There are two kinds of popular books about mathematics; bracing ones that rub against the frontiers of the subject, and those with a softer touch, aiming for something more like “math appreciation.” These books say to the reader “I know you hated this in school, but hold my hand and you’ll be fine; it’s really not so bad.” Daniel Tammet’s “Thinking in Numbers’’ is the softest of the soft, an affable if finally rather lightweight collection of essays and observations perhaps better described as “around” mathematics than about it.
Tammet, a high-functioning autistic savant, is the author of a best-selling autobiography, “Born on a Blue Day,’’ and he brings to “Thinking in Numbers’’ the memoirist’s handiness with a well-placed detail. In his new book, the details come not from his own life story but from a broad landscape of mathematical, intellectual, and literary history. One gets the sense throughout that Tammet spends a lot of time in a comfortable and well-stocked library.
The wide reading serves him well. Tammet offers a pleasant meditation on imaginary cities planned along mathematical lines by the 15th-century Florentine architect Filarete and by the American shaving magnate King Camp Gillette; he tells a convincing story about what calculus meant to Leo Tolstoy; he recounts a childhood run-in with Zeno’s paradox; and he wanders through the polyglot thicket of counting words in the world’s languages. Tammet himself is said to speak 10 – or 11, if you count Mänti, a language he devised himself and named after the Finnish word for “pine tree.”
“Thinking in Numbers’’ does not aim to be academic or authoritative; no thudding policy prescriptions here, and no footnotes. But often Tammet’s writing is so light that it floats away. “Poetry and prime numbers have this in common,” Tammet writes, “both are as unpredictable, difficult to define, and multiple-meaning as a life.” Well, OK — but this doesn’t distinguish either poetry or prime numbers from irony, good sportsmanship, or any number of other abstract entities.
Later, Tammet remarks that “the Sioux have no word for ‘late’ or ‘waiting.’ ” That sounded odd to me, so I wrote Armik Mirzayan, a linguistics professor at the University of South Dakota specializing in Lakota, to ask whether the Sioux were in fact incapable of expressing these concepts in their native language. Just in case you ever need to know this, Lakota has words for both. This kind of casual wrongness is worrying in a book whose charm is so dependent on its density of amusing facts. Maybe a few footnotes wouldn’t have been so bad.
The centerpiece of “Thinking in Numbers’’ is Tammet’s account of a strange performance in which he recited 22,514 digits of pi, from memory, to a crowded lecture hall in Oxford. This accomplishment set a European record that still stands, though Tammet is just an amateur compared with Lu Chao, a Chinese graduate student who reeled off 67,890 in 2005.
If listening to tens of thousands of digits in sequence sounds to you like a dull afternoon, I can’t blame you. But Tammet is fascinated by the celebrity mathematical constant:
“Long after my school days ended, pi’s beauty stayed with me. The digits had insinuated themselves into my mind. Those digits seemed to speak of endless possibility, illimitable adventure. At odd moments I would find myself murmuring them, a gentle reminder. Of course, I could not possess pi — the number, its beauty, or its immensity. Perhaps, in fact, it possessed me.”
This is typical Tammet – vague, lyrical, and somewhat lacking in meaning. A gentle reminder of what?
He does a good job explaining the basics; that the digits of pi never stop, nor do they repeat in a periodic pattern as do the decimal expansions of rational numbers, like 1/7 = 0.142857142857142857 . . . Rather, pi’s digits go on and on without apparent pattern, presumably containing every possible numerical sequence — your phone number, a hundred thousand 7s — somewhere down the infinite line. (Tammet states this as a fact; actually, while it seems quite likely to be the case, mathematicians don’t know whether it’s true and a proof seems totally out of reach.)
But it’s just as true for a sequence of totally random digits. And the digits of pi have no more beauty to them than the random ones do. The beauty of pi – and it really is a handsome devil of a number — lies in the rich web of interconnections between pi, geometry, number theory, probability, and more — not in a string of digits which might as well be drawn from a phone book. The digits specify pi, but they are not pi, any more than the longitude and latitude 48.8586 degrees N, 2.2942 degrees E are the Eiffel Tower.
This may be too severe a standard to apply to “Thinking in Numbers,’’ which is meant as a chat, not a lesson. You can turn to the more challenging pop-math books if you want to get to the guts of the matter; this one exists just to send the message, simple and true, that numbers are everywhere in the human world, for master memorizers and ordinary people alike.
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin- Madison. His book, “How Not to Be Wrong,” will be published in early 2014. He can be reached at email@example.com.