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I'm bringin' sexa back (why base 60)


I will begin this blog post with some un-researched speculation about why the ancient Babylonians chose to use a base 60 (sexagesimal) number system. It so happens that 60 divides evenly by the first 6 numbers, i.e. 60/1=60, 60/2=30, 60/3=20, 60/4=15, 60/5=12, 60/6=10. This allows quick and accurate calculations of whole numbers when dividing  by 1, 2, 3, 4, 5, or 6 without recurring decimals (or I suppose recurring sexagesimals) showing up. 

We see base 60 still present in certain parts of our lives, specifically in how we tell the time as possibly our measurements of degrees. 60 seconds in a minute, 60 minutes in a hour and even the 12 hours of AM and 12 of PM could be seen to be base 60 to some degree, as it's one fifth of 60. Additionally, measuring 360 degrees in a circle might come from 60x6. My guess as to why 360 was chosen is that splitting a circle into 60 parts proved too rough for accurate measurements, whereas splitting a circle into 3600 (60x60) parts proved too fine a measurement for early tools and instruments. 


Research Phase:

While I didn't have enough time to do extensive research, I did read through this blog post in Scientific American (Lamb, E. 2017). In it, the author confirms some of my speculations while also providing new information. Base 60 does indeed divide by more numbers without resulting in recurring decimals, though base 30 provides similar results. I learned that ancient Babylonians did not use fraction notation which further explains their desire to use the sexagesimal system, as fraction notation gives us, in base 10, a way to exactly represent something like 1/3. 

The relationship to our time telling system was mentioned, though 360 degrees in a circle were not. I did find a brief mention on Wikipedia of the degrees in a circle being residually sexagesimal, but there was no reference provided. Diving deeper into the sexagesimal system was a fascinating exercise and a good reminder of how culturally based our current math and number notation systems are. 


Reference

Lamb, E. (2017, September 12). The joy of sexagesimal floating-point arithmetic: One eight equals seven and thirty in this strange base 60 world. Scientific American. https://blogs.scientificamerican.com/roots-of-unity/the-joy-of-sexagesimal-floating-point-arithmetic/

Comments

  1. Amanda FritzlanSeptember 24, 2022 at 9:51 AM

    The fact that Old Babylonian math does not have fractions but does have place value is a good argument for why base 60 was developed. It's interesting to compare with ancient Egyptian math which does use unit fractions (and 2/3) and does not use a place value system for calculations.

    ReplyDelete

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