In which I freep the President December 17, 2009
Posted by Ben Webster in evil journals, math life.3 comments
In this blog (in contrast to when you meet us in person), we tend to steer away from politics. But, of course, we do make an exception for science/technology politics, and I’d like to talk to you about some of that today. The White House Office of Science and Technology Policy is holding an open web forum on access to scientific results; specifically, how to craft a policy for when to require federally funded research to be openly accessible. I recommend that all of you go and leave respectful comments encouraging as strong a requirement along these lines as possible.
You also might want to go sign this petition for open-access in the EU.
Let’s make language exams useful December 17, 2009
Posted by David Speyer in blog triumphalism, Uncategorized.30 comments
Every year, many hundreds of mathematics graduate students take language exams. In most departments, this means that they must demonstrate the ability to translates 2-3 pages of technical writing from French, German or Russian into English, with the use of a dictionary. In my experience, the usual texts are old text books, and the translations are discarded after they are graded.
I think a number of mathematicians have had the idea that all of this effort could be put to better use. Most recently, Kevin Lin just proposed this at mathoverflow.
The idea would be to take an important mathematical work that had never been translated and divide it up into 3 page chunks, across the math departments of the English speaking world. Each chunk would be assigned to 3-5 students. For each chunk, the grader would select the best translation. These would then be stitched together into a single document, producing a terrible rough draft of a translation, that could be a starting point for future editing.
Moreover, we don’t necessarily have to bring in a skilled editor immediately. Put the texts online and parcel out the first pass to volunteers. I am thinking here of a system like Distributed Proofreaders, who has done a superb job taking scans of public domain works and converting them to digital text. In my experience, web 2.0 projects work best when they rely on small inputs from many procrastinating people. And no one procrastinates like a grad student!
The point of this post is to generate discussion of this idea. A few specific questions are below the fold.
UPDATE: For those who are interested in the idea of distributed translation of mathematical texts more generally, Anton Fonarev has volunteered to create a software infrastructure for this purpose. Join the discussion at his weblog.
In Memoriam: Dr Michael Bishop December 14, 2009
Posted by Scott Morrison in Uncategorized.6 comments
Dr. Michael Bishop, one of my high school teachers, passed away last Wednesday, December 9.
I don’t know the circumstances — last I saw him, in July, he was in great health and full of his usual enthusiasm. I realise that sbseminar might not be the best place for an obituary, but I hope you’ll bear with me for a moment.
I owe a lot to Michael, and several of my fellow students who I’ve talked to in the last few days feel the same way. My decision to study physics and mathematics at university — well, maybe that was a foregone conclusion, but it was certainly strongly influenced by him! Perhaps the quickest way I can say what I need to say is that even as a high school student, he treated me, and my fellow students, as intellectual peers, and we enjoyed an experience with him much more like university (perhaps even grad school).
His “day job” was teaching chemistry, but he had little patience for the exam curriculum (indeed, he advocated that the school withdraw from the state examination system, something that was actually considered for a while during a particularly depressing curriculum revision), and where he really got going was as “Master in charge of academic extension”. For years he very successfully trained students for the International Chemistry Olympiad. He also put together “Kaleidoscope Eyes”, a magazine published in the school for all the various extension projects going on. At some point I got interested in the tautochrone and brachistochrone problems, and Mike suggested I go read Volume 2, Chapter 19 of the Feynman lectures in order to learn the calculus of variations, and I wrote a long and rambling piece about my experience solving these problems. The highpoint of “Kaleidoscope Eyes” was, for me, a piece written by two students about Hittite grammar — illustrated with a beautifully chosen extract of the Hittite legal code, and titled “Bestiality in the Ancient World“.
He also taught some extra classes — he decided that the best response to the state physics curriculum being lame was to finish teaching it a term early, and then do something fun. Thus, we got courses on Lagrangian dynamics, on special relativity, and on quantum mechanics. The quantum mechanics course was a triumph — teaching to students who’d never met a matrix or solved a differential equation, he managed to get us to the point we could successfully estimate the first ionisation energy of H_2^+ (the molecule H_2^+ is just a hydrogen molecule with only one electron: the ionisation energy is the gap between the lowest and second lowest eigenvalues)! I’m still impressed by that one. (Hints: you can estimate eigenvalues by optimising parameters in a test function, you can use bezier splines to translate “qualitative” knowledge about eigenstates into test functions, and you can guess that the second eigenstate must be antisymmetric, by orthogonality.)
I was in Australia in July and I stopped by the school one afternoon and found Michael, and we went down to Bill and Tony’s to have a coffee. He told me about his latest adventures — he’d been playing “viking chess” with some students. The rules are not well attested, so they’d decided to try to reconstruct the rules by playing variations and seeing what worked best. Experimental paleoludology!
Thank you Michael, for all you did! I suspect there’s a whole crowd of young Australian scientists out there who’ll miss you as much as I will.
Are Lax Functors Good for Anything? December 10, 2009
Posted by Chris Schommer-Pries in Category Theory.9 comments
So I’ve recently been thinking a lot about lax functors between n-categories, trying to get a better feel for what they are and why we should care. I have a few ideas about how certain lax functors could eventually be useful for TQFTs, but ever since I asked this question on MathOverflow I have started to doubt that lax functors in themselves are really good for anything.
The technical part of Godel’s proof December 7, 2009
Posted by David Speyer in Number theory.18 comments
We’ll start with a puzzle, taken from Hofstader’s Godel, Escher, Bach. In this puzzle, we are going to learn to speak in a restricted language. We will be talking about integers, so our variables will always stand for integers. We have available to us the ordinary arithmetic operations 
So we can say "
Puzzle: Within this limited vocabulary, express the statement 
Why is this puzzle important? In Godel’s proof of the undecidability of Peano Arithmetic, he took theorems and proofs and encoded them as integers. He then needed to express “
There are a lot of great popular introductions to the overall structure of Godel’s proof. Most of them gloss over HOW Godel solved this technical problem. My goal in this post is to discuss precisely this point, and ignore the larger questions. I will take the view that expressing things in the first order language of arithmetic is a worthwhile goal in its own right, and will show you how surprisingly strong this language is.
Below the fold, I’ll solve the puzzle. Then I’ll show how to express some more serious ideas.
