Fourier Transforms and the Buddhist Doctrine of No-Self

For weekly insight and inspiration — check out my newsletter!

Joseph Fourier discovered the extraordinary fact that some functions can be written as an infinite sum of harmonics. The Fourier Transform is an extension of this initial discovery, and is a highly used technique in engineering, physics and many other disciplines. The crux of it is this:

You can decompose a signal (a function of time) into its component frequencies

When two waves interact with each other, they don’t simply pass through one another, nor do they collide like particulate matter; they interfere. The height of the peak of a wave is its amplitude, and when waves interfere the result is a new waveform with a larger, smaller or similar amplitude. The more waves involved, the more complex the resultant waveform.

The above waveform is a messy combination of a couple of waves with various frequencies. Using the mathematical tool of a Fourier Transform, we can discover how many waves make up our original waveform and what each of their frequencies are.

The three peaks show that our waveform is composed of three different waves with the corresponding frequencies on the graph. What we have just done is truly astonishing. Consider a fully baked cake. We have been able to deduce both what ingredients were used, and how much of each is in the cake based only on tasting the final, delicious result.