fourth dimension

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.

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

A short explainer showing what walking through walls would look like with movement in a fourth spatial dimension, using the 4D puzzle game Miegakure.

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.

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.

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.

A PBS Space Time episode on how gravitational wave observations of a neutron star merger, GW170817, can limit the number of spacetime dimensions. It is based on a 2018 paper.

Numberphile talks with Grant Sanderson of 3Blue1Brown about a darts puzzle with a shrinking bullseye. Solving it takes the volumes of high-dimensional spheres, and the answer turns up Euler's number.

A Google Tech Talk by Laurens van der Maaten, co-creator of t-SNE, on visualizing high-dimensional data by mapping it to two dimensions. It explains how the technique works and how it compares with other visualization approaches.

3Blue1Brown explains space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations. It touches on mapping between dimensions and sensory ideas.

Michael Betancourt's lecture at MLSS Iceland 2014 on efficient Bayesian inference with Hamiltonian Monte Carlo. It covers MCMC concepts and motivation and the problems of sampling in high-dimensional distributions.

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

3Blue1Brown explains fractal dimension and shows why many fractals are not strictly self-similar. Self-similarity turns out to be a special case of the broader idea of fractional dimension.

A short video advising how to handle a police stop by politely refusing searches and not answering questions, citing Fourth and Fifth Amendment rights.

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.

The first lecture of Caltech's CS 156 Machine Learning course by Yaser Abu-Mostafa, introducing the learning problem and supervised, unsupervised and reinforcement learning. It is one of 18 lectures in the Learning from Data course.

A driver films a police DUI checkpoint on the 4th of July where a drug dog alerts on his car and he is searched without consent, though he broke no laws. He is released without charges after officers learn he was recording.

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.

Ted Nelson demonstrates Xanadu Space, his software for representing hypertext in three-dimensional space with linked, referenced content fragments.

An animated simulation comparing single-winner voting methods such as plurality, instant runoff and STAR. Colored regions show which candidate wins as a randomized electorate shifts across a two-dimensional political space, building on Ka-Ping Yee's earlier diagrams.

Jen Simmons explains the difference between CSS Flexbox and CSS Grid, and when to use each. She makes the case that Grid does not replace Flexbox and most sites use both.

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.

Morten Rand-Hendriksen's WordCamp Europe 2017 talk presents CSS Grid Layout as a native two-dimensional layout system that changes how web pages are structured, including responsive layouts independent of source order. It was given as browsers began shipping support.

A PBS Space Time episode explaining the holographic principle: the idea that our 3+1 dimensional universe may be described by information on a lower-dimensional boundary. It walks through black hole entropy and the AdS/CFT correspondence.

Google's short promo for Project Starline, a booth that shows a life-size, three-dimensional view of the person you are talking to. It presents the technology as a magic window for friends, families and co-workers who are far apart.

Jose Valim introduces Nx, the project bringing numerical computing to Elixir, covering multi-dimensional tensors, automatic differentiation and JIT compilation to CPU and GPU.

Andreas Antonopoulos argues that money has a fourth function beyond store of value, medium of exchange and unit of account, which is as a system of control. He covers the history of money and why it does not flow freely.

Kurzgesagt asks whether advanced civilizations could have existed on Earth in the deep past and left little evidence. It looks at time as a dimension for searching for alien civilizations and the limits of the geological record.