Today, I finished my first formal homework assignment since I came to Hong Kong!
Needless to say, it is the assignment of Computational Physics. As you know, I completed all the calculation one week ago, so writing the report seemed to be easy for me. However, it turned out to be quite irritating to finish the job. The lesson is: even if one have finished all the research work, and get all the result needed to write a paper, it is still very involving to actually produce the paper.
There are two problems that are relatively "theoretical" i.e. I'm required to analyse something mathematically, without using computer to do some practical calculation. Last night, when I've finished all the "practical" ones, I began to think of them. The first one was very straightforward but involving (i.e. you know how to do it right on first glimpse, but it take a lot of time to actually solve it). However, with the help of the invincible
Mathematica 7.0, I was able to finish this problem very quickly.
After that, I discussed with Bill Chow, a
seemingly capable local student who also took the course. I was in hope of finding some help, but finally I found that he was asking for my help all the time. He said he had some difficulty with the problem I had just solved, so I sent him my answer. To my surprise, instead of being grateful, he asked me why I "didn't use the Lagrange interpolation formula". I said, "It's very easy with the help of
Mathematica, anyway. If you use the Lagrange thing, you have to expand it, which is more involving." He said, "They took me a long time to solve..." I said proudly, "That's why I chose to learn
Mathematica and
Matlab!"
He was apparently envious, for I found a shortcut to do some thing that cost him hours in a minute. Soon he told me exaltedly that his answer was different from mine. I was a little nervous at the beginning. However, I gave almost blind trust to Integrated Software Packages, so I read the note again. I soon found "hints" that were very supportive to my answer. I showed him, and he, defeated, had no word to say.
The other "theoretical" problem is far more difficult, and I, as a compensation to my "rudeness", modestly asked for his opinion. He said he had no idea at all and simply threw it at me. Hence, I had to struggle through it, alone!
I didn't made any progress until 2:30 a.m. today, when I found one definition in the problem is "utterly absurd", as I wrote in the report later. After telling the professor that I modified that part so that the problem would make a little sense, I began to solve it. It was even more involving even though I modified it. With the ultimate power of
Mathematica, I got the answer, but I didn't believe it, because there were two points where a "beta" have the same value, but they turned out to be equal to 1 and 3 respectively. I returned to the note, which said the "3" was right, but it didn't discuss if the "1" is correct at that point. I spent a lot of time dealing with this annoying thing, but without any progress, hence I just left it there.
I woke up hardly before 1 p.m. (another record in Hong Kong) and had lunch. Then I turned on the computer, where Bill was waiting. He asked me for my work the moment he saw me online, and I gave him my "insane solution". As I've expected, he doubted my modification, but he soon accept its necessity. However, he distrust my result via using
Mathematica. In fact, he was hostile to it.
Bill: but sorry.. can you tell me how to expand that equation??
Pony: It's a Taylor expansion, isn't it?
Bill: yes
Pony: Then why not simply give the final result?
Bill: i want to do it by hand once..
Pony: You just do it with in the regular way we learned in Calculus, no shortcut, it seems. With some labor, you can get the correct result.
(A long silence)
Bill: OK...may be i just trust your result...==.==
Later, he talked about "steps" and "explanation" with me.
Bill: I think professor don't suppose we use mathematica to solve.
Pony: You can add a sentence like, "After eight hours of involving algebra, I finally get:"
Bill: are you kidding.....
Pony: You were talking about explanation, and you're a bit hostile to software package.
Pony: So that's the best explanation you can write.
Bill: ok...because i feel guilty that i didn't go through the step myself..
His words made me quite uncomfortable. Anyway, I'm very proud of my first report, whatever grade it will get. As to "forbid the using of ISP", I've thought of a whole set of excuse to deal with that.
The energy of the particle mentioned above. It's supposed to be a constant, but error is inevitable in computational physics, the only question is how large the error is.
