## Books: “Here’s Looking at Euclid”

### November 24, 2010

Overall, I don’t think my father was disappointed in me. He didn’t set himself up for disappointment, because he didn’t pressure me to pursue any particular career. When I said I wanted to be a priest, that was all right with him. When I became a newspaper journalist instead, that was all right, too. He was both a practicing Catholic and a newspaper reader, so he was in a good position for success.

There was, however, one thing that he might have found frustrating about the younger of his sons — Tony’s brother, as it were — and that was my inability to learn how to add several columns of figures without carrying numbers.

At slow moments in my family’s grocery store — where adding columns of figures was a frequent chore — Dad would try to show me how to add three or four columns at once, rather than starting with the right-hand column (the pennies column) and carrying the excess to the top of the column to the left. “Put down the two, and carry the four” — that was how I had learned arithmetic. I couldn’t understand the alternate method Dad tried to teach me, which annoyed me, because he could add columns of figures with his technique nearly twice as fast as I could do it with mine.

Many years later, the dawn broke in my clouded mind while I was reading a book on math. There, for Pete’s sake, was Dad’s method — explained just as I remembered Dad explaining it — but somehow I finally understood it and have used it ever since.

Like many people, I suppose, I regarded math at best as a necessary evil in elementary and high school. I didn’t go near the subject in college or graduate school. When I was in my 30s, however, I inexplicably chose to read a book on math written by Bertrand Russell, and was surprised to find that the subject was attractive. As I result, I have read many books about math, the most recent one being “Here’s Looking at Euclid” by the British journalist Alex Bellos.

In fewer than 300 pages, Bellos covers a remarkably wide range of topics. He explains the origins of mathematical concepts that we take for granted — the sixty-minute hour and sixty-second minute, for example — and how mathematical understanding has evolved since some Sumerian in the fourth millennium B.C. first pressed a stylus into a clay tablet. He writes about pi and infinity and probability (including its role in gambling), and the bell curve.

Bellos begins his book with an account of the Munduruku people of Brazil, who have a number system that goes only from one to five. Moreover, the Munduruku use only the numbers one and two to count precisely, using three, four and five more as estimates. In fact, Bellos explains, the Munduruku are baffled by others’ compulsion to enumerate people or objects and either cannot or will not answer if asked how many children they have. They know who their children are; that’s enough for them. It’s healthy, I think, to be reminded from time to time that everyone doesn’t look at the world through the lens we use.

What I particularly like reading about is the mystery and elegance that many people find in numbers. One example is the “golden proportion” or “golden ratio,” to which Bellos devotes a chapter. The definition of this term, known to mathematicians as *phi, *might be off-putting at first. Here it is as Bellos explains it: “The golden mean is the number that describes the ratio when a line is cut in two sections in such a way that the proportion of the entire line to the larger section is equal to the proportion of the larger section to the smaller section.” That number begins as 1.61803 and, like *pi, *goes on forever. It appears in many familiar geometric figures, including the five-pointed star. The 16th century mathematician Luca Pacioli, Bellos reports, “concluded that the number was a message from God, a source of secret knowledge about the inner beauty of things.” That notion may seem remote until Bellos explains how a retired dentist discovered that the golden proportion was the key to designing dentures that give an individual patient a proper smile – now a widely accepted principle in dentistry.

I’m sorry now that I once thought of math only as a nuisance, but books like this one have helped me make up for a misspent youth.