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Daniel Tammet book a crash course in the beauty of math

Thinking in Numbers
Daniel Tammet
Little, Brown

"Three point one four one five nine …" In 2004, 25-year-old Daniel Tammet sat down at a table at a museum in Oxford, England, surrounded by cameras and a rapt audience, sipped some water, and began reciting pi – the number that expresses the length of a circle's circumference divided by its diameter, and has an infinite number of decimal places. After five hours and nine minutes, he had intoned an astonishing 22,514 digits from memory, a new European record.

"Those digits seemed to speak of endless possibility, illimitable adventure," Tammet says in the most spellbinding chapter of his new book, Thinking in Numbers. "Of course, I could not possess pi – the number, its beauty, or its immensity. Perhaps, in fact, it possessed me."

Diagnosed with high-functioning autistic savant syndrome, which forms unusual brain circuits, Tammet first brought readers into his world with his bestselling 2006 autobiography, Born on a Blue Day. It vividly described his synesthesia, a condition shared by Vladimir Nabokov in which the brain associates numbers, letters, colours, sounds and shapes, so that one can be white, two may be blue and three red (I have mild synesthesia, and I was shocked then to finally read someone else describe what it feels like).

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This, the 34-year-old's third book, is a whimsical, irresistible tour through the magic of numbers. You won't find many equations here. Instead, Tammet takes us from Shakespeare's obsession with the number zero to the patterns of math within chess, to the near-mystical "googolplex," the largest number ever conceived (except, of course, for "googolplex plus one").

No one in our technology-obsessed world needs to be convinced numbers are useful. Modern Western culture is among the most number-dependent in the world, in contrast to the many tribal societies that have little use for them, as Tammet reveals. He introduces us to the African Kpelle, one of several groups who believe that counting people brings bad luck, and the amazing Amazonian Pirahã, who have no numbers in their language and live in a kind of eternal present.

Yet Tammet argues that although we're dependent on numbers, we fail to appreciate their beauty. They are not just tools that let us calculate sums, fly planes or build computers. Numbers can have personality. They can seem perfect, like 10, worshipped by Greek mathematician Pythagoras as the sum of one, two, three and four, or marvellously patterned, like the nine times table, where the digits of every answer sum to nine: 9x2=18 (1+8=9), 9x3=27 (2+7=9), etc. Like poetry, math is among the most elegant ways we have of expressing the infinite, the paradoxical and the just plain wondrous. Large numbers are actually venerated by the Indian sutras, which hold that only enlightened bodhisattvas are capable of counting to them.

It is clear enough that Tammet's brain works at a higher level than those of mere mortals. What makes him a generous and gifted author, though, is his desire (and ability) to communicate what it feels like to be him. Tammet's easy prose contrasts with the complexity of his subject, allowing the knottiest of ideas to slip unencumbered into the understanding of even the most math-challenged reader. With him, we crest the undulating waves of the "bright" and "dark" sequences further into pi than we could ever hope to tread, to the miraculous point where, he surmises, "123456789 … repeats 123,456,789 times in a row." No lover of textbooks, Tammet doesn't want to teach us math – he wants to teach us its beauty. When he writes about square roots and primes, he does so as if he is simply chatting about two old friends he's known all his life to someone who has just made their acquaintance.

Indeed, it may be that for Tammet, numbers are easier than people to befriend. His unusual brain has had consequences for relating to others. While reciting pi to the cameras in 2004, he felt not triumphant, but "completely, oppressively alone." In one sadly hopeful chapter, he attempts to use probability theory to understand his distant mother's frequently unpredictable behaviour – and fails.

Occasionally, his grand claims about numbers go a bit over my head. Can numbers really make us better people, as he claims in one breathless passage? I wish it were true, but after reading his argument, I'm not entirely convinced. Numbers also let us generalize about people, summing up whole communities in impersonal digits.

Tammet's joy in math is infectious, though. Read this book and you may find yourself turning to a spouse or cubicle-mate and saying, "Hey! Did you know that in Japanese, the opening digits of pi sound like the phrase, 'An obstetrician goes to a foreign country?' "

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Getting an answer of "Yes," as Tammet would say, would be most improbable.

Sarah Barmak is a Toronto journalist who writes about culture, science and business. She prefers words to numbers, but numbers are growing on her.

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