Babylonian Mathematics and the Curious Case of Base 60

Mathematics has had a place in history for hundreds of thousands of years; notably, the Babylonians used a base 60 place value system, a stark contrast from the base 10 we use now. When first asked about why they may have used base 60, I immediately came to a halt. Why would they? What's the relevance? It wasn't until I read the next question, asking how we still use 60s in our daily lives that allowed me to spark a train of thought. The first notable 60 used to today is in the context of time: 60 seconds is 1 minute, and 60 minutes is 1 hour. Although notable, this doesn't answer why 60 was used. I believe 60 was used however because of how it's easily divisible. I remember learning in a number theory class that 60 is the only number that can be divided by 1,2,3,4 and 5; with this in mind, it is possible 60 was used because we can divide 60 into half, thirds, quarters, fifths, sixths, and tenths (of course we can divide 60 into twentieths, thirtieths and other factors, but we don't have that many fingers)! This would make 60 a really desirable number as time could work in ones favor without having a clock. The idea of not having a clock also feeds into my next area of notability: the circle. Now the circle is not 60 degrees in nature, but like the division argument made earlier, the circle is divisible by 60 degrees.

Perhaps Babylonians were able to find out that a circle was 360 degrees, and with their knowledge of ratios and 60s, theycould use such inventions as sun dials. This would allow the Babylonians to have a makeshift way of telling the (exact) time. 

From the site Thoughtco.com's Babylonian Mathematics and the base 60 System (linked below), it's interesting to see that the reason why Babylonians used base 60 was similar to my argument of having more factors. In the article, it mentions that base 60 has factors of 1,2,3,4,5,6,10,12,15,20,30 and 60 while base 10 only has 1,2,5, and 10; in fact it's actually pointed out by the Times that the number 60 "has more divisors than any smaller positive integer" which is something I didn't know before. What was also interesting was the way they invented the systems using their hands as well. As noted above, we use a base 10 because we can count 10 on our fingers, but it doesn't seem possible to count to 60 on our fingers alone. However, the Babylonians apparently used their hands as well, using one hand to count to twelve, and the other 5 fingers counting groups of 12 --> 5 x 12 =60! The way they counted the 12 was by using the index to pinkie fingers' joints (tip, middle joint, and where the finger meets the knuckle), 3 'joints' connected to 4 fingers is 12. This was mind blowing to me, and shows how 60 is still able to be divided and counted through fingers. 

ABC Science also wrote about how the Babylonians told time, saying that "...their division of a day into 360 parts called 'ush' that each equaled four of minutes in our time system". There is also hints that the Babylonians thought that there were 360 days in the year, which is not far off from the 365 day calendar we use now. If this is true, ancient Babylonians may have influenced modern day astrology into how we perceive our heliocentric model of the solar system. 

Another way that Babylonians influenced modern day mathematics is through their writing and documentations of numbers. The Babylonians had a symbol for 10 and a symbol for 1s, when they were grouped together you can easily read, for example (<< YYY) as the number 23 --> 2 groups of 10 and 3 1s. This is very similar to how we teach younger students now. When we show them the number 28, we tell them it's 2 10s and 8 1s, sometimes even using blocks to represent a 10 vs a 1 (refer to picture). 

https://www.thoughtco.com/why-we-still-use-babylonian-mathematics-116679#:~:text=Babylonian%20math%20has%20roots%20in,according%20to%20%E2%80%8BUSA%20Today.&text=When%20the%20two%20groups%20traded,multiplied%20by%2012%20equals%2060.

https://www.abc.net.au/science/articles/2011/11/15/3364432.htm#:~:text=Ancient%20Babylonians%3A%20hours%20and%20minutes,60%20plus%20two%20or%20182.