Crumpacker: Perfect Figures
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Bunny Crumpacker, Perfect Figures : The Lore of Numbers and How we Learned to Count. New York : St. Martin's Press, 2007. xi + 271 pages, with bibliography and index.
To be honest, I'm not entirely sure what I thought of this book, but on the whole I think I liked it. I’m not going to blame Ms. Crumpacker for that, either. She's written well a book I enjoyed reading to the end, but was a bit perplexed by because it's expository form was unlike any I'd read before, so I had to figure out (in some sense) how to read it. However, I think innovation is a good thing, hence my generally positive opinion.
My shortcoming as a reader is that I tend to expect a book about the history and lore of numbers (to judge by the subtitle) to adhere to some logically historical plan of progress from one topic to another. As I've seen with some other books whose topics are numbers, the chapters are accounted for eccentrically: 1 through 12, 100, thousand, million, infinity, and those are also the subjects of each chapter. Within each chapter the author develops the ideas and presents the narrative about each number idea in a stream-of-consciousness way that almost relies more on the sound of the numbers than anything. And so our sense of the history of counting and the lore of numbers, as promised by the subtitle, develops by accretion.
But then, it's fun that way, too. It may not be the accustomed way to lay out nonfiction presentation, but I think the author's point was to induce a reaction of play in the reader and she meanders through the numbers, developing the idea that counting must have grown slowly—it's a big step from 1 tree or 2 deer to a million things.
There have been others, like the Yuroks, who used the same idea—separate counting words for sets of thins being counted—but went about it differently. They had one word for two long things, like trees, but when they counted three long things, they used a completely different word. In the flat-thing category, like leaves, there was one word for two leaves, and an altogether new word for three leaves. Then two birds had one word, and three birds had another. Again, too much to remember: counting that way can only go so far before memory dissolves. Many fills the gap. One bird, two birds, three birds, four birds, many birds. Many is an abstract idea. Eventually, the numbers gave up their concreteness and joined it.
It seems so simple to us now. Three is three, whether it's long things or short. It doesn't matter if a tree looks different from a bird; what matters is how many you have of each. The idea of a number means letting it float away in your mind and knowing that it will still be there when you come back with things to count, and knowing at the same time that a number can exist nowhere but in your mind. Whatever you're counting is real—it may very well be touchable, unless you're counting something like the dreams you've had since Monday. But numbers are not real; they're an idea. Abstract numbers are a little like bubbles. If you look at them too long, they're gone. You have to trust that they're still there, even—especially—that they exist at all. Four, after all, means four, and it always will. And it can count anything, babies or bananas. Round things don't matter, and neither do flat or long things. Four is four and that's all there is to it. What's amazing is how sophisticated that simple idea is. [pp. 61—62]
Let's take it then as a somewhat idiosyncratic but lyrically written prose poem about counting and numbers as a socio-historical idea. Phew. Or, we can just read it as a playful bit of sport with numbers, entertaining facts, and diverting quotations on every page that use that chapter's number. Why not!
For those of us who like to learn some history through etymology and the connections of words to ideas, there's plenty to satisfy us.
The Pythagoreans, ever defining in terms of numbers, believed that knowledge could be divided into four studies, the quadrivium, or four paths—a crossroads of knowledge. The first study of the quadrivium was arithmetic; the second was the study of numbers or music—music as the ancient name for the mathematical study of ratios. The third study was geometry, the study of the three dimensions: length, width, and height. Astronomy was the fourth study. All four are really about number: arithmetic is pure number, the study of multitude and quantities. Music is number in time; geometry, number in space; and astronomy, number in space and time. The quadrivium totaled one part of knowledge; the other, the trivium, from the Latin for three roads—tri-via (yes, "trivia")—presented the three basic disciplines: grammar, rhetoric, and dialectics. Grammar was considered the mechanics of language; dialectics, the mechanics of thought; and rhetoric, the use of language to teach or persuade. (A trivial bit of lore: Rome's Trevi fountain, with its three streams of water, used to be called Fontana Trivia.) Until the fifteenth century, the undergraduate degree was equivalent to the trivium; the graduate degree, the quadrivium. Add the quadrivium and the trivium together—four plus three—and you get the seven liberal, and lively, arts. [p. 69]
I have some quibbles with the author, but nothing terribly serious. It bothered me a bit that she did not always distinguish between a number and the numeral that we use to denote the number, so that phrased like "adding a zero to a number" didn't always mean clearly to me on first reading, but I don't know that anyone else would find that at all confusing.
The book is generally precise and correct with facts when facts are involved, so I found this error very curious:
Apollo 11 was the first—and is so far the only—manned spacecraft to land on the moon. [p. 197]
Of course, the Apollo missions numbered 12, 14, 15, 16, and 17 also involved humans landing on the moon. One suspects that a word sneaked in or out during editing.
Also, there's this statement:
(There's a word that includes all five vowels in their proper order: abstemious.) [p. 87]
whose wording suggests that "abstemious" is the only such word, but it is not. There is at least one other (spoiler!-->): "facetious".
-- Notes by JNS