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Craft of Writing

The Mathematics of Writing: Is There a Formula for Creative Success?

Wouldn’t it be great if there were a mathematical formula for writing? Maybe there is.

nautilus shellIn the October/September The Writer’s Chronicle poet/teacher Leslie Ullman writes of her fascination with the mathematical relationships between numbers and writing, particularly the Golden Spiral. To really understand the relationship that inspires her, check out the article (you have to be an AWP member). Essentially, it begins with a couple of ancient mathematical concepts that have persevered through the centuries. The Golden Mean was a relationship advanced by Pythagoras and Plato that established a “golden” point on a straight line segment. At that point, the smaller segment of line is .618 the length of the larger segment, and the larger segment is .618 the length of the original line. This magic .618 factor also comes into play in a variety of mathematical concepts, including the Fibonacci sequence, architectural applications like the pyramids and modern works, and many others. As importantly, it can be applied to many natural occurrences, such as branching in trees, the arrangement of a variety of flowering plants, the spirals of shells, generations of bees, and the curve of waves. It can even be applied to the measurements of DNA molecules. The Golden Mean’s ratio yields the Golden Spiral, “an orderly spiral that gets farther from its point of origin by a factor of .618 with each quarter turn it makes.”

Bear with this—here’s the writing part:

So if .618 occurs naturally as a ratio between numbers and arrangements, does it have any significance in literature?

The eight ball says, “Signs point to yes.” (Or is that the .618 ball?)

Sonnets have fourteen lines. In the Petrarchan sonnet the placement of the volta, or turning point, comes after the eighth line, which is quite close to the Golden Mean (grant some leeway here because fourteen lines is a pretty small sample size). English sonnets morphed from the Petrarchan, but maintain echoes of this same trait.

Ullman’s article focuses on poetry. But does this work in prose? The turning point in a narrative is a major key to its success. So are we naturally predisposed to react to change at a certain point in a story, to feel the narrative spiral in an orderly way from its origin to its climax and resolution?

Let’s turn to a famous short story. From my collection of digitized classics I randomly chose Chekhov’s “The Lady with the Pet Dog,” translated by Constance Garnett. Word count is 6724. That means somewhere around 4155 words we should see a shift in the character. I scrolled to that point, and just a few words before the textual Golden Mean, I found this paragraph:

Gurov did not sleep all night, and was filled with indignation. And he had a headache all next day. And the next night he slept badly; he sat up in bed, thinking, or paced up and down his room. He was sick of his children, sick of the bank; he had no desire to go anywhere or to talk of anything.

Change, my friends.

I tried another, “In the Dry,” a classic in my opinion by Breece D’J Pancake. 5126 words. The change point would be around 3168. Only a sentence later is this:

On the path to the shed, a strangeness creeps through him: he remembers walking this way—nights, years ago—and Bus yelling, “I’m going to show you something, Ottie.”

This is getting scary.

Keep in mind that to be more certain of the significance of these findings I will have to reread the stories from the start. These paragraphs may not be the greatest change or the ultimate change, but these passages are definitely turning points in the characters’ makeups, at which events have caused them to begin to rethink their present lives.

But now the real test—one of mine. I chose a published story titled “A Teaching Moment.” It contains 3923 words, so a turn should occur around 2424. Here, at exactly word 2424, is text from the story:

There was no sense bringing up commitment. I couldn’t move to take her in my arms, or invoke some other movie cliché to save the scene. I just lay there, helpless, useless. She’d managed the end of our relationship perfectly. Who knew the real reason she wanted out? But I couldn’t argue at that point. All I know is that even if she came back now, all would be forgiven.

God, I do miss her.

Yikes. Since I wrote it, I can honestly report this passage ends the second of three sections, and positions the character for his psychological change.

This is all very preliminary and could well be disproved. But I think it won’t be. A traditionally well-crafted story (or poem or novel) creates its effect on the reader by building an emotional case, and then advancing to climax and resolution. Think of it as a controlled spiral of increasing tension. Is the 61.8 percent point in the narrative the trigger where the reader’s mind is properly prepared to begin the rise to climax? This deserves more investigation.

