Saturday, March 25, 2006

On the cochlea, Golden Mean, The Da Vinci Code, and low frequency sensitivity

Physics Web reports on work published in Physics Review Letters by the applied mathematician Manoussaki and colleagues on investigating the shape of the human cochlea. The special thing about the cochlea's shape is that it is a classic example of phi, also called the Golden Mean (GM), Golden Ratio (GR), Golden Number, and the Divine Proportion. The GM is a special number that shows up in nature, art, math and music over and over again. It is a never-ending, never-repeating number that starts out 1.6180339887 and keeps going, of course. Other classic examples are the spiral shape of a nautilus shell, the Fibonacci mathematical sequence, the number of petals on many flowers, and the proportions of the human body. Dan Brown highlights it in his bestselling book, and soon to be major motion picture, The Da Vinci Code. For further information on the GM, including examples of it in nature and art, click here and here. For one mathematician's analytical perspective click here.

Getting back to the story, over the years many people have sought to explain why the cochlea is shaped the way it is and, thus far, no one has succeeded, until (possibly) now. Manoussaki, et al, theorize that its GM shape may end up giving a 20dB (decibel) boost to our auditory sensitivity at low frequencies, where humans are particularly deficient to begin with. This is thought to be due to a slight tilt along the width of the cochlea as the spiral gets bigger and bigger, thereby leading to greater movement in response to low frequency stimuli relative to a spiral without such a tilt.

Their theory has some appeal on the face of it as a partial explanation of how we can hear so well with a set of structures that takes high-powered magnification to examine closely. The ear is truly amazing...

(Image Source: Picture of human cochlea from the online picture library of the Hospital of Sick Children)