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.”