youngsub's Xanga

Monday, November 09, 2009

Mon, 09 Nov 2009 20:40:17 GMT

My uncle's father's last word was "보증서지마라" which would be roughly translated as "Do not promise your friend that you would pay for his debts in case he fails to pay for it." Korean language has a specific term for this situation.

In Korea, if you don't have enough mortgage, an alternative way to get a loan is bringing up other persons who would pay for your debt, in case you fail to pay for it. Many Koreans promise their friends that they will pay for their friends' debts out of friendship especially since their friends assure you that it will never happen that they fail to pay for it. I don't think that this system is good.

Tuesday, November 03, 2009

Tue, 03 Nov 2009 19:33:07 GMT

Yesterday, I learned the relationship between the index theorem and the chiral anomaly. It was so awesome, and beautiful.

Saturday, October 31, 2009

Sat, 31 Oct 2009 03:29:26 GMT

Some people claim that Albert Einstein was not a good student. However, here are counter-examples:

"Yesterday, Albert got his grades, once again he was ranked first,..."

(From a letter from Albert's mother Pauline Einstein to her sister Fanny Einstein, dated Aug 1st 1886, reproduced in "The Collected Papers of Albert Einstein: The early years, 1879~1902")

"He did so well at his autodidactic preparations that at the beginning of October 1895, at the age of only 16 1/2, he passed the entrance examination to the Federal Polytechnical School in Zurich, with the greatest success in the mathematical and scientific subjects but deficient results in the linguistic and historical ones. Because of these gaps in his education and because of his youth, his parents were advised to hav their son attend the final year of a Swiss secondary school, but with the prospect of certain admission the following year, despite the fact that he would still be fully six months below the prescribed age."

(Albert Einstein--A biographical sketch by Maja Winteler-Einstein (Albert's sister), reproduced in "The Collected Papers of Albert Einstein: The early years, 1879-1902")

Friday, October 30, 2009

Fri, 30 Oct 2009 19:03:33 GMT

Why I like physics more than philosophy:

I like physics because of its mathematical beauty. To learn more about that read my xanga entry on Nov 24th 2006. Here is another quote that could signify what the mathematical beauty of physics might mean:

"Every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics." (Richard Feynman, Nobel laureate in Physics in "The Character of Physical Law," p 168)

For example, it is amazing that Heisenberg's quantum mechanics and Schrodinger's quantum mechanics are equivalent, even though they may seem very different. It's amazing that they give the same results even though the actual calculations are very different. (It was Von Neumann who proved that they were equivalent.)

Another example: Feynman's quantum electrodynamics and that of Tomonaga and Schwinger's look very different but they give the same answers even though the actual calculation are very different. (It was Freeman Dyson who proved that they were equivalent.)

The very fact that there are six or seven different theoretical representations mean that physics is indeed consistent. However, even though I don't really know a lot about philosophy, I guess that it may not be true for philosophy. It seems that there aren't several equivalent constructions on ideas in philosophy. You may give several different arguments for your assertions, but that doesn't mean that these several arguments are equivalent. Has it been ever proved that philosopher A's argument and philosopher B's argument are the same even though they naively look very different?

Tuesday, October 27, 2009

Tue, 27 Oct 2009 23:30:23 GMT

Today, I asked my TF David about quadratic divergences and renormalization group equation. He convinced me that the coupling constants don't get renormalized when there is a quadratic divergence; it only gets normalized when there is a logarithmic divergence. Wow. Why didn't any textbooks that I studied mentioned this fact? I used to be confused.

Thursday, October 15, 2009

Thu, 15 Oct 2009 23:35:50 GMT

Je suis encore tres content! So ist es. So ist es. C'est ça.

Tuesday, September 29, 2009

Tue, 29 Sep 2009 16:08:29 GMT

I found out that the following Korean sentence has two meanings:

언제 쯤 올 수 있는지 확실히 알 수 있어?

1) When will you be able to know for sure whether you will come here?
2) Are you able to know for sure when you will come here?

