Music vs. Theater

Fractal expert Loren Carpenter brought my attention to a technical paper that found evidence that the distribution of shot lengths in cinema have been steadily evolving over the past 100 years to exhibit a 1/f power distribution.Your first question is probably, “what the hell is a 1/f power distribution”. And your second question is probably “why do  you have a photo of a hot girl on this post if you’re just gonna be talking about math?”  Ummm… Let’s start with the first question. It’s easier. (waving hands) It’s a distinctive pattern that seems to crop up all over biology, physics, nature and art, and there’s increasing evidence that this pattern is hard wired into the way our neurons fire. (stop waving hands). As for the second question… well,  uhhh… Let’s talk a bit about the paper first.

I find two interesting bits in this paper. First, since the entire art of cinema is only 125 years old, you can actually analyze its evolution from the earliest experiments on film. This paper claims that in just  few generations, editors and directors have unconsciously gravitated towards a film cutting style that we are neurologically wired to prefer. (Perhaps since it more closely mimics the natural rhythms of our eyes, how frequently we dart and change focus.)  However, the paper admits that other issues such as narrative, plot, and close ups of attractive people in revealing bathing suits will trump even perfectly neurologically correlated editing techniques.

The other interesting bit (and the one more immediately relevant to this blog) is that the researchers chose to sample  only “Hollywood” style films, also called “invisible style”. That is, a style of cuts and edits that seek to hide how unnatural it is to watch a two dimensional projection on a screen. This raises all sorts of questions in my mind. Do non-invisible styles show such a convergence? Do the works of non-invisible editors fail to converge because their non-natural decision making processes don’t tap into the 1/f workings of their brain. And why is it that some people (such as myself) tend to be more receptive to non-invisible works than others? What does that say about the neural patterns of the receivers?

How does this translate to other art forms? Voss and Clark showed that pitch contours of melody show a 1/f distribution in all styles of music. (Although surely there are other factors worth exploring besides pitch contour.  Harmonic rhythm?  Phrase lengths?)  This includes music from Indian raga, Mozart, and the Beatles.  However, evidence suggests that they skipped atonal and twelve tone music, much as they skipped “non-invisible” styles of filmmaking. So… what’s going on there?

I would love to see follow up work on pieces that are not “invisible”.  Can we find consistent patterns in those works?  Are there signature divergences from the tyranny of the 1/f norm?  Could we study that divergence to learn something about the artistic voice of the individual or the ethos of a particular movement or style?  A mathematical signature for expressionism?  Or minimalism?

And now for the girl. There is a connection here. Honestly. Can you figure it out? Who is well versed enough in both pop culture and math to get this really weak visual gag? Anyone? Beuler?