a therapist, I can’t say for sure.

A few years ago, Jet Propulsion Lab representatives answered a student’s question about how many digits of pi they use when calculating their spacecraft trajectories. They said they used 3.141592653589793, or 15 digits. Why not more? They explained on their website:

“Consider Earth. It is 7,926 miles in diameter at the Equator. The circumference, then, is 24,900 miles. That’s how far you would travel if you circumnavigated the globe. How far off would your odometer be if you used the limited version of pi above (meaning only 15 digits instead of a few more)? It would be off by the size of a molecule. So, your error by not using more digits of pi would be 10,000 times thinner than a hair.”

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If an Earth-sized circle’s circumference can be calculated to a molecule-width by using 15 pi digits, what could be the purpose of using (or knowing) 100 digits? None whatsoever. The pi business is strictly a numbers obsession.

Despite the fact that there are 30 trillion cells in the human body (far more than the number of stars and planets in our galaxy), human physiology is rarely associated with vastness. It’s astronomy that people most associate with enormous numerals.

Our numbers-fascination is relatively new. The word “million” didn’t come into general use until the 13th century. Before then, the largest number was a “myriad,” equal to ten thousand. The Greeks, who coined the term, would occasionally resort to myriads of myriads, and that was sufficient to express the most complex concepts.

A million seemed huge when we were kids. It became less intimidating only when we realized it was possible to count to a million in a few days. It’s really not so big: A million steps take you from here to Brooklyn. A vacation lasting a million seconds gives you only an 11-day reprieve from office misadventures.

In astronomy, we use “million” mainly in relation to the Sun, which is nearly a million miles wide and sits 93 million miles away. “Millions” also expresses the distance to the nearer planets. Venus is 26 such units, Mars 34. That’s about it.

Even less useful, astronomically, is the billion, which is a thousand million. We might say that Saturn is nearly a billion miles away from us, and that Uranus, Neptune and Pluto are a couple of billion. And the visible universe offers for our inspection about 150 billion galaxies. But that’s where a billion’s usefulness ends. The unit just isn’t very applicable much beyond Earth – although it’s convenient for taking our planet’s census of seven billion people, some of whom may contemplate the accumulated wisdom of the 60-to-100 billion people who have ever walked the face of this forgiving planet.

So we jump to a trillion. This is a million millions: suddenly a most valuable unit for government economists, physicists and astronomers. There are almost a trillion stars in our galaxy, and about the same number of planets. The light-year is equal to six trillion miles. Grasping what a trillion represents is like having a floodlight illuminate the path to understanding the cosmos.

One way to appreciate the enormity of a trillion is to count it out. Unfortunately, at the rate of five numbers a second, without stopping to eat or sleep, this exercise would still require three thousand years. A trillion seconds ago carries us back 31,000 years – to well before the dawn of recorded history.

Like Peter the Great, who had his wife’s lover beheaded and kept that head in a bottle of alcohol in her bedroom for her to contemplate, nature can also be perverse, though usually with greater subtlety. There’s no rhyme or reason for the numbers that biology or astronomy spring on us. Why does each cell in our body have 90 trillion atoms, roughly the same as the number of stars in our home cluster of galaxies? Why is there exactly the same number of Earth-Sun distances in a light-year as there are inches to the mile? Or the same number of atoms in a lungful of air as there are breaths of air in our atmosphere? Such connections are always interesting.

In any event, the trillion is the largest numeral we ever need to comprehend, for earthly as well as celestial use. But even a trillion is tiny compared with the largest number of things in the universe: the sum total of all subatomic particles such as electrons. That figure is a one followed by 86 zeroes. Still, this actual material that fills the cosmos is infinitesimally tiny when compared with the vastness of the space in which it dwells. If the observable universe were a cube 20 miles wide, 20 miles long, and 20 miles high, all the matter it contained would be as a single grain of sand.

 

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