Why Base 60?

Speculative phase:

One of the possible reason that 60 might be more convenient and significant base number than 10 is that 60 has more factors. 60 has 12 factors, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, whereas 10 only has 4 factors, 1, 2, 5, and 10. Having more factors indicates that 60 is divisible by more numbers than 10 which can be vastly convenient to use it in a system. Also, 60 might have been a more suitable base number than 10 because it represents greater quantity. Assuming that counting and recording numbers were great labour for Babylonians, having a greater base number would have been favourable to manage collected data.

One of the examples of the base number 60 in our daily lives is time. One hour is 60 minutes, one minute is 60 seconds. Hence when we talk about time, we can divide up an hour into different units, such as half an hour and quarter of an hour.

Research phase:

In our contemporary world, the significance of 60 can be found in a circle as circles have 360 degrees angle. This idea derives from fitting triangles in a circle where each of the triangle's three sides having the length of the radius of the circle. Six of these triangles can perfectly fit within a circle. Having the base number 60, Babylonians divided up the arc of the circle created by each triangle into 60 equal parts, resulting with the total of 360 parts in a circle. Hence, the angle created by an arc with the length of 1/360 of the circumference of the circle is called one degree, and a circle has 360 degrees angle. 

Another example of base number 60 is used in Chinese calendar which uses two cycles, decimal (the ten stems) and duodecimal (the twelve branches). Therefore, it takes 60 cycles for decimal and duodecimal to match again.

Citation:

Hanson, Roger. “Roger Hanson: The Origins of the Number 60 as a Counting Method.” Stuff, 19 Aug. 2015, https://www.stuff.co.nz/science/71273903/roger-hanson-the-origins-of-the-number-60-as-a-countingmethod#:~:text=The%20theory%20is%20that%20the,60%20often%20gives%20easy%20fractions.

Ferlus, Michel. "The sexagesimal cycle, from China to Southeast Asia." 23rd Annual Conference of the Southeast Asian Linguistics Society, May 2013.

Comments

  1. Amanda Fritzlan24 September 2022 at 09:34

    It's fascinating that base 60 is so useful for measuring circles! And we use it to measure the earth. I hope that you continue to explore and share connections between base 60 and the Chinese calendar.

    ReplyDelete

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