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Thursday, October 25, 2012

A Priori Intuition of Space?


The Munduruku (Mundurucu or Wuy Jugu) are an indigenous people of Brazil living in the Amazon River basin

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. See: Flexible intuitions of Euclidean geometry in an Amazonian indigene group


"Lost" Amazon Complex Found; Shapes Seen by Satellite
  Hundreds of circles, squares, and other geometric shapes once hidden by forest hint at a previously unknown ancient society that flourished in the Amazon, a new study says.

Satellite images of the upper Amazon Basin taken since 1999 have revealed more than 200 geometric earthworks spanning a distance greater than 155 miles (250 kilometers).

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