Distance in Depth: A Comparison of Explicit and Implicit Numerical Distances in the Horizontal and Radial Dimensions

Numbers are a constant presence in our daily lives: A brain devoid of the ability to process numbers would not be functional in its external environment. Comparing numerical magnitudes is a fundamental ability that requires the processing of numerical distances. From magnitude comparison tasks, a comparison distance effect (DE) emerges: It describes better performance when comparing numerically distant rather than close numbers. Unlike other signatures of number processing, the comparison DE has been assessed only implicitly, with numerical distance as nonsalient task property. Different assessments permit identification of different cognitive processes underlying a specific effect. To investigate whether explicit and implicit assessment of the comparison DE influences numerical cognition differently, we introduced the distance classification task, involving explicit classification of numbers as close or far from a reference. N = 93 healthy adults classified numbers either by magnitude or by numerical distance. To investigate associations between numerical and physical distance, response buttons were positioned horizontally (Experiment 1) or radially (Experiment 2). In both experiments, there was an advantage for both the closest and farthest numbers with respect to the reference during distance classification, but not during magnitude classification. In Experiment 2, numerically close/far numbers were classified faster with the close/far response button, respectively, suggesting radial correspondence between physical and representational distances. These findings provide new theoretical and methodological insights into the mental representation of numbers.