The Azimuth Project
Azimuth blog overview

The Azimuth Blog is where the Azimuth Project publicizes its work.

This page is an (incomplete) index of articles on the Azimuth Blog. The sections are for series, or other topic categories, and are listed alphabetically. For other articles, there is a section called Authors, with one subsection per author.

Contents

To Do

Need to add all articles from Feb 2012 up to the present.

Azimuth news

Game theory

These are notes for a course taught by John Baez in the winter quarter of 2013:

  • Part 1 - different kinds of games
  • Part 2 - two-player normal form games
  • Part 3 - Nash equilibria for pure strategies
  • Part 4 - strict dominance for pure strategies
  • Part 5 - homework problems (and cute pictures of dogs)
  • Part 6 - the assumption of mutual rationality
  • Part 7 - probabilities
  • Part 8 - independence
  • Part 9 - coin flips and binomial coefficients
  • Part 10 - cards and binomial coefficients
  • Part 11 - expected values, risk tolerance and risk aversion
  • Part 12 - Nash equilibria for mixed strategies: definitions
  • Part 13 - Nash equilibria for mixed strategies: an example
  • Part 14 - the first test, and answers to the problems
  • Part 15 - maximin strategies for zero-sum games
  • Part 16 - security values and maximin strategies
  • Part 17 - Nash equilibrium implies maximin
  • Part 18 - maximin implies Nash equilibrium... sometimes
  • Part 19 - maximin always implies Nash equilibrium, and Nash equilibria always exist
  • Part 20 - von Neumann's maximin theorem, and conclusion

Mathematics of the environment

These are notes for a course taught by John Baez in the fall quarter of 2012:

  • Part 1 - The mathematics of planet Earth.
  • Part 2 - Simple estimates of the Earth's temperature.
  • Part 3 - The greenhouse effect.
  • Part 4 - History of the Earth's climate.
  • Part 5 - A model showing bistability of the Earth's climate due to the ice albedo effect: statics.
  • Part 6 - A model showing bistability of the Earth's climate due to the ice albedo effect: dynamics.
  • Part 7 - Stochastic differential equations and stochastic resonance.
  • Part 8 - A stochastic energy balance model and Milankovitch cycles.
  • Part 9 - Changes in insolation due to changes in the eccentricity of the Earth's orbit.
  • Part 10 - Didier Paillard's model of the glacial cycles.

Information geometry

By John Baez. The web version is a bit more nicely formatted, but the blog version has comments, and of course you can post your own comments there:

  • Part 1 - the Fisher information metric from statistical mechanics. (web version)

  • Part 2 - connecting the statistical mechanics approach to the usual definition of the Fisher information metric. (web version)

  • Part 3 - the Fisher information metric on any manifold equipped with a map to the mixed states of some system. (web version)

  • Part 4 - the Fisher information metric as the real part of a complex-valued quantity whose imaginary part measures quantum uncertainty. (web version)

  • Part 5 - an example: the harmonic oscillator in a heat bath. (web version)

  • Part 6 - relative entropy. (web version)

  • Part 7 - the Fisher information metric as the matrix of second derivatives of relative entropy. (web version)

Part 8- information geometry and evolution: how natural selection resembles Bayesian inference, and how it’s related to relative entropy. (website version)

Part 9 - information geometry and evolution: the replicator equation and the decline of entropy as a successful species takes over. (website version)

Part 10 - information geometry and evoluton: how entropy changes under the replicator equation. (website version)

Part 11 - information geometry and evolution: the decline of relative information. (website version)

Part 12 - information geometry and evolution: an introduction to evolutionary game theory. (website version)

Part 13 - information geometry and evolution: the decline of relative information as a population approaches an evolutionarily stable state. (website version)

Networks and population biology

By John Baez

Network theory

Parts 2 to 24 of this series are also available as a book by John Baez and Jacob Biamonte, and as nicely formatted webpages:

