The Chronicle Review

A Humanist Apologizes to Numbers

May 28, 2013

On behalf of word people everywhere, I hereby extend this general apology to numbers. We have not always counted you as friends. I myself, an educator of the literary persuasion, have sometimes failed to live up to my pan-disciplinary liberal-arts ideals. I am tacitly complicit when advisees use foul invective in re the math requirement. I break out in hysterical yawning in the presence of anisotropic fractional maximals.

In my defense, numbers have not always been nice to me, either. I think it started with that C-plus in algebra. Numbers still seem, at times, downright vindictive. At tax time, for instance. Or when I step on a scale. My idea of an irrational number is what I see in my checkbook after paying the bills each month.

Beyond getting and spending, I guess I just don't get numbers. It has always seemed to me that the cosmic relation between the individual and the numerological is adequately summed up in a single quatrain of A.E. Housman:

To think that two and two are four,
And neither five nor three,
The heart of man has long been sore,
And long 'tis like to be.

The world is not as we would wish it to be. The numbers don't add up. Full stop.

But that can't be all there is to it. So, in a good-faith effort to remedy my ignorance, I recently picked up what I am assured is a classic among numerascenti, G.H. Hardy's "A Mathematician's Apology." Hardy was at Cambridge back in the prewar days of cricket and frock coats and "lingering in the combination room over port and walnuts," to borrow from C.P. Snow's foreword.

Chapter One begins with Professor Hardy recalling a chat with his old friend Housman (of all people), and ends with the admission that writing about mathematics, like writing about poetry, is nowhere near so wonderful as doing the thing itself. So far, so good. In Chapter Two, however, the charming Dr. Hardy transforms into the elitist Mr. Hyde, lauding his own intelligence, asserting that "good work is not done by 'humble' men," and adding, in a mean-spirited aside, that "most people can do nothing at all well."

But I am eventually rewarded with this lovely description of the beauty of mathematical proofs that Housman must have agreed would serve equally well in the service of poetry:

... There is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions.

Mon frère!

But he spoils the moment with his illustrations, Euclid's proof of the existence of an infinity of prime numbers and Pythagoras's proof of the 'irrationality' of √2. The beauty is, allegedly, manifest. In the case that it is not, the good professor assures us that "both the statements and the proofs can be mastered in about an hour by any intelligent reader, however slender his mathematical equipment."


My mathematical equipment is, apparently, more slender than he can imagine. Furthermore, I am promised that these examples are but the tiniest nail clippings from the massive hands of mathematics. There are infinitely (I use the term imprecisely, sloppily, poetically) more wondrous examples, but, alas, they are not "within the comprehension of anybody but a fairly competent mathematician."

So be it. The astringent Mr. Hardy goes back on the shelf, to be recommended to undergraduates whom I dislike. But I will not give up on numbers themselves. I want to be friends with numbers. I want them to like me. I just need to lower the bar a bit. So, as a gesture of good will, and with full disclosure of the size of my equipment, I humbly offer here:

One Humanist's Five Favorite Numbers:

1. Minus 40

Math amateurs everywhere will join me in praise of minus 40, the only number in which Fahrenheit and Celsius are a dead match. Raised on Fahrenheit, and unable to calculate in my head, I am at a loss with the other scale, despite the evident orderliness of centi-gradation. While I admit that zero makes perfect sense to denote the freezing of water, its boiling point is relevant only to the barista. I'm from the Midwest: Temperature means weather, and I will never wrap my mittens around the notion that 30 degrees is balmy and 40 is sultry. But, oh, that one beautiful place in all of numberdom where they are in concert, as if to emphasize doubly the extreme limit of human endurance. Minus 40 is Fargo in January, and the jumper cables had better work. Minus 40 is Ice Station Zebra or the blackness of interstellar space. I'm glad that numbers have the good sense to agree on that.

2. 0

Of course, right? That lacuna of numbers, with a hole in the middle to illustrate its essence, or non-essence. As perfectly symbolic in representation as its brother 1, but with a bleaker metaphorical landscape. Disaster in sports; the Jets bageled by the Dolphins again. Disaster as bank balance, rendered in redundant triplicate to add insult to penury: $0.00. Disaster as potential marriage or business partner, often paired with the oxymoronic "complete" or "total." We are unable to conceive that the Romans were unable to conceive of it. What's XIII minus XIII, Cassius? Uh, I don't know, Brutus. Let's ask Akhmed.

