computability

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

A Computerphile video in which Mark Jago of the University of Nottingham explains Turing's halting problem and how it led to the blueprint for the modern computer.

A short SIGBOVIK 2017 presentation by Tom Wildenhain showing that PowerPoint animations are Turing complete, with a working Turing machine built in slides. The talk is delivered deadpan as a serious research result.

An 11-minute animated introduction to P vs. NP and the wider landscape of complexity classes, inspired by the Complexity Zoo wiki. It assumes no background in computer science.

Polylog explains how algorithms can be turned into circuits and encoded as satisfiability problems, which lets you effectively run them backwards. It uses this to motivate breaking RSA, general reductions to SAT, and what P vs NP is really asking.

Tom Murphy's satirical SIGBOVIK 2007 presentation, delivered under a pseudonym, proving that generalized Super Mario Bros. is NP-complete. It is a short, deadpan take on a complexity theory result.

The first video in a series on extremely large numbers, introducing the topic with examples. Later parts go deep into the fast-growing hierarchy.

John Conway talks in a short Numberphile interview about his mixed feelings toward the Game of Life, his most famous invention. He says he is not especially pleased that it overshadowed his other work.

An excerpt from Hal Abelson's opening SICP lecture introducing computer science and contrasting declarative and imperative knowledge. He argues that computer science is not really a science and is more like magic or engineering of ideas.

Pro Magic player Luis Scott-Vargas triggers a mandatory-action infinite loop on Magic Online, and the game stalls in a non-terminating state.

An animated, musical visualization of Conway's Game of Life showing patterns made in the Golly program.