mspringer | May 6, 2009Sorry for the light blogging this week. Finals are this week and next, and so I'm pretty swamped. Today I'm going to pose a straightforward but slightly counterintuitive probability question, of the sort that in modified forms aren't so uncommon in physics:
A densely populated authoritarian state issues the following population control policy: each family may have one child with no restrictions. If that child is male, the family is not allowed to have more children. If that child is female, the family may have one more child. The family may not have a another child regardless of the sex…
mspringer | May 4, 2009Our excellent physics blogger Chad Orzel has a post up about the thermodynamics of Goldilocks. Seems it's a little questionable to have the porridge configured as it was in the old tale. A few wags in the comments complain that in a story with talking bears physics is the least of the concerns, but I think that misses the point. Suspension of disbelief requires that we grant the story the ability to say wild things so long as it does so in an internally consistent way. Don't, for instance, make time-travel commonplace enough so that a 13-year-old girl can use it to rearrange her school…
mspringer | May 3, 2009"I'd like to open a savings account," you tell your banker.
"Excellent!, the banker says, "our savings accounts have an interest rate of 5% and an annual percentage yield of 5.127%. It's a great deal and I think you'll like it."
5% interest is a great deal on a savings account these days. But what's all this about the difference between interest rates and annual percentage yield? You often hear about the magic of compound interest, and this particular distinction between the various types of rates are a consequence of the way this magic works.
Say you've got $100, and your banker agrees to…
mspringer | May 2, 2009Well, we've explored some groundwork in three previous posts and so it's time to put it all together. Why exactly do bosons have such weird behavior at very low temperatures, with a large fraction of their number crowding into a single quantum state? Let's plow on. If you're not familiar with the mathematics or the physics, don't worry. What you've absorbed from the previous posts will be fine - you don't need to know the details to understand the big picture.
The number of bosons is given by the grand partition function Q in the following way:
Each term in the sum is the expected number…
mspringer | April 30, 2009Normally I stay mostly on the physics beat, trying to mostly stay out of the controversy arena except occasionally when my lunatic reactionary politics crops up in something like my Social Security piece a while back. But all things considered I much prefer to a nice, collegial, uncontroversial discussion about eigenfunctions of the Dirichlet problem than charging in with guns blazing to the nearest eruption of sloppy thinking.
Nonetheless there are occasionally times it's just not possible to look away. Another ScienceBlogger brought up a piece on the Huffington Post by a well-meaning lady…
mspringer | April 29, 2009That Professor Goddard, with his 'chair' in Clark College and the countenancing of the Smithsonian Institution, does not know the relation of action to reaction, and of the need to have something better than a vacuum against which to react - to say that would be absurd. Of course he only seems to lack the knowledge ladled out daily in high schools.
- New York Times, January 30, 1929
Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th Century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere.…
mspringer | April 28, 2009Yes, it's Tuesday. Busy weekend, including a Relay for Life (you should find your local one and donate!). Today we'll get back on schedule a bit and make this one a rather more utilitarian than usual Sunday Function, playing into the last step we'll need in order to complete the Bose-Einstein condensation discussion.
In the course of our journey we will meet this somewhat alarming creature:
It's a function that takes two parameters: a more traditional variable z, and a number (lowercase Greek letter nu) denoting the particular subspecies of function g. The capital Greek letter gamma is…
mspringer | April 25, 2009[This post is tremendously nerdy Star Wars fan ranting. There is no physics. You have been warned!]
Let me get this straight: I tremendously enjoyed Star Wars: Episodes 1-3. I enjoyed them in all their badly-acted, incoherently characterized, effects-dependent glory. Every single one of them I walked into and out of the theater with a huge grin on my face. Yes, even Episode 1. They weren't works of art by any stretch, but they had enough of the classic Star Wars magic to turn me back into that wide-eyed little kid watching in wonder as Luke blew up the Death Star.
So ignore all the…
mspringer | April 24, 2009"Everybody listen up!" shouts the high school PE coach, "I'm splitting you up into N teams of equal size. I'm going to make the selection of players randomly, so with any luck the teams will be of equal skill. The players with high skills all the way down the continuum to the players with low skills are going to be partitioned among the ensemble of teams and I hope it will make all the games competitive. If it doesn't and some teams dominate while other teams collapse, I'm going to swap out players until we reach an even equilibrium. Them I'll keep scrambling things randomly just to keep…
mspringer | April 23, 2009Today we're going to have to do some groundwork to set up for a step we're going to need a post or two from now. It has to do with density in a slightly more abstract context than usual.
