John Baez’s Stuff

What’s New?

You can now see talks from the big annual applied category theory conference, ACT2020. And the proceedings of ACT2019 are now available!

Kenny Courser's thesis is out: Open Systems: a Double Categorical Approach. Read about it here and here.

Please take a copy of my diary from 2003 to July 2020!

Can we actually remove carbon dioxide from the air? Yes! Can we remove enough to make a difference? Yes! But what are the best ways, and how much can they accomplish? I explain that in my article in Nautilus, an online science magazine.







Six random permutations of a 500-element set, where

circle areas are drawn in proportion to cycle lengths.

From Analytic Combinatorics by Flajolet and Sedgewick.

Learn about random permutations, and learn how to understand their properties using a blend of old-fashioned combinatorics, category theory, and complex analysis!

Check out the slides of the talks at the special session on applied category theory at UCR, and also my research team's talks at the Fourth Symposium on Compositional Structures:

Also try my more heavy-duty talk on structured cospans at CT2019.

Read my article in Nautilus magazine: The math that takes Newton into the quantum world. And for more of the technical details, read this.

Check out this interview: A quest for beauty and clear thinking. Also check out my talk on Unsolved mysteries of fundamental physics, which is now available on video.

Together with three students at Applied Category Theory 2018, I wrote a paper on biochemical coupling through emergent conservation laws. Check out our blog posts about this!

Learn about quantum mechanics and the dodecahedron:

Then read about the glories of the 600-cell (Part 1, Part 2, Part 3), which is a 4-dimensional analogue of the icosahedron:

These posts lead up to a grand conclusion: the Kepler problem and the 600-cell!

And while you're at it, check out my new paper on the icosahedron and E8, and learn about excitonium, Wigner crystals, the universal snake-like continuum, and the connection between braids, entropy and the golden ratio!

We recently had a special session on Applied Category Theory here at UCR, and you can see slides and videos of lots of talks. And this summer at a conference on applied algebraic topology I gave an overview of algebraic topology and how it's changed our thinking about math: The Rise and Spread of Algebraic Topology. Check it out!

Learn about diamondoids and phosphorus sulfides:

A while back I gave a talk at the Stanford Complexity Group on Biology as Information Dynamics, and here's a video:

The Azimuth Backup Project is saving about 40 terabytes of US government climate data from the threat of deletion. Our Kickstarter campaign exceeded its goal by a factor of 4, so we will be well funded to store this data and copy it to many safe locations.

Check out this talk on networks and category theory:

and also my introduction to Kolmogorov complexity and related ideas:

Learn what Kosterlitz and Thouless did to win the 2016 physics Nobel Prize.

Try my articles on 'struggles with the continuum' — that is, problems with infinities in physics arising from our assumption that spacetime is a continuum:

Read about 'topological crystals':

Part 1 - the basic idea.

Part 2 - the maximal abelian cover of a graph.

Part 3 - embedding topological crystals.

Part 4 - examples of topological crystals.

Take a road trip to infinity:

Part 1: up to ε o .

. Part 2: up to the Feferman–Schütte ordinal.

Part 3: up to the small Veblen ordinal.

There's a mysterious relation between the discriminant of the icosahedral group:

and the involutes of the cubic parabola:

Learn a bit about quantum gravity, n-categories, crackpots and climate change in my interview on Physics Forums.

Anita Chowdry and I gave a joint lecture on The Harmonograph at the University of Waterloo. You can watch a video of it!

Read the tale of a doomed galaxy:

Nature and the world of human technology are full of networks. People like to draw diagrams of networks: flow charts, electrical circuit diagrams, signal-flow graphs, Bayesian networks, Feynman diagrams and the like. Mathematically minded people know that in principle these diagrams fit into a common framework: category theory. But we are still far from a unified theory of networks! Learn more here:

• Network Theory: overview. Video on YouTube.

• Network Theory I: electrical circuits and signal-flow graphs. Video on YouTube.

• Network Theory II: stochastic Petri nets, chemical reaction networks and Feynman diagrams. Video on YouTube.

• Network Theory III: Bayesian networks, information and entropy. Video on YouTube.

Last year I gave talks on What Is Climate Change and What To Do About It? at the Balsillie School of International Affairs. You can see the slides.

But if you prefer biology and algebraic topology, try my talk on Operads and the Tree of Life.

8

Part 1: integral octonions and the Coxeter group E 10 .

. Part 2: the integral octonions, 11d supergravity, and cosmological billiards.

Part 3: the integer octonions in their guise as the E 8 lattice.

lattice. Part 4: the 240 smallest integer octonions, also known as the root vectors of E 8 .

. Part 5: the geometry of the root polytope of E 8 .

. Part 6: how to multiply octonions, and the Cayley integral octonions.

Part 7: Greg Egan's proof that 2 × 2 self-adjoint matrices with integral octonion entries form a copy of the E 10 lattice.

lattice. Part 8 - my proof that 3 × 3 self-adjoint matrices with integral octonion entries form a copy of the K 27 lattice.

lattice. Part 9 - Egan's construction of the Leech lattice from the E 8 lattice.

lattice. Part 10 - fitting the Leech lattice into the exceptional Jordan algebra.

I also love Coxeter theory. Here's the Coxeter complex for the symmetry group of a dodecahedron: