Thought it might interest some to see how FFT works.
“Natural phenomena we can relate to, like sound waves, heat transfer, weather patterns, and those of a more esoteric sort, like quantum particle interactions and cosmic objects moving through gravitational fields governed by general relativity, can all have their interactions approximated by classes of functions called orthogonal functions.”
“The consistency condition which demands that new hypotheses agree with accepted theories is unreasonable because it preserves the older theory, and not the better theory. Hypotheses contradicting well-confirmed theories give us evidence that cannot be obtained in any other way. Proliferation of theories is beneficial for science, while uniformity impairs its critical power. Uniformity also endangers the free development of the individual.”
“There is no idea, however ancient and absurd, that is not capable of improving our knowledge. The whole history of thought is absorbed into science and is used for improving every single theory. Nor is political interference rejected. It may be needed to overcome the chauvinism of science that resists alternatives to the status quo.”
“No theory ever agrees with all the facts in its domain, yet it is not always the theory that is to blame. Facts are constituted by older ideologies, and a clash between facts and theories may be proof of progress. It is also a first step in our attempts to find the principles implicit in familiar observational notions.”
Terence McKenna was a fan.
Source: Paul Feyerabend’s Against Method
One mathematician who’s got first-hand experience of the fascinating interplay between physics and geometry is Shing-Tung Yau. In a new book called The shape of inner space (co-authored by Steve Nadis) Yau describes how the strange geometrical spaces he discovered turned out to be just what theoretical physicists needed in their attempt to build a theory of everything. Plus met up with Yau on his recent visit to London, to find out more.