Scientific American has an article suggesting that our natural sense of numbers may operate on a logarithmic scale rather than a linear scale.
It has long been known that our senses often work on a logarithmic scale. For example, sound intensity is measured in decibels, a logarithmic scale. Pitch is perceived on a logarithmic scale, as the Pythagoreans discovered. When moving up a chromatic scale, it’s not the differences in frequencies but the ratios of frequencies that are constant. An octave is a ratio of 2 to 1, so a half step is a ratio of 21/12 to one since there are 12 half step in an octave.
The Statistical Modeling, Causal Inference, and Social Science blog gives an interesting example combining linear and logarithmic perceptions. They quote a study suggesting that when deciding whether to walk to a new well based on information regarding arsenic levels, Bangladeshis perceived “distance to nearest safe well” linearly but perceived “arsenic level” logarithmically.
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