hash table

Technology Connections explains why single-hose portable air conditioners are inefficient and often a poor choice compared with window units. It details how the single hose pulls in warm outside air and wastes energy.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

Rune Skovbo Johansen explains Surface-Stable Fractal Dithering, a technique he invented and released as open source. It makes dithering stick to 3D surfaces and covers the experiments and shortcomings along the way, inspired by Return of the Obra Dinn.

A step-by-step animated explanation of how SHA-256 works, from padding and message schedule to the compression function and final hash, with source code for the animations.

Kaze Emanuar searches for the best sine approximation for the Nintendo 64, comparing the lookup tables in Mario 64 and Ocarina of Time with polynomial alternatives. It walks through numerics and 3rd, 4th and 5th order approximations.

A What I've Learned video arguing that industrial seed and vegetable oils have displaced saturated fats and harmed health. It covers the history of vegetable oils, the American Heart Association's role, and rising consumption.

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

3Blue1Brown illustrates how enormous the 256-bit search space is, showing how infeasible it is to find a hash or key by guessing and checking.

Yosh trains a reinforcement learning agent to drive Trackmania until he can no longer beat it. The video explains how the training works and the design choices involved.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.

Kurzgesagt explores the idea that life might have arisen shortly after the Big Bang, when the whole universe was warm enough to be habitable. It discusses what that would mean for the origin and spread of life.

Reducible's visual walkthrough of the Fast Fourier Transform, motivated by polynomial multiplication. It shows how the FFT's key ideas can be discovered by asking the right questions.

CGP Grey compares airplane boarding methods, based on an arXiv paper, and shows why the intuitive back-to-front approach is slow while random or outside-in boarding does better.

Tom Scott-style absurdist tour by Tom7 of SIGBOVIK chess projects: a tournament of 30 weird chess algorithms used to rate a color- and piece-blind chess program. Topics include mirrors, arithmetic encoding, perverted game tree search and a diluted Stockfish.

Veritasium tells the story of the Fast Fourier Transform, from its use in detecting nuclear tests to Cold War politics, and how it could have changed the arms race. It includes a short, intuitive explanation of what the Fourier transform does.

Martin Donald explains the Wave Function Collapse algorithm using Sudoku-like constraint solving and shows how he implemented it with Blender and Godot. It links demos and reference articles.

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 walkthrough of the Quake III fast inverse square root, explaining where the constant 0x5f3759df comes from. It covers IEEE 754 floats, the bit hack that approximates a logarithm, and a Newton's method refinement.

2swap explains how he solved the Klotski sliding-block puzzle by mapping its full state space as a graph and visualizing it. The video includes footage of the Guinness world-record solve and links to an interactive graph.

AlphaPhoenix uses Monte Carlo simulation and annealing-style methods to draw North Carolina congressional district maps, both gerrymandered and fair. He focuses on the fascinating computational problem rather than the politics.

Numberphile with Daniel Erman on the Josephus problem, where people in a circle are eliminated in turn. It shows how the survivor's position follows a neat pattern tied to powers of two and binary.

3Blue1Brown uses Wordle as an excuse to teach information theory and entropy, building a solver that picks guesses by expected information and incorporating word frequencies.

Matt Parker follows the community effort to speed up his slow Wordle-solving code, which ended up running hundreds of millions of times faster. He walks through the techniques contributors used.

A short CGP Grey bonus video explaining the shortest-splitline algorithm, which draws electoral districts by repeatedly splitting a state along its shortest dividing line while balancing population. It is offered as a neutral, algorithmic fix for gerrymandering.

Veritasium explains why the one-way speed of light has never been measured, only the round-trip speed, since measuring it requires synchronized clocks that assume the answer. It explores the implications for relativity.

Tom Scott explains for Computerphile why electronic voting is a bad idea, arguing that paper ballots are transparent, auditable and hard to tamper with at scale. He covers why moving voting to phones, tablets or computers undermines trust and verifiability.

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

Adam Ragusea examines whether olive oil is unsafe for high-heat cooking and whether it tastes bad when heated. He cites studies showing it is among the most stable cooking oils and that smoke-point worries are overblown.

Numberphile's Ben Sparks shows why the golden ratio is the most irrational number, using seeds, continued fractions and rational approximations. He also explains why plants use it for spacing leaves and seeds.

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.

Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.

A PBS Space Time episode asking whether Venus would be a better colonization target than Mars. It covers Venus's habitable altitudes, floating balloon habitats, and the term surfacism.

A Wendover Productions explainer on how China built the world's largest high-speed rail network so quickly and why its rail strategy differs from America's. It covers politics, social benefits and the economics of unprofitable lines.

Veritasium explores why the number 37 turns up so often, drawing on Tom Magliery's collection of 37 sightings and a poll of about 200,000 people asked to pick a random number. It covers how humans choose numbers and why 37 stands out.

Curious Droid asks what traces human civilization would leave in the geological record 65 million years from now. It considers how thin the fossil record of humanity might be.

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.

Not Just Bikes explains why upright Dutch-style bicycles are comfortable and practical, and why they are rare outside the Netherlands.

Tom Scott explains how decades of deep coal mining sank parts of Germany's Ruhr Valley and changed its drainage. Pumps run by Emschergenossenschaft must now work permanently to keep towns and cities from flooding.

Numberphile's James Grime makes the case for base 12 (dozenal) over base 10, showing how twelve's many divisors make arithmetic and everyday fractions easier.

PBS Space Time examines the Silurian hypothesis, the idea that an industrial civilization could have existed on Earth before humans. It looks at what traces such a civilization might leave in the geological record.