Tuesday, September 29, 2009

Tue, 29 Sep 2009 00:32:43 GMT

Today, I attended a seminar on physics education by Prof. Mazur of Harvard University.

He said that he had used to think that he himself was a very good lecturer, because he received 4.5 or 4.7 out of 5 on students' rating on his courses.

However, he realized that this was a misperception. There is a multiple-choice type test called FCI, which consists of about 30 questions which deal with Newtonian mechanics. This test focuses more on concepts rather than on problem solving skills. He had his students take this test before and after they took his course, and compared them. Surpisingly, he found out that there were not much differences on their performances between before and after the course.

Then, he said that the conventional physics problems checked only whether students are able to use physics formulas to plug in appropriate variables rather than whether they actually understood the concept.

As an example, he showed that students could easily solve an electric circuit problem by using Kirchhoff's laws but failed to solve another electric circuit problem that focused more on concepts which should be easier, once students understand the concept, since no algebra or no formulas are needed. 52% of students solved the conceptual problem at the same proficiency as the conventional problem. 9% of students solved the conceptual problem better than the conceptual problem, and 39% of students solved the conceptual problem worse than the conventional problem.

So, his remedy to this problem was the following:

First, he assigns students pre-class reading. Then, in the lecture, he explains things in more details. Then, he asks the students to answer a conceptual problem. Of course, students use clickers for this purpose. Then, he shows how many students choose certain answers, and ask them to talk with one another about this conceptual problem, then ask the students choose the answer for the second time. Then, he finds, most students get the problem right.

The point is that the students who have just learned these materials can explain things to each other better than the professor, because the professor has learned it such a long time ago, and forgot what conceptual misunderstandings the students may have. He called this method of teaching "peer instruction."

During the question and answer session, somebody asked how he came up with such nice conceptual problems. The professor repsonded that he assigns pre-class reading, and asks them to solve three problems after doing the pre-class reading. The first two problems are very hard, so that they cannot just copy the answers from the pre-class reading, and the third problem asks the students to write what they found most confusing. He said that he made the conceptual problems based on what the students found most confusing.

Prof. Mazur also mentioned that he could raise the students' score significantly.

I think he is right. It's much more important to learn the concepts than to learn how to use physics formulas without thinking. I also think that standardized test such as SAT should ask such questions, but I think that it may be too hard to make a bunch of such conceptual questions.

He also mentioned that he never showed the students how to solve physics problems during the lecture, but it turned out that the students who learned in this way solved physics problems better than the ones who were just taught how to solve physics problems during the lecture.

He said that you cannot be a good marathon runner just by watching a dvd which recorded marathon runners running. He emphasized that one has to solve the physics problems himself.

P.S

You can check out the video of this seminar at the following website. I think that they haven't uploaded it yet, but they will do it soon: http://www.physics.harvard.edu/about/MonColloqArch.html (9-28-09, Eric Mazur, Harvard University, 'Confessions of a Converted Lecturer')

His presentation slides are also available at http://mazur-www.harvard.edu

Thursday, September 24, 2009

Thu, 24 Sep 2009 21:48:33 GMT

Even though I could follow the derivation of the Noether's theorem step by step, I didn't understand it by heart before. Today, after looking up the wikipedia article on the Noether's theorem, I finally understood it by heart. I think that the derivation there is clearer than most of the other books. It makes manifest the reason why the coefficients of partial derivative of epsilon for the variation of Lagrangian is the Noether current, which is a quick and easy way to calculate Noether current.

Thursday, September 24, 2009

Thu, 24 Sep 2009 03:37:59 GMT

By doing physics homework, I again found out that I still needed to learn more.

One of the problems was about the mass of gauge bosons when SU(5) is broken into SU(4)xU(1) or SU(3)xSU(2)xU(1). By looking at Peskin's QFT textbook, I realized that I needed explicit forms for the generators of SU(5). However, the problem was that I didn't know what the generators of SU(5) were, even though I knew those of SU(2) or SU(3) because they are explicitly written on Prof. Georgi's Lie algebra textbook.

However, by talking with other students, I realized that the generators of SU(5) were very simple. Which means that I still need to think hard about physics.