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In briefA 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.
In briefA feature-length Defunctland documentary on the history of Disney's FastPass and FastPass+ expedited queue systems. It covers how the systems evolved and how they were designed, with simulation of their effects on park lines.
In brief3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.
In briefTom Scott explains for Computerphile how Unicode and UTF-8 grew out of messy older character encodings to become the web's standard. It covers why the design works and how it handles worldwide text.
In briefThe first video in a 55-part series by Michel van Biezen that introduces the Kalman filter and builds from the rationale through algebraic examples to the full matrix treatment. The videos are short, blackboard-style lectures.
In briefThe opening lecture of Steve Brunton's Control Bootcamp, covering the kinds of control and why closed-loop feedback matters. It starts a series that follows the control chapter of the Brunton and Kutz data-driven science book.
In briefVsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.
In briefA recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.
In briefAn older 3Blue1Brown video on why topology matters, built around the inscribed rectangle problem. It walks through how tori and Mobius strips appear in the solution. The channel later replaced it with an updated version.
In briefTom Stuart's Ruby Manor 3 talk builds FizzBuzz using nothing but Ruby lambdas, working through Church encodings of numbers, booleans and data structures. It is a hands-on introduction to lambda calculus.
In briefDavid Beazley's PyCon 2019 tutorial derives the lambda calculus from the ground up in Python, using only single-argument functions. He builds booleans, numerals and more with no other language features.
In briefLeslie Lamport argues that programmers, like architects, should write rigorous specifications before coding, especially for concurrent and distributed systems. The talk introduces the case for writing specs (the TLA+ mindset) as a way of thinking above the code.
In briefAn animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.
In briefLee Byron of Facebook explains how persistent immutable data structures work and how to use them in React apps with Immutable.js. He covers memoization benefits and avoiding coupling through shared mutable state.
In briefTom Wildenhain's guest lecture for CMU's Esoteric Programming Languages course shows that PowerPoint transitions and slides are Turing complete without macros, building up to a mind-bending fractal ending.
In brief3Blue1Brown introduces Fourier series, from the heat equation to drawing arbitrary shapes with rotating circles. It builds a visual intuition for decomposing functions into sine waves.
In briefDavid MacKay's 2007 Google Tech Talk presents Dasher, a text-entry system driven by continuous gestures and a language model, reaching about 35 words per minute with one finger and 25 hands-free. It explains the information-theory reasoning behind the design.
In briefJay Parlar's Strange Loop talk shows how model checkers such as Alloy can find complex bugs in a system's design without running or reading any code. He walks through modeling architectures and checking every possible sequence of operations, including a real security bug and a UI feature-interaction bug.
In briefjan 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.
In briefThe first lecture of Francis Su's Harvey Mudd real analysis course, covering the construction of the rational numbers. It begins a full lecture series that follows a standard analysis text.
In briefNumberphile interviews cryptographer Ron Rivest about end-to-end verifiable voting. He explains how homomorphic encryption and receipts let a voter confirm their ballot was counted without being able to prove how they voted to anyone else.
In briefNumberphile'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.
In briefMinutePhysics, 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.
In brief3Blue1Brown presents the Triangle of Power, an alternate notation that unifies powers, logarithms and roots in a single triangular symbol. The video shows how the inverse operations relate and how the notation could help.
