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How is a unit that varies in time less arbitrary than units that at least have a fixed length?
Because the day and year have meanings. They are "the time it gets for the earth to make a full rotation" and "the time to come full circle around the sun". They are of varying length, so we actually use time periods that are almost the real day and year, and call them day and year. These are fixed length.
The second is arbitrary, because we just arbitrarily decided to split up the day in 24 hours, hours into 60 minutes and minutes into 60 seconds. Why 24/60/60? Kinda arbitrary.
Now, does arbitrary mean it's bad? I don't see why. The meter is defined in a similar manner, but using multiples of 10 instead of 24/60/60.
I know the meter and second have been redefined to be based on scientific phenomena and be independent from the earth, but their length has the same arbitrary origin. And as such, they are arbitrary.
I don't see what being arbitrary has to do with being a good or bad unit of measurement.
It was created by the Babylonians, who had a base 12 numbering system. It's no more arbitrary than base 10, and in fact superior in some ways. 12 can be evenly divided by 2, 3, 4, or 6. 10 can only be evenly divided by 2 and 5.
I was referring to months which are arbitrary "to a lesser degree" but maybe I misunderstood the comment above mine