Amazon Children "Spontaneously" Understand Geometry

Davide Castelvecchi
for National Geographic News

January 19, 2006

Children of an isolated Indian group in the Amazon jungle have a seemingly natural understanding of geometry concepts, even though their language doesn't have words for them, according to a new study.

This doesn't necessarily make the children unique, the study authors say. Instead, it may mean that most human brains, regardless of education, are hardwired for a basic level of geometry comprehension.

The Mundurucú people of the Amazon River Basin don't seem to have words for "triangle," "parallel," or other geometry concepts. Even so, they are able to understand these concepts about as well as U.S. schoolchildren.

Given the same geometry exercises, U.S. adults, however, performed slightly better, on average, than Mundurucú adults.

The relatively similar abilities of the two cultures are striking, the authors said, given that the Mundurucú test subjects had received little or no schooling and lived mostly in isolation. (Read an excerpt of a National Geographic magazine article on isolated Amazon Indians.)

"This shows the deep unity underneath superficial differences—the fact that the very same problems that are difficult for the Mundurucú remain difficult for [people from developed regions], even after years of education and with our sophisticated vocabulary," said Stanislas Dehaene, the study's lead author.

The study will be published tomorrow in the journal Science. Dehaene's co-authors are Vronique Izard of the Service Hospitalier Frédéric Joliot research center in Orsay, France; Pierre Pica of the French National Center for Scientific Research in Paris; and Elizabeth Spelke of Harvard University in Cambridge, Massachusetts.

The authors plan to follow up with studies of infants and perhaps other animal species. Further studies using magnetic resonance imaging (MRI) to scan brain activity could also point to the neurological basis of some of the geometry skills.

Which of These Does Not Belong?

Dehaene is a cognitive scientist at the Service Hospitalier Frédéric Joliot research center in Orsay, France. He and his colleagues used two kinds of tests to assess the abilities of Mundurucú adults as well as children between ages 5 and 12.

The first test used visual clues such as parallel lines, curved versus straight lines, and holes.

In a specialized kind of "spot the differences" game, participants were shown sets of six figures.

Five of the six figures shared some property. The participants had to guess which figure did not belong. (In their language the Mundurucú described it as "the ugly one.")

For example, one set included a pair of nonparallel lines amid five pairs of parallel lines. Another set had six triangles, only one of which had no right angle.

Treasure Hunt

In the second test, each participant was given a map showing where to find an object hidden under one of three boxes.

The Mundurucú don't typically use maps, but they are adept at navigating their river valley home in the Brazilian state of Pará.

The boxes in the test were arranged in right triangles or isosceles triangles on the floor. The maps correctly reproduced these geometric relations. Stars on the maps marked the locations of the hidden objects.

Dehaene finds it significant that the U.S. and Mundurucú children had similar scores while U.S. adults outperformed Mundurucú adults.

The results suggest that "the concepts of geometry are grounded in extremely basic mechanisms in the human brain," he said, "whatever its culture and its education."

Brian Butterworth, a neuroscientist at Britain's University College London, agrees.

"We are born with a 'starter kit' of core concepts that helps us interpret our three-dimensional world, and this is refined by constant interaction with it," said Butterworth, who was not involved in the Mundurucú study.

"If the world has lots of straight lines, as the world of the [U.S.] subjects [in these experiments] does, then this may explain why, when they reach adulthood, they are somewhat better at dealing with problems involving straight lines," he said.

The research may also cast new light on an old conundrum: Does the brain learn concepts through words—possibly in different ways for different languages? Or does abstract thinking somehow precede speech?

Not Proof?

Rafael Núñez is a cognitive scientist at the University of California, San Diego. He believes that concepts can precede words, but he says the evidence in the new study does not constitute proof.

Although their language lacks certain words, the Mundurucú may be able to express the same concepts through metaphors.

"I could also say that in English we have few words to talk about the future," Núñez said, "because we use metaphors like 'the week ahead' and 'way back in the sixties,' which are spatial metaphors relative to front and back."

That's not the only difficulty in interpreting the data, according to Dehaene, the study's lead author. Some of the recognition may be taking place at the visual level, rather than at the level of abstract thought.

Peter Gordon, a behavioral scientist at New York's Columbia University, said that further tests would be needed for scienists to better understand the study results.

"Imagine if you did this task and had five transistors and a capacitor and had subjects pick the capacitor as being odd," he said. "Would this mean that they had concepts of electronic circuitry?"

Dehaene says the concern that the children's ability is largely visual doesn't seem to apply to the map-based test. That's because using a map requires "abstraction of geometrical information." In other words, the test subjects had to be able to understand that the shapes on the page corresponded to the boxes arranged on the floor.

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