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this post was submitted on 12 Dec 2023
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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.