Size-numerosity interaction depends retinal rather than perceived size

Walsh [1] has put forward an interesting theory 'A Theory of Magnitude' (AToM), which propounds shared visual processes for various quantity perceptions such as time, space and number. Supporting the AToM, the number of dots surrounded by smaller circles are perceived to be more numerous than dots surrounded by larger circles [2]. To examine the processing level of this size-numerosity interaction, we used the flash-lag effect, where a flashed stimulus appears to lag gradually changing stimuli, and dissociated physical from perceived size of surrounding stimuli. In the experiments, dots appeared at various timings relative to shrinking or expanding circles. In Experiment 1, participants judged the size of the surrounding circles at the time when the dots appeared. The dots perceptually lagged the changing circles about 250 ms (flash-lag effect). In Experiment 2, participants reported the number of dots. The perceived-lag between dots and surrounding circles did not affect the numerosity perception of the dots. These results suggest that the modulation of numerosity perception depends on the retinal rather than perceived size of surrounding circles and the interaction between size and numerosity perception involves visual processes earlier than perceptual registration of size of modulating stimuli.