mspringer | July 16, 2009
Yesterday I taught the basics of geometric optics to my Physics 202 students. We did plane mirrors, spherical mirrors, and thin lenses. All told it's a fairly straightforward chapter that's all theme and variations on one equation. The sign rules for object and image distances have to be remembered correctly, but that's not so difficult.
Now while students aren't necessarily going to come into class with previously built intuition for Ampere's law and all the rest of the fun equations of the electromagnetic fields, they do have many hundreds of hours of experience looking in mirrors. All…
mspringer | July 15, 2009Or: Deconstructing Dumbledore.
(Major and serious spoilers for Half-Blood Prince and Deathly Hallows follow. In fact if you haven't read them this will make very little sense.)
There's a lot of villains in the Harry Potter series. They are young and old, male and female, human and otherwise, magical and muggle. They range from indolent and reformable pests to soul-sucking embodiments of death personified. Not all of them set out to be bad. Some are good people who made bad choices; some are power-mad petty bureaucrats. But if you want to pick out the single person who caused the most…
mspringer | July 14, 2009A few days ago we briefly mentioned the chemtrail conspiracy theory in the context of water vapor in the atmosphere. Chemtrails are one of those conspiracy theories where belief is pretty much diagnostic of actual your-brain-is-defective crazy. Belief that NASA faked the moon landings is sadly more widespread, but adherents of that theory don't even have the benefit of being able to blame their dumb on wonky neurochemicals.
Though we'll never be able to send a little floating helicopter camera back in time to the grassy knoll, there is occasionally a conspiracy theory or two that actually…
mspringer | July 12, 2009Last week we did the sinc function. Let's do it again!
The function, to refresh our collective memory, is this:
Now I was thinking about jumping right into some contour integration, but on actually doing it again I see that it's a little hardcore for one post so eventually when we do it we'll have to stretch it out over probably three posts. Probably it'll be a Friday-Saturday thing culminating on an official Sunday Function. But it ain't gonna be this week. This week we're going to do three ways of computing a limit. There's more, a bunch more, but we're going to just do three.
As we…
mspringer | July 11, 2009To me this is interesting. To people like my parents, whose retirement depends significantly on their investments during their maximum earning years (ie, now), "interesting" might not be the word they'd pick. Here's a graph I pulled off of Vanguard, representing a $10,000 investment exactly 10 years ago, for three different asset types:
The top line represents an intermediate-term investment grade bond fund. Traditionally it's a low-risk category of investment, with some ups and downs but mostly a relatively stable source of modest distribution growth. The middle line is a money market…
mspringer | July 10, 2009From the front door of the physics building to my apartment is about two miles. That's not all that far, so lately I've taken to just walking instead of riding the bus. In theory it's a relaxing time to think and look at the interesting things that you miss from a vehicle, aside from being exercise. In practice all that's true, but tempered by the fact that it is as hot as a freaking autoclave outside.
This entire week the temperature has peaked out at around 100 degrees, or >310 K for those of you who think in SI. It's tolerable but not especially fun. It'll probably get quite a bit…
mspringer | July 8, 2009There's a continuum of crazy in the world of conspiracy theories. On one end are the at least somewhat plausible ideas like that Oswald didn't act alone in the JFK assassination. On the other end are the downright schizophrenically crazed theories, say that the world is actually run by evil reptilian aliens in disguise.
I'd put the chemtrail folks down toward that crazier end. They are of the opinion that the trails left by jet aircraft are in fact government chemicals of unknown but certainly nefarious purpose.
As Carl Brannen notes, if they haven't put a conspiracy interpretation behind…
mspringer | July 7, 2009Today was my first day teaching recitation for the summer session Physics 202, the algebra-based second half of intro physics. Physics 202 focuses mostly on electricity and magnetism, where the first course (Physics 201) was mostly classical mechanics.
The summer semester is split into halves for university-wide administrative reasons that are somewhat obscure. The gist of it for me is that I'm only the TA for the second half, replacing the previous guy. As it happens my first topic was electromagnetic inductance, and after going through inductance, mutual inductance, energy in an inductor…
mspringer | July 6, 2009You're all familiar with Dr. Isis, also of ScienceBlogs? She likes cute things. She likes science. Despite the fact that I'm a so-square-I'm-practically-cubic reactionary, I like both of those things too. But when physicists try to make their physics cute it's a cringe-worthy disaster waiting to happen.
