Chapter 6 - On the Relation between Numerical and Non-Numerical Magnitudes: Evidence for a General Magnitude System

Abstract

Abstract When deciding which security line at the airport might be the quickest, do we rely on the number of people in each of the lines or the non-numerical sources of information such as the physical lengths of the lines? Do the mind and brain isolate number from other magnitudes such as spatial extent, or are different magnitudes processed in integrated form? Many researchers argue for differentiation between representations of numerical and non-numerical magnitude. One prevalent view is that numerical representations engage the approximate number system (ANS), which is specific to the processing of discrete numerical magnitude. In this chapter, I outline the evidence consistent with a general magnitude system, which encompasses numerical and non-numerical magnitudes such as spatial extent (length, area, etc.) and duration. Beyond highlighting a common analog format for representing different magnitudes, this system emphasizes shared neural mechanisms in the frontoparietal cortex and overlapping representational content. In support of this model, I describe findings from human infants, children, and adults showing cognitive interactions between different representations of magnitudes and transfer of representational precision across magnitudes following training. These effects are described in the context of simple (nonverbal) discrimination tasks as well as in relation to mathematical competence. Emerging work showing that, starting early in development, the precision of both nonverbal numerical and non-numerical magnitude representations predict mathematical competence, including arithmetic and geometry, suggests an important role for a general magnitude system in learning relatively formal math concepts and computations. A general magnitude system better accommodates evidence for relations between representations of numerical and non-numerical magnitudes than does the alternative ANS model.