Guide
Why sixty seconds, sixty minutes, twenty-four hours
Why time is the last place we still count in sixties, where the twenty-four-hour day came from, and why nobody has managed to decimalise either.
Sixty, because it divides
Sixty divides evenly by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. Ten divides by 1, 2, 5 and 10. For anyone splitting a quantity without fractions — a merchant, a surveyor, an astronomer — that difference is decisive, and it is why sexagesimal counting reached us from Mesopotamia and never left.
It survives wherever dividing matters more than counting: sixty seconds, sixty minutes, 360 degrees in a circle, sixty minutes of arc in a degree. Every one of those is a place where thirds and quarters have to come out whole.
The same reasoning explains why a dozen outlived a decade in trade. Twelve splits into halves, thirds, quarters and sixths; ten manages halves and fifths.
Twenty-four, from two twelves
The Egyptian day was divided into two twelves — twelve hours of daylight and twelve of night — tracked by decan stars. Because daylight and darkness change length through the year, those hours were originally unequal, stretching in summer and shrinking in winter.
Equal hours came later, with mechanical clocks that had no way of varying them. The number stayed and the variation went, which is why we have twenty-four equal hours rather than twenty-four seasonal ones.
How well each base divides
| Number | Divides evenly by | Where it survives |
|---|---|---|
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 | Seconds, minutes, and minutes of arc. Twelve divisors against ten's four. |
| 24 | 1, 2, 3, 4, 6, 8, 12 | Hours in a day, from two Egyptian twelves. |
| 360 | twenty-four divisors in all | Degrees in a circle — close to the days in a year, and far easier to divide than 365. |
| 10 | 1, 2, 5 | Our counting base, chosen for fingers rather than for divisibility. |
The old units are not arbitrary. Every one of them was chosen by people who needed to split a quantity in as many ways as possible without leaving a remainder.
The decimal clock that failed
Revolutionary France decimalised almost everything successfully — the metre and the kilogram are still with us — and tried the same with time: ten hours in a day, a hundred minutes each, a hundred seconds each. It was official for about seventeen months and abandoned.
The metric units replaced systems that varied from town to town, so there was something to gain. Timekeeping was already universal, already worked, and every clock in the country would have had to be replaced. The reform failed on the ordinary grounds that reforms fail on, not on any argument about arithmetic.
Decimal time has been tried since and gone the same way. What survives instead is decimal notation on top of the old units: a stopwatch reads 12.47 seconds, and a navigator writes a position in degrees and decimal fractions rather than in minutes and seconds. The base stayed sexagesimal and the fractions went decimal, which is the compromise that actually stuck.