I recently finished my last term lecturing our second-year Quantum Mechanics course, which I taught for five years. It’s a required class, a mathematical introduction to one of the most important set of ideas in all of physics, and really the basis for much of what we do, whether that’s astrophysics or particle physics or almost anything else. It’s a slightly “old-fashioned” course, although it covers the important basic ideas: the Schrödinger Equation, the postulates of quantum mechanics, angular momentum, and spin, leading almost up to what is needed to understand the crowning achievement of early quantum theory: the structure of the hydrogen atom (and other atoms).
A more modern approach might start with qubits: the simplest systems that show quantum mechanical behaviour, and the study of which has led to the revolution in quantum information and quantum computing.
Moreover, the lectures rely on the so-called Copenhagen interpretation, which is the confusing and sometimes contradictory way that most physicists are taught to think about the basic ontology of quantum mechanics: what it says about what the world is “made of” and what happens when you make a quantum-mechanical measurement of that world. Indeed, it’s so confusing and contradictory that you really need another rule so that you don’t complain when you start to think too deeply about it: “shut up and calculate”. A more modern approach might also discuss the many-worlds approach, and — my current favorite — the (of course) Bayesian ideas of QBism.
The students seemed pleased with the course as it is — at the end of the term, they have the chance to give us some feedback through our “Student On-Line Evaluation” system, and my marks have been pretty consistent. Of the 200 or so students in the class, only about 90 bother to give their evaluations, which is disappointingly few. But it’s enough (I hope) to get a feeling for what they thought.
So, most students Definitely/Mostly Agree with the good things, although it’s clear that our students are most disappointed in the feedback that they receive from us (this is a more general issue for us in Physics at Imperial and more generally, and which may partially explain why most of them are unwilling to feed back to us through this form).
But much more fun and occasionally revealing are the “free-text comments”. Given the numerical scores, it’s not too surprising that there were plenty of positive ones:
Excellent lecturer - was enthusiastic and made you want to listen and learn well. Explained theory very well and clearly and showed he responded to suggestions on how to improve.
Possibly the best lecturer of this term.
Thanks for providing me with the knowledge and top level banter.
One of my favourite lecturers so far, Jaffe was entertaining and cleary very knowledgeable. He was always open to answering questions, no matter how simple they may be, and gave plenty of opportunity for students to ask them during lectures. I found this highly beneficial. His lecturing style incorporates well the blackboards, projectors and speach and he finds a nice balance between them. He can be a little erratic sometimes, which can cause confusion (e.g. suddenly remembering that he forgot to write something on the board while talking about something else completely and not really explaining what he wrote to correct it), but this is only a minor fix. Overall VERY HAPPY with this lecturer!
But some were more mixed:
One of the best, and funniest, lecturers I’ve had. However, there are some important conclusions which are non-intuitively derived from the mathematics, which would be made clearer if they were stated explicitly, e.g. by writing them on the board.
I felt this was the first time I really got a strong qualitative grasp of quantum mechanics, which I certainly owe to Prof Jaffe’s awesome lectures. Sadly I can’t quite say the same about my theoretical grasp; I felt the final third of the course less accessible, particularly when tackling angular momentum. At times, I struggled to contextualise the maths on the board, especially when using new techniques or notation. I mostly managed to follow Prof Jaffe’s derivations and explanations, but struggled to understand the greater meaning. This could be improved on next year. Apart from that, I really enjoyed going to the lectures and thought Prof Jaffe did a great job!
The course was inevitably very difficult to follow.
And several students explicitly commented on my attempts to get students to ask questions in as public a way as possible, so that everyone can benefit from the answers and — this really is true! — because there really are no embarrassing questions!
Really good at explaining and very engaging. Can seem a little abrasive at times. People don’t like asking questions in lectures, and not really liking people to ask questions in private afterwards, it ultimately means that no questions really get answered. Also, not answering questions by email makes sense, but no one really uses the blackboard form, so again no one really gets any questions answered. Though the rationale behind not answering email questions makes sense, it does seem a little unnecessarily difficult.
We are told not to ask questions privately so that everyone can learn from our doubts/misunderstandings, but I, amongst many people, don’t have the confidence to ask a question in front of 250 people during a lecture.
Forcing people to ask questions in lectures or publically on a message board is inappropriate. I understand it makes less work for you, but many students do not have the confidence to ask so openly, you are discouraging them from clarifying their understanding.
Inevitably, some of the comments were contradictory:
Would have been helpful to go through examples in lectures rather than going over the long-winded maths to derive equations/relationships that are already in the notes.
Professor Jaffe is very good at explaining the material. I really enjoyed his lectures. It was good that the important mathematics was covered in the lectures, with the bulk of the algebra that did not contribute to understanding being left to the handouts. This ensured we did not get bogged down in unnecessary mathematics and that there was more emphasis on the physics. I liked how Professor Jaffe would sometimes guide us through the important physics behind the mathematics. That made sure I did not get lost in the maths. A great lecture course!
And also inevitably, some students wanted to know more about the exam:
- It is a difficult module, however well covered. The large amount of content (between lecture notes and handouts) is useful. Could you please identify what is examinable though as it is currently unclear and I would like to focus my time appropriately?
And one comment was particularly worrying (along with my seeming “a little abrasive at times”, above):
- The lecturer was really good in lectures. however, during office hours he was a bit arrogant and did not approach the student nicely, in contrast to the behaviour of all the other professors I have spoken to
If any of the students are reading this, and are willing to comment further on this, I’d love to know more — I definitely don’t want to seem (or be!) arrogant or abrasive.
But I’m happy to see that most students don’t seem to think so, and even happier to have learned that I’ve been nominated “multiple times” for Imperial’s Student Academic Choice Awards!
