vc dimension

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.

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 Technology Connections video on JVC's LCCS, a display hybrid that cycles a color LCD shutter over a monochrome CRT to produce field-sequential color without dots or stripes. It builds on his earlier videos about analog TV and compatible color.

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.

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.

Technology Connections compares Betamax and VHS picture quality using footage from a 1979 RCA VCR and argues the Beta quality advantage was largely marketing.

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.

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.

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.

Part one of Technology Connections' account of the VHS versus Betamax format war. It argues Sony was caught off guard by JVC's cheaper, more practical VHS system.

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.