Sexagesimal

If you find this interesting you'll probably also find base 6 interesting. If you've not seen them these videos are both humorous and informative.

https://www.seximal.net/

One thing I found interesting is that French doesn't really have words for 70, 80, or 90. As if people in the past just didn't really need to go that high.

I have been thinking about the reasons a society might employ base 60 for a while. There's currently lots of speculation which makes offhand reference to reasons people have used base 10 and 20: fingers and toes are natural to count with.

So with body part counting methods in mind the hypothesis arises that sexagesimal is the product of counting base 12 on one hand and base 5 on the other hand to achieve 5×12=60. (Base 12 being achieved by ternary on 4 fingers, so the entire system is more specifically 3×4×5, not just 5×12).

However, a casual glance at https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals does not support the hypothetical 3×4×5 system, but without being a historian myself, I cannot say it altogether disproves the idea as, if I recall correctly, there are variations on these numerals. The depicted numerals have base 10 as a sub-base of 60. But most curious is the presence of rows of 3 as a sub-base of 10!

I have trouble imagining why 3 would be subdividing the decimal if it's not a remnant of counting dozenal on one hand. After all, the Romans decided base 5 to be most natural to embed in their numerals and their abacuses. https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal

A moment of thinking about the Babylonian writing system perhaps answers the mystery: they pressed a stylus into clay, which is more painstaking and cumbersome than counting on the hands. When writing numbers, it may have been deemed less tiresome to max out the stylus presses at 9 ones instead of 11 ones and also less visually confusing to make the maximal ternary symbol a nice, symmetric 3×3 square. So there is the possibility that strict adherence to the counting system of the hands was not seen as ideal for the practicalities of writing with a stylus in clay. But why not just have a rich enough inventory of symbols to eliminate the problem of too many, cumbersome presses that are really like sophisticated tally marks* and not quite the same as the number symbols of today? That would mean either having another stylus with a different stamp or creating another gesture on a medium which isn't as accommodating to quick, dexterous movements as pen and paper.

*A 1 was made with something similar to a direct, downward press with the stylus and a 10 by turning the stylus sideways to press the end differently into the clay. (If I remember correctly) This is hardly different than common tallies of today which are "one-one-one-one-slash". If faced with writing base 60 with only two symbols, one or slash, the naturally embedded dozenal might make the tallies too messy. A 3×3 square is easy to read at a glance.

If no body part counting hypothesis can be made convincing enough to explain historical usage of base 60, I think someone should critically examine what was counted or measured, not just how.

Are there Latin- or Greek-derived words for base 64 and base 256?

No concept of zero?