The Wonderful Discovery of Nothing
By Seymour Papert
This learning story was excerpted from The Connected Family: Bridging the Digital Generation Gap (Longstreet Press, 1996).
Almost all parents think that it is a good thing for their kids to do something called "learning math" and are therefore in the market for software that will "teach kids math." So far, so good. But what is not so good is that their ideas about what math is, and why the kids should learn it, are so flimsy that they are in a similar position to people who want to buy food for their kids but do not know the difference between nutritious food and junk food.
In my view 99% of what is sold is junk math.
Since that is a pretty strong statement you are entitled to ask—in fact you ought to be asking—about my qualifications. Well, just click on the word and you'll learn about my paper qualifications...like getting myself a Ph.D. in math and getting to be a professor in the math department at MIT. But the way I'd rather be judged is by listening to my stories with an open mind and seeing whether they make sense to you. A great thing about this active medium is that it is so easy for readers to take different routes...and stick in their own opinions.
When I was a kid I was told "The Hindus invented the zero." I remember wondering what they really invented. What do you mean "invent the zero?" I decided that what they invented was the round symbol we use for zero. Many years later a kindergarten girl appropriately called Dawn taught me to understand what those Hindus really invented.
Dawn was working (or playing...I don't see much difference between these things when they are done well) at a computer using a version of Logo that allowed her to control the speed of moving screen objects by typing commands like SETSPEED 100, which would make them go very fast, or SETSPEED 10, which would make them go much slower. She had investigated some speeds that seemed significant, like 55, and then turned to very slow speeds, like 5 and 1.
Suddenly she became very excited and called over first a friend and then a teacher to show something interesting. I happened to be visiting the class and shared the teachers initial puzzlement: we couldn't see what Dawn was so excited about. Nothing was happening on her screen.
Slowly it dawned on me that the point was that Nothing (with a big N) was happening. She had typed SETSPEED 0 and the moving object stopped. She was trying to tell us, but didn't have the language to do so easily, that those objects that were "standing still" were still "moving," they were moving with speed zero. She was excited about discovering that zero is also a number, speed zero is also a speed, distance zero is also a distance and so on. Up to that point zero for her was a non-number. A nothing. All, of a sudden it had joined the family of numbers.
This is the kind of discovery of which "learning math" is made. I have seen other children—and even some adults—become excited at discovering that in the version of Logo Dawn was using you can give the instruction SETSPEED -10, and the object will move backwards. Negative numbers are also numbers and negative speeds are also speeds!
I was reminded of these incidents, and chose this story for this week, because I happen to be in Russia and it happens to be February and I was told yesterday that the temperature had gone up from 10 to 20..."20 degrees of frost." Nobody here says "minus 20" or even "20 below." Everything (at least in the realm of temperatures) is expressed positively. Or maybe I should say "relatively" in a truer meaning than most people give that word: one that allows us to see going down as a kind of going up.