UC Berkeley

Numerosity perception has been studied for at least 150 years and its psychophysics have been well characterized by experimental work. However, the origins of many of its key properties remain obscure. For instance, people estimate the numerosity of small sets (up to four) much more rapidly and accurately than larger sets; people tend to underestimate larger numerosities; estimation precision and accuracy increase with exposure duration. Standard models of numerical estimation do not account for these wide ranging phenomena, with large number estimation typically characterized as a draw from Gaussian(n, w * n) where w is a person's "Weber fraction," and exact small number perception characterized separately, the result of an independent object-file system. Furthermore, the inherently perceptual nature of estimation is largely ignored in many accounts of individual differences, which are often considered evidence of disparities in innate mathematical cognition. In my dissertation, I present studies of human behavior and computational models aimed at clarifying the visual mechanisms underlying numerical estimation. Our findings help to understand, and unify, key properties of number psychophysics which have previously been explained in terms of independent mechanisms or with ad hoc modifications to existing theories. For instance, we show how the psychophysics of both small and large number estimation can be unified into a single framework with a common mechanistic origin, and in fact how myriad properties of both (including estimation precision, bias, effects of time) can be understood as downstream consequences of bounded-optimal perceptual inference.