On the internal representation of numerical magnitude and physical size

A nascent idea in the numerical cognition literature - the analogical hypothesis (Pinel, Piazza, Bihan, & Dehaene, 2004) - assumes a common noisy code for the representation of symbolic (e.g., numerals) and nonsymbolic (e.g., numerosity, physical size, luminance) magnitudes. The present work subjected this assumption to various tests from the perspective of General Recognition Theory (GRT; Ashby & Townsend, 1986) - a multidimensional extension of Signal Detection Theory (Green & Swets, 1966). The GRT was applied to the dimensions of numerical magnitude and physical size with the following goals: (a) characterizing the internal representation of these dimensions in the psychological space, and (b) assessing various types of (in)dependence and separability governing the perception of these dimensions. The results revealed various violations of independence and separability with Stroop incongruent, but not with Stroop congruent stimuli. The outcome suggests that there are deep differences in architecture between Stroop congruent and incongruent stimuli that reach well beyond the semantic relationship involved.