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 Avitsur:
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 Platonic solids, Coxeter complexes and Coxeter diagrams in this series of posts: part 1, part 2, part 3, part 4, part 5, part 6, part 7 and part 8. Here's the Coxeter complex for the symmetry group of a dodecahedron:
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:
If reading my stuff makes you want to ask questions,
take a look at this.
© 2011 John Baez
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The universe is full of magical things, patiently waiting for our wits
to grow sharper. - Eden Philpotts
baez@math.removethis.ucr.andthis.edu