June 12, 2008
The ability to map numbers onto a line is one of the foundations of mathematics. New research suggests that this ability is universal among humans, but the form of this universal mapping is logarithmic rather than linear.
Stanislas Dehaene of the College de France in Paris and his colleagues studied number sense among the Munduruku, an Amazonian native culture with a limited vocabulary of number words and spatial terms, little or no formal education, and practically no experience with maps, graphs, and rulers.
They asked a group of both adults and children to place given numbers on a line with "1" at its left end and "10" on the right. In most cases, the Mundurucu placed the given numbers on the line in a compressed, logarithmic manner, devoting more space to smaller numbers than they did to larger ones. In tests involving larger numbers, the Mundurucu placed numbers on a line with "10" at the left and "100" at the right in the same manner.
"Our findings suggest that humans have a predisposition to relate two fundamental domains of knowledge: knowledge of number and of space," Elizabeth Spelke of Harvard University says. "The Mundurucu are able to place numbers on a line in a systematic way that educated adults employ as well, under certain conditions."
When adults in the Boston area were given a similar set of tests, they produced linear mappings of numbers onto a line when presented with number words or diagrams showing countable arrays of dots. However, they produced compressing mappings when presented with sound sequences or arrays of dots too large to count.
The findings indicate that a compressed mapping of number onto space persists in adults, even after years of experience with counting, arithmetic, and measurement. Very young children also show a propensity for compressed mapping. Linear numerical mapping develops when they are between five and seven years old.
"It appears that we, as humans, can access two different methods of numerical mapping," Dehaene says. "The logarithmic, ratio-based method is the most intuitive; we inherit it from our primate evolution and we still access it in the absence of precise mathematical tools."
"Through education, we also acquire a linear mapping," he adds. "However, this does appear to be a cultural construct."
The findings of Dehaene, Spelke, and their coworkers appear in the article "Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigene Cultures," published in the May 30 Science.
Source: Harvard University, May 29, 2008; Science, May 30, 2008.