Well, it was another ridiculously busy day. I’ve a headache and I got up too early to begin the day…. dozed off a touch in Christian Roemelsberger’s (of the Perimeter Institute) excellent seminar just after lunch (triple problem for inducing sleep in seminar: (1) early start after late night, (2) lunch immediately before… (3) sitting in darkened stuffy room with a solo voice talking). Interestingly, I followed everything and only did “power-dozes”, so was able to ask intelligent questions during and after….
Taking a short break. It is after six o’clock on a week day, so I’m allowed some alcohol….this time in the form of a glass of wine. (Picked up this ad-hoc rule from my wife -back before she left- and she from her father, I gather…. it’s a nice tradition to keep up….) The rule gets broken when one is called on to go to receptions of various sorts on campus, of course…… Neccessities of work, you see. Duty calls, and all that. And on the weekends the rules are totally different.
Well, after going to sleep at 1:00am after reading postdoc applications, I got up early -6:00am- to prepare the final exam for that course I was telling you about a while back, and then I gave it at 9:00am. It was not a take-home. Those have their place, but I also like trying to set interesting exams in the classroom, where both the examiner (me) and the examined (them) have a good time. I remember this from my days as a student. I loved interesting exams. You come in the room, the scene of possible triumph or disaster. You’ve prepared, and you’re as ready as you will ever be, and the teacher hands out the papers, and then it is you vs the examiner. Fixed time, and all you have is you, your pen, and your brain. (And your sweat.) You turn over the paper and the battle begins…. Excellent drama!
One of my favourite interesting exams was when during my final exams as an undergraduate, at Imperial College, London University, 1989. The quality of my BSc. degree depended on a single week of peak performance (this was back in the day when there was little stock placed in spreading the load over the course of the year…..sudden death ruled! I could get anything from a First to a Desmond (or maybe worse), depending upon that week.). Rather late in the day, I discovered how interesting a number of my courses were as a result of studying hard in the weeks leading up to the finals, surveying the course, the careful notes I took (even when I did not understand them – a technique I stress in my students today but they ignore me), etc… I really appreciated the deeper aspects of condensed matter physics and nuclear physics in those weeks. The nuclear physics course had seemed really tedious…..just lots of rather ad-hoc looking models of things, and lots of classifying and bean-counting and no overall theme…it seemed. Things began to make more sense once I had al the course notes in front of me. Then the exam came (the lecturer was T.S. Virdee, I wonder if he is still there?) and I loved it. (I was sure that I was not going to do so well in that course as I did not like it very much, but then I got enthusiasm for it and it just overnight changed my ability to do things in it …. see my comment here on another thread about the importance of enthusiasm…) My favourite question (getting back to the point) started off as a seemingly tedious question about the “liquid drop” model of the nucleus, and you had to estimate the sizes of nuclei using a technique which estimates the force on on nucleon due to the presence of all the others…… You get out the usual numbers. But then the question took an interesting turn, which was not in the lecture course! (You can’t do that these days, you get sued….) He asked what would happen if you took into account Newton’s gravitational force as well. Well, you do the estimate and it is just not important at all…it would seem. It is vanishingly smaller than all the other forces governign the structure of a nuclues. How silly, you think, but you carry on anyway, since you’re getting points for doing what was asked. The question then takes you to the point where you increase the number of nucleons until the gravitational component does become significant. You get a huge number. You carry on anyway. You then estimate the size of this new bound object, you get …after checking the computation again for errors!… about 11 kilometers. The last question on that section is then something like “can you identify this object?”. Then it comes to you in a flash…it’s a neutron star!
That’s one of the reasons I love writing exams that take the student to new places where they learn new stuff in the act of doing it. You’re just not supposed to do that anymore….. bad practice. You’re just supposed to test students with thinly-veiled versions of what you already told them in the lectures. Very thinly. Anything challenging had better be in an open-book exam or a take-home. No arena. No drama. No sweat. Sad.
But I try to do it at graduate level still, since most graduate students in physics are not from the USA and so don’t realize that they can sue me. (Kidding…..slightly….)
It does not always work, but I think that it worked this time.
So today they started with (technical stuff coming up) examining the properties of a particular conformal minimal model – the Lee-Yang model- and I tested their conformal field theory knowledge by getting them to extract the scaling operator dimensions from the Kac table, and deducing various properties of the model from that…. critical exponents, non-unitarity, etc. Then they turned to the subject of KPZ scaling, looking at the properties of the partition function of a conformal field theory coupled now to fluctuating surfaces as opposed to fixed ones. After reflecting upon the critical exponents encountered there, they moved to the meat of the exam: solving a specific model using matrix models techniques. The matrix model allows you to actually do the sum over random surfaces explicitly (by discretising them first) and extract the KPZ behaviour (by taking a careful continuum limit) for a class of conformal models obtained by tuning to a critical point in the model and carrying out the famous “double scaling limit”, which I talked about briefly here. In the end, they get a result for the partition function of the model, and if they’ve done everything properly (I walk them through it), they see KPZ scaling and they discover that they’ve derived the model of the Lee-Yang model (from the first part of the exam) coupled to random surfaces. We’ve come full circle, and they learned how to explicitly solve one of these models on their own, and tune it too find the critical behaviour that defines the continuum limit, etc. (It was only a 90 minute exam, so my plan to have something on solitons (something else we did in the course) was dropped. There was enough computation to be done in the stuff I gave.)
I was reading their solutions on the way home on the bus just now and I think that they all enjoyed it…. A success!
It’s 7:30pm now. Better stop blogging and go back to working. Got to (1) work on documents for a proposal; due tomorrow (2) work on two dossiers for postdoctoral candidates for a fellowship; due tomorrow (3) write several sections of a collaborative project, and edit two; due tomorrow (4) finish work on an encylopeadia entry; due a month ago….
Gosh! I’d better go.