formal methods

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.

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

Veritasium shows how Hilbert's infinite hotel can still run out of room, using infinite buses of guests. It explains the surprising answer in a short animated segment.

CGP Grey compares airplane boarding methods, based on an arXiv paper, and shows why the intuitive back-to-front approach is slow while random or outside-in boarding does better.

PBS Space Time explains Roger Penrose's conformal cyclic cosmology, in which the far future of our universe becomes the big bang of the next. It explores what could come after the universe ends.

Tom Scott makes a short descriptivist argument that language keeps changing and that casual internet writing conventions, like lowercase typing and dropped full stops, are legitimate. It is part of his Language Files series, written with Gretchen McCulloch.

Bill Hammack of engineerguy explains how medieval engineers designed stone cathedrals using rules of thumb, with no science, mathematics or literacy. He uses it to define the engineering method.

PBS Space Time explains the Hubble constant tension, in which two precise, independent methods of measuring the universe's expansion rate disagree. It covers why this calls some standard cosmology into question.

A Numberphile video in which physicists Tony Padilla and Ed Copeland show a seemingly astounding result that 1+2+3+4+... equals -1/12. The argument is informal and has drawn criticism for glossing over what the result actually means.

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.

City Beautiful explains how Houston, which has no formal zoning, still shapes land use through deed restrictions, parking minimums and buffering ordinances.

Two Minute Papers covers a paper on speeding up fluid and smoke simulation with convolutional networks. It contrasts the approach with earlier regression forest methods.