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.

Sabine Hossenfelder asks whether complex numbers are just a convenient tool or necessary in physics. She discusses a recent paper arguing that quantum mechanics cannot be done with real numbers alone.

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.

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.

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.

Veritasium explores how synchronization arises spontaneously in nature, with metronomes, fireflies and bridges, drawing on Steven Strogatz's work on chaos and complexity.

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.

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.

Polylog explains how algorithms can be turned into circuits and encoded as satisfiability problems, which lets you effectively run them backwards. It uses this to motivate breaking RSA, general reductions to SAT, and what P vs NP is really asking.

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.

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.

A Veritasium video on the logistic map, showing how a simple population equation leads to chaos and bifurcation. It connects the idea to convection, neuron firing and the Mandelbrot set, with interactive animations.

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.

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.

Jared Owen's 3D animated breakdown of how a Brunswick GS-X bowling pinsetter works, showing its mechanisms for sweeping, lifting and resetting pins and balls.

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.