visual math

The American Museum of Natural History's film flies from the Himalayas out through the atmosphere and solar system to the afterglow of the Big Bang, using its Digital Universe Atlas four-dimensional map.

A short animation reconstructing a planet's looping orbit using Ptolemy's epicycles and deferents, with the epicycles tracing out the face of Homer Simpson. It shows how enough circles can reproduce nearly any shape.

A short CSI clip in which characters try to track a killer's IP address by writing a Visual Basic GUI. It is a famous example of absurd TV hacking.

A short Dyalog demonstration building Conway's Game of Life in a single line of APL, step by step. It shows how array operations replace loops.

A segment from Carl Sagan's original Cosmos explaining the fourth spatial dimension through analogy with a two-dimensional world and shadow projection.

The official music video for The Chemical Brothers' Star Guitar, directed by Michel Gondry. Visuals of a passing landscape are synced to elements of the music.

An excerpt from the 1983 BBC series Fun to Imagine in which Richard Feynman describes how he and a mathematician friend counted in their heads in different ways, one verbally and one visually. It shows that people can reach the same goal through quite different mental methods.

Bach's Toccata and Fugue in D minor on organ, shown with a Music Animation Machine bar-graph score instead of traditional notation.

The first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.

Hans Rosling uses the Gapminder animated-data tool to debunk myths about world development, with sportscaster-like energy. It shows trends in health, income and child survival across countries.

In this TED talk, Hans Rosling uses animated statistics to debunk myths about the developing world, showing how health and income have improved across countries.

Stargate Studios' 2009 virtual backlot reel shows before-and-after shots in which green screen and compositing replace locations in ordinary TV dramas and comedies. It shows how much of a seemingly real show is computer generated.

A 1983 behind-the-scenes film about making the HBO 'Feature Presentation' starship logo sequence. It shows the handcrafted miniature city, motion-control cameras and practical effects.

Alan Kay demonstrates GRaIL, a graphical input language system from around 1968 in which hand-drawn strokes become boxes, connections and dataflow-style programs.

A short video built around an animation of the roughly 10,000 galaxies in the Hubble Ultra Deep Field, placed at their measured redshift distances. It gives a brief history of deep field images and ends with a 3D fly-through.

Neuroscientist Beau Lotto runs the audience through color and pattern illusions to show that perception is shaped by context and evolutionary history rather than being a direct readout of the world. The talk is playful and hands-on, and it argues that the brain interprets ambiguous signals.

The first lecture of Andrew Ng's Stanford CS229 Machine Learning course, giving an overview of the course. It introduces supervised and unsupervised learning, learning theory and reinforcement learning.

A short clip from Carl Sagan's Cosmos in which he explains how Eratosthenes measured the circumference of the Earth using shadows in two Egyptian cities. It is a clear, visual account of an ancient scientific feat.

Debris by Farbrausch, the winner of the Breakpoint 2007 demo competition. All of its 3D visuals, textures and music come from a single 177 KB executable.

Steve Jobs demos NeXTSTEP Release 3, showing the object-oriented development environment and UI that later became the basis of Mac OS X. Midway through he builds a database-backed GUI app with Interface Builder and Enterprise Objects Framework with almost no code.

The first lecture of Leonard Susskind's Stanford Continuing Studies course on modern physics, beginning with classical mechanics. It is the start of a six-quarter sequence on the theoretical foundations of physics.

Masagin is a realtime demoscene production by Farbrausch and Neuro with music by paniq, using animated recursive SVG graphics made in Inkscape. It is a psychedelic, nested-dials audiovisual piece.

Geoff Cumming uses a simulation to show how wildly the p value varies from one replication to the next because of sampling variability. He argues for estimation and confidence intervals over null hypothesis significance testing.

In a TED talk, behavioral economist Dan Ariely uses visual illusions and his research to show that people are less rational in their decisions than they think. He covers defaults, such as organ donation rates, and how choice framing steers decisions.

A score-following video of Iannis Xenakis's 1950s orchestral piece Metastasis, showing his graphic, mathematically derived notation as the music plays. It is a landmark of post-war modernist composition.

Google's 2009 'Search Stories' ad, shown in the Super Bowl, tells the story of an American who falls in love in Paris entirely through search queries.

A short Flash animation made in 2001 by an IBM employee, set to the company's old 'Ever Onward' rally song, with imagery from IBM history.

Second half of a demonstration of the 1982 Xerox Star user interface. It shows how the Star differed from the later Lisa and Mac interfaces, with strengths in networking and printing and little direct manipulation.

A scene from the film Disclosure showing its virtual reality interface, including a 3D file system visualizer.

A short animation illustrating the proposed nanofactory concept, where nanomachines assemble atomically precise parts into larger products. It depicts how such a system might build macroscopic goods from raw materials and energy.