Lessons in Freeway Calculus

By Grace Peng

As an immigrant, I hate to see my chosen team (America) dissed by know-nothings.

The views of the governor of Pennsylvania, after an Eagles-Vikings playoff game in Philadelphia was postponed because of snow: 

"We've become a nation of wusses. The Chinese are kicking our butt in everything," he added. "If this was in China do you think the Chinese would have called off the game? People would have been marching down to the stadium, they would have walked and they would have been doing calculus on the way down."

Gov. Ed Rendell clearly doesn't understand calculus. If he did, then he'd know that calculus was basically invented to describe motion. (He should have read Steven Strogatz's Change We Can Believe In.) Therefore, anyone in motion -- whether walking to the stadium or driving in a SUV with heated leather seats -- is doing calculus.

(Thanks to my favorite math website, Wolfram MathWorld, for the figures and theorem info.)

On a more serious note, I want the general public to understand that math is a huge subject encompassing much more than arithmetic. People shouldn't give up their math education too soon just because they don't like arithmetic. Many mathematicians are only so-so at arithmetic.

Truth be told, after I finished the introductory lower-division undergraduate math courses at UC Berkeley, I hardly ever worked with actual numbers. My math homework consisted mainly of Greek symbols and other abstract notation along with copious arguments in English describing the steps of the proofs. It usually ended with relief and a big Q.E.D. as I finally signed off and could go to sleep.

Math is also so broad that mathematicians do not understand all areas of math. It would be like expecting a historian to know about the history of everything. It can't be done, though it might be fun to try.

It would be more productive to think of math as both a liberal art and a science. Not only is math the language of science, giving us a framework for describing our physical world, but it is also a construct of the human mind. As such, lessons learned from math can help us understand the human condition, moving it into the realm of humanities.

A friend who had been an English literature major and I discussed how we thought a book was mainly about one thing, and then reread it years later and thought it was mainly about something else. Was our past judgment so wrong? Or had experience and circumstance changed our perceptions?

Much as I enjoyed Steven Strogatz on the Elements of Math, I hope that readers will go beyond that. I will use the meaning of calculus as an example

When I first encountered calculus in high school, I mechanically went through the motions of "turning the crank" to learn the rules of differential and integral calculus. I thought that was what it was all about. Sure, there were pages and pages of material about limits in the textbooks, but they were just a prelude to the real stuff of finding the derivative (slope) or the integral (the area under a plot) of a function. So, if you had asked me back then, I would have agreed with Strogatz.

But then a boy that was a year ahead of me in math at Cal told me that he didn't understand calculus until he took math analysis and "proved" calculus. That freaked me out; was I so clueless and shallow that I misunderstood the whole point of calculus?

The panic intensified when I took the class he referred to: Math 104, aka "Real Analysis and Introductory Topology." Our class spent the entire semester on proofs, including six weeks to prove the compactness theorem. What did that have to do with calculus?

Looking back, I can laugh about it. I see now that calculus is such a broad topic, and touches so many aspects of our lives, that it can mean different things in different contexts.

All those weeks spent proving the limit of an infinite series exists and is unique? That tells us that there is a solution of the integral described by the series.

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James Fallows is a national correspondent for The Atlantic and has written for the magazine since the late 1970s. He has reported extensively from outside the United States and once worked as President Carter's chief speechwriter. His latest book is China Airborne. More

James Fallows is based in Washington as a national correspondent for The Atlantic. He has worked for the magazine for nearly 30 years and in that time has also lived in Seattle, Berkeley, Austin, Tokyo, Kuala Lumpur, Shanghai, and Beijing. He was raised in Redlands, California, received his undergraduate degree in American history and literature from Harvard, and received a graduate degree in economics from Oxford as a Rhodes scholar. In addition to working for The Atlantic, he has spent two years as chief White House speechwriter for Jimmy Carter, two years as the editor of US News & World Report, and six months as a program designer at Microsoft. He is an instrument-rated private pilot. He is also now the chair in U.S. media at the U.S. Studies Centre at the University of Sydney, in Australia.

Fallows has been a finalist for the National Magazine Award five times and has won once; he has also won the American Book Award for nonfiction and a N.Y. Emmy award for the documentary series Doing Business in China. He was the founding chairman of the New America Foundation. His recent books Blind Into Baghdad (2006) and Postcards From Tomorrow Square (2009) are based on his writings for The Atlantic. His latest book is China Airborne. He is married to Deborah Fallows, author of the recent book Dreaming in Chinese. They have two married sons.

Fallows welcomes and frequently quotes from reader mail sent via the "Email" button below. Unless you specify otherwise, we consider any incoming mail available for possible quotation -- but not with the sender's real name unless you explicitly state that it may be used. If you are wondering why Fallows does not use a "Comments" field below his posts, please see previous explanations here and here.

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