Counting in Base 60

Stolen entire from Essays in Idleness by David Warren

The joy of sexagesimals

For a person who loathes statistics, and in particular social (including financial) statistics, one of my more eccentric interests is in weights and measures. This has relaxed over the years of my maturity: at age sixteen it was an incurable obsession. For, as with others who have obsessions (baseball statistics; alcohol), I have never entirely escaped from it, and even the slightest indulgence will lead me back into slavery, as it were.

An example occurred yesterday, while consulting an older edition of the Encyclopaedia Britannica. (The eleventh, 1911 — always more reliable than the Wicked Paedia.) As everyone should know, the roundness of the world was known even to ancient man, especially the seafarers. The philosophers in Alexandria-by-Egypt even measured its circumference. They calculated by comparing the sun shadows at different locations. Mediaeval man of course inherited this information through Ptolemy; only in XIXth-century America was it lost (by Washington Irving, father of the Flat Earth).

Now, put this together with our archaeological record of Egyptian rulers. Not, their heads-of-state, but rather the marked strips of wood or metal used (e.g.) in schools. We have found plenty of rulers among the ruins, and the older (pre-Muslim and even pre-Christian) show that the Egyptian “cubit” was slightly over 20 British inches. So were the cubits in ancient Sumer, and elsewhere, apparently. Trade, after all, has been global for quite a few millennia. The Sumerians taught the Babylonians, who taught the Egyptians, and everyone else, the Joy of Sexagesimals.

Sexagesimals are written (invisibly) all over our planet, in for instance the lines of latitude and longitude. Indeed, the earth’s known circumference is precisely 21,160 nautical miles, which is sixty times 360 degrees. Only clowns, to my mind, would use the viciously decimalical metric system (invented in Revolutionary France) when we had a universal system of mensuration at the ready, all along. This was, and is, the nautical mile, its multiples and parts — in Babylonian, sexagesimal terms — not yet retired from shipping and aviation.

My realization yesterday is that the cubit is not merely the approximate distance from a man’s fingertip to his elbow, as the dictionaries insist. This ancient cubit is also, nearly precisely, the 60th part, of the 60th part, of the nautical mile. Break it down further into (hexidecimal) sixteenths — as the classical Greeks, classical Chinese, and our modern computer nerds would do — and we have the “digit” or “dactyl” units to replace the “inches” or (God help us) “centimetres” on the rulers of our time.

William Blake: “Bring out number, weight & measure in a year of dearth.”