> Given the attachment people have to round numbers, this would have implications. Some things would be bigger. Other things would be considered in different increments.
No, they wouldn't. This would be a very minor effect, because the primary determinant of sizes and amounts is how big you need something to be, or how much of it you need.
Instead, you'd see the same thing we already do see: contexts in which an existing unit was difficult to work with would be given their own units of a more convenient size. Consider how horses are measured in increments of four inches, or how soft drinks are sold in unit sizes of 12 ounces, 20 ounces, and 67.6 ounces.
The units aren't called that, of course; those sizes are "one can", "one bottle", and "two liters".
Some unit sizes are calibrated to geometric affinity (temperature degrees to 180 or 100, currency to 100, etc), and some are not (soft drinks).
It's likely that in a base-12 world, we'd still have "100" "cents" in a dollar. But there would be 144 (base-10) of them. That alone is interesting! But it's fine, because the collation is geometric, but the cent unit size is arbitrary.
Similarly, who knows or cares how many base-12 fluid ounces would be in a food product -- the collation (packaging) would be humanely-sized regardless.
But some units are not arbitrary, or conveniently divisible, and some collations still tend toward geometric affinity. Humans have their idiosyncrasies.
Would there be 10 base-10, or 10 base-12 amendments in the US Bill of Rights? What would the additional two amendments be?
Would there be 10 base-10, or 10 base-12 commandments in the Hebrew Bible?
Would we talk about a US president's first 100 base-10, or 100 base-12 days? Would the extra 44 days matter?
Again, none of this is profound. But if you think it isn't interesting, we'll just have to disagree.
> Would there be 10 base-10, or 10 base-12 commandments in the Hebrew Bible?
This is a case where there's no difference. Right now, Wikipedia's page on the Ten Commandments notes 15 different commandments. (Actually, 16, but two of those are "thou shalt not covet thy neighbor's house" and "thou shalt not desire thy neighbor's house", and Wikipedia knows of no tradition that thinks of those two as separate commandments.) Here it is obvious that the number of commandments is significant, at 10, and the content of the commandments is significant, but unrelated to the number. If you want 12 commandments instead, it's sufficient to renumber the existing 15 commandments, and this is clearly how the problem has been approached historically.
The same thing applies to the Bill of Rights; there are a lot more than 10 enumerated rights, but they're bundled into 10 amendments.
> Would we talk about a US president's first 100 base-10, or 100 base-12 days? Would the extra 44 days matter?
This might make a difference; 144 days is close enough to half a year that you might just mark the half year and not bother with the 144 days. Or you might mark the quarter-year, which is almost 100 days.
No, they wouldn't. This would be a very minor effect, because the primary determinant of sizes and amounts is how big you need something to be, or how much of it you need.
Instead, you'd see the same thing we already do see: contexts in which an existing unit was difficult to work with would be given their own units of a more convenient size. Consider how horses are measured in increments of four inches, or how soft drinks are sold in unit sizes of 12 ounces, 20 ounces, and 67.6 ounces.
The units aren't called that, of course; those sizes are "one can", "one bottle", and "two liters".