Amazonian indigenous culture demonstrates a universal mapping of number onto space

CAMBRIDGE, Mass. -- The ability to map numbers onto a line, a foundation of all mathematics, is universal, says a study published this week in the journal Science, but the form of this universal mapping is not linear but logarithmic. The findings illuminate both the nature and the limits of the human predisposition to measurement, a foundation for science, engineering, and much of our modern culture.

The research was conducted with the Munduruku, an Amazonian indigenous culture with a limited vocabulary of number words and spatial terms, little or no formal education, and little or no experience with maps, graphs, and rulers.

Munduruku adults and children spontaneously placed numbers on a line in a compressed, logarithmic function, such that smaller numbers appeared at greater spatial intervals. The study suggests that a propensity to relate numbers to space is universal, but that the mapping of successive integers and constant spatial intervals, as on a ruler, is culturally variable and linked in part to education.

The research was conducted by Stanislas Dehaene, professor of cognitive psychology at the College de France in Paris; Elizabeth Spelke, Marshall L. Berkman Professor of Psychology at Harvard University; Veronique Izard, a postdoctoral researcher in psychology at Harvard; and Pierre Pica of Paris VIII University in Paris.

"Our findings suggest that humans have a predisposition to relate two fundamental domains of knowledge: knowledge of number and of space," Spelke says. "The Munduruku are able to place numbers on a line in a systematic way that educated adults employ as well, under certain conditions. This convergence suggests a universal relationship between numbers and space. Nevertheless, the Munduruku do not map numbers onto a line at equal intervals, as we do when we measure objects. Both universal cognitive abilities and culture-specific experiences therefore seem to contribute to the development of a linear number line and the activities that it makes possible: measurement, mathematics, and science."

The researchers studied the ability of 33 Munduruku adults and children to map numerical representations on to a line, with "1" located at the left end of the line, and "10" at the right. In tests of larger numbers, "10" was at the left, and "100" at the right. After presentation of a number stimulus, such as spoken number word in Munduruku or Portuguese, or a visual array of dots or sequence of sounds, the Munduruku indicated the number's appropriate location on the line. The test was presented on a solar-powered laptop deep in the Amazon.