Bias toward regular form in mental shape spaces

The distribution of figural "goodness" in 2 mental shape spaces, the space of triangles and the space of quadrilaterals, was examined. In Experiment 1, participants were asked to rate the typicality of visually presented triangles and quadrilaterals (perceptual task). In Experiment 2, participants were asked to draw triangles and quadrilaterals by hand (production task). The rated typicality of a particular shape and the probability that that shape was generated by participants were each plotted as a function of shape parameters, yielding estimates of the subjective distribution of shape goodness in shape space. Compared with neutral distributions of random shapes in the same shape spaces, these distributions showed a marked bias toward regular forms (equilateral triangles and squares). Such psychologically modal shapes apparently represent ideal forms that maximize the perceptual preference for regularity and symmetry.     

How surprising is a simple pattern? Quantifying "Eureka!"

Simple patterns are compelling. When all the observed facts fit into a simple theory or "story," we are intuitively convinced that the pattern must be real rather than random. But how surprising is a simple pattern, really? That is, given a pattern of featural data, such as the properties of a set of objects, how unlikely would the pattern be if they were actually generated at random? In conventional statistics dealing with patterns of numbers, this type of question would be answered by reference to a null distribution such as the t distribution. This paper gives the analogous answer in the realm of concept learning, that is, the formation of generalizations from patterns of featural data. Using a formal but psychologically valid definition of complexity, I derive and exhibit the distribution of subjective complexity under the hypothesis of no pattern. This leads directly to a number of applications, including a statistical test indicating whether an observed pattern is sufficiently simple that it is not likely to have been an accident: literally, the "significance of simplicity."