Abstract
Studies of human adults, infants, and non-human animals demonstrate that non-symbolic numerical cognition is supported by at least two distinct cognitive systems: a “parallel individuation system” that encodes the numerical identity of individual items and an “approximate number system” that encodes the approximate numerical magnitude, or numerosity, of a set. The exact nature and role of these systems, however, have been debated for over a 100-years. Some argue that the non-symbolic representation of small numbers (<4) is carried out solely by the parallel individuation system and the non-symbolic representation of large numbers (>4) is carried out solely by the approximate number system. Others argue that all numbers are represented by the approximate number system. This debate has been fueled largely by some studies showing dissociations between small and large number processing and other studies showing similar processing of small and large numbers. Recent work has addressed this debate by showing that the two systems are present and distinct from early infancy, persist despite the acquisition of a symbolic number system, activate distinct cortical networks, and engage differentially based attentional constraints. Based on the recent discoveries, I provide a hypothesis that may explain the puzzling findings and makes testable predictions as to when each system will be engaged. In particular, when items are presented under conditions that allow selection of individuals, they will be represented as distinct mental items through parallel individuation and not as a numerical magnitude. In contrast, when items are presented outside attentional limits (e.g., too many, too close together, under high attentional load), they will be represented as a single mental numerical magnitude and not as distinct mental items. These predictions provide a basis on which researchers can further investigate the role of each system in the development of uniquely human numerical thought.
Highlights
The brain has at least two systems for representing number nonsymbolically; these systems represent number in qualitatively different ways
Individual variability in the small number range does not correlate with individual variability in the large number range and individual differences in subitizing capacity do not correlate with individual differences in large non-symbolic number comparison precision (Revkin et al, 2008; Piazza et al, 2011). Together these results suggest small number subitizing relies on a distinct cognitive mechanism from estimation of larger numbers and that, under these conditions, small numbers are not being represented as approximate numerical magnitudes
Recent work suggests that inferior IPS activity scales with the number of objects in scene up to about three to four and plateaus while the superior IPS responds to differences in object identity, but not number. These results suggest that portions of the inferior IPS support the initial selection and individuation of a limited number of objects from a scene, in contrast to the lateral occipital complex and the superior IPS, which seem to support object identification (Xu and Chun, 2006; Xu, 2009)
Summary
The brain has at least two systems for representing number nonsymbolically; these systems represent number in qualitatively different ways (see Feigenson et al, 2004 or Piazza, 2010 for reviews). If small number sets are presented beyond the limits of the brain to encode as individual object files (e.g., too close together) or if sufficient attentional/working memory resources are not available (e.g., because resources are tied up in another task), it appears that small numbers are represented as approximate numerical magnitudes like large numbers This can explain the cases where processing of small quantities shows the signatures of approximate number representation (Cordes et al, 2001; Burr et al, 2011; Hyde and Wood, 2011). If attention is not able to select individuals because the limits are surpassed (e.g., too many, they are too close together, engaged in another attention demanding task, etc.), the set is summarized by a single mental symbol and properties of the set, or ensemble statistics, will be calculated, approximate numerosity being one property of the set
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