complex numbers

Joseph Tainter lectures at a 2010 sustainability conference on why complex societies such as Rome collapse. His thesis is that rising complexity brings diminishing returns until societies cannot afford to maintain it.

The first lecture of Francis Su's Harvey Mudd real analysis course, covering the construction of the rational numbers. It begins a full lecture series that follows a standard analysis text.

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.

A 3Blue1Brown live lockdown math episode asking what Euler's formula e^(pi i) is actually saying. It builds intuition through exponentials, rotation and vectors landing on the unit circle.

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.

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.

Brian Will critiques object-oriented programming and rewrites a roughly 3800-line OO program in a procedural style, cutting code and complexity. It is part of a series of OOP critiques.

Robert Sapolsky's Stanford lecture on chaos and reductionism, which he calls one of the hardest of the course. It examines the limits of breaking systems into parts to understand them and introduces chaotic systems.

The first lecture of MIT's 6.001 (SICP) with Abelson and Sussman, giving an overview of the course and an introduction to Lisp. It argues that computer science is about managing complexity and abstraction, not computers.

The first lecture in Bartosz Milewski's category theory series for programmers. It covers the motivation and philosophy behind category theory and why composition matters for handling complexity.

Donald Knuth's 2017 Christmas Tree Lecture at Stanford about a combinatorial geometry problem whose computed numbers matched a striking formula. He tells the story of the conjecture and its sequel.

Utah State plant scientist Bruce Bugbee presents his analysis of the energy and environmental costs of vertical and indoor farming. He argues artificial lighting cannot compete with sunlight in fields or greenhouses.

Erik Demaine's MIT 6.006 lecture introducing dynamic programming through Fibonacci numbers and shortest paths. It covers memoization, subproblems and optimal substructure.

Associate Professor Simon Michaux presents estimates of the metals needed to build one generation of renewable technology to replace fossil fuels. He argues current production and reserves fall far short, with copper a key shortfall.

Nick Lane's Royal Institution lecture on the origin of life and why it is the way it is. It draws on his book The Vital Question and the alkaline hydrothermal vent theory of abiogenesis.