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# Solved: Mathematics of the blockbuster

## Study finds pattern that also describes attention spans

HOLLYWOOD’S golden age may have ended in the 1950s, but it is only recently that Tinseltown appears to have hit upon a mathematical way to capitalise on our fickle attention spans.

“Film-makers have got better and better at constructing shots so that their lengths grab our attention,” says James Cutting, a psychologist at Cornell University in Ithaca, New York. He analysed 150 Hollywood movies and found that the more recent they were, the more closely their shot lengths tended to follow a mathematical pattern that also describes human attention spans.

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”, 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 key thing is having shots of similar length that recur in a regular pattern throughout a film

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.

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.

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