Finally, best of luck to my colleague Jonathan Pritchard, who will be taking over teaching the course next year.
[Update: The bug seems fixed in the latest version, 10.0.2.]
I am in my third year teaching a course in Quantum Mechanics, and we spend a lot of time working with a very simple system known as the harmonic oscillator — the physics of a pendulum, or a spring. In fact, the simple harmonic oscillator (SHO) is ubiquitous in almost all of physics, because we can often represent the behaviour of some system as approximately the motion of an SHO, with some corrections that we can calculate using a technique called perturbation theory.
It turns out that in order to describe the state of a quantum SHO, we need to work with the Gaussian function, essentially the combination
/2), multiplied by another set of functions called Hermite polynomials. These latter functions are just, as the name says, polynomials, which means that they are just sums of terms like
a is some constant and
n is 0, 1, 2, 3, … Now, one of the properties of the Gaussian function is that it dives to zero really fast as
y gets far from zero, so fast that multiplying by any polynomial still goes to zero quickly. This, in turn, means that we can integrate polynomials, or the product of polynomials (which are just other, more complicated polynomials) multiplied by our Gaussian, and get nice (not infinite) answers.
The details depend on exactly which Hermite polynomials I pick — 7 and 16 fail, as shown, but some combinations give the correct answer, which is in fact zero unless the two numbers differ by just one. In fact, if you force Mathematica to split the calculation into separate integrals for each term, and add them up at the end, you get the right answer.
I’ve tried to report this to Wolfram, but haven’t heard back yet. Has anyone else experienced this?
Some time last year, Physics World magazine asked some of us to record videos discussing scientific topics in 100 seconds. Among others, I made one on cosmic inflation and another on what scientists can gain from blogging, which for some reason has just been posted to YouTube, and then tweeted about by FQXi (without which I would have forgotten the whole thing). There are a few other videos of me, although it turns out that there are lots of people called “Andrew Jaffe” on YouTube.
I’m posting this not (only) for the usual purposes of self-aggrandizement, but to force — or at least encourage — myself to actually do some more of that blogging which I claim is a good thing for us scientists. With any luck, you’ll be able to read about my experiences teaching last term, and the trip I’m about to take to observe at a telescope (a proper one, at the top of a high mountain, with a really big mirror).
[On a much more entertaining note, here’s a song from a former Imperial undergraduate recounting “A Brief History of the Universe”. Give it a listen!]
Nearly a decade ago, blogging was young, and its place in the academic world wasn’t clear. Back in 2005, I wrote about an anonymous article in the Chronicle of Higher Education, a so-called “advice” column admonishing academic job seekers to avoid blogging, mostly because it let the hiring committee find out things that had nothing whatever to do with their academic job, and reject them on those (inappropriate) grounds.
I thought things had changed. Many academics have blogs, and indeed many institutions encourage it (here at Imperial, there’s a College-wide list of blogs written by people at all levels, and I’ve helped teach a course on blogging for young academics). More generally, outreach has become an important component of academic life (that is, it’s at least necessary to pay it lip service when applying for funding or promotions) and blogging is usually seen as a useful way to reach a wide audience outside of one’s field.
So I was distressed to see the lament — from an academic blogger — “Want an academic job? Hold your tongue”. Things haven’t changed as much as I thought:
… [A senior academic said that] the blog, while it was to be commended for its forthright tone, was so informal and laced with profanity that the professor could not help but hold the blog against the potential faculty member…. It was the consensus that aspiring young scientists should steer clear of such activities.
Depending on the content of the blog in question, this seems somewhere between a disregard for academic freedom and a judgment of the candidate on completely irrelevant grounds. Of course, it is natural to want the personalities of our colleagues to mesh well with our own, and almost impossible to completely ignore supposedly extraneous information. But we are hiring for academic jobs, and what should matter are research and teaching ability.
Of course, I’ve been lucky: I already had a permanent job when I started blogging, and I work in the UK system which doesn’t have a tenure review process. And I admit this blog has steered clear of truly controversial topics (depending on what you think of Bayesian probability, at least).
This year, there have been a few changes to the structure of the course — although not as much to the content as I might have liked (“if it ain’t broke, don’t fix it”, although I’d still love to use more of the elegant Dirac notation and perhaps discuss quantum information a bit more). We’ve moved some of the material to the first year, so the students should already come into the course with at least some exposure to the famous Schrödinger Equation which describes the evolution of the quantum wave function. But of course all lecturers treat this material slightly differently, so I’ve tried to revisit some of that material in my own language, although perhaps a bit too quickly.
Perhaps more importantly, we’ve also changed the tutorial system. We used to attempt an imperfect rendition of the Oxbridge small-group tutorial system, but we’ve moved to something with larger groups and (we hope) a more consistent presentation of the material. We’re only on the second term with this new system, so the jury is still out, both in terms of the students’ reactions, and our own. Perhaps surprisingly, they do like the fact that there is more assessed (i.e., explicitly graded, counting towards the final mark in the course) material — coming from the US system, I would like to see yet more of this, while those brought up on the UK system prefer the final exam to carry most (ideally all!) the weight.
So far I’ve given three lectures, including a last-minute swap yesterday. The first lecture — mostly content-free — went pretty well, but I’m not too happy with my performance on the last two: I’ve made a mistake in each of the last two lectures. I’ve heard people say that the students don’t mind a few (corrected) mistakes; it humanises the teachers. But I suspect that the students would, on the whole, prefer less-human, more perfect, lecturing…
Yesterday, we were talking about a particle trapped in a finite potential well — that is, a particle confined to be in a box, but (because of the weirdness of quantum mechanics) with some probability of being found outside. That probability depends upon the energy of the particle, and because of the details of the way I defined that energy (starting at a negative number, instead of the more natural value of zero), I got confused about the signs of some of the quantities I was dealing with. I explained the concepts (I think) completely correctly, but with mistakes in the math behind them, the students (and me) got confused about the details. But many, many thanks to the students who kept pressing me on the issue and helped us puzzle out the problems.
