The Azimuth Project
Azimuth Blog

The Azimuth Blog is where the Azimuth Project publicizes its work. You can see it here.

This page is an 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.

The index is up-to-date through 8 Oct 2014. Also see Blog articles in progress.

If you want to write your own blog article, please do! But there are some stylistic and formatting issues to think about. So, please start by reading How to write a blog entry.


Algorithmic thermodynamics

By John Baez

Anasazi America

Azimuth news

Azimuth on Google Plus

The beauty of roots

By John Baez

A bet concerning neutrinos

By John Baez

Classical mechanics versus thermodynamics

By John Baez

El Niño Project

  • Part 1, John Baez, 20 Jun 2014

  • Part 2, John Baez, 24 Jun 2014

  • Part 3, John Baez, 1 Jul 2014

  • Part 4, John Baez, 8 Jul 2014

  • Part 5, John Baez, 12 Jul 2104

  • Part 6, Steven Wenner, 23 Jul 2014

  • Part 7, John Baez, 18 Aug 2014

Energy and the environment: what mathematicians can do

By John Baez

Exploring climate data

  • Part 1, John Baez and Dara O Shayda, 1 Aug 2014

  • Part 2, Blake Pollard, 16 Sep 2014

Fluid flows and infinite dimensional manifolds

By Tim van Beek

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

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. (website version)

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

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

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

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

  • Part 6 - relative entropy. (website version)

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

The mathematics of biodiversity

By John Baez

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.

Mathematics for sustainability

By John Roe

Melting permafrost

By John Baez

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


By John Baez

Quantum network theory

By Tomi Johnson

Relative entropy

By John Baez

Rolling circles and balls

By John Baez

The selected papers network

  • Part 1, by John Baez, Jun 2013

  • Part 2, by John Baez, Jun 2013

  • Part 3, by Christopher Lee, Jul 2013

  • Part 4, by Christopher Lee, Jul 2013

Stabilization wedges

By John Baez

Symmetry and the fourth dimension

By John Baez

Technology for Azimuth

This Week’s Finds

By John Baez

Towards open access to information

By John Baez


Joint authors

Leonard Adleman

John Baez

Tim van Beek

Series: Fluid flows and infinite dimensional manifolds

Ville Bergholm

Jacob Biamonte

Iuval Clejan

Eric Downes

Steve Easterbrook

Curtis Faith

Jan Galkowski

Manoj Gopalkrishnan

Marc Harper

Relative entropy in evolutionary dynamics, 22 January 2014

Arjun Jain

Alastair Jamieson-Lane

Tomi Johnson

Series: Quantum network theory

Tom Leinster

Eugene Lerman

Staffan Liljegren

Todd McKissik

Mike Pollard

John Roe

Series: Mathematics for sustainability

Vanessa Schweizer

Matteo Smerlak

Cameron Smith

Mike Stay

David Tanzer

Series: Petri net programming

Also see joint authors.

David Tweed

Also see joint articles.