Perhaps I’ll take a look at some unpublished stories and see where character change begins. Maybe the problem is not with language or theme, but with timing.

Try it for yourself. Take something you’ve read and enjoyed, or something you’ve written and look for the point at which the narrative begins to turn. I’m more than curious to know what you discover.


About Joe Ponepinto

Co-publisher, with Kelly Davio, of Tahoma Literary Review. Author of "Curtain Calls," a featured Kirkus Review. Married to Dona. Dad to Henry, the coffee-drinkin' dog.


27 thoughts on “The Mathematics of Writing: Is There a Formula for Creative Success?

  1. You are a cruel man. I have no tool to let me land on a given word. So I counted (and fudged a little). I used a favorite story of mine, On the Chopshaw Road. It was in Short Story America’s anthology and won a couple of awards.
    I decided to determine the event that signalled the major shift in the story direction. I found it and it was nowhere near the .618 number. I wanted it to work, but no. Then I thought, wait, .618 is a percentage of the whole, or 1.000, leaving a remainder of .382. And bang, the event fell right in there. Voodoo science? Massaged math? Literary alchemy? I don’t know, but it’s an interesting concept.
    (Is there actually an easier way to find that line at .618? If so, I’ll check more stories and report my findings to the Academy.)

    Posted by Jon Zech | September 28, 2013, 2:41 PM
    • No word counter in your program? If you’re using Word, it should be in the little bar at the bottom. Also in the dropdown menu under Tools.

      But this is a fascinating little concept isn’t it? And without making it too math oriented, there’s something to be said for the way in which stories resonate with readers–that subconsciously readers begin to expect change at a certain point, and good stories deliver it then.

      Posted by jpon | September 28, 2013, 2:49 PM
    • I hightlighted a story up to the confrontation, and when I lifted my finger, it told me how many words into the story I was. An old version that was rightfully critiqued as having too long of a denouement had a ratio of .536! A revision was .573. I just spent an hour or so playing with it and I’m at about .600. I could have hit .618, but I just couldn’t leave the first section untouched.

      Posted by michellemorouse | September 28, 2013, 2:56 PM
  2. I just tried this on a favorite nonfiction piece — Cheryl Strayed’s “The Love of my Life” in The Sun Magazine. The turn happens at .695.

    Something interesting to think about certainly …

    Posted by Teri | September 28, 2013, 5:27 PM
    • Somewhere way down beyond the discernible universe, in the dimensions of quantum mechanics, all this stuff is connected. Quantum writing, maybe.

      Posted by jpon | September 28, 2013, 8:33 PM
  3. What a fascinating concept! It’s really reassuring, and not at all spooky to me (well, maybe a little, but only in a good way). It makes the world make sense in a large way. I like things like that. But of course, I’ll have to tell my brother the statistics expert about it so that he can check it out too–this is submitting it to the ultimate skeptical test, since I suspect he may want to pooh-pooh it. But I’m convinced more easily, I guess. I’ve always preferred the organic metaphorical system, and this is no exception.

    Posted by shadowoperator | September 28, 2013, 7:58 PM
    • We tend to dismiss ancient knowledge in favor of what we’ve developed ourselves. But the discoverers of the Golden Mean and the Golden Spiral may have had something.

      Posted by jpon | September 28, 2013, 8:34 PM
  4. I was told that there would be no math…

    Posted by Kelly Davio | September 28, 2013, 11:08 PM
  5. Screenwriters would LOVE this! They live for such structure (which is why I’m not really a fan of screenwriting–adapted one of my novels just to do it and that’s all I’ve trucked with in screenwriting)! They have rules that state that specific things MUST happen by specific pages, such as pages 10, 15, 25, etc. (don’t hold me to these, it’s been a while), in a 120-page script, plus or minus. Be interesting how that would all play there.

    Thing I’m most curious about is how all that happened in those stores naturally, not that we now have to consciously induce that to happen.

