Abstract
Human adults in diverse cultures, children, infants, and non-human primates relate number to space, but it is not clear whether this ability reflects a specific and privileged number-space mapping. To investigate this possibility, we tested preschool children in matching tasks where the dimensions of number and length were mapped both to one another and to a third dimension, brightness. Children detected variation on all three dimensions, and they reliably performed mappings between number and length, and partially between brightness and length, but not between number and brightness. Moreover, children showed reliably better mapping of number onto the dimension of length than onto the dimension of brightness. These findings suggest that number establishes a privileged mapping with the dimension of length, and that other dimensions, including brightness, can be mapped onto length, although less efficiently. Children's adeptness at number-length mappings suggests that these two dimensions are intuitively related by the end of the preschool years.
Highlights
Number and space appear to be intimately related in the human mind
The number-space link is further suggested by neuroimaging studies, which reveal partially overlapping regions of parietal cortex activated by tasks tapping numerical and spatial cognition [9], and by studies showing that neural circuits dedicated to eye movements are recruited during arithmetic, providing evidence for spatial shifts of attention during performance of numerical addition [10]
Neglect patients who are unable to attend to the contralesional side of space have been shown to present deficits in numerical tasks that tap onto an oriented spatial representation of number [11,12]
Summary
Number and space appear to be intimately related in the human mind. Recognition of this relationship already was evident from the early description of ‘number forms’, which consist of spontaneously generated mental images where each number occupies a constant position in a spatial configuration, usually a line [1]. The mapping is present in non-human primates: the intraparietal sulcus of macaques has been shown to contain intermingled populations of neurons that respond to discrete quantity (arrays of forms varying in number), and to continuous quantity (spatial length), but even a subset of neurons that are tuned to both numerosity and length [25] None of these experiments has revealed whether the mapping of number to length is specific to these dimensions or is more general. Some evidence suggests that the number-space mappings shown by non-human animals, infants, preschool children, and adults in remote cultures reflect both the existence of a generalized magnitude system [16], and the ability to map any dimension of variation to any other [26]. By comparing children’s performance with positive vs. inverse mappings, we investigated whether there is a specific direction to each of the mappings, as has been observed for the number-length mapping in infants [24]
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