Orca Blog for March, 2019 – The Mathematics of Writing

Is there a formula for creative success?

Writers and critics disdain formulaic writing, but what if there were a mathematical formula for writing? Maybe there is.

In an article in The Writer’s Chronicle a couple of years ago, poet/teacher Leslie Ullman wrote of her fascination with the mathematical relationships between numbers and writing, particularly the Golden Spiral. To really understand the relationship that inspired her, check out the article (you have to be an AWP member). Essentially, it began 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. (Bear with me, this really does pertain to writing.) 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.”

Got that? Okay, here’s the writing part:

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. Ullman notes that 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 I couldn’t help wondering if this worked in prose as well? 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 morph in an orderly way from its origin to its climax and resolution? In the Hero’s Journey, Joseph Campbell laid out twelve steps by which the hero character in ancient literature went from average person to hero. Step 7 is the “Supreme Ordeal,” described as “…the person’s lowest point or darkest moment. The separation has been made between the old world and old self and the potential for a new world/self. By entering this stage, the person shows her/his willingness to make a change, to die and become a new person.” Step 7 is the closest to .618 in a sequence of twelve.

In that vein, Dan Harmon, the writer who created “Community,” and whose YouTube videos are quite popular with writers these days, demands that his team stick to the hero’s journey cycle and will not even entertain drafts that drift too far from the .618 rule.

Let’s see if it actually works in practice. 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.

Sounds like 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 would have to reread the stories from the start. But these passages definitely indicate turning points in the characters’ narrative arcs, 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 just my opinion 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.

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.

–Joe Ponepinto