title: Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform.
abstract: The mapping of number onto space is fundamental to measurement and mathematics. However, the mapping of young children, unschooled adults, and adults under attentional load shows strong compressive nonlinearities, thought to reflect intrinsic logarithmic encoding mechanisms, which are later "linearized" by education. Here we advance and test an alternative explanation: that the nonlinearity results from adaptive mechanisms incorporating the statistics of recent stimuli. This theory predicts that the response to the current trial should depend on the magnitude of the previous trial, whereas a static logarithmic nonlinearity predicts trialwise independence. We found a strong and highly significant relationship between numberline mapping of the current trial and the magnitude of the previous trial, in both adults and school children, with the current response influenced by up to 15% of the previous trial value. The dependency is sufficient to account for the shape of the numberline, without requiring logarithmic transform. We show that this dynamic strategy results in a reduction of reproduction error, and hence improvement in accuracy.
authors.affiliation: Neuroscience Institute, National Research Council, 56124 Pisa, Italy; and.
authors.forename: Guido Marco
authors.initials: GM
authors.lastname: Cicchini
authors.affiliation: Department of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, 50135 Florence, Italy.
authors.forename: Giovanni
authors.initials: G
authors.lastname: Anobile
authors.affiliation: Neuroscience Institute, National Research Council, 56124 Pisa, Italy; andDepartment of Neuroscience, Psychology, Pharmacology and Child Health, University of Florence, 50135 Florence, Italy dave@in.cnr.it.
authors.forename: David C
authors.initials: DC
authors.lastname: Burr
mesh_terms: D000328:Adult; D003071:Cognition / Q000502:physiology*; D006801:Humans; D008433:Mathematics; D009483:Neuropsychological Tests
keywords: Weber–Fechner law; approximate number system; numerical cognition; predictive coding; serial dependency