Wednesday, May 25, 2011

Testing nonperceptible Euclidian geometry

The NY Times reports:
Although many school-going youth might disagree, a new study finds that geometry is an intuitive subject that is easy to grasp even in the absence of formal training.

Researchers posed questions in Euclidean planar geometry to adults and children from the Munduruc├║ community, an isolated indigenous group in the Amazon. Despite having no formal education, the Munduruc├║ were able to quickly grasp concepts in planar geometry relating to points, lines and triangles.

The study appears in the current issue of Proceedings of the National Academy of Sciences.
The study says:
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. ...

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.
This did not test "nonperceptible Euclidian geometry". Angles are perceptible, and so is parallelism. If they wanted something nonperceptible, then they should have asked some abstract math questions. This study does not do what it says.

One of the coauthors is Elizabeth Spelke, a Harvard professor who claims to have done experiments showing that baby boys and girls have the same innate skills.

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