I will be out of town for a few days for Thanksgiving, so there won’t be any posts from me for the next few days.
Mathematical textbooks take pains to make their subject appear to form a unified whole. Is any such unity an illusion? Discuss.
Chris Hillman, creator of Entropy on the World Wide Web and Relativity on the World Wide Web, will be joining us as a poster on Ars Mathematica.
Discover Magazine has published a list of the 25 greatest science books. The list is almost exclusively either original works of research (such as Darwin’s The Voyage of the Beagle and The Origin of Species, the top 2 books), or popularizations of that research by experts in the field (such as The Double Helix by James Watson).
A friend of mine who’s studying econometrics asked me about the Kalman filter, which is used in estimating the parameters of a time series model. I didn’t know anything about the subject, so I was poking around online, where I discovered that the Kalman filter is rocket science: it was invented to estimate the current position and trajectory of the Apollo spacecraft. And here I thought the only concrete result of the space program was Tang.
Alexandre Borovik, who occasionally comments here, has begun uploading draft chapters of his new book, Mathematics under the Microscope: Notes on Cognitive Aspects of Mathematical Practice, here. The first three chapters are already available.
Via David Corfield.
If you ever tired of the normal this and abelian that of math, check out these lists of names that geneticists have given to fruit flies, zebrafish, and other organisms, here and here. My personal favorite is the british rail gene, which supresses the effect of the always early gene. Some of the names, like cheap date, are vaguely descriptive (the gene increases susceptibility to alcohol), while others such as pray for elves seem to indicate DMT use. And I’m sure while the first twenty times you hear a gene named sonic hedgehog, it’s funny, but soon you reach the twenty-first, and it sinks in that you’ll probably be stuck hearing it for the rest of your life…
Via Pharyngula.
In a blow to the physics weblog community, Christine Dantas has closed her weblog, and deleted all of the posts but one. She outlines her reasons on Physics Forum. She had gotten embroiled in the fight over string theory (even in the Brazilian media), and as she put it:
You see, I do not have the right temperament for “living in the blogosphere”…
and
I am a quiet person, and wish to go back to my quiet life, to my quiet readings and studies.
It’s a fairly tragic development: Christine had been teaching herself various alternate approaches to quantum gravity, and would summarize her readings. It was evolving into a handy guide to the literature. She was also unfailingly polite, an obvious rarity on the internet.
Via the comments at Not Even Wrong.
I was poking around on Wikipedia, when I came across the page for Runge’s phenomenon. Runge found an example of a smooth function such that if you interpolate it by a high-degree polynomial at fixed points over a finite interval, the approximation of the function by the polynomial becomes very bad. In fact, in the limit as the degree of the interpolated polynomial goes to infinity, the maximum difference between the function and interpolated polynomial also goes to infinity. Interpolating with polynomials is harder than it looks.
Peter spots two preprints that give two different proofs of a major open problem in algebraic geometry: the finite generation of the pluricanonical ring:
By a standard construction in algebraic geometry, this would give a particular embedding of a variety as a subvariety of projective space. Apparently for varieties of general type, this would give something even better: minimal model of the variety.