Pondering the question of why the second is defined as 1/86,400 of a day. I’d always thought it was because a second was about the length of a heartbeat, and thus measurable with the body. (Just like inches and feet and the like.) But that doesn’t really explain the exact number of 86,400 so I did some reading.

Between Wikipedia and this Scientific American article I have a basic answer.

- Egyptians used base 12 math for some astronomy related things. Why 12? Either because you can count to 12 with your finger joints or maybe because 12 = 2*2*3. Or maybe because there’s ~12 lunar cycles in a year.
- Egyptians divided daytime into 12 hours and nighttime into 12 hours. Note these hours were of variable length depending on the season.
- Sumerians and Babylonians used base 60 math. Why 60? Not sure, but 60 = 2 * 2 * 3 * 5 which makes it convenient for a lot of math.
- Greeks borrowed the Babylonian math when they did astronomy, so it was natural to divide an hour into 60 minutes and then later to divide a minute into 60 seconds.
- The etymology of “minute” is from “partes minutae primae”; first small division of the hour. Same word as the adjective “minute”, as in tiny.
- The etmology of “second” is from “partes minutae secundae”, the second division of the hour.
- Some languages have a unit of time called the “third”, 1/60 of a second. Polish (tercja) and Turkish (salise).

There’s also a nice StackExchange discussion on the history of decimal time, a sensible 100,000 seconds in a day or what have you. Including this awesome French Revolution clock, my new coveted possession.

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There’s a somewhat more detailed and nuanced discussion and speculation about Babylonian/Sumerian mathematics and the use of sexagesimal at the very beginning of Kline’s ‘Mathematical Thought From Ancient to Modern Times’. I’m just going to assume this version on archive.org is somehow legal: https://archive.org/details/MathematicalThoughtFromAncientToModernTimes

It’s a big brick of a book and not really light afternoon reading but it’s handy to have around when you wonder ‘what’s with the base 60’ or ‘why do we call this eigenvalue’.

Thanks! I skimmed that first chapter on Mesopotamia, particularly page 6, and his explanation seems to be basically that base 60 has lots of factors and so is easy to work with. (Albeit confusingly stated in terms of fusing two counting systems.)

Reading this also confirms I’m wrong about Egyptian math being base 12. Arithmetic was base 10. But for whatever reason they chose 12 hours for a day.