The Number Interval Position Effect (NIPE) in the mental bisection of numerical intervals might reflect the influence of the decimal-number system on the Gaussian representations of numerosities: A combined developmental and computational-modeling study

Abstract

Healthy adults show typical error biases when they mentally bisect number intervals without exact calculations. For a given number interval length, the bisection bias is in fact modulated by the position that the interval occupies within a ten. For intervals positioned at the beginning of tens the error bias is directed toward values that are higher than those of the true interval midpoint whereas for intervals at the end of tens the direction of the error bias is reversed toward values that are lower than that of the true midpoint (Doricchi et al., 2009; Rotondaro et al., 2015). This effect has been defined Number Interval Position Effect (NIPE). The NIPE recurs over consecutive tens and it is not found when intervals are bisected through exact calculations. For this reasons we have hypothesized that the NIPE reflects the influence that the habit of counting in tens has on the neural representations of numerosities that humans share with other species. Here, in a developmental study we demonstrate that children from preschool to fifth-grade display a NIPE that is comparable to that of healthy adults. Then, through a computational-modeling study we investigated whether the NIPE might reflect specific patterns in the Gaussian representations of numerosities that are found in the parietal and pre-frontal neuronal populations of macaque monkeys and that underlie approximate numerosity estimations also in humans. The findings of computational simulations suggest that the NIPE might reflect the influence that the learning and use of the decimal numerical system has on the phylogenetically and ontogenetically older representation of numerosities that humans share with other species. These changes in the representation of numerosities have an influence on approximate numerical estimations even when these, like in the case of the mental bisection of number intervals, are elicited by numerical symbols or words.

Keywords: Bisection; Children; Number interval; Number line; Number representation.