Flexible intuitions of Euclidean geometry in an Amazonian indigene group

Edited by Charles R. Gallistel, Rutgers University, Piscataway, NJ, and approved April 25, 2011 (received for review November 12, 2010)
May 23, 2011
108 (24) 9782-9787

Abstract

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.

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Acknowledgments

This work is part of a larger project on the nature of quantification. It is based on psychological experiments and linguistics studies conducted in the Mundurucu territory (Pará, Brazil) under the direction of P.P. in accordance with the Consehlo de Desenvolvimento Cientifico et Tecnologicico and the Fundação do Indio (Funaï; Processo 2857/04). We thank L. Braga (SARAH Network of Neurorehabilitation Hospitals, Brazil), A. Ramos (Coordenação Geral de Educação, Funaï), and C. Romeiro (Nucleo de Documentação e Pesquisa, Funaï) for discussion and advice; M. Karu, Y.-H. Liu, and C. Tawe for help with data collection; P. Stephenson (The Array Rainforest Foundation) for the satellite map of the Mundurucu territory; and D. Sutherland and T. R. Virgil for comments on the manuscript. This work was supported by the Institut National de la Santé et de la Recherche Médicale, the Fyssen Foundation (to V.I.), the Département des Sciences Humaines et Sociales of Centre National de la Recherche Scientifique (to P.P.), the National Institutes of Health (to E.S.), a McDonnell Foundation centennial fellowship (to S.D.), and a Starting Grant from the European Research Council (MathConstruction 263179) (to V.I.).

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Published in

Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 108 | No. 24
June 14, 2011
PubMed: 21606377

Classifications

Submission history

Published online: May 23, 2011
Published in issue: June 14, 2011

Keywords

  1. mathematical cognition
  2. spatial cognition
  3. culture

Acknowledgments

This work is part of a larger project on the nature of quantification. It is based on psychological experiments and linguistics studies conducted in the Mundurucu territory (Pará, Brazil) under the direction of P.P. in accordance with the Consehlo de Desenvolvimento Cientifico et Tecnologicico and the Fundação do Indio (Funaï; Processo 2857/04). We thank L. Braga (SARAH Network of Neurorehabilitation Hospitals, Brazil), A. Ramos (Coordenação Geral de Educação, Funaï), and C. Romeiro (Nucleo de Documentação e Pesquisa, Funaï) for discussion and advice; M. Karu, Y.-H. Liu, and C. Tawe for help with data collection; P. Stephenson (The Array Rainforest Foundation) for the satellite map of the Mundurucu territory; and D. Sutherland and T. R. Virgil for comments on the manuscript. This work was supported by the Institut National de la Santé et de la Recherche Médicale, the Fyssen Foundation (to V.I.), the Département des Sciences Humaines et Sociales of Centre National de la Recherche Scientifique (to P.P.), the National Institutes of Health (to E.S.), a McDonnell Foundation centennial fellowship (to S.D.), and a Starting Grant from the European Research Council (MathConstruction 263179) (to V.I.).

Notes

*This Direct Submission article had a prearranged editor.

Authors

Affiliations

Véronique Izard2,1 [email protected]
Laboratoire Psychologie de la Perception, Université Paris Descartes, 75006 Paris, France;
CNRS UMR 8158, 75006 Paris, France;
Department of Psychology, Harvard University, Cambridge, MA 02138;
Pierre Pica1
Laboratoire Structure Formelle du Langage, Université Paris 8, 93200 Saint-Denis, France;
CNRS UMR 7023, 93200 Saint Denis, France;
Elizabeth S. Spelke
Department of Psychology, Harvard University, Cambridge, MA 02138;
Stanislas Dehaene
Cognitive Neuroimaging Unit, Institut National de la Santé et de la Recherche Médicale, F-91191 Gif-sur-Yvette, France;
Commissariat à l'Energie Atomique, I2BM, NeuroSpin, F-91191 Gif-sur-Yvette, France;
Université Paris-Sud, F-91405 Orsay, France; and
Collège de France, 75005 Paris, France

Notes

2
To whom correspondence should be addressed. E-mail: [email protected].
Author contributions: V.I., P.P., E.S.S., and S.D. designed research; V.I. and P.P. performed research; V.I. and S.D. analyzed data; and V.I., P.P., E.S.S., and S.D. wrote the paper.
1
V.I. and P.P. contributed equally to this work.

Competing Interests

The authors declare no conflict of interest.

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    Flexible intuitions of Euclidean geometry in an Amazonian indigene group
    Proceedings of the National Academy of Sciences
    • Vol. 108
    • No. 24
    • pp. 9727-10022

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