Why we should love logarithms

Sunday, June 1st, 2008

Philip Ball explains why we should love logarithms — including the surprising reason that it may be more natural to think logarithmically:

Stanislas Dehaene of the Federative Institute of Research in Gif-sur-Yvette, France, and his co-workers report in Science that both adults and children of an Amazonian tribe called the Mundurucu, who have had almost no exposure to the linear counting scale of the industrialized world, judge magnitudes on a logarithmic basis.

The researchers presented their subjects with a computerized task in which they were asked to locate on a line the points that best signified the number of various stimuli (dots, sequences of tones or spoken words) in the ranges from 1 to 10 and from 10 to 100. One end of the line corresponded to 1, say, and the other to 10; where on this line should 6 sit? The results showed that the Amazonians had a clear tendency to apportion the divisions logarithmically, which means that successive numbers get progressively closer together as they get bigger.

The same behaviour has previously been seen in young children from the West. But adults instead use a linear scaling, in which the distance between each number is the same irrespective of their magnitude. This could be because adults are taught that is how numbers are ‘really’ distributed, or it could be that some intrinsic aspect of brain development creates a greater predisposition to linear scaling as we mature. To distinguish between these possibilities, Dehaene and his colleagues tested an adult population that was ‘uncontaminated’ by schooling.

The implication of their finding, they say, is that “the concept of a linear number line seems to be a cultural invention that fails to develop in the absence of formal education”.

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