mspringer | December 2, 2008If you go to Capital One's website and type in the appropriate login information, you'll see a "Welcome Matthew Springer" message and two accounts. One's a checking account and one's a money market account where I'm endeavoring to accumulate some savings. (I need to get that moved to a CD or something, the interest rate is awful). Just below those two accounts is a number representing the total amount of cash I possess. It obeys what you might call the financial analogue of the continuity equation:
This is the version you see in electrodynamics. It says that the flow of charge into or…
mspringer | December 1, 2008Well, my Thanksgiving posting break lasted longer than I thought. Real life is a more fun place than the internet though, and I hope you were having lots of fun and food and were not on the internet to notice my absence.
Among the things I did this Thanksgiving was watch Dr. Horrible's Sing-Along Blog for the first time. It is, as you know, a thing of surpassing brilliance. It warrants a few posts about its unique self-financed studio-conglomerate-free creation, because that model would probably work well in other arenas of creativity, not the least of which is science. That I'll save for…
mspringer | November 26, 2008Ok, ok, I admit there's post-1900 classical that I really like. Copland and Gershwin in particular were mentioned by a number of people, and both are great. I made my first acquaintance with Copland when I was a little kid watching a NASA documentary, and in the background of some dramatic launch was his Fanfare for the Common Man. Gave me chills.
Now to the actual post:
I'm thankful for many, many things. One of them is having the next few days off from school. Now large parts of that time off are going to be spent studying, but that's not a bad deal considering there will also be…
mspringer | November 25, 2008I'm on the road today and so can't write up an extensive post. So for today, I leave you with a picture from physics history: the 1927 Solvay conference. It proved that there's no critical mass for genius. If there were, this gathering would have exploded. A large fraction of my "Greatest Physicists" are all in the same place smiling (or glowering) for the camera:
(Click for full size)
If I had a time machine, that conference would be pretty high on my list of things to see.
mspringer | November 24, 2008Classical is how you look at it. To most people, classical music is whatever happens to be written before about 1900 that you hear played in orchestra halls and NPR. To classical fans, there's more nuance involved. More ambiguity, too.
"Classical music" is generally divided into about four eras, one of which is itself confusingly called the "classical era". They run as follows.
Baroque: From about 1600-1750. To pick a representative example of this beautiful and staggeringly diverse genre at random from playlist.com, here's Bach's Suite No. 3 In D - Air 'On The G string'
Classical: 1750-…
mspringer | November 23, 2008This function is a two-dimensional one. It's radially symmetric however, so we can specify it with only one coordinate - the distance from the origin r. It's the two-dimensional Gaussian function, and it looks like this:
As r increases, -r^2 very quickly becomes a large negative number. The exponential function falls off rapidly toward zero at negative arguments, and so as you move away from the origin the value of the function is pretty much nil.
Now if you think of that graph as a clay sculpture, you'll see that almost all of your clay will go to making that central bulge. Away from…
mspringer | November 22, 2008Take a look at the opening paragraph of this great AFP article:
It's taken more than a century, but Einstein's celebrated formula e=mc2 has finally been corroborated, thanks to a heroic computational effort by French, German and Hungarian physicists.
I'm sorry, did I say great? I meant awful. That particular equation of Einstein's was demonstrated rather convincingly in a lot of boring experiments starting almost as soon as he wrote it down. A few years later it was demonstrated rather convincingly in a particularly dramatic fashion. The particular work referenced in the article has squat…
mspringer | November 21, 2008Another former astronaut, one of the few in the extremely exclusive club of men who've walked the lunar surface, is advocating a human return.
There's not many people who'd like to see such a thing more than me. Officially it's NASA policy to get us back to the moon by... lessee, 2020 I believe is the current figure. Delays would not be unexpected. From the Kennedy speech announcing our goal of landing on the moon for the first time to Armstrong's stepping onto the Sea of Tranquility was 6 years, 8 months, and 8 days. With technology from the 60s! We are in a sorry state indeed.
Yes, yes…
mspringer | November 20, 2008One of the last things we cover in Physics 201 is heat. You all know what heat is: the atoms in a substance jiggle around or fly around freely if the substance happens to be a gas. Like all moving massive objects, these atoms have a certain kinetic energy. Now the problem is that they're all constantly moving and crashing into each other, exchanging energy back and forth. It's hard enough to keep track of the energy exchange between two colliding objects (trust me!), much less a trillion trillion of them. So we treat them as a statistical ensemble and just look at the average energy.…
mspringer | November 19, 2008#3 - James Clerk Maxwell
James Clerk Maxwell is my favorite physicist. This site takes its name from a wise thing he once said: "In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data." For all the volumes written about the philosophy of science, that sums it up pretty well. Is it built on observable facts and empirical data? If so, it's science. Otherwise it's not. Anyone, however, can come up with a clever thing to say. Almost no one in history has come up with as many brilliant…
mspringer | November 18, 2008A question before the physics: I hear Hillary Clinton is being considered for a position as Secretary of State. Let's say this is true. Why would a senator want to take that job? It's a temporary position. Eight years max, not much longer than a single term in the senate. Four years if the president doesn't get re-elected. In the senate you set your own views and political objectives. In a cabinet position you work under the orders and at the pleasure of the president. If you disagree with the president, too bad for you. Both your ideals and your reputation are largely at the mercy…
mspringer | November 17, 2008Here, straight from the Wikipedia article, is a lovely picture of a basketball in a free-flight trajectory.
