About Me

When not at work with students, I spend my time in my room either reading, calculating something using pen and paper, or using a computer. I read almost anything: from the pornographic to the profound, although my main interests are mathematics and physics. "When I get a little money I buy books; and if any is left I buy food and clothes." -Erasmus

Sunday, November 14, 2010

Sunday morning random musing

I'm listening to the standards as I type this. Among the standards, the singers whose songs populate my hard disk are Michael Buble, Tony Bennett and Frank Sinatra. I'm aware of other singers, but these two have enduring appeal for me. I grew up listening to the standards on the radio because my Dad liked listening to DWBR before he moved on to listening to classical music. Friends of mine associate this kind of music with Sunday mornings, when some FM radio stations play the oldies.

Not that I listen only to the standards. I have a mix of pop, jazz, disco, rock and who-knows-what in my music folder. But, the standards have an appeal for me because they remind me of childhood. I often sing along -- I realized much later that it's good practice for pronouncing words and sentences. I suspect that my accent owes much to Frank Sinatra. The singers of standards pronounce things well, and what they sing often comes out in the form of complete sentences set to music.

A few years ago, I read the "The Artist's Way", and among the things that appealed to me was the idea of "morning pages"-- writing that's meant to help you think. It's not supposed to be organized; if you feel like rambling or saying whatever comes to mind, go ahead. The morning pages were supposed to help the self find what it needs before the day starts. If the result were chaotic, then that's all right because the chaos of writing was the prelude to the beginning of order in the self. I don't actually recall what she said about it, but I've noticed that writing the morning pages relaxes me. I'm actually a bit shy when it comes to letting other people read my morning pages because it contains a lot of clutter. I usually write about what happened the day before, because looking back helps me think of the future.

It may seem strange to think of the scientist as an artist, but I think that science is also a creative process. The link between experiment and theory is not as solid as most people believe; one doesn't look at the data and then formulate a theory. (Recall the "scientific method" as taught in grade school) My reading of Kuhn parts of Feyerabend, scientifc biographies and physics education research has me doubting that the process of scientific creation is as straightforward as claimed by the various philosophers of science.

Formulating a scientific hypothesis is a creative act. A good experiment is also a creative act. I suspect much can be written of good experiments alone; the downside is a lot of the writing will likely be unappreciated because learning about good versus bad experimental technique is a long process. The care with which good experiments are designed is hidden from the readers of elementary physics texts because we need to cover so much during the regular semester.

We don't have enough time to explore the actual experiments, and the textbook cannot provide the nuances because it would double in size. A textbook such as Young and Freedman, already of encyclopaedic dimensions (or at least, of the same mass as an unabridged dictionary) is unattractive enough as it is.

The problem of coverage is still unresolved. Take Special Relativity as an example. The textbook that we currently use is the first edition of Spacetime Physics. In physics 73, we spend a month covering the material, and then give exams. My actual reading of Spacetime Physics was a semester because I spent a lot of time tracing how the ideas fit together, as well as solving the problems. In fact, I haven't solved all the exercises in it, just what I hope is a representative sample. I gained further experience with special relativity when I taught myself general relativity by working through the books of Bernard Schutz and James Hartle: reading and solving problems, checking for consistency and correctness. It took me years to do all that. Good thinking requires more than a semester.

In Outliers, Malcolm Gladwell says that mastery of a particular field requires 10,000 hours. I think I've spent more than that on general relativity, and I still can't say that I think my understanding is adequate. It is a lot better than people who've just finished a two semester course in GR because I've had a lot more practice.

Consider my experience with quantum mechanics. I first learned quantum mechanics during Physics 141. For every hour of class, I probably spent 3 or more hours on my own reading Dirac, as well as the textbook, and then solving problems that were not assigned by the teacher. We had problem sets with 4 questions every two weeks. My own problem-solving rate was probably about double that. (It also meant a disgraceful showing in other subjects!). Even then --let me check my academic records-- it was only worth a 2.0.

I was dissatisfied with my understanding. I was also broke, so the schoolyear after, I went on leave for a year, and during that time I taught myself complex variables (among the mathematical methods needed for quantum mechanics.) and then got myself a book on Path Integrals and quantum mechanics. I spent the whole year on those two books, when not working.

After that, I got myself a graduate level book by Sakurai and worked through all the problems in the first two chapters. I did that before enrolling in the graduate course. The course was based on that textbook, and it meant I was two chapters ahead. When Dr. Chan assigned problems, all I did was look at my files and then copy my previous work. While enrolled, I continued my problem-solving in that textbook to maintain a comfortable lead over the rest of the class. I wasn't surprised when I finished the semester with a 1.0.

My filed solutions had to satisfy a self-imposed rule due to David Mermin: they had to be well-written enough that they could serve as supplementary lecture notes. So as an added bonus, my solutions became the answer key. My classmates were at a disadvantage because they didn't do that. They didn't realize that the extra effort paid off because my search for clarity sharpened my understanding of quantum mechanics. Because I solved all the problems, I could see what ideas were important, and as a bonus there were techniques that only someone who worked all the problems would learn. I recall problems that my classmates would spend pages on while I learned a technique that allowed me to write the solution using a few lines.

I learned from various scientific biographies that this method was also used by some of the greatest physicists: Dirac, Fermi and Feynman for example. But it takes a lot of hidden work. I empathize with the stories of how long they got stuck on particular problems. I know what it feels to be groping in the dark, without anyone to consult. I recall weeks of frustration and lots of wasted paper when I couldn't solve a problem. I would eventually solve most of them, but for some of the problems, it took me more than two weeks, sometimes months of thinking, trial and error. I find it amusing when people consult me on GR (and not just GR) and at their stunned reactions to how fast I can give an answer to the particular homework problem that they've been given. But it shouldn't be surprising when you realize that there's a lot of work hidden in the fast answer. So the fast answer was actually attained by a very slow process.

After realizing how useful pre-reading was, I recruited various undergraduates and got them to take the graduate quantum mechanics course . I had them work on Sakurai's problems the summer before actually taking it. It was no surprise that they aced the class. So it's now a tradition in the theory group to read and study a semester before actually enrolling in some physics and math classes. That tradition is a source of great satisfaction for me, and I hope that it will be kept even when I leave U. P.

I'm off to S. M. to buy coffee and filters, so I'm signing out.

No comments: