[Paleopsych] NYT: Mastering the Geometry of the Jungle
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Sun Jan 29 21:01:29 UTC 2006
Mastering the Geometry of the Jungle
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
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."
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