Ars Mathematica

John Baez’s Week 235 of This Week’s Finds in Mathematical Physics is out. This week he talks about quantum computing, and his work on higher gauge theory.

If you’re comfortable with the language of schemes and representable functors, you can find a nice introduction to Grothendieck topologies here: Notes on Grothendieck topologies, fibered categories and descent theory, by Angelo Vistoli.

Bee at Backreaction has written the definitive weblog post on the experimental search for evidence of the existence of extra dimensions. (One consequence of string theory, if it’s true, is the existence of additional dimensions beyond four.)

A few universal algebra links, collected by Ralph Freese. (Universal algebra is the branch of mathematics that studies generalizations of groups, rings, and algebras. The hallmark of each family of objects that can be studied by universal algebra is that it satisfies a version of Noether’s isomorphism theorems.)

Another triumph for Wikipedia. Every time I do a web search, I’m impressed with the progress Wikipedia is making. Check out their dry but complete summary of Grothendieck topologies, and their more evocative Background and genesis of topos theory.

Rob Knop thinks that the Big Bang is a bad name for a good theory. Read this post on his weblog for more. If astronomers ever do decide to drop the name Big Bang, I hope they return to Lemaitre’s original name for the concept: the primordial atom. It has a 20s-science-fiction/evil-scientist sound to it. You can just imagine Bela Lugosi saying, “The fools. They laughed at me, but they’ll laugh no more once I have harnessed the power of the primordial atom”.