Today’s mistake was less conceptual, but no less annoying — I wrote (and said) “cotangent” when I meant “tangent” (and vice versa). In my notes, this was all completely correct, but when you’re standing up in front of 200 or so students, sometimes you miss the detail on the page in front of you. Again, this was in some sense just a mathematical detail, but (as we always stress) without the right math, you can’t really understand the concepts. So, thanks to the students who saw that I was making a mistake, and my apologies to the whole class.
There were only two specific questions, rating each of the following from “Very Good” through “Poor” (there’s a “no response” off to the right, as well):
- The structure and delivery of the teaching sessions
- The content of this module
The numerical results (at right) were pretty good. Note that 114 students — about half — responded.
The rest of the results are free-form comments. With such a big class it’s very difficult to find a style of teaching that suits everyone. Hence, the comments showed a split between the students who enjoyed the very mathematical approach of the course and those who wanted more physical examples from the beginning (not that easy in the context of an axiomatic approach to quantum mechanics — but there are a few simple system like quantum dots that exhibit some of the properties of the simplest systems we study in class; it’s clear that these should be highlighted more than I have). Similarly, some students wanted a more step-by-step approach to the mathematics, whereas others would prefer just a sketch of the proofs on the board (“put the algebra in the notes and let students work through it”).
But one set of comments especially hit home. Here’s a good example:
Frankly, I think that Prof. Jaffe has the potential to be an outstanding lecturer, one which he wastes by not being properly prepared. Just showing up to lectures and writing down on the board what was in (the previous lecturer’s) notes without thinking much about it in advance results in time spent staring at notes and board which could otherwise have been used to face the audience and explain what it is we’re doing. Maybe that sounded harsh, but he really is very good and could be outstanding if he put a little more into preparing for lectures and didn’t stick to his notes quite so much… If you actually perform the calculations, and think about the various steps yourself, then it all happens in a way, and at a pace, which suits us as students and allows us to follow.
(OK, I picked one that made an effort to heap on some praise along with the criticism.) I have to admit that this point, repeated by several students, seemed right on, for at least some of the lectures. I did always make an effort to go over the notes in detail beforehand. But these were notes indeed written by the previous lecturer, and this gives a few problems. Yes, I probably wasn’t always careful enough to go over the details of the mathematics beforehand. So sometimes I did spend too much effort trying to puzzle out exactly what I wanted to say (some students also complained about the occasional mistakes I made on the board, perhaps related to this). But sometimes the problem is more subtle: I might not always want to explain the concepts in the same way as the previous lecturer — and sometimes I might only realise this when actually doing the explaining! Either of these can happen in any lecture, but the combination of teaching this course for the first time, and doing so from someone else’s notes, certainly made it worse.
Next year, things will at least be different: I’ll be teaching for the second time, and so have some idea of the pitfalls from this past year. Moreover, our department is making some significant changes to the overall structure of the curriculum, phasing out our system of tutorials and so-called classworks for a series of three medium-sized (20 student) group sessions each week. This is happening alongside some specific changes to the quantum mechanics curriculum, with more material in the first year (happening already). My course will be shortened by a full five lectures, but I suspect that this combination of changes will give me a bit more breathing room, as well as a few different ways to make sure the material gets said in different ways, appropriate for different students.
Further criticism, comments, ideas, etc., are always welcome.
A week ago, I finished my first time teaching our second-year course in quantum mechanics. After a bit of a taster in the first year, the class concentrates on the famous Schrödinger equation, which describes the properties of a particle under the influence of an external force. The simplest version of the equation is just This relates the so-called wave function, ψ, to what we know about the external forces governing its motion, encoded in the Hamiltonian operator, Ĥ. The wave function gives the probability (technically, the probability amplitude) for getting a particular result for any measurement: its position, its velocity, its energy, etc. (See also this excellent public work by our department’s artist-in-residence.)
Over the course of the term, the class builds up the machinery to predict the properties of the hydrogen atom, which is the canonical real-world system for which we need quantum mechanics to make predictions. This is certainly a sensible endpoint for the 30 lectures.
But it did somehow seem like a very old-fashioned way to teach the course. Even back in the 1980s when I first took a university quantum mechanics class, we learned things in a way more closely related to the way quantum mechanics is used by practicing physicists: the mathematical details of Hilbert spaces, path integrals, and Dirac Notation.
Today, an up-to-date quantum course would likely start from the perspective of quantum information, distilling quantum mechanics down to its simplest constituents: qbits, systems with just two possible states (instead of the infinite possibilities usually described by the wave function). The interactions become less important, superseded by the information carried by those states.
Really, it should be thought of as a full year-long course, and indeed much of the good stuff comes in the second term when the students take “Applications of Quantum Mechanics” in which they study those atoms in greater depth, learn about fermions and bosons and ultimately understand the structure of the periodic table of elements. Later on, they can take courses in the mathematical foundations of quantum mechanics, and, yes, on quantum information, quantum field theory and on the application of quantum physics to much bigger objects in “solid-state physics”.
Despite these structural questions, I was pretty pleased with the course overall: the entire two-hundred-plus students take it at the beginning of their second year, thirty lectures, ten ungraded problem sheets and seven in-class problems called “classworks”. Still to come: a short test right after New Year’s and the final exam in June. Because it was my first time giving these lectures, and because it’s such an integral part of our teaching, I stuck to to the same notes and problems as my recent predecessors (so many, many thanks to my colleagues Paul Dauncey and Danny Segal).
