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No. 1817:
Scaling Numbers

Today, we lay numbers out on a dial. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

I was reading a murder mystery in bed the other evening — about a police chief looking for a murder weapon. It was a forty-millimeter handgun. I almost gagged. That gun would've had a barrel over an inch-and-a-half in diameter.

Then, halfway through the book, that was corrected to forty caliber (or two-fifths of an inch.) So it seems that neither author nor editor associated a mental picture with the size of the weapon. Forty-millimeter and forty-caliber were only words.

Think for a minute about numbers. They can be used to enumerate — like counting the number of people in a room or the number of years you've lived. We can also use them to express measurements — like temperature, length, or time. Then they represent arbitrary tic-marks on some sort of scale — a thermometer or a clock face.

Those marks can be close together, like millimeters, or farther apart, like inches. And here rises a really basic issue of scientific literacy. If we don't form mental pictures of those various scales, they'll never be more than noise in our heads.

Do you remember when, in 1999, people managing a Mars orbiter confused English and metric units? A 125-million-dollar mission ended up splattered over Mars' surface. And such errors become even more likely when units are compounded, as in miles per hour, degrees per inch, or square feet.

Five square inchesA tour guide in a large plant recently told us how big the plant was. "It's five miles," she said. But the place was neither that long nor that wide. So I asked, "Do you mean five square miles?" "Well," she replied, "I don't think all of them are square."

She knew the plant by appearance. But five miles were simply words that she'd been told to use. You hear this kind of misuse all the time. An advertisement proclaims that a heating unit puts out 14,000 Btu's. Well, that's nice, but how often — every month or every second?

We've carefully formed a language to express the technical complexities around us. Bowdlerizing that language is a dangerous form of malapropism. Surely any of you would react if I said a person had a "photogenic memory" or that I like "parakeet flooring." Such meaningless phrases as, "The turbine puts out one megawatt per hour," or "That wire supplies 2000 volts of power," represent a much worse form of illiteracy.

It's worse because we all traffic in electric power; we all use heating and cooling systems; and we all meter our living space in square feet, square meters, or square miles. You and I need to understand just what a megaton of explosive can do, or what a 25-mile-per-gallon fleet average means in everyday traffic.

We need to view physical units as the rich and expressive language that it is. And that is why I tremble when I imagine looking down the barrel of that forty-millimeter pistol.

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

(Theme music)

For listeners who wonder about the two examples of technical malapropism above: A megawatt is already a rate of producing power. It means "one million Joules per second." A volt is a measure of electric potential, not power. Electric power is the product of the current flowing the wire and the voltage driving it.