September 26, 2005


Kevin Drum notes that kids today are learning weird rules for dividing fractions. Strictly speaking, division can be thought of as "repeated subtraction"—that's how computers do it—but it becomes pretty cumbersome. Oddly enough, though, at some point in elementary school I learned how to subtract by nines-complement addition, and that quickly became the main way I did it. So, for instance, to figure out 8,731 minus 362, you'd take the nines complement of 362, which is 9,637, add that to 8,731, giving you 18,368, and then you lop off the first "1" and add it to the end of the sum, giving you the correct answer: 8,369. That all seems very frivolous, but I got pretty good at it, and it was fun visualizing the complementary numbers: for instance, imagining how the groove of the "5" locks in with the tooth of the "4", much like Africa and South America forming Pangea. Plus, that's how computers and mechanical adding machines all do subtraction—since it's impossible otherwise to "borrow" the one and the like. (Well, computers do twos-complement addition, but still.)

Speaking of adding machines, here's a nifty page on the Curta mechanical calculator—the first handheld mechanical calculator, which was invented by Curt Herzstark while he was a prisoner in the Buchenwald concentration camp. (Previously, accountants would lug around their adding machines in suitcases.) From what I recall, Herztstark ran into a sticking point as to how to do subtraction, because the crank only rotated one way, until he realized that you could use nines-complement addition. And, voila.
-- Brad Plumer 3:25 PM || ||