Once the students got over my funny foreign accent, bad board handwriting, and worse jokes, I think I was able to get across both the mathematics, the physical principles and, eventually, the underlying weirdness, of quantum physics. I kept to the standard Copenhagen Interpretation of quantum physics, in which we think of the aforementioned wavefunction as a real, physical thing, which evolves under that Schrödinger equation — except when we decide to make a measurement, at which point it undergoes what we call collapse, randomly and seemingly against causality: this was Einstein’s “spooky action at a distance” which seemed to indicate nature playing dice with our Universe, in contrast to the purely deterministic physics of Newton and Einstein’s own relativity. No one is satisfied with Copenhagen, although a more coherent replacement has yet to be found (I won’t enumerate the possibilities here, except to say that I find the proliferating multiverse of Everett’s Many-Worlds interpretation ontologically extravagant, and Chris Fuchs’ Quantum Bayesianism compelling but incomplete).
I am looking forward to getting this year’s SOLE results to find out for sure, but I think the students learned something, or at least enjoyed trying to, although the applause at the end of each lecture seemed somewhat tinged with British irony.
Until now, I have been forced to resist the clamour brewing among both members of my extensive readership (hi, dad!) to post a bit more often: my excuse is that, in the little over a month between early September and mid-October, I have travelled back and forth from Paris to London five times, spent a weekend in the USA, started teaching a new course, and ran a half marathon.
Ten one-way trips in six weeks is too many; the Eurostar makes it about as pleasant as it could possibly be: 2 1/4 hours from central London to central Paris by train (a flight from Heathrow to de Gaulle is faster, but the airports are less convenient and much more stressful). Most of my time in Paris was for Planck Satellite meetings, mostly devoted to the first major release of Planck data and papers next year — of course, by The Planck rules, I can’t talk about what happened. At least I have no more trips to Paris until early December (and only four or so hours a week of Planck telecons).
But in addition to three Planck meetings, I also helped out in my minor role as a member of the Scientific Organizing Committee of the Big Bang, Big Data, Big Computing meeting at the APC, which was an excellent gathering of cosmologists with computer scientists and statisticians, all doing our best to talk over the fences of jargon and habit that often keep the different fields from having productive conversations. One of my favourite talks was the technical but entertaining From mean Euler characteristics to the Gaussian kinematic formula by Robert Adler, whose work in statistics more than thirty years ago taught many in cosmology how to treat the functions that we use to describe the distribution of density and temperature in the Universe as random fields; he discussed more recent updates to that early work for much more general circumstances, the cosmological repercussions of which have yet to be digested. Another highlight was from Imperial’s own Professor David Hand, Opportunities and Challenges in Modelling and Anomaly Detection, discussing how to pull small and possibly weird (“anomalous”) signals from large amounts of data— he didn’t highlight many specific instances in cosmology, but rather gave examples with other sorts of big data, such as the distribution of prices of credit card purchases (with some particularly good anecdotes culled from gas/petrol station data).
Finally, in addition to those many days of meetings — and yes, the occasional good Parisian meal — there were a couple of instances of the most satisfying of my professional duties: two examinations for newly-minted PhDs from the Institut d’Astrophysiques de Paris and the Laboratoire Astroparticule et Cosmologie — félicitations aux Docteurs Errard et Ducout.
This week I received the results of the “Student On-Line Evaluations” for my cosmology course. As I wrote a few weeks ago, I thought that this, my fourth and final year teaching the course, had gone pretty well, and I was happy to see that the evaluations bore this out: 80% of the responses were “good” or “very good”, the remainder “satisfactory” (and no “poor” or “very poor”, I’m happy to say). I was disappointed that only 23 student (fewer than half of the total) registered their opinion on subjects like “The structure and delivery of the lectures” and “the interest and enthusiasm generated by the lecturer”.
The weakest spot was “The explanation of concepts given by the lecturer” with 5 for satisfactory, 11 for good and 7 for very good — I suppose this reflects the actual difficulty of some of the material. In the second half of the course I need to draw more heavily on concepts from particle physics and thermodynamics that undergraduate students may not have encountered before, concepts that are necessary in order to understand how the Universe evolved from its hot, dense and simple early state to today’s wonderfully complex mix of radiation, gas, galaxies, dark matter and dark energy. Without several days to devote to the nuclear physics of big-bang nucleosynthesis, or the even longer necessary to really explain the quantum field theory in curved space-time that would be necessary to get a quantitative understanding of the density perturbations produced by an early epoch of cosmic inflation, the best I can do is give a taste of these ideas.
And I really appreciated comments such as “Work with other lecturers to show them how it’s done”. So thanks to all of my students — and good luck on the exam in early June.
Somehow I’ve managed to forget my usual end-of-term post-mortem of the year’s lecturing. I think perhaps I’m only now recovering from 11 weeks of lectures, lab supervision, tutoring alongside a very busy time analysing Planck satellite data.
But a few weeks ago term ended, and I finished teaching my undergraduate cosmology course at Imperial, 27 lectures covering 14 billion years of physics. It was my fourth time teaching the class (I’ve talked about my experiences in previous years here, here, and here), but this will be the last time during this run. Our department doesn’t let us teach a course more than three or four years in a row, and I think that’s a wise policy. I think I’ve arrived at some very good ways of explaining concepts such as the curvature of space-time itself, and difficulties with our models like the 122-or-so-order-of-magnitude cosmological constant problem, but I also noticed that I wasn’t quite as excited as in previous years, working up from the experimentation of my first time through in 2009, putting it all on a firmer foundation — and writing up the lecture notes — in 2010, and refined over the last two years. This year’s teaching evaluations should come through soon, so I’ll have some feedback, and there are still about six weeks until the students’ understanding — and my explanations — are tested in the exam.
