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Miles Shuman, Elizabeth Spelke; and element size bias numerosity perception. Journal of Vision 2006;6(6):777. doi: https://doi.org/10.1167/6.6.777.
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© ARVO (1962-2015); The Authors (2016-present)
Most recent work in numerical cognition has focused on the representational level. The consensus view is that symbolic numbers (e.g. Arabic digits) and non-symbolic numerical stimuli (e.g. dot arrays) alike engage an ‘analog magnitude’ representation system; the debate has largely moved to questions such as innateness and neural localization. Here, we take a step back to examine the perceptual mechanism that enables us to extract a numerical representation from a set of elements. The most prominent current models propose that this mechanism is iterative, individuating and tagging each element (sequentially or in parallel,) then summing to obtain a numerical magnitude. The observed variability in judged number (e.g. variability proportional to N in estimation tasks) is attributed to the representational system, rather than the perceptual mechanism. An alternative possibility is that the mechanism for numerosity perception is holistic, involving (e.g.) a ‘calculation’ of element density x ‘envelope’ area, and that variability in the perceived magnitudes of these continuous quantities is an important contributor to variability in represented numerical magnitude. We tested whether parametric variation of ‘continuous quantity’ variables - element size and envelope area - would systematically bias judgments of numerosity. We found a very strong effect of envelope area (with larger, lower density arrays judged more numerous) and a significant (though smaller in magnitude) effect of element size (with arrays of smaller elements judged more numerous.) These results pose a serious challenge to iterative models of numerosity perception, and suggest that perception may be an important source of noise in numerical cognition.
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