Cheaper By The Dozen
Posted by: roscivs, in UncategorizedA dozen donuts, twelve inches in a foot, twelve pence to a a shilling, a dozen dozens in a gross. Twelve months in a year, twelve apostles for Our Lord, twelve hours on the clock, and twelve signs of the zodiac. Why is twelve such a ubiquitous number?
It turns out that twelve is a very useful number for all sorts of mathematical reasons. For instance, it has a lot of divisors: 2, 3, 4, and 6 all go into twelve evenly. There are only six numbers under 50 that have more divisors than twelve, and nearly all of those are multiples of twelve.
Why is this property of twelve beneficial? It’s because a half, a third, and a fourth are very useful and common divisions. Dividing a dozen donuts fairly among three people is trivial. Taking half a foot or a quarter of a foot results in a nice whole number of inches. Twelve apostles can be divided equally into two groups, three groups, four groups, or six groups very easily, depending on the need.
The US has been rather recalcitrant to give up its dozen-based measurement systems in favor of the ten-based metric system. But why did the rest of the world switch to begin with, if twelves are so useful? What does the metric system have to offer us? Quite simply, it aligns the counting system—which is ten-based—to the measurement system, making dividing or multiplying measurements by ten a trivial operation.
But why is our counting system ten-based? Many people assume it has to be that way, or that it’s more logical that way, but it turns out that it’s just an accident based on our number of phalanges. Ten-based systems aren’t inherently any more convenient than any other base—only when you’re dealing with tens. In tomorrow’s post, I’ll give a few examples to illustrate this idea.
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March 22nd, 2007 at 3:44 am
Ah-ha! Nice to see the old “Pre-decimal pounds were easier to navigate” argument. I always liked base-12 money–it made things simple.
Of course, people got silly about it and introduced *cough*Queen Vic*cough* the Florin and other decimal-esque pieces. And the whole thing was kludged together anyway, since the silver penny was the everyday piece of money in England for centuries, and it’s only arbitrary that 240 of them got cut out of a pound of silver. Your average craftworker, who for some reason has not been paid in kind, would see a lot of half-pennies and fourth-pennies, many of which were cut directly from the large coin, and consequently weren’t quite a fourth of a 240th of silver.
Eh… I’m nattering on. Enjoy base-12, son. It’s a dying breed.
I’m reminded also of the scene in the Illuminatus Trilogy, wherein Hagabard Celine points out that if we’d all had six fingers on our hands, there’d be a law of sixes. Clever, clever people.
September 13th, 2007 at 8:33 pm
[...] I’m fond of “13″. It’s odd, it’s prime, and when it’s on a calendar it’s alluringly spooky. In Venezuela, it is Tuesday the 13th that’s ominous. It’s just outside the environs of numeric normalcy, harking back to our base 12 days. [...]