complexity

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.

A long Lex Fridman interview with Stephen Wolfram on complexity, cellular automata, computational irreducibility and the Wolfram Physics Project.

Leonard Susskind lectures at Stanford on how gravity and quantum information theory have merged into a new way of thinking about physics. He covers entanglement and complexity, with applications from black holes to strange metals and the foundations of quantum mechanics.

Physicist Geoffrey West speaks at an FQXi conference on time about complexity and scaling laws. He covers how metabolism, growth and lifespan scale across organisms and how the same mathematics applies to cities and companies.

Lex Fridman interviews University of Glasgow chemist Lee Cronin about the origin of life, aliens, complexity and consciousness. The conversation centers on Cronin's assembly theory.

Lex Fridman interviews Donald Knuth about algorithms, complexity, The Art of Computer Programming, and his work habits. The conversation covers his approach to verifying algorithms and how he organises his time.

A /noclip interview with Tarn Adams of Bay 12 Games about Dwarf Fortress: where the ASCII simulation came from, how it works, and the plans for its Steam release. It includes his telling of the famous bug in which cats were poisoned by alcohol.

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.

Rich Hickey's Strange Loop 2011 keynote separates 'simple' (not intertwined) from 'easy' (familiar or near at hand) and argues that software complexity comes from complecting things. It offers a vocabulary for judging designs and abstractions.

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.

Kyle Hill of Because Science explains and demonstrates, using real cards, how Magic: The Gathering can be used to build a Turing machine, a computer inside the card game.

Find the Longest Path is a comedic song by Daniel J. Barrett, a Billy Joel parody that describes the NP-hard longest path problem in informal terms.

Jim Weirich's RubyConf 2012 talk derives the Y combinator step by step, live-coding in Ruby lambdas. It builds up an understanding of functional programming and lambda calculus from first principles.

Rich Hickey's Strange Loop 2011 keynote distinguishing 'simple' (not intertwined) from 'easy' (familiar or near at hand). It argues that software complexity comes from complecting things and that we should pick simple constructs.

Meredith Patterson and Sergey Bratus argue that networked software stays insecure because protocols and inputs are too complex to recognize safely. They propose using formal language theory and grammars to build secure, verifiable input handling.

Philip Wadler's Strange Loop talk on Propositions as Types, the link between logic and computation (the Curry-Howard correspondence). He traces its history through Church, Godel and Turing and shows how it shaped theorem provers and programming languages.

Christopher Domas's Derbycon 2015 talk on the M/o/Vfuscator, a compiler that emits only x86 mov instructions, showing mov is Turing complete. It explains how a full machine is built from mov and why the output is a nightmare to reverse engineer.

Rich Hickey's keynote at RailsConf 2012, a close sibling of his 'Simple Made Easy' talk. He distinguishes simple (not intertwined) from easy (familiar), and argues that software complexity comes from complecting things, with Rails-specific examples including large gem collections.

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

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.

A two-minute video of Conway's Game of Life running inside Conway's Game of Life, built from OTCA metapixels and Golly. It zooms smoothly between scales.

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.

Gabriel Lebec's Fullstack Academy talk introduces lambda calculus syntax, the history of mathematical logic, and the essence of functional programming using JavaScript. It also covers combinators, currying and Church encodings.

Scott Meyers' keynote at DConf 2014, drawing on 25 years of C++ experience to offer the D language community a plea about what it should avoid. It centers on the accumulated complexity and pitfalls of C++ as a cautionary tale.

Tom Stuart's Ruby Manor 3 talk builds FizzBuzz using nothing but Ruby lambdas, working through Church encodings of numbers, booleans and data structures. It is a hands-on introduction to lambda calculus.

David Beazley's PyCon 2019 tutorial derives the lambda calculus from the ground up in Python, using only single-argument functions. He builds booleans, numerals and more with no other language features.

Tom Wildenhain's guest lecture for CMU's Esoteric Programming Languages course shows that PowerPoint transitions and slides are Turing complete without macros, building up to a mind-bending fractal ending.

Lex Fridman interviews Stephen Wolfram for about three hours on cellular automata, computation, the Wolfram Physics Project and his career with Mathematica and Wolfram Alpha.

Matt Might's Curry On talk on ending errors in code, both software and the human genome. He covers conservative approximation of the halting problem via static analysis and a computational approach to precision medicine.

A panel with Tony Hoare, Joe Armstrong and Carl Hewitt, hosted by Francesco Cesarini, on the history and future of concurrency. The three creators of CSP, Erlang and the actor model discuss their differing approaches.

Milton Friedman explains why the US tax code is enormously complex and why meaningful reform is unlikely. He argues that politicians profit from the complexity, since tax breaks are products they sell and the code works as a tool of reward and punishment. The clip is about 14 minutes from his lecture series.

The first lecture of Michael Sipser's MIT 18.404J Theory of Computation course, covering course mechanics, finite automata, regular languages and regular expressions. It proves closure of regular languages under union and begins concatenation.

The first lecture of an MIT course on Douglas Hofstadter's Godel, Escher, Bach, covering themes like self-reference, recursion and incompleteness. The full lecture series is on YouTube.

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

A roughly four-and-a-half-hour Lex Fridman podcast conversation with Stephen Wolfram about his Wolfram Physics Project and a fundamental theory of physics, computation, life and the universe.

An excerpt from Richard Dawkins's lecture on Climbing Mount Improbable demonstrating how a complex eye can evolve through incremental steps. It answers the creationist irreducible complexity argument.

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.

Lex Fridman interviews Marcus Hutter of DeepMind about universal artificial intelligence, AIXI, Kolmogorov complexity, Solomonoff induction and the idea of intelligence as compression.

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.

2swap explores lambda calculus using John Tromp's lambda diagrams, with animated beta-reductions, asking what PLUS times PLUS gives. It touches on Church encodings and the equivalence of Turing machines and lambda calculus.