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

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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.