Geometry as a Universal mental Construction

In Stanislas Dehaene & Elizabeth Brannon (eds.), Space, Time and Number in the Brain. Oxford University Press (2011)

Authors
Pierre Pica
Centre National de la Recherche Scientifique
Abstract
Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? The spatial content of the formal theories of geometry may depart from spatial perception for two reasons: first, because in geometry, only some of the features of spatial figures are theoretically relevant; and second, because some geometric concepts go beyond any possible perceptual experience. Focusing in turn on these two aspects of geometry, we will present several lines of research on US adults and children from the age of three years, and participants from an Amazonian culture, the Mundurucu. Almost all the aspects of geometry tested proved to be shared between these two cultures. Nevertheless, some aspects involve a process of mental construction where explicit instruction seem to play a role in the US, but that can still take place in the absence of instruction in geometry.
Keywords geometry  core knowledge  mundurucu
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Cognitive Maps in Rats and Men.Edward C. Tolman - 1948 - Psychological Review 55 (4):189-208.
Reflections On Kant’s Concept Of Space.Lisa Shabel - 2003 - Studies in History and Philosophy of Science Part A 34 (1):45-57.

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