Friday, September 28, 2007

The Superposition Principle

For readers that aren't familiar with this principle, I'll give a quick introduction. The idea behind it says that you can add things. A more formal definition says that when you add two linear functions, the result is still a linear function. Woo hoo.

This is probably easiest to see with a few examples. The most common one is for waves. If you take two waves, and they overlap, at some points, you'll get constructive interference and the total wave will be even bigger. In other places, you'll get destructive interference and there won't be much of anything. You can find a nifty little Java Applet here to play with that idea if it doesn't make sense.

Another example is a bit more buggy. Most of us are familiar with the annoying whine of cicadas that crop up every summer. However, not every species comes out every year. Various breeds' eggs stay buried for longer periods of time. Most notably, there's a 13 year species, and a 17 year version. A few summers back (I believe it was 2004), both happened to be out at the same time. If one species was out, you'd have their drone, but because both species were out at the same, the superposition principle was in effect and the noise was twice as loud. Annoying, but we don't have to worry about it for another 221 years from then, which will be the next time both species are out at the same time.

But we can apply this to lots of things with periodicity. In my case, homework, tests, and meetings often come with various fixed periods. Weekly, I have ~3 homework assignments. Every ~3.5 weeks, I have another class that gives an assignment. Tests come every ~6 weeks with a bit more spread. Undergraduate committee meetings about every ~4 weeks. Lab reports every 3 weeks.

Just like cicadas, this means that every often though, all of these different things will end up piling up in the same week. Anyone want to take a stab at why I'm damn glad it's finally the weekend?

Monday, September 24, 2007

What I learned today

Physics professors love colored chalk.

All of my classes are in the same room (2005 Malott). I also teach my lab Monday nights in that room. This morning, during my first class, I noticed there was a piece of red chalk scattered amongst the pieces of typical white chalk. I got pretty excited. When I get my teacher evaluations at the end of each semester, my students frequently comment on two things: My t-shirts with witty Physics/Astronomy sayings, and my drawings. Red chalk could make my drawings even more exciting.

But when I got to my lab tonight, that nearly full stick of red was down to a nub and the chalk holder was covered with pink dust.


At least there was enough to color the eyes of my space alien red...

Sunday, September 23, 2007

Thursday, September 13, 2007

Checking in

I haven't been posting much because it's been a very busy semester for me. With 16 credit hours of junior and senior level physics classes, as well as becoming involved in KU's ballroom dancing club, time has been been a bit scarce. I've been typically spending anywhere from 8 to 16 hours on campus a day.

But in the meantime, some of my commentary was published in the Lawrence Journal World concerning the largest violation of the separation of church and state.

Also, today's Astronomy Picture of the Day was rather familiar: it's the cluster I spent the summer of 2006 researching. Nice to see that this rather ignored little cluster is getting some more time in the limelight.

Sunday, September 02, 2007

Book Review - Parallax: The Race to Measure the Cosmos

Back at the MARAC conference last April, one of the keynote speakers was by Alan Hirshfeld who was selling copies of his newest book The Electric Life of Michael Faraday. I'm not really into electricity so I didn't grab a copy, but my friend Luis told me about his last book on Parallax (which I outlined the idea of in this post).

I'd been wanting to get a copy, but never could find a bookstore that carried it. Finally, when I got back to school this semester, I checked out a copy from the library.

Overall, it was a pretty good book. One of the main points is raises is the problem of acceptance of the heliocentric model. By the time of Galileo, it was pretty well established that the "crystalline spheres" of the geocentric Ptolemaic models didn't really exist and that, while it was a nice idea, it wasn't really much more than a useful mathematical model. As long as models matched with observation, they're considered to be good. The problem for the heliocentric model is that it didn't do any better of a job than the old one. Thus, there was no reason to rock the boat and try to supplant it.

