Why is base 60 special?

              I think that Babylonians used 60 as the base rather than 10 as 60 has more factors than 10. Specifically, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, and the factors of 10 are 1, 2, 5, and 10. Since 60 has more divisors than any smaller positive integer, it is referred to as a "highly composite number". I believe Babylonians chose 60 as the base for the number notational system for efficient calculation.

             Numbers are deeply related to human civilization and life, and I think 60 survived as the base for the number notation system since it gives meaning to our lives. The units of angle and time are both expressed in a 60-base system, such as using units of minutes and seconds. 1 hour equals 60 minutes and 1 minute equals 60 seconds. Also, 360 degrees of an arc equal a full circle. A year is 360 days and this is divided into 12 months of 30 days, which are factors of 60 each.

             The commonly accepted explanation for using a sexagesimal system is that it was based on astronomy and the desire of the Babylonians to create precise calendars to chart the changing of the seasons and predict the best times for planting, which was crucial in a society with a strong agricultural foundation. When the Babylonians first developed their numbering system, they thought that there were 360 days in a year. They split this number into degrees, which represented the sun's daily motion around the sky. Then, by converting degrees into minutes, they translated this into measuring circles. (Shuttleworth, 2010)

             In my research, the advantage of the 60-base system is that 1/3 is an infinite number in decimal, but 20 (1/3 hours in 20 minutes and 1/3 minutes in 20 seconds) in the 60-base system. The decimal, unlike integers, is created by an equal division and cannot be counted one by one with a finger. Additionally, the ancient Babylonians noticed that the earth took around 360 days to revolve around the sun. As such motion is circular, the ancient Babylonians recognized that a revolution of full circle is 360 degrees.

 



References


Lamb, Evelyn. (2017). The Joy of Sexagesimal Floating-Point Arithmetic. Retrieved from

             https://blogs.scientificamerican.com/roots-of-unity/the-joy-of-sexagesimal-floating-                               point-arithmetic/

Shuttleworh, Martyn. (2010). Babylonian Mathematics and Babylonian Numerals. Retrieved Sep 13,                 2022 from https://explorable.com/babylonian-mathematics

Comments

  1. Amanda FritzlanOctober 2, 2022 at 1:50 PM

    The connections between Babylonian agricultural development, their notion of 360 days of the year, and base 60 mathematics is fascinating. Great post!

    ReplyDelete

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