mspringer | September 14, 2008Draw the graph of a function. Roughly speaking, if there's no holes, jumps, or other choppy weirdness it's a continuous function. The function is connected to itself like a curvy rope laid out on the ground, with no cuts.
Now if that function has no sharp points, it's a differentiable function. Again roughly speaking, imagine that the rope is free of kinks or sharp bends. The absolute value function is an example of a function which is not differentiable at the origin: there's a sharp point there.
It's well known that if a function is differentiable, it's also continuous. This is…
mspringer | September 13, 2008One of my favorite writers, the extraordinary David Foster Wallace, is dead after ending his own life. He was 46.
My first exposure to his work was his beautiful mathematics book Everything and More: A Compact History of Infinity. He brought his extraordinary skill as a narrative fiction writer to the story of the development of the mathematical concept of infinity, and doing so in a way that does not fall victim to the excessive simplification that plagues so much of science writing. It's equally engaging for the mathematically naive and the mathematically sophisticated, with one or two…
mspringer | September 13, 2008Yesterday I was watching Discovery's Project Earth, avoiding doing homework and grading. It's an interesting show, with ideas ranging from the interesting to the preposterous. The episode I saw proposed launching little lenses into space to scatter a small fraction of the sun's light away from earth. The tests were failures, and more damning but glossed over in the program were the sheer number of launches needed to put a significant number of lenses in space. At that point, why not just use reflective mylar sheets in space? They're much cheaper and you can put a lot more in space with…
mspringer | September 12, 2008"It's not the heat, it's the humidity."
This is said by people all over the country, especially so in the coastal south where 90+ degree heat is made that much worse by air thick enough to swim in. But heat is usually an inconvenience. Hurricanes are another matter. It's not the wind, it's the water.
I was in Baton Rouge during Katrina. We had tropical storm force winds that knocked around anything not car-sized or bolted down, downed trees, and some lost power. What's a little less well known is that New Orleans only experienced category 1 winds - low category 2 at the absolute most…
mspringer | September 12, 2008There's a comic strip called Non Sequitur. Not one of my favorites, but occasionally there's a pretty good one. Here's an example. We have a kid speculating about firing a gun on the moon. He asks:
If you were on the moon, which is a vacuum, and tried to shoot a gun, would it fire? After all combustion needs an atmosphere with oxygen... or does the casing of the bullet create its own atmosphere? If so, the bullet would travel farther in the reduced gravity, but would it travel faster than it does on the earth?
Let's take 'em one at a time.
First, the bullet would fire. Explosives…
mspringer | September 11, 2008You're probably more tired of politics than I am, but somebody has to be the voice of reason around here. I apologize to my physics-loving nonpolitical readers and urge those of you fitting that description to avoid anything I write with the politics tag. It will all be over soon.
Maybe it's because McCain now leads Obama on Intrade, but the hysteria just grows louder and louder. Take Effect Measure, here on ScienceBlogs, discussing McCain on rape. Here's the charges:
Charge: "In 1994, John McCain voted against legislation -- pushed through Congress by Joe Biden -- that helped put an end…
mspringer | September 11, 2008Reader nanoAl had an interesting observation about the post on applying an electric charge to the earth. We were trying to find out how much electric charge would need to be applied to the earth and the moon to cancel out their gravitational attraction. The answer was suprisingly little. Here's what nanoAl had to say:
Thats about 320 kg of electrons! I wonder how strong a box it'd take to contain the pressure from all that repulsive force, anyone know how to calculate it?
As a matter of fact, I do! Most people know that pressure is force per area. But fewer people know that it's also…
mspringer | September 10, 2008If you're here for the physics and not the politics, skip this entry. I wouldn't blame you. It irritates me to read politics on science sites too, but with the election only about two months away it's hard to resist the temptation. Here we go.
Neurotopia links to an article criticizing Sarah Palin. Nothing unusual. What raises an eyebrow is the contents of the criticism. In short, she's being accused of making rape victims pay for their own rape kits. Here's the news article from 2000, which mentions Wasilla in passing. Palin was mayor at the time.
Let's see what the article actually…
mspringer | September 10, 2008Ever wondered why it takes a tremendously huge rocket to launch people from the earth, but the Apollo astronauts managed to launch from the moon in a comparatively tiny lunar module? Easy, the whole thing was faked and NASA forgot to come up with a plausible explanation!
Wow, it was almost physically painful to type that even as a joke. The real reason is some very easy but still pretty cool physics. Shall we take a look?
For a given object, the gravitational potential energy per kilogram with respect to distant space is given by this easy little equation:
So to pick up one kilogram of…
mspringer | September 9, 2008There's been a lot of discussion about NASA administrator Mike Griffin's leaked email about the future of the space station. It's a fascinating, honest, and cogent look at where we stand now at the crossroads of the Shuttle and the eventual Ares/Orion system. He's precisely right on the facts. He's also too pessimistic. The failure and danger he foresees can be turned into opportunity.
