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

Thursday, August 25, 2011

Solutions Manuals to Arfken

I like teaching using Arfken's book; and the biggest reason why I like it is the non-existence of solutions manuals. Although there is an official solutions manual  (I downloaded it once just to find out if Arfken was ruined as a good source of problems; it can be found here.), it's useless for problems that ask you to prove things. What it does do is provide numerical answers, or give the final form, or give hints.

I worked through the problems in Arfken the hard way; I solved the problems one-by-one starting from chapter 5 until the chapter on integral equations. I still have a list of the problems I did not solve (I used the third edition,but teach using the 6th ed.), and as I teach, I revisit them, hoping that this time, I would be able to figure it out.

On the other hand, although I have not worked through some sections in Arfken (such as the chapter on matrices and group theory), my problem-solving in other areas of theoretical physics  does mean that I've actually solved them elsewhere. Sakurai's Modern Quantum Mechanics, chapters 1 to 3 was where I learned about Pauli matrices and the rotation group, for example. If you compare Sakurai and Arfken's group theory chapter, there will be a lot of overlap. So dedicated study elsewhere means being able to solve Arfken's problems even though, on my first pass, I skipped through the group theory.

Another example is Arfken's chapter on the calculus of variations. I've encountered the material elsewhere, in classical mechanics (Marion's and Goldstein's books), in general relativity (Hartle and Weinberg), Finkelstein's book (Nonrelativistic Mechanics, a parallel presentation of classical and quantum mechanics), and Jackson's Classical Electrodynamics.

I've collected stacks of folders with solutions, and I really have no plans of uploading them. When I do teach, I do not provide an answer key either; I do mark papers and when time permits, we solve the assigned problems on the blackboard. I usually get a student to solve it in front and then act as the hostile critic so as to root out  misunderstanding, and bad reasoning. When the student is stuck, I suggest possible lines of attack, or solve a related problem.

Why do I not provide fully-worked solutions? Providing worked solutions encourages memorization, rather than understanding. Also, the worked solutions sometimes end up being recycled by people who take the course later on. It's hard to think up good problems at that level; it's different with introductory physics where it is easier to invent easy problems.

On the other hand, people argue that without solutions manuals, they cannot be sure of their work. I think it's bosh. The problem sets of today are usually the research questions of yesterday. Cauchy's theorem and other things that we take for granted today did not come by divine revelation; these things were discovered by people who were willing to think for themselves.

Instead, what one needs is a method of eliminating self-deception. When I write my solutions, I do it in such a way that my solutions can serve as supplementary lecture notes. (This is actually an old idea, and I owe this statement to N. David Mermin. ) This means you have to express clearly, without any obscurities, how you actually reason from start to finish. You have to justify every step you make, by quoting previous theorems (that you've also proven for yourself!), etc. If the reasoning you present is tight, with no missing steps, then you can be pretty sure that your solution is correct. It does mean, however, that you have a good grasp of prerequisite material.

Solutions manuals pervert the learning process because being able to submit correct solutions to problem sets leads to self-deception. One learns by making mistakes and by being stuck in some areas, and trying various possible dead-end solutions paths. Learning the dead-ends is also important; if you do not learn the dead ends, then you will be compelled to learn them later on, when you actually have to use the methods in Arfken to solve your particular research problem. (And since it is a research problem, by definition, no solutions manuals exist!)

(addendum: one of my friends had this to say about solutions manuals: You want a solutions manual? Make one!)

Tuesday, August 23, 2011

Sign Seeker

Had a laugh while watching this. The advertising is subtle, and doesn't detract from the short film. I learned about these short films from my thesis adviser.

Sunday, August 14, 2011

The Upside (and Downside) of Irrationality

I recently read Dan Ariely's The Upside of Irrationality, and started thinking about the many irrational ways I behave. Contrary to the image of humans fostered by classical economists, Ariely claims that experiments demonstrate that humans often behave irrationally, often counter to profit maximization schemes that underlie economic models.

One example he used was on compensation schemes for executives (it's also discussed by Dan Pink in one of my favorite TED talk), and the counter-intuitive result was that although low and medium levels of compensation may improve performance, for tasks that require even rudimentary cognitive skills, extremely large rewards may actually lower performance.

I suppose that's one reason why I'm having trouble writing. The ideas are there, but if I do get it published (before I'm out of my university), I will end up with a PhD, and a USD 1000 award. Surprisingly, I find it demotivational, in the same way that Mark Twain describes in Tom Sawyer.:

"He had discovered a great law of human action, without knowing it––namely, that in order to make a man or a boy covet a thing, it is only necessary to make the thing difficult to attain. If he had been a great and wise philosopher, like the writer of this book, he would now have comprehended that Work consists of whatever a body is obliged to do, and that Play consists of whatever a body is not obliged to do. And this would help him to understand why constructing artificial flowers or performing on a treadmill is work, while rolling ten-pins or climbing Mont Blanc is only amusement. There are wealthy gentlemen in England who drive four-horse passenger-coaches twenty or thirty miles on a daily line, in the summer, because the privilege costs them considerable money; but if they were offered wages for the service, that would turn it into work and then they
would resign" 

In the Philippines, USD 1000 is a large amount of money. You can buy four netbooks with that money, and it would be about seven times the monthly minimum wage. I even know of people here whose monthly wage is  USD 70. 

Ariely's research involved paying Indians different rewards and comparing performance when the reward for completing tasks (in this case, a bunch of games) was worth a day's wage, a few week's worth of wages, and five months of wages. The most surprising finding was that those offered the biggest rewards did worse! 

Later in the book, Ariely speculates on the effects of astronomical bonuses on executives in the finance industry, and I believe, post-financial crisis, that the compensation scheme was to blame for a lot of the financial system's woes. Ariely also talks about many other things, and I plan to reread his book, as well as his other book, Predictably Irrational.

Sunday, August 7, 2011

Buying new speakers

I just bought new 2.1 channel speakers. I had an old set, but due to a problem with the power supply, I decided to scrap it and buy a new set. I missed listening to music during the mornings, and the built-in speakers of my laptops were unsatisfactory.

I knew that the usual two-speaker systems didn't give me the right sound-- I didn't get any bass. But I didn't know what I wanted exactly. My brother was the one who liked playing with speakers-- while I lived with him, his home theater system had surround sound, and he was the one who set it up. I did know that my speakers needed a subwoofer, so I decided to get the simplest cdrking system with a subwoofer.

Looking at the available products on the net was helpful, because I learned what was available. I also learned how much speakers cost. the cheapest I could find at cdrking costs PhP 200 or around USD 4.8. The more expensive ones (which I bought), with a subwoofer, costs about PhP 700 or  USD 17. I even found 5.1 channel speakers on their catalog!

Since I planned to use the speakers in my room (it's a small room!), and the input would be from my laptop, I didn't need an expensive set, so I settled for a 2.1 channel system. I brought my netbook along to test the speakers, and was disappointed with how it sounded while I was at the store. But then, we had a noisy background, so even though the speakers didn't sound good while I was at the store, I decided to get them anyway, since I knew that the components worked. I figured that as soon as I got home and tried it, I should be able to tune it so that it would sound right to me.

Once I got home, I set-up the speakers, and played some music by Sitti Navarro.  I played with the controls, just to see what the effect of eliminating the subwoofer would be like, and having the subwoofer really makes a difference. I'm quite content with the sound right now, although I do plan to get a 5.1 channel system later... Maybe when I move to another university? :-)