Base 60

     10 is a wonderfully easy base to work with when doing arithmetic. When I was doing questions on Monday in base 60, it was a lot to wrap my head around and I admit that I used a calculator to expedite my process. When thinking about when 60 would be more useful, I first thought about time. However, I'm not sure if the ancient Babylonians had a similar system to time as we did. Next, I thought about angles; I thought about 30:60:90 triangles and Pythagorean triples. I was aware that ancient Babylonians had some systems for geometry and angles. In line with angles, there are also circles as they divide cleanly into 60's. 60 is also interesting because it has so many factors, you can split it into many prime and composite numbers.

    In our culture, 60 is used often in the situations I described above. Most commonly, it is used for time and we can easily represent seconds, minutes, and hours in base 60. There are 60^2 seconds in an hour for example. I'm not too sure why 60 is used so often for space and time, but if I had to guess it would again tie into circles. Clocks are circular, so each second, the second hand would move 1/60 of the clock or 6 degrees. Then before mechanical clocks, we had sundials which involved the angles of a shadow moving across a circular disk.

    In Origin and Development of the Sexagesimal System of Numeration, Lewy suggests that the origin of the base 60 numerical system came from grain trade and harvest between Babylonians and Assyrians and they had different numerical systems that eventually evolved together. The shorted version is that land was measured in qû and kurru. Land was often irregular in shape and thus area of a field had to be determined by a ratio between seed-grain and area. Measures of capacity were ratioed in 1:10:100:300. The number 300 was important because it represented 30 qû or 1/10 kurru. A text showed that men were allotted 30 qû of grain and 30 was a easy number to work with because it had many factors and thus ways to be split. Eventually, 30 qû was insufficient and became 60 qû instead.


    Lewy, H. (1949). Origin and Development of the Sexagesimal System of Numeration. Journal of the American Oriental Society, 69(1), 1–11. https://doi.org/10.2307/595393

Comments

  1. Amanda FritzlanSeptember 24, 2022 at 10:08 AM

    Interesting point about sundials and circles and time. I enjoyed our brief conversation about the measurement of land and grain being a part of the development of base 60. I am curious about the allotment of 30 qu of grain for each man, how much it was, and if this is the amount that would feed a person or a family.

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