5 ms·
Without addressing the benefits of using base-12, the supposedly simplifying arithmetic example is atrociously awful: >The clerks then described a typical prob
by romwell 6y ago
Without addressing the benefits of using base-12, the supposedly simplifying arithmetic example is atrociously awful:
>The clerks then described a typical problem, getting the cubic content of a package measuring 2'6" x 3'6" x 4'2"
Duodecimals (or any positional system) are a bad representation of these numbers. The author proceeds with a very tedious computation of 2,6 x 3,6 in base 12.
Instead, you can do it all in your head:
2'6" x 3'6" x 4'2"
= (5/2)" x (7/2) " x (4 1/6)"
= 35 x (1 1/24) ft^3
= 35 + 35/24 ft^3
= 36 11/24 ft^3
There is more to say for the "duodecimal" musical notation, where each note lives on its own line (abolishing the sharps and flats).
This notation is called the piano roll, as it was already in use in mechanical player pianos. It's not great for writing with a pencil, but excellent for screens and editing - which is why most producers would go straight to the piano roll.
It's not, however, connected to base-12 in any way.
- Joker_vD 6y ago76 cm x 107 cm x 127 cm, should be about a cubic meter, give or take (if it was -25 cm on one side and +25 cm on another, it'd have been a 1x1x1 cube).
- romwell 6y agoI thought for a second it wouldn't work like that, but it does! You are increasing the length of one of the sides by 33%, but decreasing by 25% to get to roughly-a-cube. The product of ratios is 3/4 * 5/4 = 15/16, or about 6% underestimate. Of course, this is already pretty close, and the third side being 107 and not 100 corrects for that. In the end, that's because (1-x)(1+x) = 1-x^2, so if if the amount we're doing this with is under 20%, our error is under %4 (i.e. pretty good for rough estimates).