Imagine you want to know how many people are living in a particular region. You can multiply the population density by the land area and find out. But things get complicated if the density isn't uniform. You'd have to separately multiply the density of each small uniform sub-region by the area of each sub-region and add them all together. Mathematically we'd call this integrating the density over the…
mspringer | April 22, 2009It's been a while since we've worked on some slightly more heavy-duty physics, so I'm going to spend the next couple of days going through the basics of the theory of Bose-Einstein condensation. Let me set the stage:
Particles can be divided into two classes based on a quantum mechanical property called spin. Spin in this context isn't a physical rotation of a solid object, but an intrinsic quantum mechanical property that happens to be analogous in many ways to the physical rotations we're used to seeing in the real world. For some reason the world is constructed in such a way so that a…
mspringer | April 21, 2009Reader Timothy writes in with a question:
It seems that the north pole would get more daylight during the summer solstice than the equator does during an equinox. During the summer solstice, the north pole would get the equivalent of (24hrs)sin(23.5 ° ) = 9.57 hours of sunlight from directly overhead (the zenith). During the equinox, the equator would get the equivalent of (12 hrs / pi radians) ⫠sin θ d θ (integrating from zero to pi) = 7.64 hours of sunlight from the zenith. We only integrate from zero to pi, when the sun is above the horizon.
I am curious as the reasons why the north…
mspringer | April 19, 2009"So," Herr Schrodinger says to us, "I'm looking for a function of x. It needs to be equal to the negative of its second derivative, up to a constant factor. When x is zero, the function itself should be zero. And when x equals L for some constant L greater than zero, the function also needs to be zero. Can you find me such a function?"
Sure we can. As you know, the derivative of a function is its rate of change. Its second derivative is the rate of change of the rate of change. There are functions which are equal to their derivative (and second derivative), e^x is one of them. But we'…
mspringer | April 18, 2009An emailer sends in a link to a comment on The White Coat Underground. It's in the context of naturopathy, the idea that medical problems ought to be treated with natural means. Some of it's a good idea - eating right, exercising, that sort of thing. Those sort of things aren't going to cure much, but they're good things to do. Other aspects of naturopathy pretty much go off the deep end, as ably discussed by any number of medical bloggers on ScienceBlogs and elsewhere. The point argued by this particular commenter went as follows:
Speaking of pseudoscience, what do you all think of…
mspringer | April 17, 2009It was a dark and stormy night. Well, it was day. And it wasn't all that dark either, but it was very stormy. Yes, in College Station today it was pretty miserably wet and so was everyone on campus. Even if you had an umbrella.
Not actually very glorious.
Well, I thought, I wonder if you could do something with all this rain? Maybe generate electricity?
Unlikely, because it's a pretty obvious idea and were it practical surely someone would have tried it. But it can't hurt to run the numbers for ourselves.
The physics building at Texas A&M is five stories high, and at a very rough…
mspringer | April 16, 2009Let's say you've got one of these, and you're dusting off your computer:
(img source)
As you spray, you'll notice the can getting cold. You've probably noticed this in similar contexts: propane tanks getting cold, helium tanks getting cold, compressed air tanks running pneumatic tools getting cold, etc. It seems that when air escapes from an enclosure, it gets cold. Well, there's a reason.
Imagine if you will a elementary school gymnasium filled with kids and adults. The principle of the school announces free ice cream in the field outside of the gym and flings the doors open. The kids…
mspringer | April 14, 2009I almost titled this entry "Rocket Porn" but I wasn't sure if the management would appreciate it. Still, to the space enthusiast this is definitely pretty enthralling.
These photos are straight from my old college roommate, now an engineer at NASA's Stennis Space Center. He works in a building that overlooks the test stand for the new engines that are going to power the next generation of rockets, and it's apparently quite the show. The fuel costs alone run well into the hundreds of thousands of dollars per test and so I suppose I should temper my enthusiasm on the grounds that I spent…
mspringer | April 13, 2009I can't think of a way to relate this to physics, but it's just too cool not to share. In New York City there is an artist named Kacie Kinzer. She created small cardboard robots that can do precisely one thing - roll forward continuously. Well, that and look cute.
Attached to these robots is a flag saying "Help me!" and a description of these robots' predicament. They're trying to get to a particular destination but can't, by virtue of the fact that they have no brains or steering. And they were successful:
Over the course of the following months, throughout numerous missions, the…
mspringer | April 12, 2009Today is Easter Sunday, the most sacred and second most widely observed holy day in the Christian calendar, celebrating the resurrection of Jesus. Friday was Good Friday, the remembrance of the crucifixion. Thus after spending three days buried, Jesus rose from the dead.
Wait, three days? Let's see... Friday night to Saturday is a couple of hours, Saturday is a full day, and Sunday morning is a few more hours on top of that. So a day and a half, then. But of course all the liturgy and ceremony talks about three days.
This is because the ancients counted time as opposed to measuring it…
mspringer | April 11, 2009Mike the Mad Biologist links to a piece arguing that Social Security is fine thank you very much. Rumor to the contrary is pure political propaganda, and the fact that many young people think they'll never see a dime is a result of simple fearmongering.
I am sorry to say that they're not right. They're not even wrong, having missed the point entirely. Indeed as a factual matter their understanding of the way Social Security and its trust fund operate is fine. It's simply that "there is no crisis" does not follow from the premise that we can always borrow more.
First, consider the Social…