higher dimensions

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.

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 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.

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

Simon Peyton Jones presents linear types for Haskell, showing how practical linearity can fit into a higher-order polymorphic language. The talk covers motivations such as resource handling and relates the ideas to Rust.

Dan Worrall explains when higher sample rates help in recording and mixing, and when they do not. He goes into oversampling versus higher sample rates, and aliasing in distortion plugins.

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 1983 BBC interview in which Richard Feynman is asked how magnets work and explains why 'why' questions are hard to answer in everyday terms. He reflects on what counts as an explanation and the limits of analogy.

John Scholes builds a depth-first tree-search operator step by step in a Dyalog APL session. It covers higher-order functions and runs the search on the N-Queens problem.

The Kodak Carousel pitch scene from the Mad Men season finale, in which Don Draper sells nostalgia through a slide projector. It runs about three minutes.

Moral philosopher James Flynn explains the Flynn effect, the steady rise of IQ scores across the 20th century. He argues the shift reflects a move toward abstract, hypothetical thinking as cognitively demanding professions grew.

PolyMatter examines how universities, especially in the West, depend on foreign and Chinese student tuition and how rankings and incentives distort institutions around that money.

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.

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.

Linus Tech Tips tests whether higher frame rates and refresh rates improve gaming performance, using Shroud and other players on aim and reaction tests at 60, 144 and 240Hz. The video is sponsored by Nvidia.

A short documentary on the 2015 Yale Halloween costume controversy and the confrontation with Nicholas Christakis. Filmmaker Rob Montz investigates campus free speech and the state of the university afterward.

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.

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.

Hans Rosling's TEDxSummit talk asks whether some religions have higher birth rates and how that affects population growth. He charts data across time and religions and reaches a surprising conclusion about fertility.

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.

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.

Peter Rizun and Andrew Stone present results of tests running 1 GB blocks on a Bitcoin test network at Scaling Bitcoin Stanford. The talk argues for big-block scaling and discusses its consequences.

Colin Smith introduces Structure and Interpretation of Classical Mechanics and his Clojure port, sicmutils. He shows how higher-order functions and a symbolic algebra system can represent Lagrangian mechanics.

A clip of Jordan Peterson arguing that IQ is a strong predictor of job market success and that more complex jobs demand higher cognitive ability. He discusses what this means for people left behind.

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.

A short FoundMyFitness explainer on the trade-off between growth hormone/IGF-1 and longevity. Higher IGF-1 helps muscle and cognition, while lower levels are linked to longer lifespan and stress resistance.

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.

Billionaire Nick Hanauer warns fellow wealthy people in a TED talk that growing inequality could lead to social upheaval like pre-revolutionary France. He argues a higher minimum wage would grow the middle class and prosperity.

A five-minute demonstration of the Shepard tone, an audio illusion made from octave-separated tones that makes pitch seem to rise endlessly without ever getting higher.

A one-minute clip of Sony's keynote at E3 1995, where Steve Race takes the stage, announces the PlayStation's $299 price and leaves. It followed Sega's Saturn announcement at a higher price.

The final scene of the 1983 film WarGames, in which the WOPR computer runs through nuclear war scenarios and concludes that the only winning move is not to play. It is a six-minute clip uploaded in higher quality than earlier copies.