But what is a convolution?

Discrete convolutions, from probability to image processing and FFTs. An equally valuable form of support is to simply share the videos. ------------------ Other videos I referenced Live lecture on image convolutions for the MIT Julia lab Lecture on Discrete Fourier Transforms Reducible video on FFTs Veritasium video on FFTs A small correction for the integer multiplication algorithm mentioned at the end. A “straightforward” application of FFT results in a runtime of O(N * log(n) log(log(n)) ). That log(log(n)) term is tiny, but it is only recently in 2019, Harvey and van der Hoeven found an algorithm that removed that log(log(n)) term. Another small correction at 17:00. I describe O(N^2) as meaning "the number of operations needed scales with N^2". However, this is technically what Theta(N^2) would mean. O(N^2) would mean that the number of operations needed is at most constant times N^2, in particular, it includes algorithms whose runtimes don&actually have any N^2 term, but which are bounded by it. The distinction doesn&matter in this case, since there is an explicit N^2 term. These animations are largely made using a custom python library, manim. See the FAQ comments here: You can find code for specific videos and projects here: Music by Vincent Rubinetti. Download the music on Bandcamp: Stream the music on Spotify: Timestamps 0:00 - Where do convolutions show up? 2:07 - Add two random variables 6:28 - A simple example 7:25 - Moving averages 8:32 - Image...