Significant Digits for the Innumerate
January 12th, 2005
Suppose you ask me, “how wide is that picture frame?” (No, nevermind why you care how wide the picture frame is. This is a little device I call, “using narrative to make a semi-technical thing sound approachable.)
“About nine inches,” I would say.
Now, suppose your friend Friedrich asks you how wide the picture frame is, and I’m not in the room (let’s say I’m asleep—that’s where I’m a pirate!). You happen to know that Friedrich is of the German persuasion, and if you give him a number in English units he’ll scoff at you and possibly destroy your apartment with a Stuka divebomber.
Thinking quickly, you refer to your wristwatch calculator which you have been wearing since 1988 (in this narrative, your sense of style is atrocious). “There are 2.54 centimeters in an inch — I remember that from high school,” you think to yourself. Doing the multiplication, you smugly report to Friedrich that the picture frame is 22.86 centimeters wide.
Everybody’s happy, right? Not so fast, Copernicus.
I only told you the frame was “about nine inches” wide, remember? That could possibly mean 8.556 inches, 9.210 inches—you really can’t be sure. As a measuring device, I am lazy and inept. Do you want to be held responsible for my lax attitude? No, of course you don’t.
You are really only justified in telling Freddy-boy that the frame is about 20 centimeters wide. Giving him the extra digits of that number just give it the illusion of precision where none exists.
Friedrich measures the frame himself and gets less than 22 centimeters. He punches you in the stomach and leaves you wincing in pain on the floor, cursing me for not giving you a better figure in the first place. Sorry, I just couldn’t be bothered. (You made your bed, now lie in it, dammit!!!)
Oh yes, my point. Well, this kind of thing applies to a lot more than the picture on my desk. If I tell you that you can get $1.32 for a Euro, and $1.89 for a British Pound, you might similarly do the math and tell me that therefore, you can get 0.6984126984126984126984126984127 British Pounds per Euro. Well, you’d be nuts.