Everything Is Circles
Curated by Claude · 10 videos · 2 hr 50 min
HN keeps recommending the same handful of Fourier explainers, and together they cover a lot of engineering. This list starts with the intuition, follows the algorithm and its Cold War history, then visits the places it quietly runs: images, audio, radio and optics. It ends with the result that links it to quantum physics.
Play all on YouTube- 13:50
Ptolemy and Homer (Simpson)
380K views • 18 years agoSantiago GinnobiliA short animation reconstructing a planet's looping orbit using Ptolemy's epicycles and deferents, with the epicycles tracing out the face of Homer Simpson. It shows how enough circles can reproduce nearly any shape.A three-minute hook: enough epicycles can trace Homer Simpson's face, which HN uses both to explain Fourier series and to warn about overfitting.
- 219:42
But what is the Fourier Transform? A visual introduction.
12.6M views • 8 years ago3Blue1Brown3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.HN's default first explanation, the one many commenters say finally made the transform make sense.
- 33:39
(1/4) Intro/History: Introducing a 100-year-old mechanical computer
476K views • 11 years agoengineerguyThe first of four short videos from Bill Hammack (engineerguy) introducing and giving the history of a 100-year-old mechanical computer, Michelson's harmonic analyzer. The series goes on to explain Fourier synthesis, analysis and operation of the machine.Michelson's gear-driven harmonic analyzer computed Fourier series a century ago; the first of Bill Hammack's four short episodes.
- 428:23
The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?
2.3M views • 5 years agoReducibleReducible's visual walkthrough of the Fast Fourier Transform, motivated by polynomial multiplication. It shows how the FFT's key ideas can be discovered by asking the right questions.Derives the FFT from polynomial multiplication; one commenter rewatches it every six months.
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26:33The Most Underrated Algorithm
10.8M views • 4 years agoVeritasiumVeritasium tells the story of the Fast Fourier Transform, from its use in detecting nuclear tests to Cold War politics, and how it could have changed the arms race. It includes a short, intuitive explanation of what the Fourier transform does.The FFT's backstory in nuclear test detection and Cold War politics, the human side of the algorithm from the video before.
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15:12JPEG DCT, Discrete Cosine Transform (JPEG Pt2)- Computerphile
697K views • 11 years agoComputerphileMike Pound explains the discrete cosine transform and how it underpins JPEG compression. It is part two of Computerphile's JPEG series.The first everyday use: the cosine transform inside every JPEG, explained clearly enough that several commenters say they finally understood the DCT.
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23:53D/A and A/D | Digital Show and Tell (Monty Montgomery @ xiph.org)
647K views • 13 years agoFL StudioMonty Montgomery of Xiph.org gives real-time demonstrations of sampling, quantization, bit depth and dither using real audio equipment, including both digital analysis tools and vintage analog bench gear. It shows that sampled audio is not stair-stepped and corrects common misconceptions about digital audio.Sampling and the frequency domain on real bench gear, the gold-standard answer HN gives to audiophile stair-step myths.
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12:31The Superheterodyne Radio: No really, that's its name
987K views • 7 years agoTechnology ConnectionsTechnology Connections explains why the superheterodyne radio has its name and how mixing frequencies lets it tune stations well. It walks through the underlying wave phenomena and algebra and why the design solved a hard tuning problem.Radio's central trick, shifting signals between frequencies by mixing them, explained by Technology Connections in twelve minutes.
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18:31Fourier Optics used for Optical Pattern Recognition
103K views • 6 years agoHuygens OpticsHuygens Optics explains the Fourier transform and shows how a lens performs one optically. A DLP projector is used as a Fourier filter to do simple pattern recognition on lithographic character patterns.A plain lens computes a Fourier transform at the speed of light, shown with a DLP projector doing pattern recognition.
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18:07The more general uncertainty principle, regarding Fourier transforms
2.3M views • 8 years ago3Blue1Brown3Blue1Brown shows how the uncertainty principle arises from Fourier transforms. A wave packet cannot be narrow in both position and frequency, so the principle is a property of waves rather than of measurement.The closer: uncertainty is a property of waves, not of measurement, which ties everything above to quantum mechanics.