Next year, I’ve got the frankly daunting responsibility of teaching second-year quantum mechanics: 30 lectures, lots of problem sheets, in-class problems to work through, and of course the mindbending weirdness of the subject itself. I’d love to teach them Dirac’s very useful notation which unifies the physical concept of quantum states with the mathematical ideas of vectors, matrices and operators — and which is used by all actual practitioners from advanced undergraduates through working physicists. But I’m told that students find this an extra challenge rather than a simplification. Comments from teachers and students of quantum mechanics are welcome.
Many plays about science suffer from trying to do too much, telling a story while teaching science, but Nick Payne’s two-hander “Constellations”, now on at the Royal Court Theatre in London, has science and a scientist at its center, adding to the drama, not distracting us with jargon or science fictional twists.
“Constellations” is the story of Roland and Marianne, a beekeeper and a cosmologist. Without giving away too many spoilers, I’ll say that the play tells us the story of their relationship, as it might play out in the myriad possible universes of the multiverse, each one subtly different from the rest (while of course there would be vastly many more that are not subtly, but radically, different — but a play about empty, boring Universes would be less compelling). In one, Marianne tells Roland “I sit in front of the computer all day and analyse data from the Cosmic Microwave Background” which readers will know is pretty much exactly what I do. In others, she is still an astrophysicist, sometimes more theoretical, sometimes more observational (or she is the same, just choosing to highlight different parts of her work to impress Roland or drive him away). Sometimes we see their relationship end, sometimes continue, sometimes restart, as the play pushes forward in time and between the universes. And we return, repeatedly, to one particular version of their story, towards a climax in the future of one or more of the Universes, which puts the comedy of many of the situations into tragic relief.
Playwright Nick Payne needs one of his characters to be a scientist, able to describe the underlying ideas, but manages to avoid too much heavy-handed exposition, limiting the explicit discussion of cosmology to flirty conversations early on in their relationship (I don’t know about my peers, but I find cosmology very good for flirting, at least with the right people). Sally Hawkins’ Marianne and Rafe Spall’s Roland are improbably attractive but manage to get across at least some of the neediness and nerdiness of someone burrowed so deeply into both the technical problems and the broad themes of something like cosmology or beekeeping, making us care about them and their fate (or fates?).
I made it back onto the BBC today, this time to discuss Stephen Hawking on his 70th birthday (most of the people more qualified than me are actually at a meeting in his honour in Cambridge). (Actually, my very first appearance on the BBC, which generated one of my very first blog posts, was to talk about Hawking’s bet with Preskill and Thorne about the fate of information supposedly lost into a black hole — Hawking had originally claimed that a black hole destroys any information that fell into it, which would be a violation of the tenets of quantum mechanics, but has since, somewhat controversially, conceded.)
I have been lucky enough to meet Stephen, and was even invited to a dinner party at his house, where I got to see him posing with his Presidential Medal of Freedom, awarded by Barack Obama in 2009. So I was especially disappointed to subsequently hear that he was too ill to actually attend his conference in Cambridge. I wish him a very Happy Birthday and a speedy recovery.
It’s not hard to talk about Hawking: he’s been involved with some truly exciting breakthroughs in theoretical physics over the last few decades, perhaps most importantly for teasing out the relationship between the properties of black holes and the laws of thermodynamics. This seemingly formal analogy was realized to be much more than that with Hawking’s discovery that black holes are not, in fact, “black” — rather, they glow at a temperature inversely proportional to the mass of the black hole, emitting what has come to be called Hawking Radiation.
These are very significant discoveries, teaching us something crucial about the connections between the three great theories of physics, quantum mechanics, gravity and thermodynamics. But it’s safe to say that no one yet fully understands exactly what those relationships are.
And of course Hawking’s nonscientific accomplishments are well-known and justly valorised. He has lived with — triumphed over — ALS for far longer than any of his doctors had predicted. He has written one of the best-selling popular science books of all time, A Brief History of Time. And, needless to say, he’s done some amazing scientific work, just some of which I’ve mentioned above.
There have been very many very brilliant physicists through the centuries. So it would certainly be premature, if not churlish, to take the long view and ask where Hawking would sit in the pantheon of physicists from Archimedes through Newton, Einstein and beyond. Indeed, as my friend and colleague Peter Coles has just written, Hawking’s peers have so far decided that the time is not yet ripe to elevate him to the top of the table. (Peter has also written a short book on the subject, picking apart some of the interactions between scientists, the media and the wider public.)
I’ve spent the last few days in the northern half of Great Britain. Wednesday, I was an external examiner for a (successful!) PhD exam at the Durham University. Thursday, I was at the University of Glasgow in service to the other end of the PhD experience in the UK, giving a one-hour lecture on the Cosmic Microwave Background at the STFC summer school for incoming students.
But after the summer school I woke up early for the Caledonian Sleeper up to Fort William in the Western Highlands. I rode through some of the UK’s most spectacular landscape, hills and lochs in the morning fog:
Once I got to Fort William (a typically characterless UK town, unfortunately), I hit the trail, walking along the last few miles of the West Highland Way, taking in some detours to the Cow Hill Summit and the iron-age Dun Deardail Fort. The local hills, including Ben Nevis, the highest peak in Britain, were nestled in low-slung cloud all day:
Along the way, I spotted flora and fauna
And as an added bonus, here are the Mekons, with their own take on walking in the British countryside:
I’ve just finished another term, in fact the heaviest teaching load I’ve ever had at once: a twenty-six hour lecture course, three hours a week as one of several computer lab “demonstrators”, and another four hours or so per week in first-year student tutorials.
