A Lengthy Exercise

By Mark Trodden | August 8, 2007 9:00 am

I’ve just spent a few days living like an undergraduate; and I loved it!

For most of us, the path to a scientific paper is an extremely nonlinear one, as Sean described in his recent trilogy (I, II, III). In a collaboration this is compounded by the fact that (for theorists at least) there are several people working simultaneously. These people are calculating independently at times, mixing notations, making their own approximations, using their favorite techniques, and writing things their own ways. Regular meetings, either in person, or on video or teleconference calls then hopefully iron out the differences.

While collaboration has some of the drawbacks above, it has many positives, not least of which is the creativity and array of technical skills that several people can bring to an initially ill-formed idea. But perhaps the main reason I love collaborating, and choose to do it so often, is that I truly enjoy the process. Discussing fascinating physics with talented colleagues is a delightful part of my job, and I wouldn’t give it up for the world. So whether someone comes to me with an idea they want to discuss, or I have a good idea of my own, I frequently take advantage of having other scientists with common interests around, and more often than not collaborate.

However, one thing that one needs to do in any collaboration is to check all the equations independently. Much of this checking is ongoing as the project progresses, but sometimes you take something complicated that a collaborator has done on faith in order to push ahead and see where an idea is going, coming back later to double check the details. This has been the process in many of my collaborations, and it is a perfectly enjoyable and rigorous way to work. One checks everything, of course, but not in order, and not in one continuous sitting.

In the last week, however, I got to do something unusual, for me at least. One lengthy collaborative paper I’m working on is nearing completion and I realized that there were a number of these technical results that I needed to go over in detail. But in this case, I also felt that the paper was getting sufficiently long, and we’d changed notations sufficiently many times, that the structure of the equations appearing in the draft (but not the ideas, or the heart of the calculation, of course) had become a little murky to me. So I decided to sit down with our draft and go through every single calculation, from the beginning, to make sure not only that I checked the things I hadn’t checked before, but also that I was completely happy with the notation, the structure, and the arguments. Usually this isn’t required at this stage, but here I really felt I’d benefit from it.

And it turned out to be remarkably nostalgic fun, as well as practically useful for our paper! You see, I hadn’t quite thought of it this way, but working through a draft like this is rather like an extreme, lengthy version of the kinds of initial parts of exam questions one gets as a student. You know the kind – the ones that start

Show that such and such a result is true. Now, using this result and such and such a definition, do such a transformation and thereby prove that this unlikely looking expression is true. Interpret this in the light of this interesting observation.

This kind of problem tests a certain skill set, but not necessarily the same one that one uses to make progress on problems to which one doesn’t know the answer. It can be a bit like working out to build muscles that will be useful for a particular sport. The muscles will definitely help, but unless you have the actual skill to play the game itself, they will only get you so far.

Too many of these kinds of exercises can be dreary indeed. Nevertheless, for me there was always a bit of a thrill to sitting down in front of a clean and empty pad of paper and working my way through a maze of reasoning to get to the required answer. I’d typically hit a dead end several times before figuring out a correct strategy, and those dead ends invariably taught me something deep about problem solving in general, and the specific physics or mathematics at hand.

In this case, my task turned into the equivalent of a three day exam, with the end result being thirty or more pages of calculations (and I write quite small and neatly – yes, I am extremely anal), and a couple of Maple worksheets to help me check various approximations. I had little boxes around important results and everything. It was just like being a student again, although wasn’t accompanied by vats of coffee and a late night run to the college bar for a quick pint at last orders.

Luckily nothing major was wrong, although I found a number of typos and one missing term. However, my picture of what we’ve done is now much clearer and more coherent. It is unlikely that I’ll do anything so formally organized with many future papers, but this was such fun! It almost made me want to take a class in something technical I don’t know much about, before reality crashed in and I realized that I basically have negative time to devote to anything like that.

I probably should have been more clear at the beginning of this post – I was living the working life of an undergraduate. Hope you weren’t looking for stories of drinking games, walks of shame and quick bong hits before class, although I do hear those are the subject of Daniel‘s next post.


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About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


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