Monday, February 20, 2017


Many of the foundations of wave mechanics are based on the analyses and equations that Rayleigh derived for the theory of acoustics in his book The Theory of Sound. Erwin Schrödinger, a pioneer in quantum mechanics, studied this book and was familiar with the perturbation methods it describes. 
Excited again — found a number of articles by Atiyah, du Sautoy et al., which begin to tie together for me various threads regarding harmonics and sound.
For mathematical physicists, this material will be old news — but for the fact that they've missed the connection to what we actually hear, owing to sound's putative status as a "mental" thing. The scare quotes are there because "mental" is one of those words we all understand until we start to think about it.
Riemann discovered that the physics of music was the key to unlocking the secrets of the primes. He discovered a mysterious harmonic structure that would explain how Gauss's prime number dice actually landed when Nature chose the primes.
What Riemann discovered was that Gauss's graph is like the fundamental note played by an instrument, but that there are special harmonic waves that, when added to this graph, gradually change it into the true graph or "sound" of the primes, just as the harmonics of the clarinet change the sine wave into the square wave.
~du Sautoy
"Mathematics in the 20th Century," by Sir Michael Atiyah