Examining Knowledge of GeometryLink
In their Report "Core knowledge of geometry in an Amazonian indigene group" (20 Jan., p. 381), S. Dehaene et al. present evidence that an isolated Amazonian group, the Mundurukú, are able to understand geometric concepts. They state that geometry constitutes "a core set of intuitions present in all humans." I disagree with the basic concept of this investigation.
The central feature of Euclidean geometry is its demonstrative character and its logical structure, rather than graphical pictures of triangles, circles, etc. This logical system is built upon two pillars: (i) the concept of the "theoretical object," e.g., the abstract metaphysical idea of a circle, rather than a real constructed circle; and (ii) the deductive mathematical proof, based purely on axioms and postulates.
Other civilizations dealt with geometrical figures in a more intuitive way, and their activities cannot be characterized as geometry in the Euclidean sense. Ancient civilizations other than the Greeks did not develop a demonstrative geometry. For example, the ancient Chinese never developed a theoretical geometry (1-3).
The topic being investigated by Dehaene et al. is simply pattern recognition. It is by no means surprising that the people tested recognized different geometric figures, since they can recognize, e.g., human faces and identify different species of tree by their silhouettes.
D-29640 Schneverdingen, Germany
J. Needham, Science and Civilisation in China, vol. 3, Mathematics and the Science of the Heavens and the Earth (Cambridge University Press, Cambridge, 1959), p. 91.
G. F. Leibniz, Novissima Sinica (ed. 2, 1699), section 9.
C. Cullen, Astronomy and Mathematics in Ancient China: The Zhoubi Suanjing (Cambridge University Press, Cambridge, 1996), pp. 77, 219.
Science 2 June 2006:
Vol. 312. no. 5778, pp. 1309 - 1310