Recent studies in the field of numerical cognition quantify the impact of physical properties of an array on its enumeration, demonstrating that enumeration relies on the perception of these properties. This paper marks a shift in reasoning as it changes the focus from demonstrating this effect to explaining it. Interestingly, we were inspired by one of the very first articles in the field, “The power of numerical discrimination” by Stanley Jevons that was published in Nature in 1871. In his report, Jevons attempts to answer the question of how many objects can be perceived in “a single mental beat of attention”. We relate directly to Jevons’s records, putting forward a plausible heuristic mechanism that relies on the physical geometrical properties of the arrays to be enumerated. We use a mathematical theorem and computer simulation to show that the shape of the convex hull, the smallest polygon containing all dots in an array, is a good predictor of numerosity. We show that convex hull downsamples the spatial data, allowing quick and fairly accurate numerical estimation. Moreover, convex hull predictability changes as numerosity grows, corresponding to the psychophysical curve of enumeration shown by Jevons and many others that followed.
Computer Simulation of the Structural and Physical Properties of Minerals in the Earth's Deep-Interior.
