It's interesting to me that both duodecimal and decimal counting are recommended as being easy to calculate with.
The benefits of decimal come from our using base-10 for other purposes. I guess the best of all possible worlds would be to use duodecimal for all units (including our normal number system).
Then we'd get the ease of use of modern base-10 units plus the better factorisation of duodecimal.
(But we'd still have an impedance mismatch with the binary powers. The KB/KiB split wouldn't go away).
As an aside, I wonder how technology affects the units or systems we use. They had to rely on decimal or duodecimal systems for their units because they were doing all of their calculations manually (so did we until about 20 or so years ago btw,) but now that everyone* carries a computer on his/her pocket, what better systems could we design?
I guess binary might be an example of that. 2 values is not something that applies to everything, at least not naturally in the way the human mind works, but it is much more efficient for machines to process information, that makes sense.
How is base 10 more elegant than base 12?
1/64th might result from a binary, octal or hexadecimal system; duodecimal tens to favour things like 1/3, 1/4, 1/6, 1/9, 1/12 and so on. The elegant thing is that in duodecimal all of those are non-repeating fractions: .4, .3, .2, .14, .01 respectively. Interestingly, in duodecimal 1/5 and 1/10 are non-repeating (this is also true in binary...).
Base 12 is far more elegant than base 10, but the conversions cost make the conversion to French units look cheap--and then we'd need to convert all our units to some sort of French units mark II.
For day-to-day use, it makes sense to use a system where you can express your age (in years) in one or two digits rather than five to seven. Hence, a hexadecimal system might be preferable as a representation.
1/3 vs 0.3' ? Much elegance!
1/3+1/3+1/3==1 vs 0.3'+0.3'+0.3'==0.9'==1 or something.
One interesting thing I heard once - a journalist was discussing the merits of counting in base 12 with someone whose society already adopted this method. When the journalist asked how we would teach kids to count with their fingers, the answer was simple - use the divisions created by your knuckles!
It would mess with everyone but I think there's a pretty strong argument for base 12.
edit: okay, i finished reading and it kind of says that already. But it's still cool!
I'm pretty sure my flatmate told me the story and he watches numberphile too so you're almost certainly right either way :P
Sorry to nitpick, but "exacerbate" is to make worse. It's like "ex-acerbate". It doesn't mean "even more so" in a good way. Just thought you'd like to know.
The verb "to exacerbate" comes from French verb "exacerber", which means "to make more intense or more acute".
My post has been edited to reflect your comment.
I believe the last argument is understated: one big advantage of base 12 over base 10 is division by 3. This offers many ways of dividing a time interval into several sub-intervals of identical duration.
For base 60, this intensifies: as mentioned in the post, 60 is the smallest number divisible by 2, 3, 4, 5, and 6. This gives tremendous flexibility for dividing a time interval.