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. After an overview, I'm looking at three portions of the jigsaw puzzle in three separate talks:
• Friday 21 February 2014, 2 pm: Network Theory: overview. Also available on YouTube.
• Tuesday 25 February, 3:30 pm: Network Theory I: electrical circuits and signal-flow graphs. Also available on YouTube.
• Tuesday 4 March, 3:30 pm: Network Theory II: stochastic Petri nets, chemical reaction networks and Feynman diagrams. Also available on YouTube.
• Tuesday 11 March, 3:30 pm: Network Theory III: Bayesian networks, information and entropy..
Also try my talk on Operads and the Tree of Life.
On Azimuth, learn about the pentagram of Venus:
I'm running a new blog for the American Mathematical Society. It's called Visual Insight, it features beautiful images and explanations of math, and a new entry appears on the 1st and 15th day of each month. Check it out! The most recent entry sketches how to prove the pentagon-hexagon-decagon identity:
You can see the slides here, and click on statements in blue for more information. Or if you prefer more geometry, check out my article on rolling hypocycloids:
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.
Here's the Coxeter complex for the symmetry group of a dodecahedron:
Learn more in my series "Platonic solids and the fourth dimension":
All this is a warmup for my new series about the Cayley integral
octonions and the special geometrical features of 8, 9, and 10
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:
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:
Read about the Silk Road, the Taklamakan Desert, the Mogao Caves and surrounding areas in my diary starting in February 2013 and going on to June.
I recently gave a talk on The Foundations of Applied Mathematics, about how category theory shows up in applied math, especially when people use diagrams.
I also gave a talk at the Perimeter Institute of Theoretical Physics, called Energy and the Environment: What Physicists Can Do. You can watch a video of this talk or see the slides. To see the source of any piece of information in these slides, just click on it!
Check out my minimal surface series, and see great images like this picture of the Enneper surface by Ron Avitzur:
Read about electronics and its analogy to classical mechanics in my Network Theory series. This is just the start of a bunch of posts which will eventually study electrical circuits using higher categories.
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 M12, an amazing group with 95,040 elements:
Learn about our galactic environment. What will happen when our solar system hits the next big cloud of interstellar gas?
See my American Geophysical Union talk:
It's an introduction to a project you can join, which is all about environmental problems and how to solve them. Click the links for more details. Or, watch my related talk about The Mathematics of Planet Earth.
Learn about infinities called countable ordinals—big ones and bigger ones!—here on Google Plus.
The tallest mountain in the world is Sāgārmatha, also known as Chomolungma. But to reach it from the southeast, as most climbers do, you must pass Khumbu Icefall and Valley of Silence. Read about them in my blog.
Or if you prefer math to mountains:
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!
If you like art, check out some photos from my trip to Chiang Mai in Thailand:
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:
What's on This Site
For common questions about physics, you can't beat this:
If reading my stuff makes you want to ask questions,
take a look at this.
© 2013 John Baez