Solved: The mathematics of the Hollywood blockbuster

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.

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