geometric intuition

A SIGGRAPH 2019 course on geometric algebra. Charles Gunn gives an intro, then Steven De Keninck gives a programmer-focused course with live examples in ganja.js.

A five-minute preview of 3Blue1Brown's Essence of Linear Algebra series, which uses animation to build geometric intuition for topics from a standard linear algebra course.

An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.

Eric Weinstein's roughly three-hour presentation of Geometric Unity, his proposed theory unifying physics, given as a special episode of The Portal. It includes clarifications at the end.

Philosopher Daniel Dennett visits Google to discuss his book Intuition Pumps and Other Tools for Thinking, describing thought experiments and thinking tools across psychology, biology, computer science and physics.

A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.

The first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals. It begins a series that builds intuition for linear algebra from the basics.

Freya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.

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.

3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.

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.

3Blue1Brown builds intuition for Euler's formula, e^(pi i) = -1, using the core ideas of group theory. It treats exponentiation geometrically as rotation and scaling instead of repeated multiplication.

Richard Hamming's 1995 lecture on n-dimensional space, showing how geometric intuition about spheres and cubes breaks down in high dimensions. It is part of his course on learning to learn.

All six episodes of the 1983 BBC series Fun to Imagine, in which Richard Feynman muses on jiggling atoms, fire, rubber bands, magnets, electricity and more. He explains how to think about nature and why imagination is fun.

Andrej Karpathy's first Neural Networks: Zero to Hero lecture, which builds micrograd, a tiny autograd engine, from scratch in Python. It explains backpropagation and neural network training step by step, assuming only basic Python and some high-school calculus.

Part 1 of a lecture by physicist Albert Bartlett on the exponential function and its consequences for population growth, resource use and energy. It argues that steady growth rates quickly lead to enormous quantities.

The Eames Office's 1977 film Powers of Ten starts at a picnic in Chicago and zooms out by a factor of ten every ten seconds to the edge of the universe. It then zooms inward to a proton in a carbon atom.

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

The first part of Welch Labs' series on imaginary numbers, presenting them as the natural extension of the number line into two dimensions. It covers the history and the math with strong visuals.

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.

3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.

3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space. It is part one of a two-part series with an interactive companion site.

Cody's Lab builds a 200-billionth-scale model to show how far away the nearest stars are, using parallax and light speed. A short astronomy explainer on interstellar distances.

3Blue1Brown 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.

The 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.

Veritasium's explainer on entropy, presented as one of physics' most important and least understood concepts. It uses examples such as heat engines and the sun's energy flowing through the Earth.

Guy Steele presents a small geometric problem and compares four computational approaches: a classic sequential solution and three parallel-friendly ones. Each is illustrated pictorially and with working code, weighing total work against time to solution.

A short demo of a walking droplet on a vibrating silicone oil bath passing through a double slit and producing interference, a macro-scale analogue of pilot-wave behavior.

Matt Parker gives a hands-on Royal Institution talk on how four-dimensional shapes appear in a 3D world, with props like straw frames, Mobius strips and a knitted hat. It is a playful general-audience tour of the fourth dimension.

Sasha Rush surveys linear RNNs and state space models as replacements for attention in transformer-style models, in a talk for MLSys. It covers the foundational preliminaries and predates Mamba.

Jerobeam Fenderson shows how to draw a mushroom on an oscilloscope in XY mode using stereo audio, then animates it by modulating with a larger wave. Pd and Max4Live patches are provided.

Tsoding live-codes a JSON parser from scratch in Haskell in about 111 lines, using only the standard library. It is an edited Twitch stream that explains the intuition behind parser combinators, functors, applicatives and monads.

A university lecture from CS480/680 by Pascal Poupart on attention mechanisms and transformer networks, worked through on a chalkboard.

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.

PBS Infinite Series explains how Shor's algorithm lets a quantum computer break RSA encryption, building on earlier episodes about cryptography and the math of quantum computers. It works through the idea step by step.

A Sesame Street animation from 1979 with music composed by Philip Glass, showing geometric circle patterns.

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.

mitxela shows his KiCad plugin that rounds PCB tracks to give circuit boards organic, melted-looking layouts instead of rigid geometric ones.

Matt Parker on Numberphile explains the strange properties of spheres in higher dimensions, such as how they poke out of their bounding boxes. It uses Pythagoras to build intuition for 4D and beyond.

3Blue1Brown's chapter 4 on deep learning gives a more formal, symbol-based account of backpropagation calculus, connecting the intuition from the previous chapter to the math found in textbooks and code.