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.

Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform / G. M. Cicchini;G. Anobile;D. C. Burr. - In: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA. - ISSN 0027-8424. - ELETTRONICO. - 111:(2014), pp. 7867-7872. [10.1073/pnas.1402785111]

Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform

CICCHINI, GUIDO MARCO;ANOBILE, GIOVANNI;BURR, DAVID CHARLES
2014

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.
2014
111
7867
7872
G. M. Cicchini;G. Anobile;D. C. Burr
File in questo prodotto:
File Dimensione Formato  
Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform.pdf

accesso aperto

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Open Access
Dimensione 946.26 kB
Formato Adobe PDF
946.26 kB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/903347
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 184
  • ???jsp.display-item.citation.isi??? 176
social impact