February 17, 2009. Silver lining?

Robert Remini was not a forceful and straight forward historian as I thought. He refuses to get embroiled into any apparently partisan argument of whether one sitting president is a good one or a bed president according to his research and standards.

The TV program in this area of Henrico is very disappointed. The CSPAN bookTV program often gets co-opted by sport program such as college basket ball game. The local station too poor to pay for these programs and cable company such as COMCAST has to get involve to provide the service for the local audience.

Then the NPR program is not as bountiful as the Charlotte NPR station. Many programs that are normally available by viewers’ contributions and donations are not available here. There are more so-called Christian programs to take the place of these NPR liberal programs.

The weather turns cold again today.

Last night, Charles Rose had a panel of journalists focusing on Afghanistan. One of the panelists had the analogy of Vietnam for LBJ, Iraq for W. Bush and Afghanistan for Obama. This is the kind of bind a president find himself in all the time. What is the power of the president to do what he wants to do. Pull out or stay the course.

He is not himself when it comes to foreign policy and national interest. So much for the most powerful man in the world!

What is the most interesting foreign policy of Obama administration seem to be in the hand of Richard Holbrook instead of the hand of Hilary Clinton. The same goes with the Israel-Palestinian issue. It is in the hand of George Mitchell. This is the concept of Czar of a certain field. These are the Czar of Afghan issue, Israel-Palestinian issue, Iran issue, Iraq issue and etc.

Foreign policy issues and national interest issues are favorite subject of CR Show. I could have switch to Travis Smiles Show and skipped the CR Show. The programming feature of the PBS station in this area is so backward. It is the intent purpose to separate one group of program from the others. This is an either –or-nothing binary choice.

CEO of City Corp is the Vikram Pandit. He is very well verse in protecting the interest of share holders of the corporation. This is how he argued not to write off all the bad loans at a fire-sale price. He believes they are more valuable than what the hedge funds community happen to think. This is the answer he gave during a congressional finance committee hearing.

These CEOs are very forceful in responding to the queries from member of the US congress finance committee members. This is a very impressive show of power. This is a very long hearing that I have no time to sit through its entirety.

Blaming the Lehman Brothers for its own failure is the best way to cover up the personal animosity between Paulson and the CEOs of Lehman brother. The cases AIG and Bear Stearns are handled totally different from the Lehman Brothers case.

Tim Geithner had handled the previous two cases and save the name of these institute. The Lehman brother case was handled by Hank Paulson and he let it sink. “Inside the finance meltdown” by Frontline is a very interesting program in hindsight.

Senator Sander was wondering aloud that why Goldman Sachs CEO Bankfein was not fired from his job when he was responsible for the mess of Goldman Sachs. I don’t recall what the CEO’s answer is.

During a crisis of finance, company in US as well around the world can forsake all the promise it has made to its employees in term of Pension and other benefits including the medical insurance plan. So workers in US as well as in China are all in the same boat. One exception is they can hire a lawyer to file a lawsuit against the former employer for breach of contract in US. This is not the case for workers in Third world countries such as Thailand, Vietnam, India and China.

There are continuing meltdowns taking place day after day. What is the watch dogs group been doing in tracking government spending for the stimulus plan? More government employees for the state of California are being lay off. So the way of beating the bind of having to raise tax and price for public projects and service, government administrative workers are simply let go. This is one way for handle recession in economy.

There is some good news during the recession in term of business. The public reaction to the slowdown of income is cutting back of eat-out and learns to cook at home. The culinary school is booming as a result. So it is the silver lining of a dark cloud.

February 17, 2009. Möbius strip? Fiber bundle?

The Möbius strip is a nontrivial bundle over the circle.

Trivial bundle

Let E = B × F and let π : E → B be the projection onto the first factor. Then E is a fiber bundle (of F) over B. Here E is not just locally a product but globally one. Any such fiber bundle is called a trivial bundle. Any fibre bundle over a contractible space is trivial.

Perhaps the simplest example of a nontrivial bundle E is the Möbius strip. It has the circle that runs lengthwise along the center of the strip as a base B and a line segment for the fiber F, so the Möbius strip is a bundle of the line segment over the circle. A neighborhood U of a point x ∈ B is an arc; in the picture, this is the length of one of the squares. The preimage π ^{− 1}(U) in the picture is a (somewhat twisted) slice of the strip four squares wide and one long. The homeomorphism φ maps the preimage of U to a slice of a cylinder: curved, but not twisted.

The corresponding trivial bundle B × F would be a cylinder, but the Möbius strip has an overall “twist”. Note that this twist is visible only globally; locally the Möbius strip and the cylinder are identical (making a single vertical cut in either gives the same space).

This is a good description or intuitive feel of the definition of fiber bundle.

The fiber is also known as the pre-image of a point of Y in the function f: X -> Y.

This is the kind of interpretation of the math concept that I have yet to come across in those old math books.

Covering space of the form of Reimann surface in the topic of lifting is also a form of fiber bundle. Bundle is the entire space and fiber is just simply a small slice or subset of the bundle.