Indigenous Amazonians display core understanding of geometry (fwd)

[phil cash cash]

	 The study of geometrical understanding among the Mundurukú, who live in
remote areas along the Cururu River in Brazil, is described this week in the
journal Science. (Photos © Pierre Pica and CNRS) 		

INDIGENOUS AMAZONIANS DISPLAY CORE UNDERSTANDING OF GEOMETRY

Findings Suggest Basic Geometrical Knowledge Is A Universal Constituent
 Of The Human Mind

   BY STEVE BRADT  
FAS Communications   

  Researchers in France and at Harvard University have found that isolated
indigenous peoples deep in the Amazon readily grasp basic concepts of geometry
such as points, lines, parallelism, and right angles, and can use distance,
angle, and other relationships in maps to locate hidden objects. The results
suggest that geometry is a core set of intuitions present in all humans,
regardless of their language or schooling.  

  The study of geometrical understanding among the Mundurukú, who live in
remote areas along the Cururu River in Brazil, is described this week in the
journal Science.  

  "Although there has been a lot of research on spatial maps, navigation, and
sense of direction, there is very little work on the conceptual representations
in geometry," says co-author Stanislas Dehaene of the Collège de France in
Paris. "What is meant by 'point,' 'line,' 'parallel,' 'square' versus
'rectangle'? All are highly idealized concepts never met in physical reality.
Our work is a first start in the exploration of these concepts."  

   The work by Dehaene and colleagues suggests that such concepts are largely
universal across humans.  

  "While geometrical concepts can be enriched by culture-specific devices like
maps, or the terms of a natural language, underneath this variability lies a
shared set of geometrical concepts," says co-author Elizabeth S. Spelke, a
professor of psychology in Harvard's Faculty of Arts and Sciences. "These
concepts allow adults and children with no formal education, and minimal
spatial language, to categorize geometrical forms and to use geometrical
relationships to represent the surrounding spatial layout."  

  Dehaene, Spelke, and co-authors Véronique Izard and Pierre Pica developed
and administered two different sets of tests during visits to the Mundurukú in
2004 and 2005. Their first test, designed to assess comprehension of basic
concepts such as points, lines, parallelism, figure, congruence, and symmetry,
presented arrays of six images, one of which was subtly dissimilar. For
instance, five comparable trapezoids might be matched with a sixth
nontrapezoidal quadrilateral of similar size. The Mundurukú were then asked,
in their own language, which of the images was "weird" or "ugly."  

	 Mundurukú subjects, even those as young as 6 years old, chose the correct
image an average 66.8 percent of the time, showing competence with basic
concepts of topology, Euclidean geometry and basic geometrical figures. The
performance of both Mundurukú adults and children on the task rivaled that of
American children in separate testing done by the scientists. 		

  "If the Mundurukú share with us the conceptual primitives of geometry," the
researchers write, "they should infer the intended geometrical concept behind
each array and therefore select the discrepant image."  

  Mundurukú subjects, even those as young as 6 years old, chose the correct
image an average 66.8 percent of the time, showing competence with basic
concepts of topology, Euclidean geometry, and basic geometrical figures. The
performance of both Mundurukú adults and children on the task rivaled that of
American children in separate testing done by the scientists, while the
performance of American adults was significantly higher.  

  Dehaene, Spelke, and colleagues also administered an abstract map test where
subjects were given a simple diagram to identify which of three containers
arrayed in a triangle on the ground hid an object. Both Mundurukú adults and
children were able to relate the geometrical information on the map to
geometrical relationships in the environment, attaining an overall success rate
of 71 percent that again matched the performance of American children while
lagging behind that of American adults.  

   The superior performance of Western adults suggests that formal education
enhances or refines geometrical concepts. Nevertheless, the report concludes,
"the spontaneous understanding of geometrical concepts and maps by this remote
human community provides evidence that core geometrical knowledge ... is a
universal constituent of the human mind."  

  The study of human geometrical knowledge has a long history, dating back at
least to Socrates' probing of the intuitions of an uneducated slave in a Greek
household, chronicled by Plato approximately 2,400 years ago.  

  "Many of the references in our paper are from Plato, Riemann, and Poincaré,"
Dehaene says. "What excited us was the ability to ask experimentally some
questions which belong to a very long history of questions about the
foundations of geometry."  

  Dehaene, Izard, Pica, and Spelke's work was supported by INSERM, CNRS, the
National Institutes of Health, and the McDonnell Foundation. 
http://www.news.harvard.edu/gazette/daily/2006/01/19-amazon.html
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