The Endeavour

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 2^1/12 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.

When I was in college, my saxophone teacher recommended I study Michael Brecker. I enjoyed his music, especially his recordings with Steps Ahead, but for some reason I quit listening to Brecker sometime after college. Then earlier this year I bought Brecker’s last album Pilgrimage after reading a glowing review.

Brecker recorded Pilgrimage as he was dying of leukemia, but there’s nothing morbid about the album. It’s upbeat, complex, and beautiful. Brecker spent his final days pursuing his art surrounded by friends.

A few days ago Engines of our Ingenuity aired a piece on Wagner’s tuba. It’s an interesting story of how Richard Wagner invented a new musical instrument for his Ring of the Nibelung cycle.