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
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
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
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.
For information about Rangavalli patterns, see
Image created by N.
As the child walks the circle, shown in black,
her pull-toy traces the path shown in red.
The Engines of Our Ingenuity is
Copyright © 1988-1998 by John H.
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