What’s Math Got to Do with it?

The Writer’s Page by Donna Jo Napoli

I was once in mathematics. Now I’m in writing. What’s math got to do with it? A lot.

During my first year in college, I took the required freshman writing course. There was one fiction assignment. The day after I turned it in, I got a phone call from the professor, who said I really ought to be a novelist. I decided then and there never to take another English course. I simply was not going to be lured into a vocation that was so financially unstable.

I grew up in a family where money was always an issue. My father gambled. Some people look down on a family man who gambles. But I bet many of you gamble — you just call it investing in the stock market. Either way, you’re hoping to make a bundle without ever having to do any physical or intellectual work to get it. That’s gambling, to my way of thinking. So I’m not complaining about my father. I loved him. I’m simply saying that the money came and the money went. When he’d make money at work, he’d gamble it — sometimes completely away. Then we’d get kicked out of where we were living and my parents would fight and I’d go sit in a tree and read a book and live in the world I created inside my head.

One day in third grade I came home to find everything I owned out on the sidewalk. We’d been evicted yet again. And I vowed to myself that when I grew up and became a parent, my own family would never be evicted. Later, in high school, when the financial situation of my family got desperate, I remember vowing further that my children would never go to bed hungry.

In sum, no way was I going to be a starving writer. I quickly expunged the English teacher’s comment from my head and majored in mathematics, a subject I loved, and I then went on to graduate school and, via a serendipitous series of events, became a linguist. Writing came much later, after a personal tragedy led me to find solace in the pencil.

And, in fact, it was the pencil, not the pen. Mathematics taught me that: pencils have those nifty little devices called erasers. Pencils announce to the world that everybody makes mistakes. Pencils affirm that we can, perhaps with a little help from our friends, recognize our mistakes, and they boldly offer us a chance to correct them. Pencils serve much better than pens.

So that’s the personal side of how I came through mathematics and eventually wound up as a writer, but it’s not the end of the connection.

In mathematics, I learned that the shorter proof was the better proof. If you can do it in five steps, why take fifteen? And it isn’t just a matter of brevity. Brevity might be the soul of wit, but it doesn’t have much to do with mathematics. Instead, it’s a matter of clarity. The proof with fewer steps — the more “elegant” proof — gets to the heart of the matter in a more direct way.

Writing can take a lesson from mathematics here — all writing, but especially writing for children. For many children, reading is a chore. What right do we have to ask a child to read a word that isn’t doing any job? For me the first step in writing is telling: I talk myself through the scene I want to write. By telling it in ordinary words, as cleanly as I can, to my blank computer screen, I get a handle on what’s essential in the scene.

In mathematics, I learned not to defend what I had done in the face of a superior solution to the problem. In the academic world, defending one’s own work is way too often the name of the game. But in mathematics, that attitude has no place. A superior solution stands out like a beacon—it glows. I was not a terrific mathematics student, and I therefore may well have had more lessons in humility to learn than most mathematics students. But even the really top students sat back in admiration when a solution superior to their own was presented.

Let me stress that last point. Too often we think of mathematics problems as having only one solution, because, after all, there’s a right answer to be contrasted with so many wrong answers. In fact, though, you can solve a mathematics problem in various ways. You might offer an algebraic solution or, instead, a geometric solution. You might simply argue your way to a solution with ordinary words, perhaps by assuming the opposite of what you wish to prove, and showing that such an assumption leads to contradiction. Indeed, there may even be more than one answer to a given problem, depending on how you define the elements that are to be operated on and the operations that manipulate them. So the commonly accepted divergence between mathematics and the humanities might be illusory, after all.

But even if you maintain a clear line between mathematical-type problems and humanities-type problems, writers can still learn a lesson from mathematics here — a practical lesson. When an editor marks a passage for cutting, it’s quite possible the editor is a fool. But if she’s too much of a fool, she won’t last in the business. And if she’s been around a while, chances are she isn’t a fool at all. It’s easy to fall in love with our own words—to covet, even, our own ideas. But that’s stupid and, in the end, destructive. If we are to benefit from criticism, we have to stop defending. That’s an absolute rule. My credo is that the reader’s reaction (whether it be my editor, my children, children I’ve accosted on the street, whoever) is never wrong.

