The high school chemistry teacher would say something. Maybe it would chime something in my head a week later, maybe several years later: maybe in a college physics class, maybe in my early twenties while drinking a beer in the Whitehorse … maybe never … maybe now. There’s no telling when a point will strike one as significant, when a metaphor of Shakespeare’s will suddenly explain to one a conundrum of Russell’s … A thought about the physicists’ concept of significant numbers just came to me. Thoughts on the subject have come before, but this association was I think new to me.
First, what is it?
If someone says to you, “She’s in her sixties,” and then someone asks you, “How old are you,” and you answer, “I’m seventy-three years and eight months and um, twelve days, and … um,” that person may well shut you up, and say, “So, you’re in your seventies.” “Seventies” is as exact a quantity as they want.
If the recipe calls for a handful of flour and a pinch of salt, you’re wasting your time if the next time you bake you count the salt grains. If you do count the salt grains, then count the flour particles too.
Several times at K. I quoted a story by mathematician John Allen Paulos: A Mathematician Reads the Newspaper:
|Someone visits the natural history museum. Walking through the dinosaur room, the museum guard seems friendly, anxious to talk. The visitor cooperates: “I wonder how old that dinosaur is?”
The guard answers promptly: “One hundred fifty million and nine years.”
“That an odd number,” the visitor responds. “How do you know such a precise figure?”
“Well,” the guard begins, “on first working here I was told the dinosaur was one hundred fifty million years old, and I’ve been here for nine years, so …”
Sorry, Mister: your nine years don’t count in that figure.
OK: that’s “significant number”: in doing calculations, if each and every quanity is reliable to six places, then you can calculate with numbers, all reliable to six places. If one of your quantities is vaugue, reliable only to two places, throw out your excessively accurate numbers, round everything down; otherwise, you’re kidding yourself, misleading others.
Now: here’s how that came back at me:
If the priest tells the parents how many of the boys in the class touched themselves, without telling the boys how many of the parents touched themselves, you have a prison guard with a 150,000,009 year old dinosaur.
If you have statistics on suicides in Sweden, the US, Italy, but only Sweden is half-way truthful about such things, then throw out all your data, you don’t have any significant data.