Learning and extrapolating a periodic function

How people learn continuous functional relationships remains a poorly understood capacity. In this article, I argue that the mere presence of nonmonotonic extrapolation of periodic functions neither threatens existing theories of function learning nor distinguishes between them. However, I show that merely learning periodic functions is extremely difficult. It is only when stimuli are presented numerically, rather than as numberless quantities, that participants learn anything like a periodic function. In addition, I show that even then, people do not regularly extrapolate periodically. The lesson is that careful methodologies will be required to understand a psychological capacity that is as idiosyncratic as the learning of complex functions appears to be.