  • Part 1 - toward a general theory of networks.
  • Part 2 - stochastic Petri nets; the master equation versus the rate equation.
  • Part 3 - the rate equation of a stochastic Petri net, and applications to chemistry and infectious disease.
  • Part 4 - the master equation of a stochastic Petri net, and analogies to quantum field theory.
  • Part 5 - the stochastic Petri net for a Poisson process; analogies between quantum theory and probability theory.
  • Part 6 - the master equation in terms of annihilation and creation operators.
  • Part 7 - a stochastic Petri net from population biology whose rate equation is the logistic equation; an equilibrium solution of the corresponding master equation.
  • Part 8 - the rate equation and master equation of a stochastic Petri net; the role of Feynman diagrams.
  • Part 9 - the Anderson–Craciun–Kurtz theorem, which gives equilibrium solutions of the master equation from complex balanced equilibrium solutions of the rate equation; coherent states.
  • Part 10 - an example of the Anderson-Craciun-Kurtz theorem.
  • Part 11 - a stochastic version of Noether's theorem.
  • Part 12 - comparing quantum mechanics and stochastic mechanics.
  • Part 13 - comparing the quantum and stochastic versions of Noether's theorem.
  • Part 14 - an example: chemistry and the Desargues graph. There's also a special post on answers to the puzzle for this part.
  • Part 15 - Markov processes and quantum processes coming from graph Laplacians, illustrated using the Desargues graph.
  • Part 16 - Dirichlet operators and electrical circuits made of resistors.
  • Part 17 - reaction networks versus Petri nets; the deficiency zero theorem.
  • Part 18 - an example of the deficiency zero theorem: a diatomic gas.
  • Part 19 - an example of Noether's theorem and the Anderson–Craciun–Kurtz theorem: a diatomic gas.
  • Part 20 - Dirichlet operators and the Perron–Frobenius theorem.
  • Part 21 - warmup for the proof of the deficiency zero theorem: the concept of deficiency.
  • Part 22 - warmup for the proof of the deficiency zero theorem: reformulating the rate equation.
  • Part 23 - warmup for the proof of the deficiency zero theorem: finding the equilibria of a Markov process, and describing its Hamiltonian in a slick way.
  • Part 24 - proof of the deficiency zero theorem.
  • Part 25 - Petri nets, logic, and computation: the reachability problem for Petri nets.

Petri net programming

By David Tanzer

Stabilization wedges

By John Baez

This Week’s Finds

By John Baez

This Week’s Finds in mathematical physics (week 300)

This Week’s Finds (week 301)

This Week’s Finds (week 302)

This Week’s Finds (week 303)

This Week’s Finds (week 304)

This Week’s Finds (week 305)

This Week’s Finds (week 306)

This Week’s Finds (week 307)

This Week’s Finds (week 308)

This Week’s Finds (week 309)

This Week’s Finds (week 310)

This Week’s Finds (week 311)

This Week’s Finds (week 312)

This Week’s Finds (week 313)

This Week’s Finds (week 314)

This Week’s Finds (week 315)

This Week’s Finds (week 316)

This Week’s Finds (week 317)

This Week’s Finds (week 318)

