Sexagesimal Supremacy

 Speculative Phase

I will admit, I did spoil my speculative phase somewhat by discussing with my group in-class why we thought that Babylonians used a sexagesimal system. Tim suggested that one of the driving factors for the use of the sexagesimal system is that 60 is divisible by many of the smallest numbers, including 2,3,4,5,6, and 10. The power of this, as Tim pointed out, is that it is very easy to reduce a quantity by a half, or a third, or a quarter in the sexagesimal system. As far as I know (pre-research), Babylonians primarily used their number system for commerce and accounting, where it would be useful to be able to, say, figure out how much of your grain stock would remain if you lost a quarter to a mold infestation, or had to pay a tenth of it in taxes. 

I imagine the fact that we still use 60 for time (60 seconds in a minute, 60 minutes in an hour) is a result of the Babylonians utilizing the sexagesimal system. I think I recall learning at some point that they were one of the earliest people to study Mathematics and Astronomy, and since timekeeping is so closely linked to celestial bodies, it would make sense that the use of the number 60 to quantify time might have taken root during the time of the Babylonians and persisted to this day.


Research Phase

My research phase was limited to an article in Scientific American, which confirmed, more-or-less, what I had previously speculated to be true regarding the high divisibility of 60 being a reason for its use as a base. I was particularly intrigued by a discussion in the article about the representability of fractions in base 10 compared to base 60. 

According to Evelyn Lamb, writing in Scientific American, Babylonians did not have the modern concept of fractions, but had to represent fractions as decimals. In a base-10 system, for instance, the fraction 1/3 has no simple form, but must be written as 0.3333…, with the implication that the 3’s repeat forever. Even terminating decimals, like 1/4, must be written with two digits (0.25). In the sexagesimal system, on the other hand, the number 1/2, 1/3, 1/4, 1/5, 1/6, and 1/10 can all be written as decimals (gesimals?) with only one digit, which is a great convenience when you have to write your numbers on clay tablets, where space is limited and mistakes may be difficult to correct. 




Lamb, E. (2017, September 12). The joy of sexagesimal floating-point arithmetic. Scientific American Blog Network. Retrieved September 13, 2022, from https://blogs.scientificamerican.com/roots-of-unity/the-joy-of-sexagesimal-floating-point-arithmetic/# 



Comments

  1. Amanda FritzlanOctober 9, 2022 at 4:45 PM

    Interesting discussion about base 60 and decimals/gesimals:) It is amazing that the Bablyonians and the Egyptians had such different approaches to fractions or decimals.

    ReplyDelete

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