arrow's theorem

PBS Space Time explains Noether's theorem: conservation laws such as energy and momentum are consequences of deeper symmetries. It also covers why those laws hold only under certain conditions.

MinutePhysics, with 3Blue1Brown, explains Bell's theorem using a Venn diagram paradox and polarizing filters. It shows why no local hidden variable theory can reproduce quantum correlations.

3Blue1Brown presents Bayes' theorem through a geometric diagram, showing how evidence should update beliefs. It works through the Kahneman and Tversky style questions and base rates.

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.

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.

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

Sabine Hossenfelder explains superdeterminism as an interpretation of quantum mechanics, addressing common objections and misconceptions, including the worry that it kills free will or science. She ties it to Bell's theorem and hidden variables.

Veritasium explains quantum entanglement and spooky action at a distance, walking through Bell's inequality and the experiments that rule out hidden variables, in under ten minutes.

Veritasium explores why energy is not conserved in general relativity, using Emmy Noether's theorem linking symmetries to conservation laws. Physicists interviewed explain energy loss in an expanding universe.

Veritasium explains Bayes' theorem with examples and introduces the 'Bayesian trap', where repeated events get mistaken for inevitable ones. It discusses how priors shape our expectations and behavior.

Veritasium explains the Dzhanibekov effect, also called the tennis racket theorem, where a spinning object flips unexpectedly about its intermediate axis. The video gives an intuitive account of the underlying rotational dynamics, drawing on Terry Tao's explanation and the original papers.

A ten-minute explainer from Hypermind on the wisdom of crowds, covering Galton's discovery and the diversity theorem. It argues that collective intelligence comes from diversity, independence and aggregation.

Posy gives a short history of the computer mouse cursor, from early straight pointers to the tilted arrow, comparing Apple and Windows designs. He then explains why he designed his own cursor set and offers it as a free download.

Numberphile's Tony Padilla and Matt Parker discuss Graham's number, once the largest number used in a mathematical proof, and how enormous it is.

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.

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.

Bill Hammack of Engineer Guy explains the engineering behind the aluminum beverage can: why it is cylindrical, how it is manufactured, why it narrows at the top, the double seam, and how the pull tab works.

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

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.

FortNine explains how Harley-Davidson ended up in decline, from a narrow lifestyle niche and an aging customer base to the pandemic hitting a company already in trouble.

An RSA Animate summary of Iain McGilchrist's lecture on the divided brain, arguing the brain's two hemispheres attend to the world differently and that this has shaped culture and society.

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.

A Veritasium video on AlphaFold, DeepMind's protein structure prediction system, and the protein design work it enabled. It features interviews with John Jumper and with David Baker's protein design group and explains why predicting protein folding matters.

Corridor Crew tracks down Disney's lost sodium vapor prism process, used for Mary Poppins-era transparency mattes. They explain how a narrow sodium wavelength and a beam splitter enabled better compositing than green screen.

A short Not Just Bikes video on the 1960s plans (Plan Jokinen) to cut highways through Amsterdam to accommodate cars. It shows how radically different the city would look had they succeeded.

Tom Scott visits the Strid at Bolton Abbey in Yorkshire, a deceptively narrow stretch of river with dangerous currents. He covers its reputation and the 12th-century legend of the Boy of Egremont.