Here's a quick precis of the situation as it stands. The shuttle is being retired. There is a non-negotiable finite number of possible shuttle launches remaining due to the fact that the external tanks…
mspringer | September 8, 2008There's got to be what, probably one or two Metalocalypse fans in the readership? The rest of you will probably be pretty confused, but bear with me. Quick primer: the show is about an absurdly successful but actually incompetent death metal band called Dethklok.
The season finale was last night. Holy cow that was a great episode. The last five minutes are worth their weight in gold. I won't say what happens for the benefit of those who watch the show but haven't seen the finale yet, but it's brutal stuff. The body count is even higher than usual and my own favorite character is at…
mspringer | September 7, 2008Take as our starting point this function, defined on the positive whole numbers:
All it does is add together the fractions above, stopping when you hit the fraction specified by your particular choice of n. As you increase n and thus add more fractions to the sum, you'll end up with a plot of the function that looks like this:
As you keep adding more and more fractions the sum will get larger and larger, but the rate of growth will be very slow. I've stopped plotting at n = 100, where the last fraction is of course 1/10000. But even though the growth rate keeps slowing down, how do I…
mspringer | September 6, 2008Friday I met my first ScienceBlogger in person. Nick Anthis from The Scientific Activist was in town, and as he's a former Aggie we got to trade a few stories about the university and the different kinds of work we're doing. He's a cool dude! It was very nice meeting him, and I think it might just inspire me to try to organize a reader meet-up at some point. College Station is tiny and in the middle of nowhere, but I think there's a few other Texas ScienceBloggers as well so maybe we could have a group meet somewhere big and convenient like Dallas or Houston. We'll worry about that later…
mspringer | September 5, 2008I've taught seven recitation sections as a graduate student, and this semester I'm teaching three more. Between them it's several hundred hours of standing in front of a classroom teaching. That's nothing compared to career teachers and professors, but it's a decent bit of experience as far as TA teaching goes. I put a fairly large amount of effort into teaching, with preparing lectures and example problems, grading quizzes and lab reports, conducting extra review sessions, and answering questions by email. Does that make me a good TA? I'd like to think so. But what do my students say…
mspringer | September 4, 2008Teaching Physics 201 has me digging out some of my old favorite concept-y problems. Nothing dramatic in the mathematics, but at the 201 level you can't even assume knowledge of derivatives. But you can try to catch their minds with interesting examples. Here's a classic one:
You've got the earth and the moon. They have mass and so they attract each other with gravity. Both the earth and the moon are pretty large, and so the attraction is considerable. On the scale of earthbound undergraduate lab equipment however, gravity from anything but the earth is pretty hard to measure. Pretty…
mspringer | September 3, 2008Physics is a continuous thing, progressing steadily forward with only rare dramatic leaps. This is not the kind of style that makes for flashy news stories in the popular press. When there are interesting things being reported, they're usually wrong. "Faster than light" laser pulses, quantum teleportation, invisibility cloaks... if it's in the popular press it's probably not anything remotely resembling what they tell you it is. It's like asking me to report on avant-garde fashion.
But every once in a while some interesting things pop up. Today two things did. The first is the sun.
The…
mspringer | September 2, 2008In honor of Physics 201 which I'm teaching this semester, I present a very elementary statics problem.
Here we have a board of uniform composition and weight W. It has length l and the supports are separated by a distance s. What are the two forces (call them A and B) on the boards?
The board isn't moving. It's just sitting there, and so if there's no acceleration there's no net forces. That gives us
Hmm. That's two unknown quantities with one equation. Not enough. Fortunately there's another equation we can use involving the torque. Torque is the angular equivalent of force. Get a…
mspringer | September 1, 2008Fundamentally, you can start off with the Standard Model. It's not perfect, but it's a pretty good description of the particles and forces of nature especially at the mostly low energies of our soar system. Using quantum mechanics you can built up those particles into distinct nuclei, and calculate how they can fuse to form new nuclei. Tack on even a rudimentary Newtonian understanding of gravity and you're already able to describe stars from scratch.
Keep going with atoms and eventually things move out of the physics building into the chemistry building as those atoms combine to form…
mspringer | August 31, 2008We can't graph here, this is bat country! Complex bat country.
...well ok, let's stop and take a look anyway. But no graph.
You've seen this jewel of mathematics. It's Euler's identity.
It comes from the more general expression right below this paragraph, which is today's Sunday Function. You might wonder where this expression comes from. It's a long story, but if you want to plow through it, I commend you.
Set θ = π, and Euler's identity pops right out. But let's set θ = π/2 instead and see what happens:
In other words, we've just figured out a new way to write the imaginary number…
mspringer | August 30, 2008First, a Public Service Announcement: As a decade-long former south Louisiana resident who was in Baton Rouge for Katrina, I have some advice. If you're in Louisiana anywhere south of about Alexandria, now's the time to start packing. You might be ok sticking around till Saturday night or possibly Sunday morning to see if it turns, but that's really pushing it. If you're actually in New Orleans you should leave now regardless. Now to our regularly scheduled post.
Science. On TV it goes something like this: Scientist gets brilliant idea. Scientist goes to lab, puts serious expression…