Group Theory in the Bedroom

And Other Mathematical Diversions

Brian Hayes

Hill & Wang: 282 pp., $25

IN A desperate attempt to reach the vast and uninterested lay public, mathematicians are forever shrouding their discipline in come-hither clothes. The choice of title for this essay collection by Brian Hayes, a columnist for American Scientist, is an example.

"Group Theory in the Bedroom" -- wow, what's in the offing here? Well, the title essay is a piece about how most efficiently to flip a mattress, which one should do periodically to keep it from getting lumpy. Sorry. "Group theory" is a mathematical tool for dealing with symmetry, and symmetry apparently has a lot to do with how you ought to flip a mattress -- if you think about it.

The other approach would be to not think about it and just do it. But Hayes is besotted with mathematics (his column is titled "Computing Science"), and he can't seem to do anything without getting caught up in the mathematical implications. When an Internet service provider informs him that if he wants "brian" as an e-mail handle he will have to be "brian13311," it gets him thinking about names and naming, which produces a column that spans the problem of the finiteness of labels from the efforts of Adam through those of Linnaeus and on up to the current relentless replacement of area codes.

In an essay titled "Dividing the Continent," Hayes recalls a coast-to-coast road trip whose high point (figuratively speaking) was achievement of the Continental Divide, "the spine of the continent," where "rain falling on one side trickles into the Pacific, and on the other side into the Atlantic." At his particular latitude, this was Monida Pass, at 6,823 feet, on the Idaho-Montana border. He spent the rest of the trip, amid some of the most glorious scenery on the planet, wondering how this could be, because higher elevations lay ahead of him. "Since I'm a computer-dependent person, my instinct was to address the question in algorithmic terms," he writes. And so he does. In this and other essays, you may follow his reasoning, if you're sufficiently adept.

If you're not, you may be put off by some of these exercises -- say, a discussion of why we don't have a base-3, or ternary, system of counting (something we probably don't need to know). "As an example," Hayes explains, "the decimal number 19 . . . is interpreted as follows: (1 x 33) - (1 x 32) + (0 x 31) + (1 x 30), or in other words [sic] 27 - 9 + 0 + 1." Yup. Q.E.D., as mathematicians like to say. Still, when Hayes does avail himself of words, he's a graceful writer. And if you love numbers, grids and graphs, you'll love this book. Taken singly, his columns are refreshing in an eccentric sort of way. It's just that when grouped, as in "Group Theory," they may make you want to go lie down on that unflipped mattress, lumpy or not. *