In his In Retrospect article “Out of the darkness” (Nature 442, 986; 2006), Jay M. Pasachoff notes the impact of Fred Hoyle's novel The Black Cloud (first published in 1957) and its contemporary relevance. We would like to add a further aspect: the contribution of two ideas in Hoyle's book to vision research and to our understanding of the perceptual guidance of action.

The characters in the book discover an ominous black cloud that appears to be heading towards Earth. Will the cloud hit Earth and, if so, when? The first question is solved when the characters examine the relative speed at which the cloud is translating across the night sky to the rate at which it is looming, or seeming to get larger. The second question is tackled with a bit of impromptu algebra in which the time until impact is calculated from the ratio of the current size of the cloud to its rate of change. A mathematical derivation of the formula is provided.

A footballer wishing to head an approaching ball needs to know where the ball is going relative to the head, and when it will hit or pass the head. The player could estimate the trajectory of the ball from knowledge of its position and velocity. However, David Lee realized in the 1970s that the brain can use the ratio of size to its rate of change, previously identified by Hoyle, to estimate the imminence of arrival. David Regan realized soon afterwards that the brain can use the ratio of lateral speed to looming rate to calculate where an object is travelling. These elegant solutions bypass the need to know position and velocity, so that the two quantities of interest can be estimated directly. This human ability is important for the characters in Hoyle's story because the position and velocity of the cloud are unknown.

An ability to estimate these quantities is of use not just for heading a ball, but also when trying to cross a street full of cars, return a tennis serve or pick up a cup of coffee while rushing past your desk. Since the early work of Lee and Regan, a considerable amount of research in areas including psychophysics, motor action, neurophysiology and computational modelling has followed (see D. Regan and R. Gray Trends in Cognitive Sciences 4, 99–107; 2000). The whole body of work that exists today can be traced back to a casual footnote and a couple of sketches in a science-fiction novel.