Two dissociated systems of core knowledge for geometry

Overview

Animals use the geometry of their surroundings to establish their orientation. However, the system of geometry-informed navigation fails to reach abstraction in two points. First, it fails to encode some geometric information, namely angles. Second, it also fails to recognise geometry in 2D displays, a main domain of Euclidean geometry. . As reviewed in the present chapter, this system is sensitive to angle and length, while it ignores distinctions of sense: it is thus complementary to the geometry-informed navigation system, which encodes length and sense, but not angle.

Summary

Our results indicate that when classifying shapes, sensitivity to angle and size is universal, while sensitivity to sense is not

Geometry as a universal mental construction

Space, Time and Number in the Brain

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
December 2011
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