A Number Sense as an Emergent Property of the Manipulating Brain

The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which this ability is developed is still poorly understood. In particular, it is not known whether acquiring such a {\em number sense} is possible without supervision from a teacher. To explore this question, we propose a model in which spontaneous and undirected manipulation of small objects trains perception to predict the resulting scene changes. We find that, from this task, an image representation emerges that exhibits regularities that foreshadow numbers and quantity. These include distinct categories for zero and the first few natural numbers, a notion of order, and a signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate the number of objects in the scene, as well as {\em subitization}, i.e. the ability to recognize at a glance the exact number of objects in small scenes. We conclude that important aspects of a facility with numbers and quantities may be learned without explicit teacher supervision.