Friday, February 23, 2007

Tests I remember well

There has been a great deal of foolishness written over the case of Marcus Ross, the YEC who, quite appropriately, was awarded a PhD in Geology (or some related field.) All the discussion had me reminiscing about my own most memorable exams. There are three that percolate to the top of the heap. One very bad, and two very good.

My worst test experience came in an undergraduate course that was supposed to be an easy A. It was a course on Mathematical Logic. A sure (so I thought) no-brainer given it was a math course required by philosophy majors (heh) who are notoriously math-phobic. What happened to me in this course is so ingrained in my psyche that I still dream about it, and I included it, with only minor, inconsequential fictionalization, in my not-so-best-selling novel Here, Eyeball This! (Still the only novel to start with the word: Acetone.) So, if you'll forgive me, I'll just post an excerpt. Here the protagonist, Aaron, a physics grad student and a Teaching Assistant (TA), is flirting with an undergraduate in his class. (Scandalous!)

         The day before, right before heading home for winter break, Leila stopped by his office to say goodbye. The topic of grading came up, and she asked him about his policy.
          "Why don't you take attendance? Most of the TAs do."
         She sat in her favorite spot, on the floor just under the whiteboard. The same place where, one night, she had remained invisible to Hiroshi.
          "I don't know, I guess because I never went to class. Unless it was mandatory. So I'd feel like a hypocrite."
          "You didn't go to class? Naughty boy. How about now?"
          "I always go now, ever since starting grad school."
          "And skipping class never affected your grade?"
          "Oh yeah, once it did. Once I got really burned. Unbelievable. I mean, it was bad. You know the dream where you show up to class totally unprepared for a test with no place to hide? Well that happened to me."
         "Tell me, tell me." She smiled, anticipating his humiliation as only a true enemy or a true friend can.
          "You know the Math Logic course?"
          "Yeah, but I don't plan on taking it. Paula just had it. It's all symbols."
         In Mathematical Logic, students applied the rules of logic to prove propositions. A typical problem looked like:

       Let P denote a unitary predicate
       symbol and f a binary function.
       For the following, find a structure
       that satisfies the formula:

       $ν0 (Pν0 Ù "  ν1P fν0ν1)

         It's intimidating if you don't know what the symbols mean. But if you knew the language and had decent math skills, it's simple.
          "Well, I took it for an easy A. You know, it's a joint offering from math and philosophy. Since the philosophy majors stink at math, it seemed like it'd be a breeze.
          "So I went to class the first day. The prof's name was Potinger. He probably still teaches it. I listened while he went through his syllabus and grading policy. I just wanted to know his rules on attendance. Finally, he tells us, 'I don't take attendance, this here is college folks, and you're not kids anymore. I urge you to come to class, but I'm not going to waste time calling out the role.' That's all I needed to hear, that's what they all say."
          "Yep. Always the same line, like we haven't heard it before."
          "Exactly. So anyway, I had two friends in the class who would tell me the assignments. Potinger always gave problems right from the book. I'd do them, and these guys would turn them in for me. The next time I bothered to go to class was for the midterm. I aced it without breaking a sweat. Like I said, the class had a bunch of philosophy majors.
          "Now Potinger was a trip. He referred to himself in third person on the exam. One of the problems required a symbolic proof that 'Potinger was benevolent'."
         Leila made a yuck, that's weird face.
          "Yeah, I know," Aaron said. "So anyway, I finished the exam in about twenty minutes, got up, and turned it in. 'Nice of you to show up,' he said when I handed it to him. I returned his lob with something like, 'Always a pleasure, your benevolence.'"
          "Smart aleck."
          "Not for long. After the midterm, my so-called friends thought it'd be funny not to bother mentioning that Potinger introduced his own private notation for each and every logical symbol and operation. He still gave problems from the book, but he did his lectures and examples with his own symbol set. I just kept turning in the homework using the standard language."
          "What time was the class?"
          "Ahh, it was early. Eight o'clock. You have a point?"
         Leila held up her hands. "Yes, I do. That's why they did it. Your buddies trudged through the early morning slush while you slept nice and cozy in your jammies. What'd you expect?"
         He had never thought of that. "You're probably right. Too bad you weren't around to give me advice."
         She nodded. "Your life would be much better. So what happened?"
          "You can guess. The time bomb exploded at the final. I showed up for the first time since the midterm. Potinger had written the final in his own private, bizzaro symbology. I'm not exaggerating, I couldn't even read it. It might as well have been in Sanskrit. Without the staple in the upper left, I couldn't even be sure that I wasn't holding it upside down."
         Leila grinned from ear-to-ear. "So what did you do?"
          "Nothing I could do. Like I said, this is the stuff nightmares are made of. Only this was for real. The only thing missing was that I wasn't sitting there in my underwear. I got up and left, and got a big, fat zero. Potinger was beside himself. He knew what happened. 'Nice of you to show up,' he says, just like before. This time I had no snappy comeback."
          "Did you flunk?" A strange question when asked by someone who struggled to control her laughter.
          "No, it turns out Potinger really is benevolent, at least with his grading policy. The final only counted for a quarter of the overall grade, so I got a C. It's the worst grade I ever got in a math course, and I got it in the easiest math class I ever took."

