Area, not number, dominates estimates of visual quantities

Abstract

The study of numerical estimation collectively spans hundreds of papers and hundreds of thousands of citations. Interest in this topic hinges on one assumption: that we can approximate number independently of continuous spatial dimensions (e.g., area). Accordingly, many studies have specifically tried to demonstrate sensitivity specific to number while controlling other dimensions. However, recent work demonstrates that perceived area (based on psychophysical judgments) differs from true area (i.e., a precise pixel count). This difference raises concerns about most past studies of approximate number, by asking if they have systematically controlled for the wrong dimension(s). Building on recent findings that the percept of area may be systematically illusory, the current study examines the relation between perceived area and number. Four experiments reveal that (1) perceived area, but not mathematical area, strongly influences numerosity judgments, (2) perceived area influences perceived number but not the reverse, (3) number acuity is greatly reduced in stimuli controlled for perceived area, and (4) the ability to make area discriminations on the basis of ‘additive area’ but not mathematical area predicts number discrimination ability. Together, these findings highlight a potentially serious confound in prior work, raising new theoretical and methodological challenges for the field.