Ask a member of the Pirahã tribe to count a cluster of pebbles, and even the brightest member of this isolated Amazonian tribe will probably respond with a blank stare. This is because the Pirahã do not have words for precise quantities or the action of counting--instead they quantify objects approximately, using words analogous to our "few" and "many." Even their word for one, "hói," might be more accurately translated as "about one," says Peter Gordon, PhD, a psychology professor at Columbia University Teachers College, who studies the tribe.
For example, when Gordon placed nine objects on a table and asked seven Pirahã adults to make a group out of an equal number of nuts, not one of them used exactly nine nuts, according to research by Gordon published in the Oct. 15 special issue of Science (Vol. 306, No. 5695), focused on cognition and behavior.
The finding suggests that language, especially number-words, plays a critical role in people's comprehension of quantity, Gordon says. However, other researchers paint a slightly different picture--one where humans, and some animals, are born with the ability to perceive numbers and even predict the result of simple mathematical operations such as addition and subtraction.
One such researcher, Rochel Gelman, PhD, a psychology professor at Rutgers University and co-director of the Rutgers University Center for Cognitive Science, holds that people are born with skeletal principles for abstracting numerosity. Research by psychologist Karen Wynn, PhD, at Yale University supports this proposal. She has found that infants can notice when the number of items in a group has changed, Gelman notes.
Cross-cultural research also converges on the idea that, although different cultures develop different counting words, they all share similar properties--such as attaching one unique word to each counted object, and using the last number-word to stand for the entire group of objects, she notes. The finding suggests that the ability to use natural numbers shares a common core, regardless of culture, says Gelman.
But why, then, would the Pirahã tribe seem to lack the ability to appreciate exact quantities of objects? The answer to this puzzle may shed light on the subtle ways language can shape thought and even make ideas possible.
No need for numbers
Some argue that--at least until recently--the Pirahã haven't needed a counting system. Because they don't trade with the outside world, they can simply indicate by gesture that they would like to exchange, for example, this basket of nuts for that chicken. Cultures with more elaborate trade systems--especially those that use currency--require the ability to label specific quantities, notes Gordon.
As a result, the tasks Gordon gave the Pirahã people in his Science study may have seemed alien to them. In one typical test, the researcher set out a group of one to 10 nuts and asked each participant to place an equal number of batteries--used because of their availability and size--on the table. The participants performed perfectly when matching sets of up to three batteries, but at four batteries the accuracy rate dropped to about 75 percent, and by nine none of the Pirahã got the right answer.
The accuracy level dropped even more dramatically when Gordon showed the participants the group of batteries for only a moment before covering them--which required the Pirahã to remember and recall the number of objects. On this task, the accuracy rate dropped to 75 percent at three objects, and few participants correctly matched anything more than six objects.
While Gordon did not make a formal comparison, he says that during informal tests, American college students performed all of these tasks with 100 percent accuracy.
"Though [college students] do less well if you don't let them count," he adds. "Counting is the key to performing these sorts of tasks."
However, making approximate comparisons may be within the grasp of people without number-words, suggests research on the Amazonian Mynduruku tribe, also published in the Oct. 15 issue of Science.
In fact, while language can advance people's concept of number, infants and even some animals appear to be born with an innate understanding of numbers.
In one of the first experiments showing infant perceptions of number, published in Child Development (Vol. 54, No. 3), Sue Antell, PhD, psychology professor at the University of Maryland, showed hours-old infants two arrays of two to six black dots. After they gazed at the displays, the researcher changed the display of one of the arrays, and participants tended to gaze at the changed display.
Animals such as chimpanzees and even pigeons have shown similar results, says Gelman, who researches how children develop number concepts. And it suggests that people are born with an internal representation system for numbers that operates regardless of language.
Further bolstering this idea is an experiment summarized in a recent article by Gelman and Randy Gallistel, PhD, a psychology professor at the Rutgers University Center for Cognitive Science, which also appeared in the Oct. 15 issue of Science. In this experiment, participants named which of two numbers--as represented by Arabic numerals, such as "2" and "3"--was the larger. Participants, even mathematicians, took a little bit longer to distinguish between the closer numbers, such as "2 and 3," as compared with "2 and 5." This phenomenon, related to the principle known as Weber's Law, suggests that even those highly proficient in the language of mathematics rely on mental representations of numbers, Gelman says.
"But there is one important limitation to internal representations of number," says Gelman. "They are imprecise," for quantities greater than three.
And perhaps a language-based counting system allows us to refine our instinctual sense of number, she notes. It is even possible that language-based counting systems and internal representations of numbers operate somewhat independently of each other, Gallistel adds.
However, says Gordon, the example of the Pirahã tribe shows that language may have more sway over numerical concepts than many previously imagined.
"The lack of number-words seems to preclude the ability to entertain concepts of exact number," Gordon says. "There may be other ways to learn and represent exact numbers, but in the normal course of human learning, language is the route we take."
Gelman, R., & Gallistel C.R. (2004). Language and the origin of numerical concepts. Science, 306(5695), 441–443.
Gordon, P.F. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496–499.
Miller, K.F., Smith, C.M., Zhu, J., & Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science, 6(1), 56–60.
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