Rational Number Representation by the Approximate Number System

Abstract

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck 2021a). Prior work has demonstrated that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here we use a well-known “connectedness illusion” to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) may involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results support and refine the hypothesis that the ANS represents full-blown rational numbers.