Speculative phase:
When initially thinking about why the Babylonian people used base 60, I though of time and 60 seconds, 60 minutes etc. but quickly came to the conclusion that it is unlikely the Babylonian people had an understanding of time to this level of detail. I thought of of how 60 can be divided by 1,2,3,4,5,6 which allows for easy conversions which could be possible.
Today we still use 60 for several things including the most obvious being time including seconds and minutes. It is also common practice to quote car acceleration speeds from 0-60mph which relates back to the division by time making for easy conversions.
Research phase:
Although I could not come to a clear conclusion on why Babylonian people used base 60 there are some interesting facts that may lead to why including: base 60 is the smallest integer with the most divisors and furthermore the Pythagorean theorem is based on Babylonian math.
Winston, you've made an interesting connection between how we talk about velocity and base sixty.
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