3Blue1Brown
4 HN recommenders · recommended in 8 months, 2020–2025
24:47 · 19M views · Jun 30, 2019
3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles. It builds a visual intuition for decomposing functions into sine waves.
Recommended as the visual explanation that makes Fourier series and transforms click, even for laypeople.
8 comments from Hacker News
I wouldn’t call this 3blue1brown video a reference, but until I watched this (coming from an audio background), I didn’t quite grasp that a continuous stencil of any complex silhouette could be described in terms of a set of contributing vectors. Helped click that there is a perfect visual analogy to the deconstruction of complex audio to sine waves. this video
3B1B is incredible. I loved his video ( this video ) using Fourier series to make epicycle animations. I worked through the details to make my own: [LINK]
You can use epicycles to draw the actual orbits of planets. That's what "epicycles" are, or were: a fairly accurate model of the observed orbits of planets relative to Earth built through a composition of circular motions. One way to think about it is that you start by modeling the motion as a simple circular orbit. You then look at how the observed data differs from your circular model and add an epicycle whose parameters minimize the difference between your new model and your observations. Repeat this process until you get as close as you want to get. The success of heliocentric elliptic-orbit model isn't that it's able to represent something impossible with epicycles, but that it's dramatically simpler. Kepler's three laws are: 1) The orbit of a planet is an ellipse with the Sun at one of the two foci. 2) A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3) The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. In contrast, the epicycle models had 40-80 cycles with parameters tuned to match the observed data. I really like this video on how Fourier series work: this video
> It remains a badge of honor for many who like to describe themselves as highly cultured or artistic to describe themselves as mathematically challenged, or to say that their brains aren’t wired for mathematics. Because many of those they hold in high esteem have made similar claims, there is no real social penalty to them for doing so. For many scientific illiteracy is in the same category as mathematical illiteracy -- but the problem starts there already. Everybody should at least know what a Fourier transformation does -- it's not necessary to exercise it rigorously, but at least an idea... I think this video is enough to give even laymans an idea: this video
Warning: Bit of a 'Hitch hikers guide to the galaxy"/conway game of life yak shave for a reply. Nice start to providing a simple way to visually interact/experiment/manipulate different multiple Neural network concepts by loading/transforming any traditional code (working or not) & reshuffling/tesselating the structual representation of the code to generate a turing tape path via color execution paths. Switching to pi calculus could provide the theory to support coroutine/coprossing/ threading" multiple interacting tape paths/color combinations/path diffs/scaled recusion to perform assembly language instructions. Raster graphics without the yak ( [LINK] ) Feed back between tape & "traditional code" as neural network layer(s)! Flexiable code (via tessilations) without changing the actual imported source code! So, complete svg (tape interactions) web page as code source on how to interact with web page, ( this video ) what's displayed/played, documentation & usage manual included within code structure! Unicode permits implied piping rich kern font without all the tech fluff. Unicode fails because allows infinate multics and is there for k&r incomplete. But, this approach is way more dimensional/colorful than unicode/tech stuff. ?? can one's code unintentially provide a wordle problem & solution in one package ?? ( [LINK] ) ?? turing complete fourier transforms [LINK] toolkit concepts: Neural networks / analog stuff : [LINK] perceptrons: [LINK] spreadsheets (: [LINK] (turing spread