Of course, readers disagree a lot. If I get fourteen readers, chances are I’ll have fourteen different reactions. But those reactions are fact, not to be questioned. This is how the reader responded to my work, period. And if a reader has a reaction that is not among the reactions I want, then it’s my job to figure out how the reader got there and how I can change what I wrote to make it more likely that I’ll get the reactions I’m after.

Don’t misunderstand me. I’m not saying every reader is a great critic. I don’t pretend to know what a great critic would be. And neither my children nor my editors can offer concrete solutions to problems in my writing. They don’t know my characters the same way I know them; they don’t understand the story the same way I understand it. So solutions that might work for them won’t generally work for me. I am, therefore, in no way suggesting that writers should ask readers for solutions. If they did, they’d go nuts, anyway, with all the opposing solutions they’d get. Instead, writers should ask readers their reactions. They should listen with respect, and they should revise accordingly. Many solutions can work, but, with a little good fortune, one will stand out as superior.

Mathematics also taught me how to deal with complexity. When I’d be doing a problem and my husband would interrupt me to talk about something like dinner or walking the dog, almost invariably I’d want to shoot poison darts at him. It would often have taken me the better part of an hour to get inside a proof, and then a brief interruption would bring me back to the surface and I’d have to make that difficult and slow dive all over again. There may be many things you can study to teach you how to put together multiple parts in an intricate way, but certainly higher algebra is among them.

The tie-in to writing of this mathematics lesson is plotting. Every plot has its assumptions and its logic, and mathematics teaches one to uncover assumptions and to argue logically. That much is indisputable. But there’s something about geometry that I think helps me — something that visual arts clearly draw on, but that verbal arts and music can as well, I believe.

Sometimes when I’m writing, I feel like my story opens with a single, poorly defined shape. Think about Iran, for a moment.

If I told you it was the shape of a heart, you’d say I was silly. But from far out in space, or perhaps after having shared a nice bottle of wine with me, you might agree. There is something heart-shaped about Iran (just as there is something pentagonal about France, and something bootlike about Italy). I saw this shape when I started writing Beast, a love story that opens in Persia in 1500.

As my story progressed, the shape became more defined. Yes, it’s definitely a heart, with the pointed tip slanting off to the right side. And now everything will start to play: I’ll see the heart reflected across a vertical axis, then across a horizontal one. I’ll see it rotated. I’ll see it translated to one side. I’ll see it translated and rotated (in what’s called a “glide reflection”).

Every symmetry that mathematics taught me will help me to recognize the patterns of my story. I’ll be surprised when a detail moves from the back of my mind into consciousness, simply telling me to use it now — telling me this is the time for that particular symmetry. It’s a mysterious process, shaping a story, but I’m convinced that the training for it in my case came from mathematics training.

My discussion of mathematics has so far focused on the abstract, on the habits of mind that mathematics hones, on the way mathematics disciplines thought. But perhaps the greatest benefit of studying mathematics for the writer is of a different nature. Mathematics isn’t easy. Maybe no theoretical field is. To do math problems, you have to focus and work and work. Or at least I do. I have to read something multiple times. I have to solve a zillion problems before I really get a glimpse of what it’s all about. But if

I keep at it, I get it. (Sometimes, anyway.) So mathematics teaches persistence.

And there may be no more important quality for a writer than persistence. I spent fourteen long years gathering letters of rejection before an editor finally bought one of my stories. I made every mistake it was possible to make. But I kept at it. Part of getting published is having a good manuscript. But that’s only part. Another part is luck: having your manuscript get onto the right person’s desk at the right moment. And another part — for me probably the most important part — is persistence. If I hadn’t kept writing, early in the morning before my children woke and late into the night when everyone else was asleep, I wouldn’t have improved, and I’d never have sold that first story, from which all the rest of it followed.

So mathematics does have a lot to do with writing, at least for me. I doubt I’ll ever have the courage to call myself a mathematician. But, then, it took me decades to have the courage to introduce myself as a writer. So who knows? And, in the end, who cares? That’s part of my point. The benefits of mathematics are sitting there for all of us to reap on whatever paths we follow.

Donna Jo Napoli is co-author with Richard Tchen of a mathematics tale in picture-book form, How Hungry Are You?, to be published by Simon and Schuster in 2001. Her novel Beast was reviewed in the September/October 2000 issue of the Horn Book.

From the January/February 2001 issue of The Horn Book Magazine.

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