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# A Natural Log: Our Innate Sense of Numbers is Logarithmic, Not Linear

People without math training naturally think in terms of ratios

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.

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### 10 Comments

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1. 1. Quasimodo 08:05 AM 8/5/08

Now you're talking! Cool report. Yay.

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2. 2. inboulder 04:57 PM 8/5/08

1,2,3, ... many. Ok, who thought humans who can't differentiate between 20 and 27 dots are going to space them correct?

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3. 3. squall211 06:33 PM 8/5/08

Its interesting research, especially how the investigators actually tested indigenous tribes.

It 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

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4. 4. Tan Boon Tee 10:28 PM 8/5/08

While not knowing the exact methodology and analysis of the experiment, I cannot be sure if the tentative conclusion means much.

I 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?

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5. 5. AF 01:05 AM 8/6/08

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.
Regardless 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.

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6. 6. omz99 02:08 AM 8/6/08

So I guess Zeno's paradox is indeed absurd.

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7. 7. riemannzeta 11:10 PM 8/6/08

Logarithmic thinking or linguistic deficiency? There is linguistic evidence of "one, two, many" thinking in primitive cultures.

http://www.newscientist.com/article.ns?id=dn6303

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8. 8. minasto 06:35 AM 8/8/08

I think I need more Explanation to understand you well....and not to missunderstand you.........

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9. 9. elmousetrap 12:11 PM 8/11/08

muy interesante :D

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10. 10. tehtheory 01:28 AM 12/3/12

Where does an innate concept of number leave the belief of mathematicians that number and maths are abstract, human inventions?

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