And why isn’t twelve “two-teen”? Why do bagels come in dozens? Why are there two sets of 12 hours in a day? And why 12 inches to the foot?
Like much of northern Europe, England once had a hybrid system of counting based on both 10 (decimal) and 12 (duodecimal). Today, almost all our daily commerce is measured in base 10, from cents, dimes and dollars to gallons of gas (never 5¾ gallons) to mileposts by the side of the highway to the number of reps in a workout. However, plenty of remnants of the long-gone base-12 system survive. In the U.S. For instance, lumber is specified in inches (two-by-fours), eggs are sold in dozens (but in 10s in Europe), and precious metal dealers still use 12 troy ounces to a troy pound. It was only in 1971 that Britain abandoned a currency system that originated with Charlemagne 1,200 years ago: 12 pennies in a shilling and 20 shillings in a pound. (The 20 persists in the word “score,” as in Lincoln’s “Four score and seven years ago.”)
Much of the English language is descended from Old Germanic, and even before the emergence of Old English, ancient Germanic societies generally used base-12 (duodecimal) to count. We know this from several lines of evidence:
The linguistic fossils “eleven” and “twelve” derive from Proto-Germanic ainalif (one left) and twalif (two left), from a time when the count paused at twelve before starting with the more logical thirteen (Old English þreotīene, three plus 10).
The Old Norse word hundrað, our “hundred,” equaled 120, not 100.
Side notes in early Germanic manuscripts sometimes explained that numbers in the adjacent text use the “tenty-wise” (decimal) counting system, not the duodecimal that the reader presumably expected.
Our words “dozen” and “gross” are survivors from base-12 Proto-Germanic.
Note that a duodecimal system is arguably more useful than a decimal one in trade, since 12 is divisible by 2, 3, 4 and 6, as opposed to only 2 and 5 for 10. Finger-counting (dactylonomy) by twelves is common in some Asian countries, with the thumb acting as a pointer, touching the three finger bones of each finger in turn, starting with the outermost bone of the little finger, up to 12. The other hand counts completed 12s, up to 144.
In passing: A “great gross,” meaning 12 gross or 1,728, “is used in commerce and manufacturing for bulk items, e.g., pencils, fasteners,” according to Wikipedia. Note that 1,728 (12 cubed) plus 1 (one cubed) equals 1,729, the “taxicab number.” After his friend told him he’d ridden in a taxi with that number, Indian mathematician Ramanujan observed that it’s the smallest number expressible as the sum of two cubes in two different ways, since 1,729 is also 9 cubed plus 10 cubed.
The Indian-Arabic decimal system (popularized in Europe during the Renaissance) probably gained superiority over the 12-based system because of our 10 digits. Cultures that once used base 12 include ancient Egypt, Sumeria and Babylonia. If you’re not sufficiently confused by now, remember it was the Babylonians who gave us our 60 seconds, 60 minutes and 24-hour timekeeping, along with 360 degrees in a circle.
Barry Evans (he/him, barryevans9@yahoo.com, planethumboldt.substack.com) remembers chanting his “times” tables up to, not 10 x 10, but 12 x 12.
This article appears in One School, Nine Students.