For several years, the stock market has been booming while most Americans are facing increasingly worse financial situations. In 2006, the personal savings rate went negative for the second year in a row -- something that hasn't happened since the Great Depression. Every time Bush talks about the economy recently, he tells us how the economy is "strong." Piffle. The economy might be growing, but it is anything but strong. "Growing but extremely fragile" is a more accurate characterization.
Nevertheless, when the stock market has a shock, the axiom still holds. The stock market isn't the economy. Bad news on Wall Street might actually be a good thing for America right now. It's about time that the rich and powerful catch a gust of the ill winds that have been ravishing America's poor and middle class. Maybe they will put down their cognac long enough to help us do something about it.
Next, Abers calculated the classical cross section for a sphere (it's just the cross sectional area of the sphere) and the cross section to propagating plane wave (four times as big). In the region of small-angle deflections, the wave equation undergoes constructive interference. Both calculations is pretty fundamental, so I'll revisit it once I finish the homework for the variational principle.
Update: Here is once case where I am deeply grateful for Abers' book. His lectures match the book exactly, so if I miss something in class, I know I can always find it later. My hunch was correct; he working through the Born series for spherically symmetric potentials.
It would be bad enough if it weren't for the surly attitude and lousy service from the major airlines. The IRS is better at customer service than the major carriers. They really are. The first time I had to file a tax return, I didn't even know where to start. I called the IRS. They were polite, answered all my questions, and explained how to fix things if I made a mistake. The told me how to file for an extension, if I needed to. They gave me a list of local certified tax accountants if I wanted more technical advice. They were even cheerful about it. Good luck finding that kind of treatment from an airline official on a busy day.
That said, I've always liked JetBlue. They are one of the few bright spots in an otherwise rotten industry. If there was some way that I could board their flights without having to run the gauntlet of idiotic airport hassle/security, I might actually enjoy flying.
Last weekend was a very bad weekend for JetBlue. Leaving thousands of passengers stranded and angry, it seemed that their effort to be the Good Airline might have finally broken. Fortunately, that seems not to be the case.
Dear JetBlue Customers,Sincere apologies are rare in our culture. The best you'll hear in most cases is something like, "We are sorry that this unfortunate thing has happened." So, when the CEO of a major airline sends an email to his company's customers that says, "Words cannot express how truly sorry we are for the anxiety, frustration and inconvenience that we caused." He doesn't even blame the storm, or the facilities, or bad luck. This is called "taking responsibility." It's something that grown-ups are supposed to do, but that CEOs and presidents and small children usually do not.
We are sorry and embarrassed. But most of all, we are deeply sorry.
Last week was the worst operational week in JetBlue's seven year history. Following the severe winter ice storm in the Northeast, we subjected our customers to unacceptable delays, flight cancellations, lost baggage, and other major inconveniences. The storm disrupted the movement of aircraft, and, more importantly, disrupted the movement of JetBlue's pilot and inflight crewmembers who were depending on those planes to get them to the airports where they were scheduled to serve you. With the busy President's Day weekend upon us, rebooking opportunities were scarce and hold times at 1-800-JETBLUE were unacceptably long or not even available, further hindering our recovery efforts.
Words cannot express how truly sorry we are for the anxiety, frustration and inconvenience that we caused. This is especially saddening because JetBlue was founded on the promise of bringing humanity back to air travel and making the experience of flying happier and easier for everyone who chooses to fly with us. We know we failed to deliver on this promise last week.
We are committed to you, our valued customers, and are taking immediate corrective steps to regain your confidence in us. We have begun putting a comprehensive plan in place to provide better and more timely information to you, more tools and resources for our crewmembers and improved procedures for handling operational difficulties in the future. We are confident, as a result of these actions, that JetBlue will emerge as a more reliable and even more customer responsive airline than ever before.
Most importantly, we have published the JetBlue Airways Customer Bill of Rights—our official commitment to you of how we will handle operational interruptions going forward—including details of compensation. I have a video message to share with you about this industry leading action.
You deserved better—a lot better—from us last week. Nothing is more important than regaining your trust and all of us here hope you will give us the opportunity to welcome you onboard again soon and provide you the positive JetBlue Experience you have come to expect from us.
