A base-12 metric system would be absolutely gorgeous. Geometry and trigonometry would be greatly simplified with a duodecimal unit circle. Our 360-degree circle is a truly ugly hack to make geometry play nice with a decimal number system.
Our base-10 number system would be as ugly to a duodecimal society as a base-7 system would be to us.
Base-6 wouldn’t be bad at all. “100” in base 6 is 36 in base 10. Their metricated unit circle would have three times as many “degree” divisions as we have hours on a clock.
Base 7 or 14 would require something akin to the sexagesimal abstraction layer we use to make base-10 play nice with angles.
A base-12 metric system would be absolutely gorgeous. Geometry and trigonometry would be greatly simplified with a duodecimal unit circle. Our 360-degree circle is a truly ugly hack to make geometry play nice with a decimal number system.
Our base-10 number system would be as ugly to a duodecimal society as a base-7 system would be to us.
On the last point, a better comparison would be base 6 or base 14.
10 = 2 × 5
6 = 2 × 3
14 = 2 × 7
Or maybe a better way of thinking about it is the percentage of numbers that divide nicely in the base, as a percentage.
Base 10 has 2, 5, 10 = 30%
So maybe base 3 is the closest, at 33% of numbers being easily divisible.
Either way, 7 is a significantly worse base than 10.
Base-6 wouldn’t be bad at all. “100” in base 6 is 36 in base 10. Their metricated unit circle would have three times as many “degree” divisions as we have hours on a clock.
Base 7 or 14 would require something akin to the sexagesimal abstraction layer we use to make base-10 play nice with angles.
You’re not alone, but the idea of a movment to duodecimal hasn’t had traction in a long time: https://en.wikipedia.org/wiki/Duodecimal#Advocacy_and_“dozenalism”
Also, ancient Egypt was hip to his idea: https://hsm.stackexchange.com/a/2881
Fun fact, you can count from 1 to 12 on one hand by touching your thumb to count your finger bones, as there are 12 of them. https://en.wikipedia.org/wiki/Finger-counting#Asia