Engines of Our Ingenuity

No. 2825: INNUMERACY

by John H. Lienhard

Today, innumeracy. The University of Houston's College of Engineering presents this series about the machines that make our civilization run and about the people whose ingenuity created them.

A generation ago, all the talk was about illiteracy in America. How our language skills were slipping. Now the pendulum has shifted. We see our schools falling behind in math and science. Well, math and science deal with the quantifiable world around us. And, it all comes to rest upon our unease with elementary arithmetic.

Writer Douglas Hofstadter saw it coming in the early '80s. He coined the term, innumeracy for our rising inability to see reality in numerical terms.

"That'll be $15.21," says the store clerk. I hand over a twenty-dollar bill and 21 cents. The clerk hands back my coins. Then he pushes a button on the cash register. It serves up $4.79 in change. No mental manipulation of numbers is even allowed. And my pocket groans with small change.

Our innumeracy appears in such small things: Consider the matter of round-off. Suppose my cat needs around three ounces of canned meat daily. I find 2.3-ounce cans. Not enough. I go on and find 2.8 ounce cans. That's close enough so I buy them. Common sense says that one can is roughly two ounces, the other is roughly three.

Or go to the gas station. The pump price says $3.49. But every gas station tacks on another number -- another point-nine in teensy tiny type. We should mentally add another penny. That gas is really three-fifty per gallon. Yet people always quote the lower number. A penny per gallon isn't much. But over a lifetime it comes to a few hundred dollars.

Almost $3.50

Our failure to ingest the idea of sensible round-off leads to the insane convention of pricing everything one dollar or one penny less than the round-off price. And we're suckered in by it. If we have no real sense of what numbers mean, we really do see an item as less expensive than it really is.

Actual -- typical -- used car ad

That sort of fudging is universal. We have a nice hybrid car. It has a readout that tells us what mileage we're getting. I've kept careful track of miles driven and gallons consumed. Sure enough, the display consistently says we're doing five percent better than we really are. The car maker can fudge the numbers that way because he can generally rely on us not to question them.

Actually, only about 52 mpg

A salesman tells me that a $140 item is on sale at 40 percent off -- it's only a hundred dollars. When I try to explain that 40 percent off $140 dollars leaves 84, not 100, dollars, he looks at me blankly -- and stands his ground.

So innumeracy reveals itself in the small stuff. But the real damage is done when politicians and Ponzi schemers begin using far worse sleight of hand with billions, nay trillions, of dollars. And woe betide anyone who's left without the tools needed to question them.

And so it is: math, science -- and economics -- are quantita-tive. If we aren't grounded, from the beginning, in elementary arithmetic, our complex, high-tech world becomes a very dangerous place.

I'm John Lienhard at the University of Houston, where we’re interested in the way inventive minds work.

(Theme music)


For more on the idea of innumeracy, see this web page on Hof-stadter's ideas. See also: J. A. Paulos, Innumeracy. (Hill & Wang, 2001).

This episode was first aired on August 27, 2012



The Engines of Our Ingenuity is Copyright © 1988-2012 by John H. Lienhard.