Monday morning, 10:25. Intro to Deductive Logic. Professor Carson has told us what to expect on the exam, where to pick up our assignments, and tied up all the loose ends in the course material. As if finishing a thirteen week stage show, the auditorium full of students give her a round of applause which she modestly acknowledges.
Tuesday morning, 9:50. String Theory. Professor Cline has finished his own thirteen week performance by introducing the “brane action”. The last line in my notes reads “Branes cannot go faster than light”, next to an equation that says the same thing in mathematical terms (dx^a/dt squared less than one, for those interested). The last assignments are laid out to be picked up and class is over, but there is no applause for the end of a physics class.
Tuesday afternoon, 13:05. Electromagnetic Waves. Professor Lovejoy finished teaching 45 minutes prior, and the floor has been passed on to a group of students to make a presentation. Time is short, so we rush through each of the questions. Roughly two minutes is given to the topic of a particle starting to move before you start to move it. We didn’t even get a chance to start talking about how a particle in a gravitational field radiates energy even though you don’t give it any to radiate. It doesn’t matter—the few people that stayed until the end of class aren’t paying attention anyway. Being pushed out by the next class I don’t know if anybody heard the last things the Professor was saying, but I’m sure if it was important we’ll hear it in the next electromagnetism class.
That’s the way it goes in the physics department. No class is ever really finished, since there’s always another one to continue on. Themodynamics was followed by Statistical Mechanics, which is followed again by Advanced Stat Mech, and probably further still by graduate school classes. Within one semester there is no sense of wonder. There may be a few plot twists along the way as we find that one of Newton’s Laws is violated, or that a particle might have a negative mass, but there is no climax. No denouement.
Now, Professor Bisson, he knew how to take his class—the topic was human evolution—and make a story out of it. His last lecture came back full circle to touch on the things he had told us on the first day and wrapped everything up nicely. It’s more important in an Arts class, I suppose, where each class tends to be more of a little unit on its own, with things in common to other classes but always with a difference scope and perspective. On the last page of my notes I have written “We are unique, in that we are the only large mammal to cover such a huge range and remain a single species.” No equation needed. That was a lecture that deserved applause.
My String Theory textbook, by Barton Zwiebach, started very well with an introduction to the topic, including its motivations, its current status, and the possibility of experimental tests. There were no equations to look at, only a qualitative summary of what our goals in the book were and why we were bothering at all. However, 543 pages later, at the end of the last chapter, we find this less than satisfying conclusion:
Once this is proven, one can finally show that G’ coincides with G. This means that S and T generate the full modular group (see Problem 23.6). It also follows that Fo is a fundamental domain for the modular group.
Nice to know, I suppose, for the context of that chapter. But is there no final word? No wrapping up of our wonderful adventure together? Didn’t our three painful months together mean anything to you, Barton!? You think you can just brush it off, teasing me by telling me what Fo can be, without any thought or care of what our separation means. No, Barton, it’s too late. Go back to your modular groups. I just wanted to say goodbye, that’s all.
can be complex, but there is a finite answer for any 
.
which is valid down to 
. Then you can find not only
.
