Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures

Abstract

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education.

Figure 1

Number mapping task with numbers 1–10. A horizontal segment, labelled with a set of one dot on the left and a set of 10 dots on the right, was constantly present on screen. Numbers were presented visually as sets of dots or auditorily as sequences of tones (see 24), Mundurucu numerals or Portuguese numerals. For Mundurucu numerals, a rough translation into Arabic numerals is provided (e.g. “pũg põgbi xex xep bodi” ≈ “one handful (and) two on the side” ≈ 7; “xex xep põgbi” ≈ “two handfuls” ≈ 10). For each stimulus, participants pointed to a place on the line, and the experimenter clicked it with the computer mouse, which made a small bar appear.

Figure 2

Average location of numbers on the horizontal segment, separately for Mundurucu participants (left column) and for American participants (right column). Data are mean +/− standard error of the mean. Graphs of performance broken down by age group and education are available as supplementary material (24).