I very clearly recall my first exposure to chicken pox, and the suffering that resulted.
But who can remember the first time they were exposed to negative numbers? I sure don’t. I’m tempted, however, to blame my initial exposure on my eighth grade math teacher, Mrs. Hagemann. Mrs. Hagemann stood about 5 foot 2 in her clunky black heels; she wore flower print dresses and schoolmarmish wire-rim glasses, and kept her hair dyed to a slightly unnatural shade of auburn.
If you met her on the street, you’d probably peg her as a librarian — you know, the type of older woman who can shelve books with great accuracy while simultaneously being able to frighten children enough to prevent loud whispering and giggling. You would never guess that Mrs. Hageman understood mathematics deeply enough to explain ‘negative numbers’ to distracted, homone-infected eighth graders.
But Mrs. Hagemann not only explained negative numbers to us; she actually made us believe that they existed. She illustrated them on the chalkboard, using a “number line.” Zero was in the middle. On the right were the “positive numbers.” On the left were the “negative numbers.” By the time I left her class in June, Mrs, Hagemann had me convinced that numbers like “−5” had a meaningful essence.
Before we go any farther… a quick refresher course, in case you’ve forgotten everything you were supposed to remember about negative numbers. (Maybe, like me, you were momentarily distracted by certain eighth grade girls in their mini-skirts?)
First, remember that a “positive number” times a “positve number” is “positive” and a “positive number” times a “negative number” is “negative” but a “negative number” times a “negative number” is “positive”. Same with division, except backwards.
In the beginning, God made each of us with ten fingers. And unless we played with fireworks or hunting knives when we were kids, we probably still have ten fingers. Obviously, then, God wanted all of us to be able to count to ten. (Or even up to twenty, until shoes became popular.)
But counting to ten wasn’t good enough for the mathematicians. In an effort to boost their salaries, they came up with clever ways to make mathematics seem too complicated for the ordinary person. First they invented fractions, and then square roots, and then geometry. Then they started telling us they could calculate, using numbers, how fast a cannon ball would accelerate when dropped from the Leaning Tower of Pisa. And when the next total eclipse would happen. Important things.
To make these kinds of calculations look even more complicated, they borrowed the idea of “zero” from the Arabs. So now they could talk about the number of fingers on the hand of, say, a pirate who’d had his hand whacked completely off.
Meanwhile, over in China and India, the mathematicians were more concerned with practical matters like bookkeeping and debt collection, and they invented negative numbers — to clearly calculate and show, in black and white, how much money you owed your banker. The Arabs borrowed this clever mathematical device, and handed the idea over to the Europeans during the 15th century — right around the time European real estate companies were discovering cheap waterfront property in the Western Hemisphere.
Certain European mathematicians were drawn to the idea of negative numbers, like flies to manure. Other (more sensible?) European mathematicians noted that a negative number like, say, “−5” means “five less than nothing” and they asked (very sensibly) how anything can be “less than nothing?”
Unfortunately for all of us, however, those pesky negative numbers turned out to be very useful for doing algebra and trigonometry and calculus. And those advanced math skills, in turn, informed science and technology — and led us into a modern world where, for example, science and technology could (with the help of negative numbers) send a couple of middle-aged men 225,000 miles to the surface of the moon, to do some rock collecting.
With more achievements like that, waiting for us around the corner, the mathematicians knew they needed to come up with ways to teach innocent eighth graders about negative numbers — and trick them into believing that these imaginary numbers are real.
As a result, we Americans now generally believe that numbers like “−17,000,000,000,000” exist. That’s the amount of dollars that our democratically elected federal government believes the American taxpayers currently owe to the investment bankers on Wall Street … and in Beijing and Tokyo.
Thanks a lot, Mrs. Hagemann…
Underrated writer Louis Cannon grew up in the vast American West, although his ex-wife, given the slightest opportunity, will deny that he ever grew up at all.