Chaos Theory, Movie Rhythms . . . and the Fractal Geometry of Stories?

A couple of months ago, while cruising the Web, I came across a piece written by Canadian blogger Jay Stone called “Chaos Theory and the Rhythm of Movies” (http://communities.canada.com/shareit/blogs/stonereport/archive/2010/02.aspx). He referenced an article in the journal Psychological Science in which authors James Cutting, Jordan DeLong, and Christine Nothelfer of Cornell “used the sophisticated tools of modern perception research to deconstruct 70 years of film, shot by shot,” looking for a pattern called the 1/f fluctuation. “The 1/f fluctuation is a concept from chaos theory, and it means a pattern of attention that occurs naturally in the human mind,” Stone writes. “Indeed, it’s a rhythm that appears throughout nature, in music, in engineering, economics, and elsewhere.” The Cornell authors, by measuring “the duration of every shot in every scene of 150 of the most popular films released from 1935 to 2005,” established that modern movies, particularly those made since 1980, “were more likely to approach this natural pattern of human attention.” Action movies, in particular, “most closely approximate the 1/f pattern, followed by adventure, animation, comedy and drama.” Among the movies they studied that have nearly perfect 1/f rhythms are Hitchcock’s The 39 Steps (1935), Nicholas Ray’s Rebel Without a Cause (1955), and Wolfgang Petersen’s The Perfect Storm (1955).

I found this to be fascinating, but I was mystified by exactly what the “1/f fluctuation” is. I’m not a physicist; I’ve read one book on chaos theory and a few other titles that tried their best to explain Einstein’s universe to me, but I’m not about to be able to explain what the 1/f fluctuation has to do with the attention spans of movie audiences or engineers or economists. The paper itself, “Attention and the Evolution of Hollywood Films” (http://people.psych.cornell.edu/~jec7/pubs/cuttingetalpsychsci10.pdf) is sufficiently technical to have me feeling out of my depth as I read it trying to find a clear answer to my simple question.

A wonderful article on the PhysOrg website, however, clarified it for me (http://www.physorg.com/news185781475.html): Cutting and coauthors “found that the magnitude of the waves increased as their frequency decreased, a pattern known as pink noise, or 1/f fluctuation, which means that attention spans of the same lengths recurred at regular intervals. The same pattern has been found by Benoit Mandelbrot (the chaos theorist) in the annual flood levels of the Nile, and has been seen by others in air turbulence, and also in music.” Furthermore, “Cutting said the significant thing is that shots of similar lengths recur in a regular pattern through the film.”

Okay. Got it. Same lengths recurring at regular intervals. That sounds (ho ho) like a noise pattern to me, as well as Nile flooding and, interestingly, also hints at what many of us find to be appealing about some landscapes and naturescapes, as one of these articles points out. It is a kind of “sweet spot” that we all appreciate, as Stuart Fox says in an article on popsci.com: “Cutting doesn’t believe that this increasing conformity to the 1/f fluctuation resulted from a conscious decision on the part of the directors. Rather, he theorizes that films which fall into people’s viewing sweet spot better hold their attention, and thus seem more gripping, and make more money. Then the other directors naturally copy the pace of the more exciting, more profitable movies, and the 1/f fluctuation trend spreads. However, this formula seems a better predictor of box office than quality. For instance, Cutting found that the Star Wars prequels all conformed nearly perfectly to the 1/f fluctuation. Sure, all three of those movies made a ton of money, but man, did they suck” (http://www.popsci.com/technology/article/2010-02/mathematician-cracks-box-office-gold-code).

It sounds to me as though what Cutting and his coauthors established was a formula for how successful montage is in films. If I recall my film theory correctly, montage (a term introduced and widely used by Russian filmmakers and film theorists in the 1920s) is how a movie’s separate shots are put together in a certain rhythm in order to gain maximum effect from an audience. The Odessa steps sequence in Battleship Potemkin is perhaps the best-known example. So what is going on appears to be a style of montage or film editing in modern movies that, through the random (chaos theory) repetition of sequences of shots of a certain length, matches our natural human heartbeat as well as our natural human attention span. A pulse beat, a rhythm.

None of these authors talks about language in this regard, or poetry. This is a mathematical model, so the discussion in the formal science papers had to do with sine waves and fractals. These are not the elements that I typically get involved with during my work day, although talk of fractals led to me another fine website (http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html) that contains this sentence: “Fractals are unpredictable in specific details yet deterministic when viewed as a total pattern—in many ways this reflects what we observe in the small details and total pattern of life in all its physical and mental varieties, too.”

Whoa. The first part of that sentence is as good a definition as any for what occurs during the process of editing a movie: “Shots are unpredictable in specific details yet deterministic when viewed as a total pattern”—that is, a sequence in a movie. You put the shots together into a sequence such as the Odessa steps slaughter or the chase through the marsh in The 39 Steps, and what do you have? Pulse beat racing and pure, undivided attention.

Back to language and poetry. Doesn’t it make sense that language itself, the popular rhythm of sounds, syllables, and words, would also lend itself to the attention-grabbing rule of the 1/f fluctuation? I wouldn’t know how to design such a study, but it makes sense to me that the meter and beat of great verse and appealing prose really must, in some way, approximate this fluctuation. Is it possible that at the root of some fiction that critics find intellectually unsatisfying but which audiences love is this 1/f fluctuation? Is this same pulse beat at work in comedy, in the timing of comics’ and great actors’ delivery? I really want to know. If I could figure this out, why, I would start writing my stories with this in mind; perhaps it would make my fiction more appealing to a wide, general audience!

This isn’t the whole story, of course. As Cutting himself noted in his paper, his favorite type of movies are film noirs, and few of them accommodate this 1/f fluctuation pattern. Still, they are satisfying. So it really does come down to attention span in the moment, the undistracted attention of an audience glued to the screen—and, perhaps, to the un-put-downableness of some stories? If this is part of the appeal of the Harry Potter books or the Twilight series, whatever their flaws, I’d like to determine this and bottle it and sell it at writers’ conventions. Little glass bottles of Honest Dave’s 1/f Storytelling Formula and Writers’ Block Cure: Guaranteed to Win You Lots of Sales and Audience Devotion.

Hmmm…. Wait a minute. Pride and Prejudice and Zombies and 1/f! I’m onto something….

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One Response to Chaos Theory, Movie Rhythms . . . and the Fractal Geometry of Stories?

  1. Ted says:

    Interesting consideration, no doubt. But you could argue dramatic arcs and rhythms 1/f-ing fluctuation at a time for ten-thousand years, and your agent would still respond with that blank stare, blink it all away vapidly, and ask you if you had accumulated enough Twitter and blogosphere followers yet to make it worth her while trying to market your book.

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