    Isn’t Life fascinating?

    Posted by fpdorchak | September 29, 2013, 10:37 AM
    • Indeed it is. Very doubtful that those authors consciously planned for a turn at that point in their stories–I know I certainly didn’t. Perhaps that’s one of the things that keeps good writing separate from the obviously formulaic type Hollywood product. The writing is still organic, and it shows.

      Posted by jpon | September 29, 2013, 12:00 PM
  6. brilliant stuff. I’ve known about this stuff and have wondered at the implications for writing. Now that I write poetry, I’ve consciously managed working turns and voltas along these lines — though it is a rhythm that, as you say, comes naturally. But if something is not working right, the order of things is one area I start at. Great post as usual. thanks

    Posted by Robert Hoffman | September 29, 2013, 3:31 PM
    • Thanks Robert. Yes, we can analyze and assign numbers and ratios, but the writing must still come organically.

      Posted by jpon | September 30, 2013, 1:27 AM
  7. I never thought of it as mathematics, but the relationship between it and narrative writing stands to reason. In my course manual with the Institute of Children’s Literature, one of the lessons focuses on properly structuring a story. The “beginning” of a short story should constitute no more than 25% of the total word count. So if a story is 1,000 words, a reader should know the who, the what, and the why of the plot by around word 250. According to the same lesson, denouement should comprise approx.10% of the text. The middle 65% should build toward climax, which occurs right before the denouement. I like this idea of breaking it down into numbers, if nothing else for helping me keep word count and structure.

    Posted by Gwen Stephens | September 29, 2013, 10:23 PM
    • Interesting that they’ve broken so much of writing down by numbers. But of course the key is to be able to write without having those things in your conscious mind. It’s similar to what I teach writers who I mentor–my system is to create a series of filters that avoid mistakes and bad writing, and to internalize them so they come into play naturally, without diverting the writing process.

      Posted by jpon | September 30, 2013, 1:32 AM
  8. Edit: Ullman’s article focuses on poetry. But does this work in prose? The turning point in a narrative is a major key to its success. Ullman’s article focuses on poetry. But does this work in prose? The turning point in a narrative is a major key to its success.

    Just sayin ;)

    Posted by Richard | September 30, 2013, 12:12 AM
  9. yup, it’s creepy. happily, i can’t add or subtract so i’ll have to write it all and read it all just by the feel.

    Posted by Stephanie Barbé Hammer | September 30, 2013, 5:55 AM
  10. I absolutely love that those ideas, which I fell in love with and even thought about in my sleep while I was writing my essay, are taking on new life through all of you. Now you’re all having the same experience I had, and it isn’t about us as writers, it’s about the energies inherent in the ideas themselves. And maybe a little about our own curiosity…
    Thank you, Joe, for generating such an interesting discussion.

    Posted by Leslie Ullman | September 30, 2013, 2:19 PM
    • I hope other readers of The Writer’s Chronicle found these ideas as interesting and inspirational as the people who commented here. Thanks, Leslie, for the essay and for connecting modern writers with these ancient, but still very applicable concepts.

      Posted by jpon | September 30, 2013, 2:37 PM
  11. Incredible. In Middlemarch, Will Ladislaw enters Dorothea’s life at .615.

    Posted by MK | October 2, 2013, 5:03 PM
  12. Great observation!…………Your story is featured on Golden Ratio Updates:

    Posted by Robert | October 7, 2013, 2:24 AM
    • Fascinating site. I had no idea there were so many real world applications of the GR. Thank you for including my blog.

      Posted by jpon | October 7, 2013, 9:48 AM
  13. Reblogged this on Notwithstandingtheforegoing2 and commented:
    Math and Writing?? The magic .618 factor Fibonacci sequence? In stories? plot structure? I have admitted , only now my admiration for mathematics.It was my achilles for years, carrying abacus, then scratch pad and then calculator and charts in pocket sized memos.Now freedom with a formulaic reasoning.Oh, what shall i write??

    Posted by Priscilla | November 18, 2013, 1:04 AM

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