For those from outside of the Imperial system: our tutorials are small group meetings during which we go over a selection of the problem sheets handed out during the week in the lecture courses; here, like most of the UK, these are not explicitly marked, but instead the students get the solutions a week or so after they are handed out. The tutorial session is one of the few chances for any sort of discussion or feedback.
The tutorials can be fun and even challenging (but I’m glad I get to see the answers before the students). It is heartening to see the students trying — sometimes struggling — to really understand the problems. However, the fourth hour in a week going over the same problems can get repetitive; there aren’t that many different questions the students ask.
On the other hand, lab demonstrating doesn’t offer much intellectual at all. I have mostly supervised computer labs, which involves standing around while the students work their way through a “script”, writing programs and (we hope) learning about programming. I admit that I don’t think this is a particularly efficient use of my time: although considerable overall high-level organization is needed, the labs themselves could be (and indeed are, partially) monitored by graduate students. Unfortunately, they don’t get more than beer money for their trouble — and postdocs don’t get paid at all.
The best part of undergraduate teaching for me, though, is lecturing. When it goes well, it can be a remarkably effective way of communicating. Of course, it doesn’t always go well. Sometimes I’m not as well-prepared as I would like, or sometimes I don’t even understand the material as well as I need to. Sometimes the students don’t have the background that I thought they did. And sometimes the material is just hard, too hard to really get the first time through. Even problem sheets and studying for exams isn’t always enough: I certainly admit that I didn’t really understand much of the material that I now use every day until I was in graduate school, applying it in the course of my research. And some stuff I didn’t understand until I had to teach it (which implies that there is plenty of physics that I still don’t understand, so still much more to learn).
This term’s Cosmology course felt pretty good: after three years not only do I understand the material, but also I understand something about how to explain it to not-yet-expert upper-level physics students. The downside of this is that my explanations get a bit longer every year, so it gets harder and harder to squeeze in the most exciting material which inevitably has to come at the end, building on the foundation of the rest of the course.
This year, the Physics Department has an artist-in-residence, Geraldine Cox. Among her many other cool projects, she has been lurking in the back of our lecture theatres, sketching furiously. Many thanks to her for these pictures of me at the blackboard, in one of my favorite striped shirts:
(The graph on the upper left is labeled “Do we live in a special time?” — We seem to live at a time labeled by the vertical line, just as the Universe is transitioning from being mostly made of “matter” — the middle of the three plateaus in the graph — to mostly something very like Einstein’s cosmological constant, or the so-called “Dark Energy” — the rightmost plateau, which may go on infinitely far to the right. So we might have expected to find ourselves near a plateau rather than a one of the few times in between. This is an anthropic argument, and must be treated with care.)
As always, I welcome feedback, anonymous or otherwise, from any of my students on this course or any other. (When I asked for some comments a few weeks into the term, the most amusing came from the student who praised my voice and asked if I was a singer — which doesn’t jibe with the other, less positive, comments on my American accent….)
Finally, today was one of the high points of post-graduate teaching: one of my students, Jude Bowyer, passed his PhD viva with his thesis, Local Methods for the Cosmic Microwave Background. Well done to the soon-to-be Dr. Bowyer!
This week is the 100th anniversary of one of the most important events in the Labor movement (at least back in the US): the Triangle Shirtwaist Factory fire, a disaster in which the garment factory’s sweatshop conditions led to the death of almost 150 workers, mostly Jewish immigrant women, locked by their bosses into their lower-Manhattan factory while the fire raged. This tragedy had remarkably swift and positive repercussions, spurring the growth of the once-powerful International Ladies’ Garment Workers’ Union and resulting in a new regime of labor laws actually intended to help workers and not their employers. (The New York Times is commemorating the fire on one of their blogs.)
So I am saddened and a little guilty that I will not be participating in the labor action being called for this week by my own union. The University and College Union represents academics in UK higher education institutions. In this precarious time for Universities, especially here in England, I am glad, in principle, that there is a union representing academics, a group of people who certainly aren’t in it for the money, and deserve at least a modicum of recompense, job security, and respect.
In principle. In practice the UCU has spent much of the last decade or so in the news not fighting for workers’ rights but because of the stance of some of its more radical (but sadly misguided) members toward Israel than for trying to improve the condition of its own workers.
Now, however, they’re trying to take on an issue that will certainly impact all of us (academics): pensions, which our employers contend have to dwindle in the light of supposed economic realities. I suspect and fear that, in the long run, the employers may actually be right, given the ageing and long-lived population, as is well known. But I also suspect that they are not negotiating with everything appropriate on the table. Hence, an impasse, and one that if not resolved will certainly harm all of us: academics, administrators and, not least, students. During this last week of our term, with only two hours of lectures left in my course, I would have preferred “action short of a strike” that would have enabled me to fulfil my teaching duties and my responsibilities toward my (blameless) students. Although, yes, I appreciate that the whole point of a strike is to cause harm, and show how indispensable we workers are, but this relies on generating sympathy for the workers, and anger directed at the employers. But with the rather woeful PR job by the UCU, I doubt many of our students would have known why their lecturers aren’t around.
As a scientist, I am used to my work being read by my peers, and I’ve made it into the occasional magazine or newspaper article, and even the odd TV and radio slot. But last week I travelled to Venice’s Architecture Biennale for the culmination of the first phase of the Architectural Association’s Beyond Entropy art/science project (which I’ve described before). I took a vaporetto to the island of San Giorgio, and next to one of Venice’s more spectacular Palladian churches, I saw the Beyond Entropy banner hanging over the entrance:
(I took these pictures, but there are many much more professional ones taken by the AA’s Valerie Bennett.)