Founder and CEO
The Passenger's Bill of Rights is a good idea. It's what airlines should have been doing all along.
Taking responsibility when things go wrong is probably the most important function of a leader. It's something that our current national leadership is notoriously bad at. It should come as little surprise, then, that JetBlue is the only US carrier that is a significant contributor to the Democratic party.
We began examining the geometry of the scattering problem. The scattering geometry is this: A target sits at the origin of a spherical coordinate system. A beam of particles is directed at the target. The target is treated as a macroscopic object, so the beam is expressed in terms of a "probability current." This is simply a way of treating a continuous stream of traveling wave functions. Of course, each wave function must be normalized, but because the beam is switched on for an arbitrary length of time (forever) the beam itself is not. Thus, the probability current formalism describes the flux of probability through the surface. Typically, one would choose the surface to be the beam-facing surface of the target.
Some sort of interaction occurs among the particles in the target and the particles in the beam; usually, the particles in the beam are scattered off of a potential in the target. The Rutherford scattering experiment is an example of a beam scattered by a potential. Alternatively, interaction with the beam could change the state of the target; a photon beam could excite the valence electrons in the target, which would eventually return to the unexcited state and re-emit the photons, or beam of positrons could annihilate with electrons in the target, or a beam of high-energy neutrons could smash the target nuclei into assorted atomic debris. If the beam is scattered by the target without changing the state of the target, this is called elastic scattering.
The scattering problem is useful because because beam-target interactions will divert the beam into a characteristic angular distribution of beam particles. The scattering problem can be used to study the properties of the target, the beam, the interaction, or any combination thereof.
Nonrelativistic elastic scattering
To introduce the technique, we consider a beam of nonrelativistic, spinless particles scattered elastically by a fixed potential. Because the number of collisions in a given time will vary with the beam intensity, it is convenient to eliminate the time interval from the equations by expressing the problem in terms of a cross section. The term is an analogy to the classical collision problem; one may imagine the target as a cloud of spheres with a given radius. The classical cross section of such a system would be the sum of the two-dimensional area presented by each sphere to the beam per unit volume of the target. One can think of it roughly as the "effective area" per unit area of the target, or as the "opacity" of the target.
For Coulomb scattering, the beam and the target will not actually contact one another (otherwise we would have to take other forces into account, and it wouldn't be Coulomb scattering any more). The cross section is then the area within which a beam particle will "significantly" interact with a target particle. Rather than specifying some arbitrary definition of "significantly," it is better to define the problem in terms of a differential cross section which scatters the the beam into a differential solid angle. This is better illustrated by a picture, so I'll stop blathering about the geometry.
As I mentioned above, the beam is not normalizable. Generally, one treats it as a plane wave. The scattering problem amounts to calculating over what solid angle the probability current passing through a given differential cross section will be scattered by a potential.
I was about a quarter of the way across a quiet residential street. A woman driving a brown sedan came down the street I was crossing and stopped at the stop sign. She was a car-length past the line for the stop sign, but not yet into the intersection. She looked up and down the street she was about to cross. I was about ten feet away from the driver side window when she came to a stop. She paused a good long time while looking, so it appeared she was yielding to me. I continued across the street.
I was, by this point, in front of her car. While looking around, she must have somehow failed to notice the large man wearing the bright orange reflectorized jacket. She stepped on the gas, and I fell on her hood to avoid having my knees snapped.
She did not touch the breaks. She simply threw her hands up and let the car roll slowly into the intersection. This is probably the right thing to do if you hit someone at low speed. If you slam on the brakes, you'll toss them off the hood and in front of your car.
I got up on my elbow and looked at her to see what her reaction was. She looked like she was scared shitless. She was about 50 or 60 years old, with short hair in little curls. She had reading glasses on a string around her neck. I did not feel like lecturing someone's grandmother about sharing the road, so I got off her hood and walked away. After sitting in the intersection for twenty or thirty seconds, she drove away.
It occurs to me that people in Los Angeles simply do not look for pedestrians. It is so fantastically unlikely that you will ever encounter anyone proceeding on foot that people forget to take the possibility into account. One is as likely to encounter a unicorn as a pedestrian when motoring in quiet residential neighborhoods. The lady was definitely being cautious. She paused at the stop light for a good long time, and carefully looked each way several times. However, she was just looking for other cars. It must have completely slipped her mind that she ought to look for things other than cars.
