title: Linear mapping of numbers onto space requires attention.
abstract: Mapping of number onto space is fundamental to mathematics and measurement. Previous research suggests that while typical adults with mathematical schooling map numbers veridically onto a linear scale, pre-school children and adults without formal mathematics training, as well as individuals with dyscalculia, show strong compressive, logarithmic-like non-linearities when mapping both symbolic and non-symbolic numbers onto the numberline. Here we show that the use of the linear scale is dependent on attentional resources. We asked typical adults to position clouds of dots on a numberline of various lengths. In agreement with previous research, they did so veridically under normal conditions, but when asked to perform a concurrent attentionally-demanding conjunction task, the mapping followed a compressive, non-linear function. We model the non-linearity both by the commonly assumed logarithmic transform, and also with a Bayesian model of central tendency. These results suggest that veridical representation numerosity requires attentional mechanisms.
authors.affiliation: Department of Psychology, University of Florence, Via S. Salvi 12, Florence, Italy.
authors.forename: Giovanni
authors.initials: G
authors.lastname: Anobile
authors.forename: Guido Marco
authors.initials: GM
authors.lastname: Cicchini
authors.forename: David C
authors.initials: DC
authors.lastname: Burr
mesh_terms: D000328:Adult; D001288:Attention / Q000502:physiology*; D001499:Bayes Theorem; D003071:Cognition / Q000502:physiology; D005260:Female; D006801:Humans; D007092:Imagination / Q000502:physiology*; D008297:Male; D008433:Mathematics; D009483:Neuropsychological Tests