Mathematics as Play

June 2, 2014


Bart Simpson as a maze. From Math Bytes.
Book Review
Philip J. Davis

Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing.
By Tim Chartier, Princeton University Press, Princeton, New Jersey, 2014, 152 pages, $24.95.

Of what use is mathematics? Over the years, answers have ranged widely. In The Handmaiden of the Sciences (1937), E.T. Bell was reflecting a common opinion. Earlier, Bertrand Russell considered mathematics the cat's meow because of its logic. Another opinion has God as a mathematician who created the cosmos along mathematical lines.*

It is also the case that the use of mathematics has been panned and subjected to derision: Recently, path-breaking but controversial French economist Thomas Piketty berated his profession for its "childish passion" for mathematical economics and neglect of its history. Other have looked on the knowledge and use of mathematics as an ego trip.

So who needs mathematics? How much math does a checkout clerk in the supermarket need to know? Does your primary care physician need to know any mathematics other than, perhaps, the qualitative distinction between low- and high-dose aspirin tablets? Is 81 mg vs. 325 mg of any importance to a physician other than as identifiers for prescriptions?

And yet, during a recent hospitalization for several days, I was impressed by the extent to which medical diagnosis and practice have been computerized, chipified, graphisized, netisized by pieces of hardware/software to which I had been hooked up. I began to feel that as far as the doctors and nurses were concerned, my identity had been replaced by a vector of numbers. Talk about identity theft!

How much and what mathematics should be required for a diploma are currently hot topics in educational circles and in the media. NECAP (the New England Common Assessment Program in K–12 math, reading, and writing) has both elicited praise and aroused fury.

All this points to mathematics as utilitarian: for use in analyzing and describing, interpreting, planning, constructing, predicting, prescribing, preventing, teaching, and---alas---occasionally in doing damage.

Yet mathematics has another face, one that I became aware of long ago as a 6th grader. One day, on the top of the family piano, I found four old volumes, bearing the title . Among which are all those commonly performed with the cards. By Rational Recreations: in which the principle of numbers and natural philosophy are clearly and copiously elucidated by a series of entertaining interesting experiments. Among which are all those commonly performed with the cards. By William Hooper, MD, they were published in London, in 1787.

I assume that my older brother, who was then a graduate student at MIT, found and bought these books because he was amused by their experiments in physics (pneumatics, hydrology, pyrotechnics). Many of the card tricks in the books have mathematical underpinnings. Then there are numerical tricks that go like this: Think of a number (but don't tell me); do this and that, and tell me what your number is now. Then your number was such and such.

Mathematical play, though rarely imposed by physical necessity or moral duty, can lead to insight and development. Nathalie Sinclair, in Mathematics and the Aesthetic, writes that

"[Johan] Huizinga [in a path-breaking study of human play] alluded to the possibility that in ‘mathematical play', the mathematician is aesthetically exploring certain structures or trying to impose or reveal structures and patterns."

Tim Chartier, a professor of mathematics at Davidson College, has put together a delightful book of recreational mathematics. His presentation of a large array of topics is accompanied by excellent graphics, many in color. The book has plenty of competition---the recent Dover catalog for mathematics and science lists easily 50 books under "recreational mathematics." But Chartier has his own, often novel selections, which should attract wide popular attention. Among them are: the game of 30 questions, creating fractal islands, ranking athletic teams (or, in the case of Google's PageRank, web pages), image identification and alteration, the topology of doodling, painting via number theory, a game called google-opoly, Bart Simpson as a maze, and many, many others.

In sum, a fun book.

Books Mentioned in this Review
William Hooper, Rational Recreations; a free online version is available at http://books.google.com/books/about/Rational_Recreations.html?id=iOQ4AAAAMAAJ.
Johan Huizinga, Homo Ludens: A Study of the Play-Element in Human Culture, Beacon Press, 1971.
Nathalie Sinclair, David Pimm, and William Higginson, eds., Mathematics and the Aesthetic: New Approaches to an Ancient Infinity, Canadian Mathematical Society Books in Mathematics, Springer, 2006.

*See my article "A Brief Look at Mathematics and Theology," Humanistic Mathematics Network Journal, 27 (2004).

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at philip_davis@brown.edu.


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