Man Must Measure

It just appeared one day, out of nowhere, on the desk by the bedroom window. I picked it up and looked at it. It was a big book with not many pages in it, and with an arresting title in big black letters on the front, which read: MAN MUST MEASURE.

I must have been 7 or 8 years old, and I was living with my mother in my grandparent’s house when I drank in those words, which seemed to possess the force of a veritable Commandment.

I opened it, and discovered that it was both lavishly illustrated and also filled with numbers and diagrams. It was the strangest and most terrifying book I had ever encountered.

I began to read the book, a little fearful that I wasn’t supposed to be reading it. Much of it seemed incomprehensible, but on the third or fourth page I came across this:

I studied the picture on the right very closely. What on earth were they doing? What were those strange lines in the sand? Little by little, I gradually understood that they were marking out the corner of a pyramid, and the semi-circular lines drawn in the sand were what they used to make the corner exactly square. They drew the lines in the sand, and then they drove stakes into the lines, and finally they brought rectangular stones and fitted them next to the stakes.

I tried it out for myself. My grandfather had an old compass somewhere, which he unearthed for me, and fitted a pencil into. And with these and a ruler I was soon drawing right angles (although for the life of me I couldn’t see what was “right” about them).

Deeper still in the book, I came across another drawing full of semi-circles:

With my grandfather’s compass, I soon replicated this too.

It was an astonishing book, full of astonishing things of a kind that I had never imagined before. It was a book about mathematics and numbers and geometry. It included a demonstration of the Theorem of Pythagoras (which was entirely beyond my comprehension), sextants, clocks, candles, a map of the city of Alexandria, and even a brief history of the world – all in just 70 pages.

I spent hours reading the book, until one day, just as suddenly as it had appeared, it vanished.

But I never forgot it. I never forgot its single Commandment. I wasn’t quite sure why Man had to Measure, but the tremendous power of the book nevertheless impressed that message upon me ineradicably. It’s one reason why, right now, my principal objection to antismoking pseudoscience is that nothing is measured accurately: they’re drawing pictures with stretchy rulers and bendy compasses.

Man Must Measure was one of the formative books of my childhood. It was certainly the strangest and most terrifying book. And three or four years later, at school, when we were taught geometry, I found that I knew half of it already.

And so when I found a secondhand copy online a couple of months ago, priced £19.87, I bought it immediately, surprised that it was so cheap. It remains a brilliant book, even though it’s 60 years old. It does something that most dry, abstract, mathematical textbooks always fail to do: it brings numbers and geometry to life. And it does it by marrying art to mathematics, and showing how to do it.

So I would thoroughly recommend anyone to buy a copy, if only as an investment. I would have happily paid 10 times that amount for it. It hasn’t dated very much either, although the drawing whose caption reads, “Japanese businessmen use the abacus with great skill,” is undoubtedly incorrect. It was probably true in 1955, but I rather suspect that most Japanese businessmen haven’t the first clue how to use an abacus these days.

But if you do buy one, then you must find a boy or girl of about 8 years of age, and arrange for the book to be left on a table in their bedroom for a few weeks. And you might also take the precaution of providing the parents with a compass and a ruler as well. And when you come back to retrieve the book, and you learn that the child has been asking for compasses and rulers, you will know that you have successfully cast the spell of mathematics upon another receptive mind.