Hours have 60 minutes of 60 seconds each. A degree of angular measurement also has 60 minutes of 60 seconds each. Is this a coincidence? Did the terms minute and second simply mean 1/60 and 1/3600 and were applied to both cases separately? Or was there a relationship beyond this? It’s interesting that when one is using a chronometer to determine longitude, one uses minutes and seconds of time to determine minutes and seconds of angular distance (in terms of circumference) on the globe.

Hours and other things were originally divided into first small parts (pars minuta prima) and then second small parts. Sixty was used because it was a number that could be divided evenly into two, three, or five.

And the 36 multiple comes from ancient Babylonia belief that it was a magic number, given approx 360 days in a year, it all seemed to fit. If you also assume the earth’s orbit is circular, as people tended to back then, 360 degrees becomes a good unit to use for that circle, and measuring all circles, and spheres. Even the Earth, which isn’t really a sphere. But whatever, in spite of all the qualifiers you have to add for the real world, it all stated with Babylonian mathematics, starting from their calendar.

The base-60 system originated in Babylonia by 2000 BC, which had arithmetic and algebra more advanced than that of ancient Greece. Minutes and seconds are simply the places corresponding to tenths and hundredths in decimal system. (1/60 of a second is a “third,” though that term is now highly obsolescent.)

I think 360 degrees was chosen as the size of a circle in part because there are about that many days in a year. Don’t know about 24 hours per day, but Wikipedia shows that convention to be very ancient.

24 hours in a day goes back to the practice of counting by dozens. From sunrise to sunset the day was divided into a dozen hours, and from sunset to sunrise the night was also divided into a dozen hours.

If your method of timekeeping is a sundial, it’s easy to see that the length of hours has to vary throughout the year, with long hours in the summer and short hours in the winter.

**The Romans**, never afraid to make life complicated, actually varied the length of hours throughout the *day*, then switched the hours between summer and winter.

So using the same terms for both angles and time is just coincidental, then?

Not exactly but sorta. One-sixtieth is reasonably termed one *pars minuta* (tiny or ‘my-NEWT’ part) of that which is being divided … hours and degrees (either of a circle or on the Earth’s surface) being the two main units so divided. If it becomes useful to subdivide a *pars minuta*, it is to be regarded as the primary division (*Pars minuta prima*) and be split into 60 secondary subdivisions (*partes minutae secondae*). The terms ‘minute’ and ‘second’ derive from this.

Coincidental in that hours and degrees both use the same subdivision system, not coincidental in that the system is a logical consequence of fractionating on a base-60 system.

By analogy, the dollar, pound, Yuan, Euro, ruble, and several now-defunct European currencies are subdivided into 100 lesser units, often termed ‘cents’ from the Latin for ‘hundred’. The entire metric system depends on subdivision by powers of ten, identified by prefixes such as kilo-, centi-, milli-, and the like. There is no essential relationship between a meter, a litre, a farad, and a gram, but each takes the SI prefixes with identical meaning. The coincidence lies in the fact of which (more than one) basic units are so subdivided.

I remember reading that the Babylonans had a 24 hour day with each hour composed of 60 minutes, and that they had obtained the concept for a 24 hour day from the Egyptians, but the Babylonians took it further and made the hour a fixed length throughout the year, rather than varying it (iirc the Egyptians divided the day into a fixed number of daylight hours, a fixed number of twlight hours, and a fixed number of darkness hours). They then realized that the hour was too long for some time tracking purposes, so they divided it by one of their favorite numbers, 60. The Babylonian number system was a combination of base 10 and base 60, so it made sense (just like it makes sense to US to divide something into tenths).

What is fascinating is that the arbitrary hours minutes seconds ends up with a measure that matches seconds ( as close as biologically possible) to human pulse rate. At least, the unexcited human pulse.

The Babylonians were aware of what the real length the year is, but found 360 official days a useful thing to use. As noted above, their number system was mostly based upon 60. The simple reason is that 60 is a very useful number, since it is divisible by 2,3,4,5,6,10,12,15, and 30. 360 is a similarly useful number. 24 and 12 are pretty nice numbers too. 24 is divisible by 2,3,4,6,8,12. Makes sharing out things trivial.

When you think about the neatness of these numbers, use of 10 as a base looks a little stupid. 12 would have been a much nicer number to have based our number system on. 60 was OK for the Babylonians, but it was a bit unwieldy. There were not individual symbols for the 60 numbers, rather they were built up with a rudimentary base 10 mechanism. But they had a positional notation that worked much as our does based upon it (and included a form of zero.)

Notice how surfing the net shortens hours?

Not very close. Pulse rates vary widely but I believe the average is around 72 beats per minute, which means seconds are off by twenty percent.

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Pre-decimal British currency was based on 12.

12 pennies to the shilling, 240 pennies to the pound.

Australia and New Zealand went decimal in the 60s, and the UK itself in the 70s, precisely *because* the old system was so difficult. I like old things in general, but decimal currency is a *much* better idea.

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The Babylonians counted with hands differently: they did use the fingers of one hand, but used the joints of four fingers for the other hand. That’s why their math was based on fives and twelves.

It’s a much better idea in a world using base-ten for maths. If we’d used base-twelve for everything instead of just for various goods and money, decimal currency would never even have been suggested, except in tricky math problems.