Before arriving, I didn’t know what to expect from the project: small-scale, low-key, amateurish? In this setting, it was clearly big and serious. And inside this lovely building were these, the prototypes for our time machine:
Last year I traveled to South America to witness the launch of our several-hundred million-Euro Planck satellite, surely a big and serious project. But the sight of my own work — our texts, flywheels and gyroscopes — sitting on a plywood plinth, plausibly described as something at least related to the very different creative process of art, was nearly as disconcerting (despite the lack of highly explosive rocket fuel).
I’ll leave any assessment of the overall quality to others, although it became obvious that these pieces really are prototypes for what could become more finished works, but we have a long way to go. Nonetheless, let me explicitly thank my collaborators, Shin Egashira (whom I will also congratulate on his wedding which gave him an excellent reason to not show up in Venice) and Scrap Marshall, a student at the Architectural Association who joined us toward the end of the project and did an enormous amount of practical and creative work getting our pieces together. From speaking to members of some of the other groups, we were lucky to all be based in London, and to eventually come to see our project in similar ways, albeit from different directions; some of the more widely-dispersed groups had to deal with significantly greater practical problems, and the interpersonal ones those ended up causing.
That first day was dedicated to the AA’s visiting school, and the next day was the centrepiece: a marathon symposium of more than thirty talks, dedicated to the themes of “entropy” and “energy”. Remarkably, none of our projects addressed the ecological, societal and political aspects of these topics, while many of the speakers attacked them directly, from Richard Burdett and Reinier de Graaf’s complementary discussions of the bleak picture for energy and climate if we keep to “business as usual” in our habits of consumption and production, to Italian Green Party politician Grazia Francescato’s hopeful discussion of “Green Jobs and Green Economy”. There were a few talks on science per se, from Angelo Merlina’s brief introduction to the LHC at CERN (of which a third talked about cosmology, and a third was pre-recorded), to one of my favourites, biophysicist Tania Saxl’s description of the amazing mechanism behind the motion of rotating bacterial flagella. There was also an inexplicable prerecorded description of “parallel worlds” in film from de Gruyter and Thys, a performance from the Arazzi Laptop ensemble, and contributions from Serpentine Gallery curator Hans-Ulrik Obrist (which was interesting but mostly about himself) and Charles Jencks. Jencks tackled the overlap between science, art and architecture head-on, each as a different metaphorical system for describing and interacting with the world. This culminates in his Scottish Garden of Cosmic Speculation, a hugely symbolic landscape replete with double helixes and grassy knolls in the form of black hole spacetime diagrams (I admit I’ve also found these supposed metaphors a bit too, well, literal for my taste — with insufficient information to be effective teaching tools, but too didactic to be truly beautiful.) I think the most important thing I learned was that, in their own way, the architects are just as nerdy as us scientists, but just better looking dressed.
Also, there was plenty of fine food and free-flowing sparkling wine (which meant that I probably missed about half of the presentations).
Finally, I would like to thank everyone from the AA who made the project happen (and will continue to do so, if further funding is forthcoming): Artemis Doupa, Sylvie Taher, Esther McLaughlin, Aram Mooradian and most especially the ever-enthusiastic project director, Stefano Rabolli Pansera. Thanks also to the AA visiting students, and all of the other participants, especially Ariel Schlesinger and Wilfredo Prieto for giving me a glimpse of the Architecture Biennale through artists’ eyes.
We get most of the official feedback on our teaching through a mechanism called SOLE — Student On-Line Evaluations — which asks a bunch of questions on the typical “Very Poor” … “Very Good” scale. I’ve written about my results before — they are useful, and there is even some space for ad-hoc comments, but the questionnaire format is a bit antiseptic.
On some occasions, however, students make an extra effort to let you know how they feel. Last year, I received an anonymous paper letter in the old-fashioned snail-mail post from a student in my cosmology course which said, among other statements, that I should “show appropriate humility and shame by not teaching any undergraduate courses at all this coming year.” Well, that year has come and gone, and I was not absolved of teaching responsibilities, so I soldiered on.
Today, I received another anonymous letter, from a most assuredly different student, who said that this year’s cosmology course “is without a doubt the most interesting undergraduate course I have taken at Imperial.” This would have left me ecstatic, except that this otherwise well-intentioned and obviously smart student managed to put the envelope in the mailbox with insufficient postage, which meant that I had to trudge across to the local mail facility and pay the missing 10p, along with a full £1 fee/fine! (If the author of the letter happens to read this, please consider a donation of £1.10 plus appropriate interest to the charity of your choice!).
It would be self-serving of me to make too much of this, beyond noting that, although I did make some significant changes in this year’s course, these letters more likely indicate the very different reactions that a given course can engender, rather than a vast improvement in my teaching.
My apologies to both students if they would have preferred I not quote them on-line, but such is the price of anonymity.
I just received the SOLE (Student On-Line Evaluation) results for my cosmology course. Overall, I was pleased: averaging between “good” and “very good” for “the structure and organisation of the lectures”, “the approachability of” and “the interest and enthusiasm generated by” the lecturer, as well as for “the support materials” (my lecture notes), although only “good” for “the explanation of concepts given by the lecture”, with an evenly-dispersed smattering of “poor” and “very good” —- you can’t please all of the people all of the time. That last, of course, is the crux of any course, and especially one with as many seemingly weird concepts as cosmology (the big bang itself, inflation, baryogenesis, …). So perhaps a bit of confusion is to be expected. Still, must try harder.
