Every glance at a clock uses a Sumerian counting system around 5,000 years old
Sixty minutes to the hour and 360 degrees to the circle are leftovers from base 60, a way of counting that began with the Sumerians in the 3rd millennium BC. Its appeal is simple: sixty splits cleanly into halves, thirds, quarters, fifths and sixths, which made dividing goods and fractions far less painful.
Sixty has twelve divisors, and it is the smallest number divisible by every whole number from 1 to 6. An hour can therefore be carved evenly into chunks of 30, 20, 15, 12, 10 or 5 minutes, and many more. Mesopotamian merchants exploited this: a talent of roughly 30 kilograms was split into 60 minas, each of 60 shekels, units whose descendants survived for millennia.
The Babylonian version was not pure base 60. Each digit was built from wedge marks for units up to nine plus wider marks for tens, so base ten hid inside it. Worse, there was no zero at first, so the symbols for 1 and 60 looked identical and readers had to work out values from context. Later texts added a placeholder, but only between digits, never at the end. Historian Otto Neugebauer warned that the system's origins and use were messier and less consistent than often portrayed.
Astronomers kept it alive. Ptolemy's Almagest, written in the second century AD, used base 60 for fractions, and his table of chords went unrivalled as a large trigonometric reference for over a millennium. Around 1000, al-Biruni divided the hour into minutes, seconds, thirds and fourths. European astronomers still calculated this way as late as 1671, and Tamil astronomers of the late 18th century reckoned with shells using mixed decimal and base-60 notation. Medieval Latin names for successive fractions, minuta and minuta secunda, gave us minute and second.
The system turns up elsewhere too: the Chinese calendar's stems and branches repeat every 60 steps, and the Ekari people of Western New Guinea developed base-60 counting on their own. It can still cause trouble. Version 1.1 of the YAML data format read some network addresses as base-60 numbers, confusion that led to the feature being dropped in version 1.2.
Source: Sexagesimal
