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. Everything fits together!

We may then reconstruct the “foot” as two-thirds of this, and break it down hexidecimally, as the classical Greeks, or classical Chinese, would do — into sixteen “digit” or “dactyl” units to replace the “inches” or (God help us) “centimetres” on our contemporary rulers. This longer foot (about 13.5 Anglo-American ┬áinches) will prove more useful in ergonomic design. Trust me.

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


POSTSCRIPTUM. — My cybernetophile son defends “metric” as a system of hard precision for use with machines, for the very reason that “base ten” is so fraction-averse. He concedes, however, that “beautiful sexagesimal relationships” are more appropriate for the humans, who think in fractions and approximations.