The specific written comments were mostly positive (it’s clear the students really liked those typed-up lecture notes), but I remain puzzled by comments like this: “Sometimes 2-3 mins of explanation (which is generally good) is reduced to one or two words on the board which are difficult to understand when going over notes later.” Indeed — I expect the student to take his or her own notes on those “2-3 mins of explanation”, if they were useful and interesting. But many of the comments were quite helpful, about the pace of the lectures, the prerequisites for the course, and, especially, the order in which I use the six sliding blackboards in the classroom.
So, thanks to the students for the feedback (and good luck on the exam…).
I’ve just finished teaching my eleven-week winter-term Cosmology course at Imperial. Like all lecturing, it was exhilerating, and exhausting. And like usual, I am somewhat embarrassed to say that I think I understand the subject better than when I started out. (I hope that the students can say some of the same things. Comments from them welcome, either way.)
It’s my second year, and I think I am slowly getting the hang of it. It’s hard to fit all of the interesting and up-to-date research in cosmology into 26 lectures, starting from scratch. This time I spent a little more time in the early lectures trying to give a heuristic explanation of some of the more advanced background topics, like the interpretation of the metric in Einstein’s General Relativity, and the physics behind the transition of the Universe from and ionized plasma to a neutral gas.
In a way, much of this was prelude to some of the most most exciting research in modern cosmology, the growth of large-scale structure from its first seeds into the pattern of galaxies we observe in the Universe today. Explaining this requires a lot of background: early-Universe thermodynamics and why the Universe started out hot, dense, and dominated by radiation; enough relativity to motivate how structure grows differently on large and small scales; and the generation of the initial conditions for structure, or at least our best current idea, inflation, which takes initial quantum randomness and blows it up to the size of the observable Universe (and solves quite a few other problems besides). All of this, and the background required even to get to these topics, barely fit into those 26 lectures (and I admit I was a little rushed toward the end…). And it was even harder to compress them down into four hours of postgraduate lectures.
Alongside this, I decided that none of the available textbooks had quite the right point of view for my discussion, at least not at the undergraduate level I was aiming for (and there are some very good textbooks out there, including Andrew Liddle, An Introduction to Modern Cosmology; Michael Rowan-Robinson, Cosmology; and Peter Schneider, Extragalactic Astronomy and Cosmology: An Introduction). So I also wrote a hundred or so pages of notes (which are available from my Imperial website, if you’re interested in a crash course).
I’m often puzzled by exactly what students want from the 26 hours of lectures themselves. Many, it seems to me, would prefer to merely transcribe my board notes without having to pay close attention to what I am actually saying; perhaps note-taking is not a skill that students perfect at school nowadays. I hope at least that those written notes make it a bit easier to both listen and think during the lectures. (Again, constructive criticism is more than welcome.)
This week I’ll be giving a review (just half an hour!) of cosmology at the IOP’s High-Energy and Astroparticle Physics 2010 meeting. And then I get to indulge in some of my hobbies, like doing scientific research.
The students in my cosmology course had their exam last week.
There’s no doubt that they found the course tough this year — it was my first time teaching it, and I departed pretty significantly from the previous syllabus. Classically, cosmology was the study of the overall “world model” — the few parameters that describe the overall contents and geometry of the Universe, and courses have usually just concentrated upon the enumeration of these different models. But over the last decade or two we’ve narrowed down to what is becoming a standard model, and we cosmologists have begun to concentrate upon the growth of structure: the galaxies and clusters of galaxies that make the Universe interesting, not least because we need them for our own existence. Moreover, that structure directly teaches us about those contents which make them up and the geometry in which they are embedded. I wanted to give the students a chance to learn about the physics behind this large-scale structure, not traditionally at the heart of undergraduate cosmology courses.
Unfortunately, this also meant that the traditional undergraduate textbooks didn’t cover this material at the depth I needed, and so the students were forced to rely on my lectures and the notes they took there (and eventually a scanned and difficult-to-read copy of my written notes).
I sensed a bit of worry in the increasing numbers of questions from students in the weeks before the exam, and heard rumors of worries. But the day of the exam rolled around, and indeed when I re-read the questions it didn’t seem too bad, although there were some grumbles evident in the examination room.
Later I learned that there was a “record-breaking” number of complaints about the exam. I gather it was perceived to be difficult and unfamiliar.
So marking the exams in the past week, I was happy to find that the students performed just fine: the right “bell-shaped curve”, the correct mean, etc. (Of course I should point out that all results are subject to final approval by the Physics Department Examiners Committee.) I admit some puzzlement, therefore, about the reaction to the exam. Were they worried because the questions were different from those they had seen before? That, I admit, was the point of the exam — to test if they have actually learned something. Which, I am happy to point out, it seems that they had!
There was one question that almost all students got wrong, however. I asked about the “Cosmological Constant Problem” and whether it could be solved by the theory of cosmic inflation. The Cosmological Constant is a number that appears in General Relativity, and, although we can’t predict it for certain, we are pretty sure that if it’s not strictly zero, in most theories we would estimate that it ought to have a value something like 10120 (that is 1 followed by 120 zeros!) times greater than that observed in the Universe today. I suppose I didn’t write on the board the words “Cosmological Constant Problem” next to that extraordinarily large number. (In the end, I reapportioned the small number of marks associated with that problem.) Inflation involves something very much like the cosmological constant, but occurring in the very early Universe — so inflation can’t help us with the 120 zeroes, alas.
Next year, I’ll be sure to spell all of this out, but I’ll also show this movie of my old grad-school friend, collaborator, and colleague Lloyd Knox, now a professor at the University of California, Davis, singing this song about Dark Energy (of which the cosmological constant is a particular manifestation):
The scientifically-accurate lyrics are sung to the tune of Neutral Milk Hotel’s “In the Aeroplane over the Sea”.
Finally, I’d welcome comments on the course or the exam, anonymous or otherwise, from any students who may come across this post.