four chords

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

Huygens 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.

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.

Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.

3Blue1Brown 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.

Reducible'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.

The 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.

Veritasium 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.

CGP Grey argues that the two-day weekend is poorly structured and proposes taking days off midweek, such as Wednesday and Sunday, instead.

Hans Rosling uses augmented-reality animation to show 200 countries over 200 years in four minutes, built from 120,000 data points. It tracks life expectancy and income to show the world's development.

A four-minute Not Just Bikes comparison of grocery shopping in Amsterdam versus car-centric North America, arguing that frequent small fresh-food trips beat bulk shopping. It ties this to land use and reduced food waste.

3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space. It is part one of a two-part series with an interactive companion site.

Mick West analyzes the Navy's Gimbal UFO video and gives four checkable observations suggesting it is an infrared glare that appears to rotate because the camera rotates while tracking. He argues the object is likely a hot craft hidden behind the glare.

A short Wendover Productions explainer on ETOPS, the rules that let twin-engine jets fly long routes over oceans. It covers the economics that favored twinjets like the 787 over four-engine aircraft like the A380 and 747.

Historia Civilis traces the history of work and time discipline, comparing modern working hours with those of medieval peasants and the changes brought by clocks and industrialization. It draws on works such as Schor's The Overworked American.

A video essay from Every Frame a Painting on animator Satoshi Kon and his editing style, which distorts and warps space and time. It draws on his four features and one TV series.

A School of Life video arguing that everyone marries someone who is somewhat wrong for them, and that this is unavoidable. It is a four-minute version of an essay by Alain de Botton.

A four-minute minutephysics video arguing that causal models and causal networks let statistics infer causation from correlation. It touches on Reichenbach's principle, common causes, feedback and quantum causal discovery.

A US Chemical Safety Board video explaining how sugar dust explosions at the Imperial Sugar plant in Georgia killed fourteen workers in 2008.

A four-minute 2006 explainer on trusted computing, describing what it is and whether users should support it, with a skeptical DRM angle.

Rick Beato analyzes a pop song he argues is among the most harmonically complex ever, breaking down its chords and key changes. It is a music theory deep dive aimed at general music fans.