Engines of Our Ingenuity


No. 1633:
STUDYING CALCULUS

by John H. Lienhard

Click here for audio of Episode 1633.

Today, a mathematician misses the point. 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.

A surprising number of otherwise educated people have never studied calculus. They don't know what it does or what it's for. Calculus is a form of math that deals specifically with change.

For example, suppose you open a plug in the bottom of a tank. You can use calculus to find out how long it'll take to drain as the water level drops. If I floor the accelerator, and I know my car's maximum acceleration at any speed, then the calculus will tell me how fast I'll be going after, say, eight seconds.

Now I've just found a disturbing old book from 1824, entitled A Short View of the First Principles of the Differential Calculus. It's by the Rev. Arthur Browne at Cambridge University. Browne begins with a long Preface, setting out his objectives. He's teaching calculus to young men who'll go on to become clerics, lawyers, and statesmen. That situation worries him.

He allows that it's important for students to develop a sense of logic and order, but is calculus worth the trouble? He concludes that it probably is not, except as a brief exercise in logic, undistracted by any problem-solving. So he gives us two hundred pages of propositions and demonstrations. No hierarchy of ideas! The last words on the last page are merely the end of a dangling calculation about the curvature of a parabola. He says nothing whatsoever about the subject's utility.

In his Preface, Browne mentions that some people are anxious to see Cambridge become "eminent in scientific pursuits." That strikes him as nonsense. The only purpose of universities, he says, is "that they may continually yield a supply of men, well qualified to fill the various offices, both in Church and State."

What is so odd about Browne's cynicism is that Cambridge was just becoming the focus of a mathematical revolution in England. The great astronomer John Herschel had finished his studies in mathematics in 1814. He'd stayed on to translate French work in math. France was then far ahead of England in mathematics, and Browne took particular care to sneer at highfalutin French mathemeticians.

Herschel's friend Charles Babbage, inventor of the first programmable computer, also finished math at Cambridge. Both were driving England toward a deeper understanding of math and of its use.

Browne shows us how we can miss the vitality around us by trying to freeze the world in place. So much life swirled about him in 1824. Cambridge, the calculus, learning itself -- they were all energized by a world in motion, a world changing. The new calculus had already become, for Browne, a virtue that lay beyond either utility or evolution. College was about serving a static nation with the same students who had served that nation last year.

I went looking for Browne in biographical encyclopedias. He was not to be found. The calculus is, as I said, about change. And Browne was one of those who chose to be left behind by change.

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

(Theme music)


Browne, the Rev. A., A Short View of the First Principles of the Differential Calculus. Cambridge: J. Deighton & Sons, Cambridge, 1824





The Engines of Our Ingenuity is Copyright © 1988-2001 by John H. Lienhard.