What would you see if put a white sphere in a mirrored spheroid and lit it with red, green and blue light from different directions? This image by John Valentine shows the answer! For more images, and more of the underlying math, visit Visual Insight.
My new talk on split octonions and the rolling ball features some nice WebGL animations made by Geoffrey Dixon. Philip Gibbs, Karine Bagdasaryan and I found a new improved universal covering — progress on a 100-year-old geometry problem. And speaking of geometry....
Read about the group theory of compound polyhedra on Visual Insight.
On a more serious note, check out the Azimuth El Niño Project:
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.
For fun, I've been continuing to study the octonions, E_{8}, the exceptional Jordan algebra, the Leech lattice and related structures:
I also love Coxeter theory. Here's the Coxeter complex for the symmetry group of a dodecahedron:
You can learn more about this 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.
Doug Adams said 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.
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