Can your ears do math?
Yes they can and do according to researchers, Jacob Oppenheim and Marcelo Magnasco. As any audio “golden ears” will tell you, ears are the perfect transducer. Microphones and speakers merely perform loose translations of the real acoustic energy.
Oppenheim and Magnasco’s research shows that some human ears are capable of transforming air movement into identifiable sounds and with timing far in excess of what has previously been thought possible with predictions made by Fourier transformation.
Scientists assumed that ears used Fourier transformation to make the conversion from air pressure to understandable sound. In non-geek speak, that means changing sound as a mathematical function of time and turning it into a selection of discrete frequencies. For those engineers with a math background, we know it as ‘integration’.
The human ear turns out to be a pretty good integrator, in fact according to Oppenheim and Magnasco, sometimes as much as ten times better than the math predicts. The researchers assembled a group of 12 composers and musicians and then tested them to see if they could analyze a sound beyond the uncertainty limit of Fourier analysis. Said the authors, "Our subjects often exceeded the uncertainty limit, sometimes by more than tenfold.”
Cornell University released the authors’ report last month and a pdf can be obtained here. If you’d like a less ethereal (easer-to-understand account of the research), the website motherboard has a good description.