You probably expect a parabolic trajectory, and we do get pretty close. There are some deviations. The resistance of the atmosphere is the largest, and the rotation of the ball will itself result in aerodynamic effects that distort the flight of the ball from its idealized trajectory.
But in fact even in a perfect vacuum with no external forces but gravity we still won't get a parabola. We'll get a section of an ellipse.
Why? Newton's laws tell us that if you're in the…
mspringer | November 16, 2008Here's sin(x).
What, you don't believe me? Ok, ok, I'm leaving something out. Let's do some background before I tell you what it is.
The first thing we need is the incredibly interesting and important Euler's formula. It's the key that relates the exponential and trigonometric functions. We won't pause to figure out why it's true, for now we'll just take it as a given:
Now replace x with -x, and we'll use the fact that cos(x) is the same as cos(-x), and sin(-x) is the same as -sin(x).
So that's two ways of saying the same thing. Now we'll subtract the second equation from the first.…
mspringer | November 15, 2008So what would the elementary quantum of solace be? The soliton? I haven't actually seen Quantum of Solace yet, but I'm going to make a point to go at some time this week. The last Bond flick was great, and I have high hopes for this one. Most sequels don't quite live up to their predecessors, but by most accounts this one comes quite close. And this is the year that gave us The Dark Knight, after all.
Wall-E is about to be out in a few days, and that is probably the best or second best film of the last year. Seen it yet? If not, for shame. Go buy it. (That's the Blu-Ray version, but…
mspringer | November 14, 2008I thought about linking this Forbes article on the economic situation simply because it's interesting. What actually made me link it was the sentence at the end:
And reality tells us that we barely avoided, only a week ago, a total systemic financial meltdown; that the policy actions are now finally more aggressive and systematic, and more appropriate; that it will take a long while for interbank and credit markets to mend; that further important policy actions are needed to avoid the meltdown and an even more severe recession; that central banks, instead of being the lenders of last resort…
mspringer | November 13, 2008It is a capital mistake to theorize before you have all the evidence. It biases the judgment.
- S. Holmes
Built on Facts is going on a brief (2 day) semi-hiatus as I've got a classical mechanics exam this Friday. It's not a total break though. The posts will be there, but they'll just be short. With all respect to Mr. Holmes, why don't we ignore him just for the moment and make today a bit of a survey day? Specifically, a survey about what we think about physics for which we have no (or very little) experimental data! Short answer format:
Does each exist or not?
1. A way for a massive…
mspringer | November 12, 2008Today in my recitation we discussed several problems in acoustics. One of them involved beats. This happens when two tones which are very close in pitch are played at the same time. There's a demonstration on the Wikipedia article. I'll solve the problem here since if it confused people in class there's probably people googling it. It's an easy problem, the difficulty comes from a lack of clarity in this section of the book.
This problem is Young and Geller 12.54:
A violinist is tuning her instrument to concert A (440 Hz). She plays a note while listening to an electronically generated…
mspringer | November 11, 2008Let's say you have a table. This table is better than your average table. It's perfectly level, absolutely flat to within the thickness of an atom over its entire surface. In fact, this table isn't even made of atoms. You called up Plato and ordered the platonic ideal of a flat table.
Now you set this table down in your dining room and have Plato's deliverymen install the table so that it's perfectly flat with respect to the earth's surface. Then you take a ping-pong ball and set it down toward the edge of the table. What happens?
It doesn't stay still. It will roll to the center of…
mspringer | November 10, 2008There's been an article in the Guardian that's been circulating around various science blogs recently. There's a proposal to make what small autonomous nuclear reactors, install them underground, and let them power local areas.
Nuclear power plants smaller than a garden shed and able to power 20,000 homes will be on sale within five years, say scientists at Los Alamos, the US government laboratory which developed the first atomic bomb.
The miniature reactors will be factory-sealed, contain no weapons-grade material, have no moving parts and will be nearly impossible to steal because they…
mspringer | November 9, 2008Math-averse readers! Do not be scared off! You can enjoy this entry even if as far as you're concerned the equations are pretty pictures of Cypriot syllabary.
Not long ago we looked at adding up lots of consecutive integers. Multiplying consecutive integers is also interesting, and not only that it has a tremendous number of uses all throughout physics and pure mathematics. The function that multiplies the integers from 1 to n is called the factorial function, and rather unusually it's denoted with an exclamation point, like this:
Here I'm using dots to denote multiplication, as is…