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How Your Ears Do Math Better Than Mathematicians

pigrabbitbear (2519384) writes | about a year and a half ago

Math 0

pigrabbitbear writes "The assumption was that ears use something akin to a Fourier transformation. A Fourier transform, named after the French mathematician who also identified the Greenhouse Effect, is essentially when a sound wave is stretched way out until its details are revealed. In more mathy terms, you take a signal, which is a mathematical function of time--a mechanical thing of air molecules traveling through space--and turn it into an array, or series of different frequencies. The Fourier transform is found all over science, and not just sound.

The transformation is done through what's called an "integration" of the original, mechanical function of time. (If you've taken calculus, you should remember integration.) Basically, this is taking that function and recovering information from it by mathematically slicing it up into tiny bits. It's pretty neat. This, it turns out, is how we get meaning (words, music, whatever) from sound (that big wave in the ocean). Or so scientists have thought.

Turns out this might not be quite the case. Researchers at Rockefeller University devised an experiment to test the limit of this kind of analysis via Fourier transformation.

Rockefeller researchers, Jacob Oppenheim and Marcelo Magnasco, took a group of 12 composers and musicians and tested them to see if they could analyze a sound beyond the uncertainty limit of Fourier analysis. And guess what? They busted it down. "Our subjects often exceeded the uncertainty limit, sometimes by more than tenfold, mostly through remarkable timing acuity," the authors write in Physical Review Letters."

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