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.

Tod's Workshop fires full-weight medieval arrows from a 160lb English warbow at reproduced medieval armour. Armour curator Dr Tobias Capwell, an archer and bowyer give historical context and discuss the results.

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.

Chris Stucchio presents the ethical principles behind algorithmic decision making and shows with examples from lending, criminology and education that they cannot all be satisfied at once. The talk frames AI fairness as a set of quantitative tradeoffs.

The first lecture of N J Wildberger's History of Mathematics course, starting with Pythagoras' theorem and following Stillwell's text. It emphasizes the flow of ideas over proofs.

Numberphile talks with mathematician Ron Graham about the magnitude of Graham's number, building up from arrow notation to show how impossibly large it is. It is part of a series of videos on this number.

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.

Mathematician Kevin Buzzard explains why he believes the Lean theorem prover will shape the future of mathematics, and describes digitizing his university curriculum in Lean with undergraduates, plus the cultural challenges.

Physicist Carlo Rovelli gives a public lecture at the Royal Institution on how our understanding of time has changed, from Boltzmann and Einstein to quantum theory and loop quantum gravity. He blends physics, philosophy and art to argue that time is stranger than everyday intuition suggests.

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.

Leonard Susskind's Santa Fe Institute talk on the arrow of time: why the past differs from the future when physics equations are time-symmetric. He covers entropy, cosmology and Boltzmann brains.

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.

Short British Pathe newsreel footage of the 1940 collapse of the Tacoma Narrows Bridge as it twisted and swayed in the wind. The only casualty was a dog left in a stalled car.

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.

A demo of a raycasting 3D engine built entirely from in-game mechanisms in vanilla Factorio 0.17. It renders simple 3D scenes, producing a new frame every 45 game ticks, with the video sped up to compensate for low UPS.

Andrej Karpathy's CVPR 2021 presentation on Tesla's Autopilot, covering its vision-based approach, sensor choices and the scale of Tesla's deep learning compute cluster. This upload is a lower-quality copy of the talk.

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.

The first video of 3Blue1Brown's Essence of Calculus series, which builds toward integrals, derivatives, and the fundamental theorem of calculus from a simple geometry question. It aims to make viewers feel they could have invented calculus themselves.

Philip Wadler's Strange Loop talk on Propositions as Types, the link between logic and computation (the Curry-Howard correspondence). He traces its history through Church, Godel and Turing and shows how it shaped theorem provers and programming languages.

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.

The original trailer for Threads, the 1984 British TV film depicting the aftermath of a nuclear attack on Sheffield. The trailer hints at the film's bleak tone.

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.

A 36C3 talk by Bunnie Huang arguing that open source is necessary but not sufficient for trustworthy hardware, because verifying hardware is destructive and so creates a time-of-check/time-of-use gap. It surveys supply chain security and classes of hardware attacks, and presents the Betrusted approach to narrowing that gap.

Technology Connections experiments with filtering white and colored LEDs to make holiday lights look less garish. He explains why narrowband LED strings look harsh compared with incandescent bulbs.

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.

José Valim's ElixirConf US 2023 closing keynote on the foundations of the Elixir type system, covering set-theoretic types and gradual typing with strong arrows.

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.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

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.