Freytag & Fibonacci


Herein is a “sidebar”, stemming from the essay at OPEN: Journal of Art & Literature. It’s simply for anyone who is not familiar with Gustav Freytag’s insight into basic dramatic form.  

Also, below Freytag, is a note for anyone innocent of how we’re surrounded by, indeed, cosmically-immersed in, beautiful, reliable, virtually eternal Fibonacci numbers.

Reader is linking here from page 13 in the essay The Long of the Short of It, in OPEN:JA&L, and can link back to that essay clicking here on: #TheLongOfTheShort


               / \               

/       \

______/                              a

Freytag? It’s on the test! Skip this next paragraph if you yawn and check your phone when teachers drag out good old Gustav, but for the beginning creative writer:

 Freytag’s pyramid: the ‘inverted check mark,’ also called

Freytag’s triangle, does nothing more or less than delineate all basic dramatic (i.e., having conflict) plot structure. The dots to connect along the outline of this inverted checkmark are

1) the set up, which will give you the situation and the so-called point of attack (that point at which you can first state what the dramatic question i —will he get home, will she get to the ball and hook up with the Prince, etc., ad inf.).

2) Then comes an array of hurdles—called complications, actual resisters to solving the dramatic question (will she get to the ball? Not if step-mom has any say in it).

3), 4), 5)… No set number of these, but in each the complication gets resolved, only to lead to yet another one: Yes, she will get to the ball, thanks to F.G., but, there’s a curfew, little lady.

These complications and their resolutions leading to more complications cause the dramatic tension to mount (suspense)—hence the line of ‘rising action’ in the diagram of the upside-down check mark. Finally, at the highest point of tension, the over-all conflict is resolved—the climax—and then comes a brief spell of ‘falling action’ and the final resolution—the dénouement, a lovely French word that literally means the un-knotting, the untying of the forgone snarl of complications: Prince finds his girl through her dental records—no, her shoe size—and marries her and they move on into an implied happily-ever-after. (When all the girl really wanted was to go to a dance! Some things work out better than expected.)

Again, in sum:

Cinderella is in the cinders, gets an invitation to the ball (point of attack), is blocked by step-mother (complication), saved by Fairy Godmother, but given a curfew (one complication resolved, leading to another); she goes, she meets Prince, flees at midnight (complication: girl is gone), is tracked and found by Prince with her size 6 ½ shoe (a recognition climax) happily ever after (dénouement). This pattern found in virtually all dramatic form is called Freytag’s triangle, or pyramid, after a mid-19th century German novelist and playwright, Gustav Freytag. He taught, too, till he gave it up for writing, actually becoming quite popular.

The scheme is admittedly a bit formulaic, but try to find a play, even a movie without it:

The point I was making in the craft essay in OPEN: JA&L, is that that tiny little clip from an answer to a mathematical question in Quora, sounds like a narrative short short because it has nodal points that more or less fit the Freytag dramatic structure. In fact, I’ll bet you could duplicate this structure with only your tone of voice—no words necessary: the heart would step up its pitter-pat a half step just hearing your voice tones emulate those that would, with words, carry you through intro, attack, complications, climax, resolution. And it was an added delight to find ‘Freytag’ embedded in Fibonacci lore, kind of a miniature tour de force; hence, I called it Fibonacci Sprezzatura!


0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 . . .   [What’s the next number?]

Now to Fibonacci himself: My closing point regarding the ‘found flash’ in OPEN, entitled Fibonacci Sprezzatura, was that the thing on the page can be very short, ink-wise, but this one still able to squeeze in the moves of Freytag’s five phases of dramatic structure, thus a dramatic narrative, as well as give a respectful nod to the beautiful math in natural things: such as the arrangement of seeds or buds on a stem, or bracts of a pinecone, or the scales on a pineapple. This mathematical progression fairly abounds in nature. The arrangement of limbs on a tree, or leaves on a stem, the uncurling of a fern, the spirals of shells, the curve of waves. Everything from the seed arrangement on the calyx of a sunflower to actual galaxies in space. Everything’s hardly an exaggeration: the number of possible ancestors derivable from the male’s X chromosome line. I wouldn’t be surprised if our axons and dendrites didn’t branch out toward each other in Fibonacci progressions. I don’t know, but dendrite does mean tree.

Fibonacci was a brilliant theoretical mathematician by the name of Leonardo Pisano, living in Pisa in the early Middle Ages. He was given the name Fibonacci, it’s said, from his family name: son of Bonaccis: filius Bonacci fi’bonacci. It’s also said it came from Bigolo, which translates n’er-do-well or loafer, maybe dubbed that by those who had no patience with theoretical math or his persistent arguments advocating the use of Arabic numerals over Roman. Image if the West were still using Roman numerals! Man, what’s the square root of stupid.

His book, The Book of Calculations (Liber Abacci, 1202), discloses the famous number sequence, discovered in India a millennium earlier; but Fibonacci introduces it to the West. Those “Arabic numerals,” by the way were originally Hindu, from around 700 CE—we just copied them from Arabic translations, hence ‘Arabic.’ We should call them Hindu-Arabic, at least.

The formula for this neat progression is beyond my computer’s graphics, but it basically describes a sequence of numbers built out of their own sequence, creating a series where each number, starting with 1 (or 0), can be found by simply adding together the two numbers preceding it. Hence, 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on: 5 is sum of 2 and 3; 21 = 8+13. You can start at 0, but Fibonacci used 1. You can go backwards. You can predict turning points in the stock market, they say. They also say you can’t. The tao of Dow. Music of the spheres. Speaking of, look at a chromatic scale: made up of 13 keys, and in the span of an octave, 5 of the notes are black, 8 are white. It has its way with the actual notes, too—the frequencies. Enough. A good, hardly used Liber Abaci is only $89 at amazon. …13, 21, 34, 55, 89!

It’ll follow you home, so, keep it.