The Magic Number 4 ± 0: A New Look at Visual Numerosity Judgements

Abstract

Visual numerosity judgements were made for tachistoscopically presented linear arrays of dots or lines. The interelement interval (which could be specified in spatial frequency terms) was constant for a given array but varied across conditions. A clear limit in the accuracy of numerosity judgements was found to be set at 4 for regularly spaced elements with spatial frequencies below approximately 10 cycles/deg (element and interelement interval of 0·05 deg). This limit in terms of accuracy is accompanied by a fast and almost constant response time for arrays of 4 or less, compared to response times for arrays of more than 4 elements. The limit in accuracy falls to 2 elements rather than 4 for spacing narrower than 0·05 deg although with such spacing the elements are still easily resolved. The limit of 4 is found if the stimulus is a bright afterimage, lasting for approximately 60 s. This result suggests that the limit is independent of the time allowed for a single fixation and is a perceptual limit rather than a limit in some memory buffer. ‘Numerosity’ units are proposed to account for the results.