What You Can't Say

This is one of my favorite essays. I like the way Paul Graham writes and the way he thinks. Rather, I like that he thinks very profoundly about what he writes and that this shines through his otherwise mostly colloquial and casual writing. Besides, it references Fight Club and talks about Noam Chomsky and 'Physics vs Literature' all in the same piece!

Needless to say, what I think about the 'Physics vs Literature' part is one of those things we can't say. Yes, really and despite the fact that I love Literature and have tremendous amounts of respect for Professors, students and practitioners of this finest art. ;-)

There isn't much to say about the piece that it doesn't say already. So go read it!

Finally, most other essays on Paul Graham's site also make for very good reading -- well, you may have to be some sort of a nerd to like some (maybe most) of them, but still.

Uncle Vanya

It is due to Paul that I was introduced to Chekhov, and boy am I glad! I read Uncle Vanya in one sitting the first time around (which means it can't be very long :-). While the play seemed to be very well done, I just did not like it. It reminded me of the house my mom and I stayed at for a while when I was very little (2, 3 or perhaps 4). The house belonged to my great-grandparents and was an old large house from feudal times. I did not like it there at all. The house had a very sinister and melancholic feel to it, specially at night. Being reminded of this must've made me not like the play, I guess. There was a certain je ne sais quoi about Vanya and Sonya that I liked in a "I want to befriend them" type of way. Not enough to like the play, however. It seemed so depressing, just like that old house and so void of deeper meaning. Then, in class, Paul showed the film Vanya on 42nd Street. That changed everything. The movie is fantastic. It has a prerequisite of having read the play (according to me) even though it sticks to it word for word. I was pleasantly surprised by the way Vanya and Sonya were played -- it matched the afromentioned je ne sais quoi. I still don't know what is it exactly, so I'll stick to the french double-dyadic phrase :-).

I read and re-read Uncle Vanya having watched the movie and it was wonderful. I found that there was a lot more to the play than I had originally thought.

My favorite feature is either the sociological commentary or the characters -- both, rather. The characters are so well developed in such a short time and it is easy to identify with facets of all of them. I love how Chekhov is able to tell such long stories about his characters with so few words and events. Every conversation tells you a bit about the characters involved as much as it advances the play. He's got a way with diction and imagery that allows him to paint an intricate picture with just a few strokes (I find this in his other plays, too).

Somehow Vanya's bitterness is both sad and upbringing at the same time and his are such wonderfully executed commentaries about the stasis in late 19th century Russia. Oh I love it! The doctor is also easy to relate to and his interactions paint a protrayal that is upbringing but sad. Dare I call the doctor and Vanya dual characters? For the class I wrote a short paper about this.

It is easy to make the doctor an ideologist from the get-go, but Vanya not so much -- he's always bitter about everything! Furthermore, he is always skeptical about what the doctor says and is not afraid to let him know. But, they get drunk and the reader finds they have more in common than he may originally think. Specially, they share a love for the professor's wife, Yelena. I think Yelena almost serves as a metaphor for ideological change as I argue in the paper.

Finally, the overall feeling that the play leaves one with is bittersweet. Of course, this after one has gotten past unpleasant childhood memories! I place special value on bittersweetness for it seems a lot easier to leave a very dark and unhappy feeling and even more so to leave a happy and cheerful pink one. Bittersweet seems much more real and yet that much harder to accomplish.

QM Texts

I've been studying quantum for my quals. It is my nth time around reading Sakurai's book and some sections s have been read n+m_s times :-). Sakurai's Modern Quantum Mechanics is a great book... as long as you are a graduate student, have had QM before and (if it is your first time reading it) have plenty of other books to read alongside it. What makes it good is its approach to quantum theory. What makes it bad is that Sakurai seems to assume that you have some kind of intuition about this stuff and fails to provide explanations sometimes. This is fine if it is your nth time around, but not for newcomers -- even having had undergrad QM.

The usual approach in most texts (like Messiah, Griffiths, Shankar) is some variation of:

what's wrong with classical physics => old quantum theory => modern QM => the cool stuff of quantum theory

Sakurai's is more like:

the cool stuff of quantum theory => modern QM with a hint of what's to come if you keep going in physics (I think... I haven't kept going, yet :-)

I think this is the right way to go about it, not just for a graduate student, but for an undergrad as well. Let me expand on what I mean:

When I was an undergrad, we used Griffiths. The book was good (as should be expected after reading his E&M book). It takes the 'brute force' way into quantum mechanics: PDEs, wave functions, lots of messy integrals and the like. Those are all necessary evils; however, I believe Feynman said that he thought the whole PDE-approach to QM was not really necessary to gain insight into the fundamentals. I think he meant: start with the formalism and the simplest example of it! You don't need PDEs, those just come when your matrix representations of operators become infinite dimensional. And sure, you need to get there at some point, but at heart all you really need to understand the trickery is a spin 1/2 system and its 2x2 matrices. You can even get to Schrodinger's equation using only operators and algebra. I like to call the later this the 'algebraic' approach to QM. Instead of solving PDEs you play with commutators and construct "helper" operators to get to the eigenvalues and eigenstates you are interested in and so forth. This is precisely what Sakurai does and it is fantastic.

There is a couple of sections in Sakurai that seem to be misplaced: the 'stat mech' section in the middle of the 'angular momentum' chapter, and the one about Bell Inequalities in the same chapter. I think they should both be in their own (short) chapters. This is, of course, no real problem, just something to be aware of. The more important problem is that the text is unaccessible to an undergrad and I'll say why at the very end.

Since last year I have been thinking about writing a set of 'notes' to go alongside with Sakurai in an attempt to make it suitable for an undergrad's first-time around. If I pass the quantum qual and take QFT, that may have to wait til summer ;-), otherwise I'll do it as I go through the class here.

Shankar's book is also excellent. Specially the Math and Classical Mechanics reviews that are at the beginning. Nobody should attept to study QM without having spent some time reviewing this material and having it become second nature. I also like that Shankar is very clear (more so than Sakurai), explains things quite a bit (again, more so than Sakurai) and that has the exersies mixed-in with the text. With Sakurai it takes a bit of work to figure out when it is your time to try the next problem from the end of the chapter, but that's very minor as well.

Like I said before, Griffiths is also very good, specially when you get into the situation where you follow the math but have lost "the picture". He also includes a Math review in chapter 3 albeit not as good as Shankar's.

Now, on to why my 'notes' for Sakurai seem to be a good project and why I think it is important that we teach QM this way. The way we teach Physics needs to evolve according to what is relevant in current research. Sure there is a lot to be gained by following the historical path, or by following the messier but conceptually more familiar path (PDE-approach). But, there is much more to be gained by following the conceptual approach that exposes the fundamentals of the theory as...hmmm...well...fundamental. Afterall, the point of science education is producing new scientists, not so much producing new science historians!

Here are the QM books that sit on my bookshelf:
Sakurai
Griffiths
Shankar
Messiah (a true bargain compared to the others!)