Channeling Euclid

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Science  24 Jun 2011:
Vol. 332, Issue 6037, pp. 1483
DOI: 10.1126/science.332.6037.1483-a

Behavioral research has explored how human and animal understanding of space reflects principles of Euclidean geometry. Though perception of the environment can affect many mental processes, Kant argued for an a priori, innate spatial intuition. Such intuition might underpin the ability to understand geometric concepts that are not observable in nature, such as an infinitely thin line or infinitely large plane. To address the universality of Euclidean concepts, Izard et al. tested a population indigenous to the Amazon, the Mundurucu, who have no formal training in geometry. This group of both children and adults was compared to mathematically educated U.S. adults, comparably aged French children, and younger U.S. children. Among other queries, people were shown dots and lines, representing villages and paths, projected on a plane or sphere, and asked whether a line could be drawn through a point and never cross another line. The Mundurucu responses were similar to those of U.S. adults and French children, reflecting strong application of Euclidean principles. The younger U.S. children responded similarly but were more error-prone. Across cultures, people were biased to erroneously apply Euclidean principles to spheres. The authors propose that new research explore whether understanding of abstract geometry is innate but only emergent at a certain time in development, or whether it is learned as a result of experiences so general that all humans are exposed to them.

Proc. Natl. Acad. Sci. U.S.A. 108, 9782 (2011).

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