The perception of number from long-term memory

The perception of numerosity is supported by two systems: an exact system for small quantities, and an approximate system for large quantities. Two properties arise from the combination of these two systems: the accuracy of numerosity judgments changes qualitatively above the capacity limit for exact representations, and the ability to discriminate two quantities depends on the numerical distance between the quantities and the relationship of this distance to the absolute magnitudes. These well-characterized aspects of number cognition have typically been studied in judgments of numerosity based on visual arrays. Across four experiments we demonstrate remarkably similar effects in numerosity judgments based on incidental long-term memory. These results suggest that similar mechanisms and constraints may operate when estimating numerosity from representations of external sensory input and internal representations derived from long-term memory.