One bit of pedantry to complain about: this (really clever) essay is really only describing Fourier Decomposition, the idea that any function can be described in a vector space of sinusoidal basis functions. The Fourier Transform is an algorithm that exploits some (also really clever, and obviously of critical practical impact) factoring representations to compute that sum of functions in N*log(N) time in the number of data points instead of the naive N^2 summation of products.