Research in face recognition has tended to focus on discriminating between individuals, or "telling people apart." It has recently become clear that it is also necessary to understand how images of the same person can vary, or "telling people together." Learning a new face, and tracking its representation as it changes from unfamiliar to familiar, involves an abstraction of the variability in different images of that person's face. Here, we present an application of principal components analysis computed across different photos of the same person. We demonstrate that people vary in systematic ways, and that this variability is idiosyncratic--the dimensions of variability in one face do not generalize well to another. Learning a new face therefore entails learning how that face varies. We present evidence for this proposal and suggest that it provides an explanation for various effects in face recognition. We conclude by making a number of testable predictions derived from this framework.