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Low-functioning pinhead...
January 29, 2005
Linear Deficit
I’m teaching advanced mechanics, for juniors and seniors, this semester. And, once again, I’m driven bonkers by one of those educational peculiarities of UT (at least, I think it’s peculiar to UT).
I’m lecturing about damped, coupled harmonic oscillators (surely, the most basic problem in all of advanced mechanics), and I say, “OK, by introducing the velocities as independent dynamical variables, we can write Newton’s 2nd Law as a system of coupled 1st-order linear differential equations.” We can cast those equations in matrix form
where
and is a certain matrix. The solution is
and I then go on to explain that we can compute the exponential of a matrix if we know how to diagonalize it. Blank stares. And we can diagonalize , if we know its eigenvectors and eigenvalues. Uncomfortable rustling. “OK,” I ask this collection of junior and senior physics majors, “who knows how to find the eigenvectors and eigenvalues of a matrix?”
Slightly less than half the class raises their hands.
Whoa!
The problem, you see, is that, unlike most places, where linear algebra is bundled into 2nd-year calculus, the UT Math Department has unbundled it into a separate course. And, nowhere in the curriculum of the UT Physics Department is that course listed as a prerequisite. Thus students can hit my course or, G-d forbid, the Quantum Mechanics course, without so much as a passing acquaintance with linear algebra.
Having taught both courses before, I was prepared for this debacle. A brief review of finding the eigenvectors and eigenvalues of a matrix ensued. And then we exponentiated and found the general solution to the coupled harmonic oscillator problem.
Finally, we got to case where some of the eigenvalues of coincide. In this case (called “critical damping” in the case of the 1D harmonic oscillator), I explained that cannot be diagonalized. Instead, the best we can do (but still good enough for exponentiating it) is to put in Jordan Canonical Form.
“So, who knows what Jordan Canonical Form is?”
No one raised their hand …
January 27, 2005
Can’t Complain About the Weather
As you may have noticed, I now sport the local weather forecast on my sidebar. This is partly a technical “because it’s there,” and partly an artifact of the fact that my former office did not have a window.
The forecast is powered by NOAA’s XML service that I blogged about previously. One of the cool things about the internet is that, in response to my complaints, NOAA’s Director of Internet Services, Bob Bunge, chimed in to say that they were working on my issues. I’d like to thank Bob and especially John Schattel for working with me to iron out the bugs in their service.
Some were quite amusing:
The trouble revolves around our decision to calculate the sunrise and sunset times and base the decision to use “night” when the data time occurs after the sun has set. This logic does not return the correct result in the central time zone at this time of year [mid-winter].
Anyway, it took a while, but it looks like the bugs in their service are mostly squashed. So, despite having moved offices in the interim, I now sport the local forecast on my sidebar.
I’ve gotten a couple of emails asking me how I deal with NOAA’s XML service, so here’s a brief summary.
- NOAA updates the current conditions hourly, at 20 past the hour. I use a (completely trivial) script to retrieve the current conditions and cache them locally.
- The forecasts are updated hourly, at 50 past the hour. The forecast data is retrieved via SOAP and cached using the script described previously.
- To put things together, I run yet another script twice an hour, i.e. after each NOAA update. It parses the aforementioned XML files, using
XML::Simple, and spits out a file containing an XHTML fragment which I can include in my sidebar. Up to 7 days of forecasts can be produced. I settled for two.
Note that after haranguing NOAA for not using XML tools to assemble their XML, I copped out and generate my XHTML with a few simple-minded print statements as well. Using XML::Simple to assemble the desired XHTML document from the data would have been kinda painful. And, hey, nothing else in this sprawling expanse of blogging software does it “right” either.
January 25, 2005
Another MT Mail Exploit.
The MovableType Comment/Trackback/… system (which uses email to notify the blog owner of newly posted comments/trackbacks) is vulnerable to being exploited by spammers. (Surprised?)
Update now, before the spammers get around to your blog.
January 22, 2005
rel=”nofollow”
By now, you’ve surely heard about the announcement. Google (and other leading search engines) will now respect a new attribute to hyperlinks. There has been a deluge of comment, both pro and con. Phil Ringnalda has a nice list of links in his piece. I’m too