[Paleopsych] NYT: Mastering the Geometry of the Jungle

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Mastering the Geometry of the Jungle
http://www.nytimes.com/2006/01/24/science/24geom.html

    By NICHOLAS BAKALAR

    An indigenous group called the Mundurukú, who live in isolated
    villages in several Brazilian states in the Amazon jungles, have no
    words in their language for square, rectangle, triangle or any other
    geometric shape except circles.

    The members use no measuring instruments or compasses, they have no
    maps, and their words for directions are limited to sunrise, sunset,
    upstream and downstream. The Mundurukú language has few words for
    numbers beyond five except "few" and "many," and even those words are
    not used consistently.

    Yet, researchers have discovered, they appear to understand many
    principles of geometry as well as American children do, and in some
    cases almost as well as American adults. An article describing the
    findings appears in the Jan. 20 issue of Science.

    "Across cultures that live extremely different lives, we see common
    foundational sets of abilities," said Elizabeth Spelke, a co-author of
    the paper and a professor of psychology at Harvard, "and they are not
    just low-level kinds of abilities that humans share with other
    animals, but abilities that are at the center of human thinking at its
    highest reaches."

    To test their understanding of geometry, the researchers presented 44
    members of a Mundurukú group and 54 Americans with a series of slides
    illustrating various geometric concepts. Each slide had six images.
    Five of them were examples of the concept; one was not.

    The Mundurukú subjects, tested by a native speaker of Mundurukú
    working with a linguist, were asked to identify the image that was
    "weird" or "ugly." For example, to test the concept of right angles, a
    slide shows five right triangles and one isosceles triangle. The
    isosceles triangle is the correct answer.

    In data that do not appear in the article but were presented by e-mail
    from the authors, Mundurukú children scored the same as American
    children - 64 percent right - while Mundurukú adults scored 83 percent
    compared with 86 percent for the American adults.

    The researchers also tested the Mundurukú with maps, demonstrating
    that people who had never seen a map before could use one correctly to
    orient themselves in space and to locate objects previously hidden in
    containers laid out on the ground.

    The indigenous people were able to use the maps to find the objects,
    even when they were presented with the maps at varying angles so that
    they had to turn them mentally to match the pattern on the ground in
    front of them. Dr. Spelke found this particularly significant.

    "The Mundurukú, who aren't themselves in a culture that relies on
    symbols of any kind, when they were presented with maps were able to
    spontaneously extract the geometric information in them," she said.

    The idea that an understanding of geometry may be a universal quality
    of the human mind dates back at least as far as Plato. In the Meno
    dialogue by Plato, written about 380 B.C., he describes Socrates as he
    elicited correct answers to geometric puzzles from a young slave who
    had never studied the subject.

    Do these findings among the Mundurukú confirm Socrates' contention
    that concepts of geometry are innate? Stanislas Dehaene, another
    co-author and a professor of psychology at the College of France, is
    not willing to go quite that far. People learn things, after all, just
    by living in the world.

    "In our article we do not use the word 'innate,' " he said in an
    e-mail message. "We do not know whether this core knowledge is present
    very early on - the youngest subjects we tested were 5 years old - or
    to what extent it is learned. The Mundurukú, like all of us, do
    interact with 3-D objects, navigate in a complex spatial environment,
    and so on."

    Instead, Dr. Dehaene described an innate ability, rather than an
    innate knowledge. "Our current thinking is that the human brain has
    been predisposed by millions of years of evolution to 'internalize,'
    either very early on or through very fast learning, various mental
    representations of the external world, including representations of
    space, time and number," he explained.

    "I have proposed that such representations provide a universal
    foundation for the cultural constructions of mathematics," he added.

    Dr. Spelke sees in these results evidence of the universality of human
    thought processes. "Geometry is central to the development of science
    and the arts," she said. "The profile of abilities that the Mundurukú
    show is qualitatively very similar to what we see in our own culture.
    This suggests that we are finding some of the common ground at the
    center of human knowledge."