I WAS DEEPLY ROOTED

New Zealand Listener, Volume 10, Issue 260, 16 June 1944, Page 13

I WAS DEEPLY ROOTED

(Written for "The Listener" by

R.L.

M.)

WAS sitting in the library mugging up American Politics for an essay I had to do, when I heard someone say "Excuse me, but do you know.how to work out the square root of a number?" I admit that this baffled, me a little. When you're sitting in the Library reading about American politics, you simply don’t expect anyone to have such bad taste as to request information-especi-ally information pretaining to the lower sphere of knowledge. And I was just on the point of discovering the exact relationship of President to Congress, too. However, When I looked up and found the questioner was a rather bright young lass wearing a bow in her hair and a puzzled expression, I decided that it was very meet, right, and my bounden duty to help her in her trouble. The damsel-in-distress touch always works, doesn’t it? Then I realised with awful suddenness that I didn’t know how to find the square root of a number. It was like those General Knowledge tests-you

feel you ought to know the answer, but you never do know it, and then you read the answer and you say, of course! Having realised that I didn’t know how to do it, I asked myself, "Should I admit my ignorance, or should I play for time, in the hope that divine afflatus might descend?" I decided to stall. "Why do you want to know?" I asked, and immediately I’d spoken, I realised how silly it sounded. That was her business, anyway. And besides, she might be "doing" abnormal psychology or something like that, and it might embarrass her to answer. "I’m doing Education III.," said the girl. (That -was a relief, anyway.) "There’s a lot of statistical stuff in it. I want to find the square root of one point four nine five three." The "point" got me. If it had just been plain one four nine five three I might have tried to bluff it out-but one point four, etc.-oh no! The divine afflatus stopped in its descent, went into reverse, and shot upwards out of sight. "T haven’t the slightest idea," I said, trying to make my tone of voice mean

"Isn’t it funny, but I, who know so much about everything else, simply don’t know how to do such a simple thing as work out the square root of a number." It was a valiant effort, but I think it failed. I haven’t yet reached that pinnacle of fame, where you can say that you don’t know something, and everybody thinks you’re being funny. "I think you divide it in pairs from the left," said the’ educationist helpfully. "Or is it from the right? I can’t remember." (continued on next page)

| WAS DEEPLY ROOTED (continued from previous page)

I couldn’t remember either, but I suddenly remembered something else-that there was a very large mathematics section in the Library. And, having "done" Logic 1 last year, I reasoned thus: "I may possibly have lost caste through my display of ignorance. I do not wish to lose caste, especially in the presence of an intellectual female who wears such a cute little bow in her hair. I can regain caste by finding out the solution of this problem. I can find out the solution by looking it up. Therefore--" "T’ll go and look it up for you," I syllogised. She looked awfully grateful. So I went over to the Mathematics section. ok Bg * T was a pretty grim quarter. There were shelves and shelves of books full of symbols and figures and formulae. I didn’t like to ask any of the people reading in the vicinity how to find the square root of a number, or what book they’d recommend me to look up, because I thought that perhaps they mightn’t have known, and then they’d have been even more embarrassed than I was because that’s the sort of thing you expect people to know if they read mathematical books in a Library. So I collected a large pile of big books that looked like compendia of mathematical knowledge-sort of Will Durant-Van Loon books that tell you everything you want to know-and I took*them back to the girl with the bow in her hair. Her hair was slightly auburn, and I like auburn hair. "We ought to be able to find out from these," I said. It was a big pile. * a * O I started going through them. There was a History of Mathematics and an introduction to the Philosophy of Arithmetic and a Principles of Mathematics and even a Principles of Relativity which had got in by mistake, and lots of others. I thought I’d better employ the genetic approach, so I opened the History of Mathematics and looked up "square root" in the index. . Well, there was a lot about square roots in this book. I found that Archimedes in his "Mensuration of the Circle" worked out a number of them. Even Omar Khayyam, that worthiest of pagans, besides "elevating to a method the solution of algebraic equation by intersecting conics,’ worked out square roots. And an individual with the intriguing name of Tabit Ibn Korra worked them out in Arabic. But unhappily, this book didn’t tell you how Archimedes and Omar and Tabit worked out, square roots. It told you almost everything else, though. The Principles of Relativity I discarded after a brief browse. For one thing, it hadn’t got an index-which I always think is so thoughtless-and for another thing it ended as follows: ‘These are convariant tensors of the First Order," and I always feel that a book should have a nice comfortable "l’envoi" at the end and not finish up baldly and brutally with "These are convariant tensors of the First Ordér." Foundations of Mathematics hadn't got an index either, and Principles of (continued on next page)

(continued from previous page) Mathematics was a bit soulful-all except an interesting bit about "Zeno’s attacks on the continuum," which I read through because I am sentimental and remembered my James Jeans-Auden-Van Gogh adolescence. But in the Philosophy of Arithmetic I got hot on the trail. It told you how to work out the square root analytically. This was good. "By the principles of involution, we see that there will be two figures in the root, hence the number consists of the square of the 10’s plus the units of the root, which equals the square of the 10’s plus twice the 10’s into the units plus the square of the units." The book then told you how to work it out synthetically, but I didn’t read any more because we only wanted one method. I put a piece of paper in the book to mark the place. Then there was a book on Higher Arithmetic, which was even better, because there on page 47 was an illustration of the working out of a square root,

and, sure enough, the figures were divided into pairs from the left (or was it from the right?) just as my learned girl friend had stated. And there was a lot of helpful comment written in tiny type beside it, such as: "20 has been found, and 20’, or f', subtracted, thus 147.56 must contain 2fn plus n* or 2.20.m plus n*. Therefore, by dividing by 2.20, or 40, n can be found approximately. Therefore n equals 3. Therefore 2fn plus n’, or 2.20.3 plus 3? 299 equals 129 equals 2fn plus n’. This was, I felt, the real goods, so I put another piece of paper in the place. There was my lost caste, under the table there. I had only to stretch out my hand to pick it up. * * * ‘THEN I took the last book, which was an enormous volume full of figures and tables and cobwebs. It took me a little while to discover what it dealt with. It was, I found, all about the relations of Jupiter and Saturn. There were no illustrations; there was nothing except logarithms and formulae. There were 544 pages. I suddenly felt very humble. "Here you are," I said, taking up the two books I’d marked. "This’ll show you how to do it. It’s really quite simple." My voice seemed to echo in a curious manner. I looked up. The girl with the bow in her hair had gone. So had everyone else except the Librarian, who was waiting to put the lights out and looking at me in a rather unkindly fashion. These Librarians just don’t appreciate the search for Knowledge for its own sake.