Logarithms – nature or nurture?

Scottish mathematician John Napier first “discovered” logarithms in 1614, but a recent study published in Nature suggests this counting scheme could be innate in all humans.

Teenage mathematics students would argue that using logarithm tables is anything but instinctive, but researchers have found an Amazonian tribe that judges magnitudes on a logarithmic basis despite a lack of exposure to the linear counting scale of the industrialised world.

Members of the Munduruncu tribe 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 one to 10 and from 10 to 100. They clearly apportioned the divisions logarithmically, which means that successive numbers get progressively closer together as they get bigger.

The researchers argue that our linear scaling, in which the distance between each number is the same, irrespective of their magnitude, is a cultural invention. And numerous examples of logarithms in nature and in our intuitive thinking support that argument. The phenomenon of life speeding up as we get older is an example familiar to us all, as each passing year becomes a smaller proportion of our whole life.

The magnitudes occurring in nature take on most meaning when expressed logarithmically. The fentometre (10–15m) is the scale of the atomic nucleus, the nanometre (10–9m) that of molecular systems, and the micrometre (10–6m) the scale of the living cell.

The immense variation in the size of earthquakes is measured using the logarithmic magnitude scale, while the same is true of the decibel scale for sound intensity and the pH scale. Younger pharmacists may still remember the log scales used in pharmacokinetics graphs explaining how the body distributes and metabolises drugs.

But logarithms were not Napier’s only claim to fame. He was also the first to use the decimal point and he proposed the first mechanical means of calculation, making him the grandfather of modern day calculators.

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