Ars Mathematica

I’ve come across this guide to quantum field theory textbooks. Since QFT is on my to-do list of things to learn before I die, this list may come in handy.

People always post interesting links in the comments to Scott Aaronson’s weblog. For example, the other day Paul Beame posted two links that explain the connections between random walks on graphs and electrical networks. One is a complete book on the subject by Doyle and Snell. The other is an article by Chandra, Raghavan, Ruzzo, Smolensky, and Tiwari that further develops the theory.

The 2007 Abel Prize has been announced. The winner is S. R. Srinivasa Varadhan for his work on large deviations in probability. Large deviations are asymptotic estimates of rare events. They are of practical importance, for example, in justifying the results of statistical mechanics. Cosma Shalizi’s notebook on large deviations provides an overview and many more links.

I find it interesting that the Abel Prize has taken a turn towards the applied in recent years. The first two awards, to Serre and to Atiyah and Singer, track the expectations of pure mathematicians. In the last three years, though, one prize has gone to Peter Lax, who works in applied PDEs, and now this year Varadhan. (The other winner is Lennart Carleson.)

Terence Tao has a thoughtful post that explains why proving existence results for Navier-Stokes equations is so hard.

I ran across the oddest anecdote about Einstein. Einstein was teaching a class in Germany in 1918. When in the aftermath of World War I Kaiser Wilhelm abdicated, he put a sign on the classroom door that said “Class cancelled because of revolution.” (This link mentions the story.)

Mark Srednicki has written a new textbook on quantum field theory. The final version is not available electronically, but a prepublication draft is.

It’s common for authors to take down the manuscript when the book is published, so it’s nice to see it when an author bucks the trend. Srednicki adopts a reasonable compromise in keeping the final-but-one version available on his site (he warns “This draft contains numerous errors (mostly minor) that are corrected in the published version”).

Sean at Cosmic Variance notes that NASA has discovered that everyone is apathetic about their new planned mission to the Moon and then Mars, and that they are in the market for a celebrity spokesperson to change that. They are throwing around obvious names, like David Duchovny and Patrick Stewart, when the answer is obvious. There is only one man for the job of selling the new Mars mission:

Dave Chappelle (warning: long, not safe for work, and you probably won’t think it’s funny).And if NASA is looking for a marketing slogan, they could do worse than what John Baez says here: “the scientific equivalent of putting a goldfish bowl on top of Mount Everest.” Think about it — we’ll never know what’ll happen to that goldfish unless we try. Dare to dream.

Dave Bacon explains why he is not a Bohmist. While I doubt it will turn out to be a correct interpretation of quantum mechanics, I think the Bohm interpretation deserves to be better known, since its existence contradicts a certain amount of conventional wisdom on the meaning of quantum mechanics.

I had no idea that David Bohm himself was driven out of the country by McCarthyism.

ArXiv has announced a new numbering scheme for preprints. Instead of yymmnnn, they will now use yymm.nnnn. In a time of dizzying change, arXiv has taken from us one of the few constancies we had. Won’t they think of the children?

From Asymptotia, I just learned about the Antikythera mechanism, an ancient Greek analog computer. Its full capabilities are not yet known, but the device’s thirty interlocking gears simulate the movements of the Sun, Moon, and Earth well-enough to predict eclipses. Not much is known about the history of the mechanism, which uses technology that was not reinvented until the fourteenth century.