How wondrously humane it would be to live in a world without zeros. And more convenient in at least one way, as we would not constantly be confusing it with the upper-case glyph of the 15th letter of the alphabet in flight reservations and passwords.

3. 6.02214 X 1023

When I lived in Denver, in the 1970s, my favorite eatery was a sprouts-and-tofu place in the Cheesman Park neighborhood called Avogadro's Number. I loved it more for the name than for the food. In the universe I inhabited then, the primary definitions of "number" were as follows: 1. n. a pretty girl; 2. n. what said pretty girl was wearing; 3. n. a self-rolled marijuana cigarette (slang); SYN. jay, doobie; see, for example, side two, track one of Neil Young LP Tonight's The Night. So, I thought, Wow, man, whichever. That Avogadro must be one hip dude.

But I also thought Avogadro was Mexican for avocado. Those years are a little blurry in my memory.

Anyway, at some point someone informed me that it was a real number, and a doozie, man, to the 23rd freaking power. What's more, it was a number that a lot of people knew about, and it was useful in some scientific kind of way. The revelation blew my mind. I was like, "No way, man. That's so cool."

I must confess being captivated, now as then, less by the digits than by the pure joy of the name. The double trochee, the internal rhyme, the suggestion of a semitropical pale-green color and fruit. As for the number itself, aside from its awesome size and seeming randomness, I can't say much about it. I read that it has to do with mole, which I take as a marginal vindication of one of my original mismeanings.

It's also known, I learn, as the Avogadro Constant (plus article, minus possessive) which is totally lacking in poetic appeal. You wouldn't have hung out in a diner by that name. You couldn't drive away in your Chevy Vega, belting out, along with Neil on the cassette tape, "Guess I'll roll another constant for the road." That wouldn't even make sense.

4. 0.9999

 All right, another confession: I don't have a fourth favorite number. I have a fifth but lack a fourth—mystery to be revealed shortly. So I asked my favorite mathematician, Bill Rosenthal, of LaGuardia Community College, in Queens. He happily responded, "My very favorite number is the unending decimal expansion 0.999... . This number is my favorite because The Mathematical Authorities believe it is equal to 1, most other sane people believe it is less than 1, and there are equally good reasons for going with either belief—or with both."

Bill is one of the rare mathematicians who relishes ambiguity.

5. 5

 OK, that's why I saved the fifth for five,
or five for fifth, if you prefer. It is,
as you suspect, in deference, to Chaucer,
Milton, Shakespeare, Wordsworth, Byron, Keats.

An earlier draft had this ode to iambic pentameter unfurling down the page for dozens of lines, embedded with precious examples from the masters. But when I opened the file again, and saw my work, I had the epiphany that (wait for it) not all readers love iambic pentameter. That, in fact, the very sight of a disciplined cadre of lines marching down the page, like a lexical Roman legion, strikes fear and hatred into the hearts of most readers, as sight of the real thing once did to Goths and Gauls. As the sight of pages of theorems and formulas do to me and mine.

So let me eighty-six the heroic couplets and readjust my visor on fivers: a new take, starting with the observation that in centuries past, booze came in quarts. The quarts were often short, not quite a quart, four-fifths, perhaps (25.6 ounces). One couldn't pull a pistol on every seller of a short quart, as one could not cut off the thumb of every devious miller. So instead of bemoaning human nature, it was simpler to change the scale. And thus was born the concept and concrete incarnation of the fifth, which referred to one-fifth of a gallon, which—shazam!—is exactly the same as four-fifths of a quart.

But when it came to going metric, unlike Fahrenheit and Celsius, more like me and my checkbook, the numbers of disparate systems did not line up. They were, at some point, slightly fudged. Thus the fifth came to mean the metric three-fourths of a liter, aka 750 ml, which became the worldwide standard for volume in bottles of wine and spirits.

This adjustment cost the tippling public seven milliliters per bottle, but no one seems to have noticed or minded. Which leads me, by way of conclusion, to my own, happier version of Housman's grievance:

The news that fifths of wine or rum
Are neither quart nor liter,
Has never made a heart turn glum,
Nor branded barman cheater.

Here's to numbers. Huzzah.

Jon Volkmer is director of creative writing at Ursinus College.