Arithmetic education is accompanied by another important change: the learning of systematic links between numbers and space. The intuition of the spatial scale of numbers plays an essential role in mathematics, from the notion of measurement (geo-metry) to the study of irrational numbers, the real line, Cartesian coordinates or the complex plane. Numerous studies have demonstrated the automaticity of the link between numbers and space in adult humans: the simple presentation of an Arabic numeral is enough to bias motor responses and visuo-spatial attention, towards the right for large numbers and the left for small numbers. This "SNARC effect"(spatial-numerical association of response codes) depends on attentional and cultural variables such as the direction of writing - the direction of the effect tends to reverse in cultures that read from right to left (Dehaene, Bossini, & Giraux, 1993).
The number-space association itself seems to derive from the very close anatomical links between the middle intraparietal region, involved in number coding, and neighboring regions involved in space coding. In particular, a circuit links the LIP and VIP areas, which are involved in eye movement and the encoding of relevant positions in space. With Ed Hubbard, based on a detailed review of these issues, I proposed that this VIP-LIP circuit be partly recycled for elementary arithmetic (Hubbard, Piazza, Pinel, & Dehaene, 2005). Together with André Knops and Mariagrazia Ranzini, we have obtained functional MRI, evoked potentials and behavioral data that point in this direction. Indeed, the simple presentation of a number induces lateralized activation of posterior parietal regions (a plausible homologue of the LIP area in humans). In addition, addition and subtraction automatically evoke movement to the right and left respectively. These spatial-numerical links remain unconscious in most test subjects. However, in rare individuals, their access to consciousness could perhaps explain the phenomenon of digital synesthesia. In fact, these individuals claim to literally see numbers in well-defined spatial positions on an internal spatial scale.
