complex systems

An 11-minute animated introduction to P vs. NP and the wider landscape of complexity classes, inspired by the Complexity Zoo wiki. It assumes no background in computer science.

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.

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.

WonderWhy surveys complex international borders, including enclaves like Vatican City, San Marino and Lesotho, the enclave-within-enclave town of Baarle, and the India-Bangladesh Cooch Behar region.

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 PBS Infinite Series episode explaining the mathematics of quantum computers, including how qubits store complex numbers and how quantum computation differs from classical computation. Hosted by Kelsey Houston-Edwards.

A short Healthcare Triage episode by Aaron Carroll arguing that milk gets an undeserved pass in efforts to improve diets. It examines claims about calcium and bone strength and concludes you don't need to drink milk.

Numberphile's James Grime introduces quaternions, a type of number beyond the complex numbers, building up from real and complex numbers and explaining why they are useful.

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.

3Blue1Brown shows how pi emerges from prime numbers via complex numbers and sums of squares, culminating in a formula for approximating pi.

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.

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.

3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.

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.

A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

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.

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.

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.

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

NASA's animated explanation of the Curiosity rover's Mars landing, which relied on a complex automated sequence taking about seven minutes. It features NASA engineers discussing the risks before the 2012 landing.

Scott Manley explains the plumbing of rocket engines, including pressure-fed, gas generator, expander and staged combustion cycles. He shows why more complex designs exist and what they gain.

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.

PBS Space Time, together with It's Okay to be Smart and PBS Eons, asks how a universe drifting toward disorder produced something as complex as life. It presents the idea that the laws of physics, through thermodynamics, may actually favor the emergence of life.

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.

A two-minute clip in which Milton Friedman uses a humble pencil to show how thousands of strangers across many countries cooperate, without central direction, to make a simple product. It is a short visual version of the 'I, Pencil' essay's argument about free markets and dispersed knowledge.

A video arguing that exercise matters for the brain as much as the body, linking movement, the nervous system and BDNF to learning and memory. It draws on research connecting complex movement to brain development.

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.