Of course, if she had stopped behind the line, she probably would have seen me. That is why they put the line where it is. However, from behind the line, she could not have safely looked down the intersecting street. In such circumstances, you are supposed to stop twice: Once to look for pedestrians (and obey the stop sign), and once to check for cars. Sometimes you can do both at once, but not always.
Modern roads really are a curious invention. Contrary to most people's assumptions, our roads do not exist to allow people to move quickly. It would be simpler (and probably cheaper) to design vehicles that can drive fast without the expense and complexity of a road. The US Army has lots and lots of such vehicles. The problem is that such vehicles are extremely dangerous, which is why we only use them for weapons.
The reason why they are dangerous is that they must be used under complex conditions. The desert basins of Southern California are ideal territory for tanks. However, very few people can safely operate a tank under any circumstances. Safely operating a tank among pedestrians, pets, houses, gardens, mailboxes, fireplugs and wildlife is probably an impossible task.
So, we build roads. Modern roads exist to minimize complexity. This allows drivers to operate on a smaller set of assumptions. This is probably the only reason that most normal people are able to drive at all. I consider myself to be a pretty safe driver, but I know that I don't have the skill, attentiveness and reaction time needed to safely operate a tank in a populated area. If I had to move a tank across Los Angeles, I would would disassemble it and carry each piece in a pickup truck.
No matter how carefully we design our roads, they are a fiction. The real world is too complicated for people to safely drive a vehicle at 25 miles an hour, so we have invented a simpler world where it is safe. Los Angeles is exceedingly good at this. Our roads are logical, the signs are large and easy to read, the lanes are carefully marked, and the stop signs and crosswalks are thoughtfully placed. Unfortunately, the real world always has a way of impinging on our carefully constructed fiction. Unfortunately, the bits of the real world that include cats, dogs and small children do not stand much of a chance against 3000 pound steel projectiles. It is especially alarming when you realize that these projectiles are controlled by people who have just barely enough skill to safely navigate in an imaginary cartoon universe where cats, dogs and small children do not exist.
Evidently, pedestrians in crosswalks are fading out of the fictional world in which ordinary people must live in order to operate a motor vehicle. This is a very scary thought, and it doesn't say anything good at all about Our Fair City.
Once the separation distance had been found (approximately), we calculated the energy spectrum of rotation for the hydrogen molecule. To calculate the vibrational energy spectrum, we expanded the Coulomb potential of the atom to second order. This potential is simply the harmonic oscillator problem. With the correct dimensions, the harmonic oscillator yields a good small-amplitude approximation of the vibrational energy spectrum.
It was noted that for various diatomic molecules, the rotational energy spectrum will also depend on the nuclear spin. Atoms with nuclear spin 1/2 will behave as fermions, and atoms with nuclear spin 0 will behave as bosons. Depending on the nuclear spin, symmetry may forbid certain energy levels. This is a critically important feature of matter that determines the statistical behavior of bulk quantities of the material.
In other news, we will evidently be skipping the WKB approximation so that we can spend more time on scattering.
"In the eyes of the government and courts of California, marriage shall be hereby defined as none of its goddamned business."If gay people are ever allowed to get married in California, it won't be by convincing straight people to care. That isn't to say that straight people don't care; 2,909,370 people voted against Proposition 22. Gay people will win the right to marry when straight people start getting uncomfortable about having the government rummaging around in their married life. Then gay people and straight people can rally behind the same slogan: It's none of your goddamned business. A proudly American sentiment.
Democrats reflexively package their arguments in the terms of wonderful programs and insightful social policy. This isn't going to work for these kinds of issues. Most straight people still feel uncomfortable about actively supporting a policy that will lead to men kissing other men on TV. But most straight people probably would support a policy that would grant them a little more freedom and privacy.
From there, it's easy. Americans will generally be comfortable reasoning that what other people do with their privacy and freedom is their own damn business. It's simply a matter of framing the debate in such a way that the bible thumpers are bossing "regular people" around.
RussellThe notes are posted, and I will summarize them in a future post.
I finished the application of the variational principle to two-electron atoms like helium, then started on the Born-Oppenheimer approximation. I will post some notes soon to replace the discussion in section 7.6.1.