Authors

Joint authors

Babylon and the square root of 2, John Baez and Richard Elwes, Dec 2011

John Baez

The faculty of 1000, Jan 2012

A quantum Hammersley-Clifford theorem, Jan 2012

How to cut carbon emissions and save money, Jan 2012

Ban Elsevier, Jan 2012

I, Robot, Jan 2012

Classical mechanics versus thermodynamics (part 2), Jan 2012

Classical mechanics versus thermodynamics (part 2), Jan 2012

Going on strike, Jan 2012

The beauty of roots (part 2), Jan 2012

Quantropy (part 1), Dec 2011

Melting permafrost (part 3), Dec 2011

Melting permafrost (part 2), Dec 2011

What’s up with solar power, Dec 2011

The beauty of roots, Dec 2011

The global amphibian crisis, Dec 2011

Mathematics 1001, Dec 2011

Probabilities versus amplitudes, Dec 2011

A bet concerning neutrinos (part 4), Dec 2011

Quantum theory talks in Asia and Australia, Nov 2011

Liquid light, Nov 2011

New climate sensitivity estimate, Nov 2011

Lynn Margulis, Nov 2011

Wild cats of Sumatra, Nov 2011

Eskimo words for snow, Nov 2011

Azimuth on Google Plus (part 4), Nov 2011

Apocalypse, retreat or revolution?, Nov 2011

Major transitions in evolution, Oct 2011

The complexity barrier, Oct 2011

Buycotts, Oct 2011

A math puzzle coming from chemistry, Oct 2011

Bioremediation and ecological restoration job, Oct 2011

A bet concerning neutrinos (part 3), Oct 2011

The decline effect, Oct 2011

The Science Code Manifesto, Oct 2011

Chaitin’s theorem and the surprise examination paradox, Oct 2011

A bet concerning neutrinos (part 2), Oct 2011

The network of global corporate control, Oct 2011

The Lifeboat foundation, Apr 2011

A bet concerning neutrinos, Sep 2011

American oil boom, Sep 2011

The Malay archipelago, Oct 2011

NSF funding for research in Asia, Sep 2011

Climate reality project, Sep 2011

Fool’s gold, Sep 2011

Mathematics of planet earth at Banff, Sep 2011

US weather disasters in 2011, Sep 2011

Melting permafrost, Sep 2011

Bayesian computations of expected utility, Aug 2011

Environmental news from China, Aug 2011

Rationality in humans and monkeys, Jul 2011

Heat wave in the USA, Jul 2011

Australian carbon tax, Jul 2011

Food price spike, Jul 2011

Operads and the tree of life, Jul 2011

Mathematics and the environment in Iran, Jun 2011

Calculating catastrophe, Jun 2011

How sea level rise will affect New York, Jun 2011

Earth system research for global sustainability, Jun 2011

A characterization of entropy, Jun 2011

The Stockholm memorandum, Jun 2011

Is life improbable?, May 2011

The one best thing everyone could do to slow down climate change, May 2011

Outsourcing carbon emissions, May 2011

The melting of Greenland and West Antartica, May 2011

Conferences on math and climate change, May 2011

A question about graduate schools, May 2011

Moore’s law for solar power?, May 2011

Time to wake up?, May 2011

Equinox summit, Apr 2011

What to do?, Apr 2011

The genetic code, Apr 2011

The threefold way, Apr 2011

Chemistry puzzle, Apr 2011

The environment and sustainability institute, Mar 2011

Energy and the environment: what mathematicians can do (part 2), Mar 2011

Mathematics of planet earth, Mar 2011

Energy and the environment: what mathematicians can do (part 1), Mar 2011

Tsunami, Mar 2011

Summer program on climate software, Mar 2011

Guess who wrote this?, Mar 2011

Child Earth, Feb 2011

Rényi entropy and free energy, Feb 2011

Carbon dioxide puzzles, Feb 2011

Petri nets, Jan 2011

Postdoc positions in climate mathematics, Jan 2011

Quantum information processing 2011 (Day 2), Jan 2011

Quantum information processing 2011 (Day 1), Jan 2011

Mathematical economics, Jan 2011

Algorithmic thermodynamics (part 2), Jan 2011

Welcome to the greenhouse, Jan 2011

Adapting to a hotter earth, Dec 2010

Carbon trading in California, Dec 2010

Cancún, Dec 2010

Quantum foundations mailing list, Dec 2010

Archimede: concentrated solar power, Dec 2010

Solèr’s theorem, Dec 2010

State observable duality (part 1), Nov 2010

Carbon emissions in 2009, Nov 2010

Fossil fuel subsidies, Nov 2010

The Azolla event, Nov 2010

Out future, Nov 2010

The 2010 Singapore energy lecture, Nov 2010

The art of math, Oct 2010

Entropy and uncertainty, Oct 2010

Energy return on energy invested, Oct 2010

Algorithmic thermodynamics, Oct 2010

A geometry puzzle, Oct 2010

Power density, Oct 2010

Recommended reading, Oct 2010

Ashtekar on black hole evaporation, Sep 2010

Jacob Biamonte on tensor networks, Sep 2010

Quantum entanglement from feedback control, Sep 2010

Math and the environment in Montreal, Sep 2010

The Siberian tiger, Sep 2010

Quantum dots in cavities, Sep 2010

Sustainability in Palo Alto, Sep 2010

How long would Uranium last?, Sep 2010

Cap and trade in China, Aug 2010

Björn Lomborg’s new book, Aug 2010

Probability puzzles, Aug 2010

Control of cold molecular ions, Aug 2010

Dying coral reefs, Aug 2010

Quantum control theory, Aug 2010

Trends in quantum information processing, Aug 2010

The geometry of quantum phase transitions, Aug 2010

Quantum phase measurement via flux qubits, Aug 2010

Curriki, Aug 2010

Thermodynamics and Wick rotation, Aug 2010

Introduction to climate change, Aug 2010

How hot is too hot?, Jul 2010

High temperature superconductivity, Jul 2010

Elizabeth Kolbert on overfishing, Jul 2010

Climate stabilization targets, Jul 2010

Bose statistics and classical fields, Jul 2010

Turning renewable energy into fuels, Jul 2010

Breaking temperature records, Jul 2010

Quantum steganography, Jul 2010

News about the Younger Dryas, Jul 2010

Tim van Beek

Putting the Earth in a box, June 2011

A quantum of warmth, July 2011

Eddy who?, Aug 2011

Your model is verified, but not valid! Huh?, Jun 2011

Eric Downes

Crooks’ fluctuation theorem, Apr 2011

Curtis Faith

Seven rules for risk and uncertainty, Jan 2011

Curtis Faith on the Azimuth Project, Jan 2011

Tom Leinster

Measuring biodiversity, Nov 2011

Cameron Smith

Hierarchical organization and biological evolution (part 1), Aug 2011

Mike Stay

Extremal principles in classical, statistical and quantum mechanics, Jan 2012