In the mail today was a flier from the city municipal water supply. It contained information about the various tested properties of the city water, including contaminant levels and that sort of thing. Among the properties listed was:
Diluted Conductance: 882 μmhos/cm
*Cringe* What they'…
mspringer | July 5, 2009I first met this function sometime in the year 2001 in the manual for a graphing calculator. The manual said that the function had no "closed-form analytic antiderivative" but nonetheless the calculator could integrate it numerically. At the time I had no idea what any of that meant, but upon taking a high school calculus class I met the function again as a demonstration of the concept of a limit. In my freshman calculus class in college I met the it yet again and learned that while this function and all continuous functions have an antiderivative, the antiderivative can't always be…
mspringer | July 4, 2009Today you should grill some good food, shoot some fireworks, spend time with your family and friends, and take a few minutes to remember awesome magnitude of what our forefathers did on that July in 1776:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes…
mspringer | July 3, 2009Last night I saw a classic conservation of momentum problem in person. It was about midnight, and I was on a service road beside west Houston's Beltway 8 (avoiding the tolls) when I slowed down to stop at a red light. In my rear view mirror I saw the red and blue flash of emergency lights approaching, so with the room I had left I crept over a bit to the right to let them by. Whoosh! A car blew by my left side at high speed, swerving in front of me and speeding into the intersection heedless of the light. My neurons barely had time to start cooking up some surprise when a black pickup…
mspringer | June 29, 2009The National Weather Service does a very useful thing for people who live in an area expexted to experience severe weather danger. I have a little Firefox app in my browser that links to the NWS and advises me of the current conditions and forecast for the next few days, and as part of its mechanical duties it advises me of the various severe weather alerts that happen. They're popping up at the rate of several times per week now, when the sky is a beautiful crystal blue. Why? Severe heat. Welcome to the southern summer!
I regret to say that I have an advisory of my own: a travel alert…
mspringer | June 28, 2009I've been away from campus visiting family during the first part of the summer, in one of those rare confluences of events where research, classes, and teaching all find themselves on temporary hiatus. While it's pretty rare, I'm glad to take it. It is giving me Mathematica withdrawals though, especially with being able to easily make nice graphical plots and do some of the number-crunching I sometimes need for the more technical posts around here. Fortunately this is the last Sunday I'll have that problem, as I'll be back in Texas soon (and all those responsibilities will come roaring…
mspringer | June 27, 2009There's a lot not to like about the Waxman-Markey cap-and-trade bill that passed the House this last week. You'd expect the right not to like it, but this bill has many people of all political opinions unhappy.
From the left: The bill is a huge 1300ish page monstrosity developed behind closed doors. What we do know about what's in the bill is not promising. Greenpeace opposes it and lists several reasons. The "cap" is weak, flexible, and full of loopholes. The "trade" part is shot full of offsets and concessions to the dirtiest power generation coal plants. Even if everything goes as…
mspringer | June 26, 2009Alas for Michael Jackson. Talented musician, deeply broken human being. Most of my knowledge of him was through cultural osmosis rather than his actual music, and I'm young enough so that I can't really remember the time before he was a punchline about changing skin color, disastrous plastic surgery, and child molestation. Well, de mortuis nil nisi bonum.
His death reminds me of my undergrad thermodynamics book, of all things. As you know, an object at a particular temperature will radiate light with a particular spectrum depending on the material. Heat something up enough, and it will…
mspringer | June 24, 2009Chad Orzel's got a great post up about the physics of Lord of the Rings. It's about Legolas the elf and his excellent eyesight. His eyes are so good that in fact they're probably operating well beyond the physical diffraction limits of any optical device with a human-sized pupil. Some speculation was discussed about how his eyes might plausibly be so good without magic: maybe he can see in the short-wavelength UV, maybe he can do interferometry(!), maybe elf pupils are bigger than we think, maybe the Middle Earth "league" is shorter than our identically-named unit of distance, along with a…
mspringer | June 23, 2009Yesterday we dumped a bucket of electrons on the Statue of Liberty and watched what happened. The most important thing we saw is that all the charge immediately distributes itself over the outside surface of the statue in such a way so that the electric field within the statue is zero. We also noted that the field was high on sharp points like the spikes in the crown, but we left that without further explanation. Today we fix that.
Fields can be funny things. In the case of electric fields and gravitational fields and numerous others, the fields are vector fields. This means that a given…
mspringer | June 22, 2009Today we need an example of something weirdly-shaped and electrically conductive. There's no shortage of such things, so we might as well go with the iconic. This is the Statue of Liberty:
It's made out of copper, which over the years has taken on a decidedly not-copper color due to chemical reactions between the copper surface and the surrounding atmosphere. But it's still copper and thus a very good conductor of electricity. Unfortunately for our purposes here the statue is also hollow, and in fact the copper is only a few millimeters thick. This isn't unusual, almost all metal…
mspringer | June 21, 2009If you want to kill some time, try to think of all the different definitions of the word "set". You have chess sets, sets in tennis, sets of dishes, sets musicians play, sets as abstract mathematical entities, television sets. You can set a table, set a clock, set someone straight, set a price, set out on a journey. That's just scratching the surface. The Oxford English Dictionary lists literally hundreds of different senses of the word. And yet if I set out (ha!) a particular instance of the word, you'll process its meaning instantly.
You'd think mathematics could avoid the ambiguity…