Author’s Response: Is Number Sense a Patchwork?

Stanislas Dehaene I would like to thank the commentators for raising excellent questions that illustrate the extent of what we do not yet know about the organization of the number system. The most critical comments seem to revolve around the multifaceted nature of the concept of number. Should we really postulate a single number sense, or is there a patchwork of representations and abilities, each underlying a specific set of tasks and experiments? If only for the sake of economy, I would like to defend the idea that a single, analog representation of quantities underlies the core of our numerical abilities and intuitions. In the course of development and education, however, this central representation becomes connected to other cognitive systems, including word comprehension and production and object tracking devices. What is at stake is to what extent the initial quantity system is altered through these interactions; and to what extent the adult concept of number is based solely on the quantity system as opposed to an integration of multiple senses of numbers. Giaquinto argues the number line is a " culturally supplied representation " , a visual tool learned from school that we use to convene a concrete image of numbers, and that must therefore be distinguished from the biologically inherited quantity representation that underlies number sense. He further argues that the distance and magnitude effects that are seen in the number comparison task " could well be accounted for in terms of the operations of 'scanning' and 'zooming in' postulated by Kosslyn in his theory of the visual imagery system ". If it was literally true that number comparison relies on visual imagery, would