information theory

3Blue1Brown uses Wordle as an excuse to teach information theory and entropy, building a solver that picks guesses by expected information and incorporating word frequencies.

A PBS Space Time episode asking whether the universe's information can ever truly be lost, tying quantum mechanics, determinism and black holes together. It sets up the black hole information paradox.

3Blue1Brown's discovery-oriented introduction to error correction codes, building up Hamming codes from the puzzle of locating a flipped bit. It explains the parity-check idea and why it is so efficient.

3Blue1Brown builds intuition for Euler's formula, e^(pi i) = -1, using the core ideas of group theory. It treats exponentiation geometrically as rotation and scaling instead of repeated multiplication.

ScienceClic gives a 15-minute animated introduction to quantum field theory, covering fields, spin, conserved quantities, the standard model and interactions.

Adam Neely analyzes vaporwave through music theory, timbre and nostalgia, and includes a parody track made for the video. He also touches on the phenomenology of music.

Veritasium explores the Prisoner's Dilemma and Axelrod's tournaments, showing why tit-for-tat and forgiving strategies win in repeated games. It extends the ideas to cooperation in evolution and conflict.

A PBS Space Time episode introducing de Broglie-Bohm pilot wave theory, an interpretation of quantum mechanics that avoids much of the strangeness of the mainstream views. It is aimed at curious lay viewers.

PBS Space Time episode on the black hole information paradox, covering how black holes seem to destroy information, the no-hair conjecture and the proposed role of the event horizon. It is part of a series on black holes.

Looking Glass Universe explains de Broglie-Bohm pilot wave theory (Bohmian mechanics) as an alternative to the standard interpretation of quantum mechanics. The video lays out the pros and cons of the theory and links to related videos on contextuality and entanglement.

Isaac Arthur examines the Dark Forest theory, Cixin Liu's proposed solution to the Fermi Paradox in which civilizations stay silent and may destroy any that reveal themselves. He tests the theory's underlying assumptions and arguments.

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

CGP Grey's animated adaptation of The Dictator's Handbook, explaining how rulers stay in power by keeping a small group of key supporters happy rather than ruling fairly. It lays out selectorate theory and how resources shape regimes.

An animated Sprouts video presenting Dietrich Bonhoeffer's argument that stupidity is more dangerous than evil, because reason cannot reach stupid people. It frames stupidity as a social and moral phenomenon.

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

Monty 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.

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.

Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.

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.

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.

Mike Pound explains the discrete cosine transform and how it underpins JPEG compression. It is part two of Computerphile's JPEG series.

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.

Tom Scott explains for Computerphile how Unicode and UTF-8 grew out of messy older character encodings to become the web's standard. It covers why the design works and how it handles worldwide text.

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.

Physicist Angela Collier argues that dark matter is not a theory but a set of observations, covering rotation curves, the CMB and why modified gravity struggles to explain them.

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.

Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

Technology 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.

Tom Scott explains why confetti and snow wreck video quality, using interframe compression and bitrate. He demonstrates it live by changing the quality on screen.

A two-minute demonstration of the loudness war, showing how heavy dynamic range compression in CD mastering makes music louder while degrading sound quality. It uses audio examples so you can hear the distortion.

Tom Scott explains for Computerphile how floating point numbers work, why moving the binary point is fast, and why it handles money badly.

Vsauce explores how human reasoning works, drawing on the social theory of reason and the extended mind thesis, made in partnership with Bill Gates around climate change.

Tom Scott explains why hold music sounds worse than it used to, tracing it to old telephone exchanges and the audio compression applied by modern switches. It is a short visit to the Milton Keynes Museum.

A 105-minute technical deep dive from Noise In Space evaluating whether Starlink satellites could work as synthetic aperture radar. It covers SAR signal-to-noise, amplifiers, antennas, duplexing, phased array beamforming and simulations of V2 Mini and V3 satellites.

GoldenSound publishes music on Tidal to test MQA, a deep dive into the format's claims and problems including its leaky filter. Testing begins around the 5:45 mark.

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.

Veritasium builds a QR code by hand to explain how it works. It covers the history of Morse code and barcodes, how QR codes encode data, why damaged codes still scan, and how safe they are.

A vlogbrothers video tracing how the claim that people eat a credit card of plastic every week spread. It walks through the funded talking point, the misleading amplification, and the peer review that missed it.

Vox Earworm explains why John Coltrane's Giant Steps is so hard to improvise over: it is fast and moves through three keys. Musicians Braxton Cook and Adam Neely walk the host through the underlying music theory.

Veritasium shows silicone oil droplets bouncing on a vibrating bath, a physical analogue of pilot wave theory that reproduces quantum-like behavior such as double-slit patterns.