The Babylonians probably used a base 60 system because it is an easy way to count with fingers. They would use base 10 for the smaller numbers, since we have 10 fingers. But to get to 60, we can use the knuckles of our fingers. Our index, middle, ring, and pinky finger all have 3 notches, and we can use our thumb to keep track of which notch we are on. This means that on one hand, we can get to 12. So, with our other hand, we can all 5 fingers to keep track of how many times we have counted up to 12. So, with 5 fingers on the other hand, we can count to 5 x 12 = 60! (Exclamation mark, not factorial)
Now, when it comes to using base 60, I can’t really think of anything outside of keeping time, since we have 60 seconds in a minute and 60 minutes in an hour. If I were to guess, having 60s is helpful with the position of the sun. Since sundials are one of the earliest types of clocks, ancient civilizations probably realized that small segments of time can be divided into exactly 60s, making this base number quite useful. The angle of 60 is also useful, since that is a third of a triangle and a sixth of a circle. I can see this being useful in learns of architecture since it’s a nice number to divide with.
And, from the research that I’ve done, the most prominent theory is that not only is counting by the knuckles simple, 60 is also a very nice number to be dividing with. It is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, making it useful for base 10 as well. This ease of division also makes fractions simpler, since the Babylonians used a lot of fractions in a lot of different areas such as measurement, currencies, and weighing crops. With this base 60 system, the Babylonians were able to approximate square roots and Pythagorean Triples, which inspired Greek architecture and modern mathematics. In Ancient Greek, as well as Mesopotamia, base 60 is useful in Astronomy. For example, the sky is 360 degrees, a circle, and if we divide that by 12 constellations, we get 30, which gives us 12 months and 30 days. And in the modern times, we still use a similar calendar system! Of course, base 60 is prevalent globally since almost all cultures use the 60 minute 60 seconds time system.
Sources:
https://www.parabola.unsw.edu.au/sites/default/files/2024-05/vol60_no1_5.pdf
Great post, Leon! And thanks for sharing all the links to the sources.
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