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A guy I know owns this clock, which basically proves that everything in life is pointless and arbitrary:
Also why the seemingly arbitrary graduations, 24 hours, 60 minutes, 60 seconds. If it was say 10 hours in a day, 100 minutes in an hour, 100 seconds in a minute, seconds would be close to the same amount of time. Same with latitude and longitude, why 360 degrees in a circle with 60 minutes in a degree and 60 seconds in a minute.
Morning, midday, evening and night are arbitrary. Why not just morning and night? Why not morning, mid-midday, midday, evening, mid-evening, and night?
The number of seasons is likewise arbitrary. Some Native American tribes had more than 4 seasons.
These numbers aren’t arbitrary, they are from different base numbering systems.
60 can easily divide by 2, 3, 4, 5, 6, and 10.
12 can easily divide by 2, 3, 4, and 6 (notice how much overlap there is).
10 only divides easily by 2 and 5. Common fractions like 1/4 or 1/3 now require decimals.
Basically, base 12 and base 60 make it significantly easier to think and work in common fractions.
It is also historically significant, as base 12 used to be more common than modern base 10. Our timekeeping system dates back to the ancient Babylonians, who worked in base 12. This influence is still felt in other places, such as the fact that eleven and twelve have unique names in many languages rather than following the same pattern as everything that comes after them.
The short explanation is that those numbers are more easily divided by a larger set of denominators. 24 is divisible by 2, 3, 4, 6, 8, and 12. 100 is divisble by 2, 5, 10, 25, and 50. 60 is divisible by 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, and 30.
Metric is great for scaling up and down ad infinitum, but it sucks for fractions. Fractions are easier for daily use without precision measuring equipment.
The units of time we use come from a bronze age civilisation that used base twelve instead of base ten. They'd count on their hands using the finger joints of one for single digits, and then the joints of the other for multiples.
That's called Decimal time and revolutionary France already tried it.
Other commenters hit on the reasoning, just adding that they're called highly composite numbers. My favorite!
Boy, do the French have a decimal time for ya!
Of course, you could always go metric