Mad science: Cum on feel the pink noise.

Neuromathematics, the dauntingly named practice of mathematically modeling neurological processes, may have revealed the deep structure of the language of film editing. James Cutting, a psychologist at Cornell in Ithaca, New York. From a survey of 150 Hollywood movies, Cutting proposes that the pattern of editing in narrative film reflects the pattern of focus and distraction found in the human brain.

In the 1990s, a team at the University of Texas, Austin, measured the attention spans of volunteers as they performed hundreds of consecutive trials. When they turned these measurements into a series of waves using a mathematical trick called a Fourier transform, the waves increased in magnitude as their frequency decreased.

This property is known as a 1/f fluctuation, or "pink noise", [pink noise (left above) is imaged in relation to white noise (right above) - CRwM] and in this case it meant that attention spans of particular lengths were recurring at regular intervals. The pioneering chaos theorist Benoit Mandelbrot found that annual flood levels of the Nile follow this pattern; others have observed it in music and air turbulence.

To find out whether the length of camera shots in films might follow 1/f too, Cutting measured the duration of every shot in 150 high-grossing Hollywood movies in various genres released between 1935 and 2005. He then turned these into a series of waves for each film. He found that later films were more likely to obey the 1/f law than earlier ones (Psychological Science, in press). But he stresses that it isn't just fast-paced action films like Die Hard II that follow 1/f. Rather, the important thing is having shots of similar length that recur in a regular pattern throughout a film.

The text can get a little dense, but the executive summary goes something like this: When human's focus on something, they don't throw an intense laser beam of concentration on it. Rather, we look for patterns that define the object observed and groove along on those patterns. To many breaks in the pattern and the object starts to require serious expenditures in energy to puzzle through it. Too much similarity, we zone out.

Cutting's argument is that the editing techniques of Hollywood style narrative follow the generalized pattern of human attention. They fall in the sweet spot that requires our attention but doesn't overly tax the system. Cutter, in a refreshingly non-Bordwellean turn, doesn't suggest this formal element "explains" movies.

Cutting suggests that obeying 1/f may make films more gripping because they resonate with the rhythm of human attention spans, but he doubts that directors are deliberately using mathematics to make movies. Instead, he thinks films that happen to be edited in this way might be more likely to be successful, which in turn would encourage others to copy their style. This would explain why a greater number of recent films tend to follow 1/f.

Cutting, a film noir fan, is the first to admit that shot-pacing isn't everything: he found that the lengths of shots in film noir movies are typically random and not correlated with one another on any timescale. Star Wars Episode III (pictured), however, which he describes as "just dreadful", adheres rigidly to 1/f. He says that a good narrative and strong acting are probably most important.

Cutting's work does jibe with some other work in the field:

The attention theory chimes with other recent work, Tim Smith at the University of Edinburgh, UK, tracks the eye movements of movie-goers. He has shown that the editing style of modern films results in more people being focused on the same areas of the screen at the same time. He has interpreted this as a sign that audiences are more attentive to the film.

UPDATE: Another article discussing the same work by Cutting and others gives Cutting's hypothesis on just how the pink noise pattern became so prevalent in Hollywood blockbusters.

These researchers don't believe that filmmakers have deliberately crafted their movies to match this pattern in nature. Instead, they believe the relatively young art form has gone through a kind of natural selection, as the edited rhythms of shot sequences were either successful or unsuccessful in producing more coherent and gripping films. The most engaging and successful films were subsequently imitated by other filmmakers, so that over time and through cultural transmission the industry as a whole evolved toward an imitation of this natural cognitive pattern.