Base 60 Homework

Image source: https://i.ytimg.com/vi/FxTencmpDLc/maxresdefault.jpg

1) When I first began thinking about base 60, all I could really come up with was that 60 is divisible by many numbers. It has 12 factors while 10 has 4 so it would be more convenient for division. However, this made me question why that would be significant. I realized I didn't know a lot about the historical and cultural context of the Babylonian people as more questions came to mind. What were they needing to count? How was 60 related to time? I wasn't sure how they were measuring time so I wasn't sure if they counted 60 seconds in a minute etc. What type of currency did they use (if they did) and how would counting by 60 be connected to that? How did they measure distance? Were they concerned with speed? I also wondered if the choice may have had something to do with the frequency of full moons, which are about every 29-30 days. I had all these questions but absolutely no idea because I hadn't really thought about it before, and I couldn't make educated guesses because I lacked the background information about Babylonian civilization.

2) The obvious connection with modern times was time (60 minutes in an hour, 60 seconds in a minute). I wasn't able to come up with many other ideas except maybe 60 miles/hour being a speed limit in the States but Imperial units aren't actually in base 60 so that isn't really related. I wasn't familiar with the Chinese zodiac system and couldn't think of any systems across other cultures either.

3) When I began my research, I looked for general knowledge about the significance of base 60 in Babylonian and other cultures. 60 being divisible by many numbers was a contributing factor to why they chose that system, but not in the way I had expected. In an article by O'Connor and Robertson, they describe how Babylonians used a table of reciprocals to multiply. The Babylonians used approximations for numbers that were not divisible so, as O'Connor and Robertson describe, if the fraction 1/13 was used, they would say 7/91 ~ 7 x 1/90, and indicate an approximation was used here. Thus, there was clearly an advantage to have a base with a high level of divisibility so less approximations would have to be made. Aside from that, 60 was also significant because the Babylonians devised the system of splitting the day into 24 hours with 60 minutes per hour and 60 seconds per minute. They represented these times with fractions to account for minutes and seconds (O'Connor and Robertson, 2000).

In terms of other uses of base 60, the Chinese Sexagenary Cycle is another ancient one. This time and space system consists of 10 heavenly stems and 12 earthly branches. A year consists of one heavenly branch and one earthly branch. The heavenly branch and earthly branch change sequentially each year (i.e. 1-1, 2-2 ... 1-11, 2-12, 3-1...10-12) until they reach the 60th year (10-12), at which point the cycle restarts. Base 60 has also been used by others in history including Plato's musical marriage allegory which involves the number 60^4 = 12 960 000, and by astronomers throughout history (see list on Wikipedia). One of the major points I missed was that 60 is a significant number in geometry with regards to angles. I was quite annoyed with myself for not thinking of that!