I'll present an overview of some recent work in my lab seeking the cognitive foundations of number. First, I'll present evidence against "two systems" accounts in which large and small numbers draw on distinct representational resources. People's behavior is predicted by one system with bounded information processing capacity, and moreover the functioning of this system is tightly integrated with perceptual processes such as visual memory. Second, I'll present some of our cross-cultural work suggesting that representation of integers, large exact numbers, are highly dependent on culture, and likely rely on a general algorithm- and structure-learning processes whose functioning can be seen across diverse tasks. Finally, I will outline some upcoming work that formalizes what inferences are justified from behavioral data, with the numerical representations used in insect path integration as a key example.
