Image: Dietmar Klement/iStockPhoto
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 Mundurukú, an Amazonian culture with little exposure to modern math or measuring devices. The Mundurukú 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"
This article was originally published with the title A Natural Log.
See what we're tweeting about
10 Comments
Add CommentNow you're talking! Cool report. Yay.
Reply | Report Abuse | Link to this1,2,3, ... many. Ok, who thought humans who can't differentiate between 20 and 27 dots are going to space them correct?
Reply | Report Abuse | Link to thisIts interesting research, especially how the investigators actually tested indigenous tribes.
Reply | Report Abuse | Link to thisIt makes sense, the ability to quickly group objects into relatively broad categories is probably an evolutionary advantage.
Peter
How Your Electronics Work
http://www.howyourelectronicswork.com
While not knowing the exact methodology and analysis of the experiment, I cannot be sure if the tentative conclusion means much.
Reply | Report Abuse | Link to thisI suspect that when people are shown numbers presented as hard-to-count groups of dots, it would only be natural for them to line up in ascending or descending orders.
To find out further if a logarithmic number line could indeed be an intuitive mathematical concept, why not carry out more research in countries (like Finland, Hungary, or East Asian) where children are thought to be more mathematically inclined?
With hindsight perhaps not too surprising: a linear scale is extremely inefficient when dealing with more a couple of orders of magnitude. So some form of "data compression" is needed to stay "on top" of the quantities that we experience.
Reply | Report Abuse | Link to thisRegardless of whether we live in a rainforest or are surrounded by computers every day, we have to deal with many more orders of magnitude than a representation on a linear scale can handle. For example, it is practically impossible to produce any implementation of a linear scale that can simultaneously represent, say, seconds and years in a meaningfull, usable way. The introduction of different units at different orders of magnitude (second, year) is in itself the simplest example of a logarithmic scale.
So I guess Zeno's paradox is indeed absurd.
Reply | Report Abuse | Link to thisLogarithmic thinking or linguistic deficiency? There is linguistic evidence of "one, two, many" thinking in primitive cultures.
Reply | Report Abuse | Link to thishttp://www.newscientist.com/article.ns?id=dn6303
I think I need more Explanation to understand you well....and not to missunderstand you.........
Reply | Report Abuse | Link to thismuy interesante :D
Reply | Report Abuse | Link to thisWhere does an innate concept of number leave the belief of mathematicians that number and maths are abstract, human inventions?
Reply | Report Abuse | Link to this