Physicists have been interested in human hearing since the work of Helmholtz in the mid-nineteenth century. Helmholtz thought that our hearing organ, the cochlea, contained a number of elements tuned to different frequencies, like a harp, but subsequent experiments proved this model to be wrong. Now physicists at the IMEDEA institute in Spain and Rockefeller University claim to have shown that the cochlea can be understood in terms of a nonlinear phenomenon known as a Hopf bifurcation (V M Eguiluz et al. 2000 Phys. Rev. Lett. 84 5232).
In 1960 von Bekesy published the results of his classic measurements on the cochlea, which suggested that the ear was essentially a linear device. However, von Bekesy conducted his experiments on cadavers, and more recent experiments on live cochleas suggest that hearing is essentially nonlinear. The nonlinearity is thought to arise from a biological power supply that leads to positive feedback within the cochlea. Indeed, experiments have revealed a variety of different and seemingly unrelated nonlinear behaviours in human hearing. Moreover, the response of the cochlea remains nonlinear for even the faintest of sounds.
The IMEDEA-Rockefeller team claim that these phenomena can all be explained in terms of solutions to the Hopf equation, a simple-looking nonlinear first-order differential equation that is widely studied for its dynamical properties. For certain values of the control parameter in the Hopf equation, the solutions to the equation exhibit compression of the dynamic range, sharp tuning for small inputs and broad tuning for large inputs – features also observed in human hearing. The next challenge, both theoretically and experimentally, is to link this macroscopic view of the ear to the microscopic behaviour of the individual hair cells in the cochlea.