Yes, that really happened to me.

My other two indelible exam memories are much more pleasant. Both are from grad school, and both involve the late Dick Cutkosky.

Cutkosky was a first-class particle theorist with a mathematical style. He came of age in the 60's, which might have been just about the best time ever to be a physicist. Thanks to Sputnik there was plenty of money for physics, the colleges hadn't dumbed-down to accommodate the deluge of inferior students seeking draft deferrals (not that I blame them) and the physics problems were real and tangible—not crap like Boltzmann's Brains and the Superstring Landscape with 101000 sets of constants to choose from. (New and improved! Version 2.0! We've squared the mere 10500 choices in Version 1.0!)

I had Cutkosky for Quantum III, which was concerned with many-particle systems. Very cool stuff that nuclear physicists love, like Hartree-Fock calculations. For his final, Cutkosky gave an oral exam. (Which is not a bad policy.) His method was well known to the students—he'd query you on the course material, but then, to separate the wheat from the chaff, he'd go off in some unexpected direction, to see if you could generalize and think on your feet. No point asking for hints from the students who went before you, because he went down a different rabbit trail with each wounded animal that had to face him. Besides, grad school is highly competitive—your classmates would be just as likely to feed you disinformation as anything useful. Anyway, the hour before my exam I'm in the science library. I'd been looking over a Quantum book by Gordon Baym. Not our text, but a book I always liked for its rather unconventional style. For some reason, I notice that Baym had a chapter on Atomic Physics. Not part of our course's content, but like I said I enjoyed his book and was sick of studying, so for no particular reason I read the chapter and then headed off to my exam.

I get through Cutkosky's grilling regarding our material without a hitch. Then off he goes, into left field.

He asks me about Atomic Physics. And he asks as if, in anticipation of taking me in that direction, he had spent the last hour as I had, reading Baym's book. He asked me five or six questions and, only because I had just read the chapter, I fired the answers right back. I didn't pretend to ponder the question, or to slow the pace so that time would expire, I just let him have it. It was sooooo satisfying.

The final story comes a few years later, and I'm giving my PhD defense. Cutkosky is on my committee, and the only examiner that scares the bejeebies out of me. As I am giving my presentation, I look over, and he's sleeping! I take this to be a good sign. Anyway, I finish and the questions begin. When it gets to Cutkosky I'm feeling a bit nervous. He asks me a mathematical question:

"You did that three-body part using relative coordinates. Is the way you set them up unique?"

Now, it wasn't a horrible question, and I probably would have answered it more-or-less correctly with some thought, but, in that environment, it would not have been fun. But I didn't have to struggle at all. History repeated itself. Up to an hour prior to my defense, I had never considered the question. I had followed someone else's scheme for defining my relative coordinates, and never thought much about it. But, in the hour before my defense, sitting in my office watching the clock, I picked up an obscure paper on my office mate's desk, which described a similar calculation. The author wrote: we note that this choice for relative coordinates is not unique, there are in fact three different ways to define the relative coordinates. So without skipping a beat I answered Cutkosky's question with:

"No, this choice for relative coordinates is not unique, there are in fact three different ways to define the relative coordinates."

The only danger would be that he would ask me to work out those other two ways—which would have been tough to do on the spot. But he didn't. He seemed very happy with my answer. He nodded, and said he had nothing further to ask.

Man, it sure is better to be lucky than good!

No comments:

Post a Comment