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.

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 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.

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.

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.

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.

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.

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.

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.

Tom Scott explains YouTube's 11-character video IDs, which are base-64 encoded 64-bit numbers, and whether YouTube could ever run out of them. It covers counting systems and base 64 briefly.

Tom Scott and Matt Parker investigate some of the small deceptions and oddities of the London Underground, such as misleading signage and map distortions.