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How not to develop a sense of number

Opfer, John EMcCrink, Koleen.  Behavioral and Brain Sciences; New York Vol. 40,  (2017). DOI:10.1017/S0140525X16002223

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The mechanism of numerosity perception is often depicted as a solitary creature, living alone in the intraparietal sulcus (IPS) (its presumed birthplace), with nothing to feed it but number, and serving just the function for which it was born – giving the rest of the brain an approximation of “how many.” Although copies of this mechanism are thought to exist in the brains of an astonishing range of organisms – even those with no homologue to IPS – it is consistently predicted to have the same basic properties (noise and ratio dependence) everywhere one finds it, regardless of its age, the genes in its cells, or its history of activity.

This portrait of the numerosity mechanism – only slightly exaggerated – is in dire need of revision, and we thank Leibovich et al. for pointing toward a major issue for any future theory. As the authors note, our perception of numerosity is influenced by the spatial characteristics of the set (Frith & Frith 1972; Gebuis et al. 2014). Similarly, our perception of space is influenced by numerical aspects of the set (de Hevia et al. 2008). Two major – but still unsettled – issues arise from these findings. The simpler issue is describing the relation between two groups of processors: those that register the number of a set (numerosity detectors) and those that register the non-numerical spatial characteristics of the set (e.g., spatial frequency). The harder issue is to explain how this relation does or does not change over time (for a review of evidence, see McCrink & Opfer 2014); this is the purpose of a developmental theory.

Although the authors have succeeded in describing the rich interactions that exist between space and number, the cornerstone of their article – their developmental theory – suffers from three major weaknesses.

First and foremost, the argument is structurally flawed. According to the authors, the number of items in a set and...