Sept 21 - Babylonian Mathematics

 

    The number 60 is convenient for a number system base because it has so many factors (1, 60, 2, 30, 3, 20, 4, 15, 5, 12, 6, 10). The large number of factors allow for easy representation using fractions. Unlike say base 10 which only has 1/10, 1/5, 1/2 and 1, a base 60 system has access to 1/60, 1/30, 1/20, 1/15, 1/12, 1/10, 1/2, 1/3, 1/4, 1/5, 1/6 and 1. The large draw back is that the next order of magnitude is 3600, a significant difference from 100 in our base 10 system. This means the Babylonians would require significant space to write out large numbers. I assume that they didn’t need numbers of that magnitude, as they likely used mathematics in construction, taxation and other day-to-day societal functions where numbers that large would not appear, and so this limitation was not a noticeable detriment.

    Of course, a base 60 system didn’t end with Babylonian civilization, we still use one to tell time. Again, I think its largely due to the plethora of fractions available from 60; they allow us to quickly and clearly track and communicate time. We also use a multiple of 60 to measure angles and circles (though that’s technically base 360, it’s similar). Our current base 10 system allows very precise measurements, in the form of decimals, due to its usage of only ten symbols. Without that precision a fractional system makes more sense for searching the night’s sky or otherwise measuring circles and spheres.

    Based on the two articles linked at the bottom of this post, we don't know exactly why the Babylonians chose base 60, though it is accepted that it was likely due to its divisibility, being the lowest common factor of 1, 2, 3, 4, 5 and 6. It has also been posited that the base 60 system originated from the mixing of a base 5 society and a base 12 society. Our use of 60s in measuring time can be linked to ancient Greece, and in fact we defined a second as a fraction of a solar day until 1967 with the advent of atomic time. 

https://www.thoughtco.com/why-we-still-use-babylonian-mathematics-116679

https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/#:~:text=The%20Babylonians%20made%20astronomical%20calculations,the%20first%20six%20counting%20numbers