linear systems

A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

Primer uses simulations to compare voting systems such as first-past-the-post, approval, ranked choice and others. It shows how each system behaves and can be manipulated, with links to further voting theory resources.

Huygens Optics explores the idea that space is a non-linear elastic medium, and uses simulations to show how wave energy might be confined locally into particle-like objects. It touches on inertia, the Schwinger limit and the vacuum as a medium.

Adam Neely tests the claims for tuning to A=432 Hz by trying the unusual tuning systems that its proponents' numerology requires. He compares how they sound against standard tuning and temperaments.

Musician Adam Neely examines whether certain keys sound sadder than others, looking at the history of tuning systems and temperaments and at how instrument timbre shapes the emotional character we hear. It draws on historical aesthetics writing and audio examples.

CGP Grey explains first-past-the-post voting and why it pushes elections toward two dominant parties. It is the first in his series on electoral systems.

An animated simulation comparing single-winner voting methods such as plurality, instant runoff and STAR. Colored regions show which candidate wins as a randomized electorate shifts across a two-dimensional political space, building on Ka-Ping Yee's earlier diagrams.

A Vox Borders episode with Johnny Harris explaining how China is gradually erasing the line between mainland China and Hong Kong since the 1997 handover. It describes the one country, two systems arrangement and its expiration date.

Historia Civilis explains the origins and governing system of the Iroquois (Haudenosaunee) Confederacy. It covers the Great Law and the league's surprisingly intricate legal and political structure.

A six-minute explainer from Undefined Behavior on range (score) voting. It follows an earlier video on Arrow's Theorem and shows how range voting seems to satisfy the criteria Arrow's Theorem says no ranked system can.

Yuta, a Japanese YouTuber, explains whether Japanese speakers can read Chinese text. He shows how shared kanji let people guess meanings while the two languages remain completely different.

Tom 7 (suckerpinch) delivers a long, comedic digression on gradient descent and floating-point imprecision. He shows how rounding behavior can supply the nonlinearity needed to build a neural network.

Tom Scott visits ThyssenKrupp's test tower in Rottweil to see the Multi, a rope-free elevator that uses linear motors to move cabins sideways as well as vertically.

Veritasium explains why no voting system can be perfectly fair, drawing on Arrow's theorem and the work of Eric Maskin. It looks at problems with systems like first-past-the-post and ranked-choice voting.

CGP Grey explains the Single Transferable Vote, a proportional ranked-ballot system, and why politicians have little incentive to adopt it. It is a short animated explainer of how multi-winner ranked voting works.

CGP Grey explains Mixed-Member Proportional representation, the system used in New Zealand where voters get two votes. It covers how it differs from first-past-the-post.

A Smarter Every Day episode from aboard a nuclear submarine on how the crew makes breathable air. It covers oxygen generation from seawater, oxygen candles and CO2 scrubbing with amine.

jan Misali presents an humorous but earnest case for counting in base 6 (seximal) instead of base 10 or 12, comparing the arithmetic advantages of each.

The Center for Election Science explains favorite betrayal in instant-runoff voting: in some elections, ranking your favorite first can cause your least favorite to win. It contrasts this with plurality voting's spoiler problem.

Technology Connections explains that US household power is split-phase, with two 120V legs that combine to 240V for large appliances. It covers the breaker panel and how the system works.

A short CGP Grey animation showing how the US electoral college lets a candidate win the presidency with as little as about 22 percent of the popular vote. It lays out the arithmetic of winning states by narrow margins.

CGP Grey explains how the 2015 UK general election showed the flaws of first-past-the-post voting, with parties like UKIP winning many votes but few seats.

jan Misali traces the history of the letter W, including why it is called double u. The video is part of a series of deep dives into individual letters.

A short narrated video describing how reintroducing wolves to Yellowstone triggered a trophic cascade that changed wildlife, vegetation and even river courses. This is a remastered HD version of George Monbiot's viral piece.

Brian Douglas introduces Braitenberg vehicles, simple robots whose sensors are wired directly to motors yet show surprisingly lifelike behavior. He draws on Valentino Braitenberg's book Vehicles.

3Blue1Brown, in collaboration with minutephysics, introduces the math of superposition and quantum states using polarized light. It builds up the quantum behavior of photons as a simple counting and probability problem.

A short explainer from 2swap on the chaotic behavior of double pendulums. It examines how predictable the system is for some starting conditions and whether closed-form solutions exist.

Yuta asks whether native Japanese speakers can actually write kanji by hand, showing that many struggle to recall characters from memory.

MinutePhysics explains that computers store brightness nonlinearly, so blurring and blending colors in raw RGB gives wrong, dark results. It shows why mixed colors, such as in gradients, look off.

Veritasium explains why bicycles are stable, arguing that gyroscopic effects are not the answer. The video shows countersteering and an experiment where riders blocked from steering the opposite way cannot turn.

Not Just Bikes explains why cars rarely crash into buildings in the Netherlands, attributing it to street design that forgives mistakes and to systematic crash investigation. It contrasts this with North American acceptance of such crashes.

Captain Disillusion's comedic, fast-paced explainer on how color works in cameras, displays and video. It covers the biology of color perception and what it means for screens.

Veritasium explains why many real-world systems follow power laws rather than normal distributions. It covers self-organized criticality, with simulations of sandpiles, magnetism and forest fires.

Real Engineering explains the engineering behind the James Webb Space Telescope, including its folding mirror, sunshield, orbit and cooling systems, and why deployment was so difficult.

Robert Miles introduces the first of several videos on the paper 'Concrete Problems in AI Safety', focusing on how AI systems can cause accidental negative side effects. It explains the problem in accessible terms.

Computerphile interview with Prof. Ross Anderson on how Chip and PIN payment systems are being compromised, and the attacks researchers have seen.

Two Minute Papers covers OpenAI's multi-agent hide-and-seek experiment, in which agents learned emergent tool use and found ways to break the game's rules. It summarizes the 'Emergent Tool Use from Multi-Agent Interaction' paper.

An MTA video on communications-based train control, the system meant to replace the New York City subway's century-old signaling. It also shows the mechanical interlocks and signals in use today.

Veritasium visits the US Navy's Crane facility to test top night vision goggles. It explains how image intensifier tubes and thermal or digital systems work and compares the generations of the technology.