Today, an obituary brings back memories. 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.
Mathematics was a labor until I reached calculus. Then, a fast-talking young instructor from New York turned up with a book by one Frank Loxley Griffin. Suddenly math was no longer about manipulating symbols. It was about building shapes in space. It was about the way things move and unfold. Griffin's book, propelled by that young man, made me see how math could throw light on the inscrutability of the everyday world. Griffin's book transmuted the dreaded story problems of algebra into an adventure.
That was half a century ago, but it all came back in Monday's New York Times. There I found an obituary for a man named Peter Griffin, who'd died of prostate cancer. He was only 61. Then I looked at the fine print: this was my textbook author's grandson.
The younger Griffin was also a noted mathematician, but he was no conventional academic. When he was about the same age as my calculus instructor, teaching math at California State University, he proposed a new course on the mathematics of gambling. Since Griffin knew little about gambling, he went off to Nevada to practice. There he lost his shirt, and he came back angry. He set about to diagnose gambling; and blackjack caught his eye.
Years before, a book titled Beat the Dealer had sold over 700,000 copies. It showed players how they could beat the house in the long run by keeping track of cards. Griffin had a phenomenal capacity for counting cards. But he didn't have the patience for doing it long hours on end. He could've make money, no doubt. But it wasn't worth the labor. Instead, he published his own Theory of Blackjack in 1979. The sixth edition is just coming out. It's a winning mix of penetrating analysis and good humor.
All this was a reminder of the way Griffin's grandfather, and that young calculus teacher, had shown me the power of math to transform commonplace things. Monday ended with yet one more echo of the world that unfolded in my first calculus course: A colleague showed me a graph he'd plotted -- a lovely seven-pointed star. The seven teardrop-shaped points were formed by one continuous curve. It was just like a traditional Rangavalli pattern from India.
"What's this?" I asked. "A child walks in a circle," he said, "pulling a wheeled toy on the end of stick. The toy tries to move in a straight line, so it swings away from the circle until it's pulled in the reverse direction. Then it moves back inward, and the process repeats inside the circle. This graph is the toy's path."
The problem of plotting that curve turned up in a modern book, one that showed how to solve a problem, once formulated, with a few lines of computer code. The game has no doubt changed. But the driving influence of people like Frank and Peter Griffin is still with us. They're out there ready to take students into a magic land where the obvious world gives up secrets we never expected to find.
I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.
(Theme music)
Thomas, R. McG, Jr., Peter Griffin, Solver of Blackjack, Dies at 61. The New York Times, OBITUARIES, Monday, November 2, 1998.
The Griffin calculus book was actually two books:
Griffin, F. L., An Introduction to Mathematical Analysis. Revised Edition. New York: Houghton Mifflin Co., 1936.
Griffin, F. L., Mathematical Analysis: A Higher Course. New York: Houghton Mifflin, Co. 1927.
I am grateful to N. Shamsundar, UH Mechanical Engineering Department, who did the pull-toy/Rangavalli-pattern plot and who, himself, represents the impetus and tradition of teachers like the Griffins.
As the child walks the circle, shown in black,
her pull-toy traces the path shown in red.
Image created by N. Shamsundar