We then calculated the energies of various two electron systems. It was noted that the perturbational approach seems to converge very slowly, and that the second order calculation would be a nightmare. Onwards to variational methods!
We then rushed through an introduction to the variational method. The variational method can be thought of as a generalization of perturbation theory, but only for the ground state. It works as follows: You assume a priori that there is an eigenstate of the Hamiltonian with a minimum energy, and you make a guess about what it might be (this only works if your guess is "reasonable"). The "true" ground state will be the eigenfunction that minimizes the energy. So, you guess its form, and tweak whatever parameters it has until you find the minimum energy. If you guessed the exact form of the function, and you do enough tweaking, in theory you can find the exact eigenfunction.
A little more formally, you know that each eigenstate spans all of function space. So, the ground state will span all of function space. So, whatever you guess, it must be a linear combination of the eigenstates. So, you write the trial function as a sum over the eigenfunctions with some coefficient for each one (you can always do this). Each eigenstate corresponds to an energy eigenvalue, so you can replace the sum over eigenfunctions with a sum over their corresponding energies (and their coefficients). As you vary your trial functions and evaluate the sum, the lowest possible value you can find will be the case where the coefficient of the ground state is 1, and 0 for all the others.
This seemed almost offensive to me. I was eleven or twelve years old, so not very much time had passed since my Dinosaurs are Awesome! phase. I knew that palaeontologists had a pretty good idea of what killed the dinosaurs. Like any recovering dinosaur-enthusiast, I knew about the K-T boundary and its abundance of rare isotopes of iridium and chromium. It seemed like pretty solid evidence to me; an asteroid impact had caused the mass extinction. The big question was whether or not the Chicxulub crater was the site of the impact. Our textbook's claim that scientists have "no idea" what killed the dinosaurs was very unsettling. The fact that no one really seemed to care about the misleading characterization of the topic was disturbing.
In freshman year biology class, we began our discussion of genetics by examining the inheritance patterns of various genetic diseases. To my horror, several students repeatedly expressed the opinion that the world would be better if we simply sterilized or exterminated everyone with, for example, cystic fibrosis. Then we wouldn't have to worry about it any more. The teacher was appalled. By the time evolution came around, I was was resigned to the necessity of ignoring everything my classmates had to say.
Then there was global warming. In my elementary school science classes, we learned that carbon dioxide and water vapor are greenhouse gases. We learned that both gases are emitted by combustion. We also learned that fossil fuels are the decomposed remains of dead plants and animals. We learned about the global carbon cycle. And yet, the question of whether or not humans could cause global warming was considered "dubious."
In high school, virtually no one thought humans could cause global warming. When I competed on our policy debate team, judges would often throw out your whole case if you impact scenario involved global warming. We were coached to avoid the topic. If our opponents raised the issue, we were given canned arguments designed to undermine the whole idea of global warming. The canned arguments didn't attempt to prove or disprove anything; they merely created doubt and confusion about the issue. I seem to recall that our teams used a popular anti-global-warming brief from Baylor University, though I can't find a reference to it. They were devastatingly effective. Later on, I noticed that same arguments turned up in newspaper editorials and political messages.
Nevertheless, it always seemed so obvious to me that global warming was a real threat, and that the burning of fossil fuels was the most likely cause. I recently began to wonder why it was that I remained convinced of its dangers despite spending a decade of my formative years among a consensus of global-warming naysayers. Why was I so convinced?
Obviously, I hadn't read the scientific literature and I hadn't conducted studies myself. Whatever convinced me, it wasn't exactly careful evaluation of the evidence. I suppose it must have been the hours and hours I spent playing my favorite video game.
SimEarth is a toy model, and the real feedback systems in the environment are vastly more complicated. Global warming in SimEarth was a fairly simple effect. However, tinkering with the simulation did give me an intuitive appreciation for the complexity of interdependent systems. The Earth is vastly more complicated that even the most sophisticated computer simulations. SimEarth teaches an exceedingly important lesson: When you disturb a complex nonlinear system, there are always consequences. Even when you understand every single rule governing a system, you often cannot predict the outcome.
If you don't believe me, fire up SimEarth, and try to guide a civilization of intelligent amphibians to the stars.