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

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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).

This is consistent with our analysis in chapter 5 of our book of decisions of Bangladeshis about whether to switch wells because of arsenic in drinking water. Among households with dangerous wells (arsenic content higher than 50 (in some units)), we predicted whether a household switches wells, given two predictors:
– distance to the nearest safe well;
– arsenic level of their existing well.
The data were consistent with the model that people weight “distance to nearest safe well” linearly but weight “arsenic level” on the log scale. As we discuss in our book, this makes psychological sense: distance is something you perceive directly and linearly, by walking (it takes twice as much time and effort to walk 200m as to walk 100m), whereas arsenic level is just a number and, as such, going from 50 to 100 seems about the same, psychologically, as going from 100 to 200 or 200 to 400–even though, in reality, that last jump is four times as bad as the first (arsenic being a cumulative poison).

3 Comments

  1. Thom Baguley says:

    It does make psychological sense, but I'm a bit worried that this gets reported as a new insight. AFAICT the novelty of the study is in the cross-cultural comparison and maybe also the idea that a linear scale has to be learned. The idea that distances between things are represented this way is far from novel. It is (in essence) generalizing the Weber-Fechner law that is over 100 years old.

    I'm sure the original article mentions this, but it surely a good science journalist should pick up that this idea is much older than May 30th 2008?

  2. really nice example given there!!

    and a really good way of explaining the Weber-Fechner law!

    Cheers.