Unless, of course, observations could be made that were in agreement with the heliocentric model that the geocentric one could not explain. Since an Earth orbiting the Sun gives a larger baseline than the simple width of the Earth as it rotates on its axis would, this would mean that the heliocentric model would allow for measurements of stellar parallax while the geocentric one would not.

Astronomy classes often tell of Galileo's observations of Jupiter and its four largest moons and how, seeing that smaller bodies could orbit larger ones, this convinced the astronomical community of the reality of the heliocentric model. However, this is a bit of a stretch. While it was compelling, what was really needed to put the nail in the coffin was the determination of parallax.

But this is no easy feat. Even the closest star only has a parallax angle of .75 arc seconds (recall 60 arcminutes = 1 degree & 60 arc second = 1 arcminute). In other words, .0002ยบ. That's a tiny angle! Given the additional problem of the distortion of the atmosphere, the wobble of Earth's orbit, and a host of other detrimental factors, it's quite a challenge to take on. Of course, that's just for the nearest star. If a star is further, it will make an even smaller angle. So aside from just measuring the angle, there's also the trick of choosing the right star.

But that didn't stop a long line of astronomers from trying.

The infamous Tycho Brahe was one of the first to attempt this despite not believing in the heliocentric model and having his own Tychonic model. However, his instrument was only a large quadrant and far too coarse to measure such small angles.

To improve accuracy, the invention of the telescope was needed. Although Galileo was the pioneer of the basic telescope design, the quality of the optics was still far too poor to allow for precise angles. In the late 1600's, Robert Hooke attempted to measure parallax, but still with no success.

By 1725, James Bradley and Samuel Molyneux picked up the challenge, but although they claimed that their telescope could measure to better than one arcsecond (approaching the necessary limit), they chose the wrong star (Gamma Draconis). However, while they failed to measure any movement due to parallax, the two did discover another oddity: There is another movement that had not been expected. What they had discovered was the annual aberration of starlight. While this wasn't what they had been looking for, it was ultimately an observation that fit only with the heliocentric model and could not be explained by the geocentric one. Although the heliocentric model was now proven beyond any reasonable doubt, a measurement of stellar parallax had still never been made. Astronomers continued to look for it.

In the 1780's renowned astronomer William Herschel picked up the task. Working under the assumption that all stars were really about the same overall brightness (a completely unfounded and incorrect assumption), his idea was to observe systems of visual double stars (stars which are close together but are not bound gravitationally). Under his assumption, the fainter one would be further away and provide a measuring stick by which to measure the parallax of the brighter and presumably closer star. He cataloged thousands of double star systems. In 1802, he decided to go back to several to check their separations again, but discovered that although they had changed with respect to one another, the manner in which they had done so was inconsistent with parallax. Instead, they were orbiting around one another. His method was doomed to failure.

The next to join the race was Thomas Henderson, who assumed that stars that drifted the most quickly (what's known as proper motion) were the ones that were nearest to us for the same reason that a car nearby looks to move much faster while a plane which is actually moving far faster, seems to glide slowly across the sky. Working in the southern hemisphere, he chose the star with the highest proper motion he could find: Alpha Centauri. Since southern observatories weren't as well equipped, he was using an inferior telescope, but by 1833, with 19 measurements, he had appeared to have determined a parallax. But by then he had moved back to England. He decided to wait for his assistant still at the southern observatory to make additional observations before announcing anything definite.

in 1834, William Bessel turned his attention to trying to determine a measurable parallax. He turned his attention to 61 Cygni which also had a high proper motion. But right behind him was Wilhelm Struve who had at his disposal a telescope made by the legendary Fraunhaufer, with the ability to measure stellar positions to a few hundreds of a second of arc. Struve was looking at Vega. By the end of 1837, Struve had determined a parallax angle of 1/8 of an arcsecond, but since he only had 17 measurements, he decided to wait for more before making his announcement.

