You can learn about category theory applied to electrical circuits and control theory in my lectures on YouTube and my blog articles on Azimuth.
For the math of this amazing image by Greg Egan, check out my Google+ post, or for more detail my article on the n-Category Café.
Check out the Azimuth El Niño Project here:
I gave a talk on "Spans and the Categorified Heisenberg Algebra" at Université Paris 7. An annotated video prepared by Stéphane Dugowson can be found here.
This spring I also gave a talk on network theory at a workshop called Category Theory at the Crossroads.
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! Try the above slides for an overview that touches on the role of higher categories. Or, try these:
• 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.
Or if you prefer more geometry, check out my article on rolling hypocycloids:
Here's the Coxeter complex for the symmetry group of a dodecahedron:
Learn more in my series "Platonic solids and the fourth dimension": part 1, part 2, part 3, part 4, part 5, part 6, part 7, part 8, part 9, part 10, part 11, part 12, and part 13.
All this is a warmup for my new series about the Cayley integral octonions and the special geometrical features of 8, 9, and 10 dimensions:
The answer to life, the universe and everything is 42. But you may not know why. Now I have found out. The answer is related to Egyptian fractions and Archimedean tilings:
Check out my minimal surface series, and see great images like this picture of the Enneper surface by Ron Avitzur:
Click the boxes to hear and read about some pieces I made with Greg Egan's QuasiMusic program, which translates quasicrystals into sound:
Starting with this picture by Bob Harris, learn how we can build the Mathieu group M_{12}, an amazing group with 95,040 elements:
Read my series on the mathematical delights of rolling circles and balls!
Learn about infinities called countable ordinals—big ones and bigger ones!—here on Google Plus. Or if you prefer large finite numbers...
There's a math puzzle whose answer is a really huge number. How huge? According to Harvey Friedman, it's incomprehensibly huge. Now Friedman is an expert on enormous infinite numbers and how their existence affects ordinary math. So when he says a finite number is incomprehensibly huge, that's scary. It's like seeing a seasoned tiger hunter running through the jungle with his shotgun, yelling "Help! It's a giant ant!" For more, read this.
In week319 of This Week's Finds, learn about catastrophe theory in climate physics! This is the first issue that features a program you can play with on your browser. It's a simple climate model that illustrates how a small increase in the amount of sunlight hitting the Earth could have a big effects on the climate, by melting snow and revealing darker soil. It was made by Allan Erskine.
Also on my blog, learn about ice, its many forms and crystal structures, how it resembles diamonds, and what scientists do with a machine that uses 80 times the world's electrical power for the few nanoseconds it's running.
If you like astronomy, read about the moon called Dysnomia, a planet whose atmosphere liquifies and then freezes every year, the reason so many objects in the outer solar system are red, why the same chemicals you find in the tarry buildup on a barbecue grill are also seen in outer space... and whether life on Earth could have been started by complex compounds from comets!
Archimedean tilings are beautiful patterns whose possibility is predicted — but not guaranteed — by solutions to a simple equation. I'll explain what that equation says, where it comes from, and what happens when things don't quite work!
If you plot all the roots of polynomials whose coefficients are 1 and -1, say polynomials of some large degree like 24, you get a picture like this:
How can we understand the amazing patterns here? Read The Beauty of Roots for some answers!
For common questions about physics, you can't beat this:
I don't maintain this Physics FAQ - Don Koks does, so please send any comments about it to him, not me!
If reading my stuff makes you want to ask questions,
take a look at this.
© 2013 John Baez
baez@math.removethis.ucr.andthis.edu