We humans seem to be born with a number line in our head. But a May 30 study in Science suggests it may look less like an evenly segmented ruler and more like a logarithmic slide rule on which the distance between two numbers represents their ratio (when divided) rather than their difference (when subtracted).
The mathematical idea of a number line—a line of numbers placed in order at equal intervals—is a simple yet surprisingly powerful tool, useful for everything from taking measurements to geometry and calculus.
Previous studies of Westerners showed that people tend to map numbers on a linear scale, with the numerals evenly spaced along the line. But if the numbers are presented as hard-to-count groups of dots, people will logarithmically group the larger numbers closer together on one end of the scale in what researchers call a “compression effect.” Preschoolers also group numbers this way before they begin their formal education in math.
To investigate which number-line concept is innate, neuroscientist Stanislas Dehaene of the College of France in Paris worked with the Munduruk, an Amazonian culture with little exposure to modern math or measuring devices. The Munduruk were immediately able to place numbers on a line when asked, but they grouped them logarithmically.
Dehaene says the research suggests that a logarithmic number line might be an intuitive mathematical concept, whereas the idea of a linear number line might have to be learned.
Editor's Note: This story was originally printed with the title "A Natural Log"