Bessel then redoubled his efforts on 61 Cygni. By October of 1838, he had compiled hundreds of measurements and announced his findings: a definitive parallax angle of .314 arcseconds. Henderson published his results of Alpha Centauri only two months later and Struve, his results for Vega during the following year.

Overall, this book wasn't a bad read. It explores the lives of the people involved more than necessary, but this adds a nice bit of flavor. For people more familiar with astronomy, parts tend to get boring when basic concepts are explained in great detail, but this makes it easily accessible for even someone who's never read anything on astronomy in their lives. My biggest dislike was that Hirshfeld tends to weave in personal anecdotes that add absolutely nothing to the story he's telling. While the majority of the book is a good historical recounting, these bits, although intended to bridge topics, break the simple chronological flow and seem highly out of place.

Still, it's a book I'd recommend reading. Assuming you can find a copy...

Saturday, September 01, 2007

Don't Fuck With Texas.

It seems Texas does a good enough job of fucking itself up. Texas has just passed a new big of legislation, HB 3678 which explicitly defines the extent to which a student can express themselves religiously.

PZ has a screed up about the bill, but I'm not sure he, or Texas Citizens for Science, read the full version of it as there's slight changes in the statements that are quoted. They quote a rather dangerous sounding passage:
Students may express their beliefs about religion in homework, artwork, and other written and oral assignments free from discrimination based on the religious content of their submissions. Students shall neither be penalized nor rewarded on account of religious content.
In other words, this makes it sound like it's perfectly OK to just answer "Goddidit" to every question you ever face!

But in the final version, nestled right between those two sentences is a qualifying statement:
Homework and classroom assignments must be judged by ordinary academic standards of substance and relevance and against other legitimate pedagogical concerns identified by the school district.
Oops! It looks like "Goddidit" isn't an acceptable answer because it doesn't meet the standards expected of... well, just about any class I could think of. Certainly not science.

Essentially what the bill seems to be saying is that students have the right to turn in their biology homework and as long as it has the correct answers on it, they can fill it with all sorts of rants about how great Jesus is and how the teacher is going to Hell for teaching evolution. The evil atheist teacher can't take off points for the student expressing their religious viewpoint. As if any teacher really does.

Similarly, students are allowed to express their religious views in class, so long as it doesn't create a "legitimate pedagogical concern", such as wasting the classes time.

The bill also makes another stipulation:
Students may organize prayer groups, religious clubs, "see you at the pole" gatherings, or other religious gatherings before, during, and after school to the same extent that students are permitted to organize other noncurricular student activities and groups. Religious groups must be given the same access to school facilities for assembling as is given to other noncurricular groups without discrimination based on the religious content of the students' expression.
This one seems like a throwaway bit of excess given that the Federal Equal Access Act passed in 1984 says almost the exact same thing.

So overall, I don't see this bill as a big deal. Students have always had the right to express themselves, even if it's religiously. What this bill is doing, is making sure it's clear that students expressing themselves is different than the government funded school expressing and promoting religion.

But although this particular bill is a bit of a waste of paper and legislative time, Texas has been hard at work with other stupid bills as of late. HB 1034, passed in June, adds the phrase "one state under God" to the Texas pledge. I've already written my views on what I think of the "under God" phrase for the national pledge, and the exact same applies here: It's blatantly unconstitutional.

The main reason is that the Endorsement Tests requires that any government act not give the impression to non-adherents that they're outsiders. Even the parents at local schools realize that those that don't choose to say the pledge, or even those words, are considered outsiders. "They would have to say it ... to fit in," one parent said.

But just in case that wasn't enough stupidity, SB 83 (2003) made the pledge mandatory without a signed parental release form. This is in direct opposition to the 1943 Supreme Court case West Virginia State Board of Education v. Barnette which ruled it was unconstitutional to require students to recite the pledge or salute the flag.

So while Texas passes one bill that seems to be rather worthless, it seems the Texas legislature needs to review a few basic supreme court cases.