2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?

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Director of the Bristol Cognitive Development Centre in the Experimental Psychology Department at the University of Bristol; Author, The Self-Illusion

Complexity Out of Simplicity

As a scientist dealing with complex behavioral and cognitive processes, my deep and elegant explanation comes not from psychology (which is rarely elegant) but from the mathematics of physics. For my money, Fourier's theorem has all the simplicity and yet more power than other familiar explanations in science. Stated simply, any complex pattern, whether in time or space, can be described as a series of overlapping sine waves of multiple frequencies and various amplitudes.

I first encountered Fourier's theorem when I was a Ph.D. student in Cambridge working on visual development. There, I met Fergus Campbell who in the 1960's had demonstrated that not only was Fourier theorem an elegant way of analyzing complex visual patterns, but it was also biologically plausible. This insight was later to become a cornerstone of various computational models of vision. But why restrict the analysis to vision?

In effect, any complex physical event can be reduced to the mathematical simplicity of sine waves. It doesn't matter whether it is Van Gogh's Starry Night, Mozart's Requiem, Chanel's No. 5, Rodin's Thinker or a Waldorf salad. Any complex pattern in the environment can be translated into neural patterns that in turn, can be decomposed into the multitude of sine wave activity arising from the output of populations of neurons.

Maybe I have some physics envy, but to quote Lord Kelvin, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." You don't get much higher praise than that.