More Than A Hint Of The Old Days, II

A strange but satisfying aspect of my time here (I’m at the Aspen Center for Physics, recall) has been the fact that due to some odd serendipity, there’s a ton of people from the “old days”. Which ones? My Princeton years, in the early 90s, as a postdoc at the Institute for Advanced Study (and later at Princeton University). These are not all people doing what I do, but in a wide range of fields such as high energy physics, astrophysics, condensed matter physics. Several of us were postdocs together. I’ve been chatting with people I’ve not seen for a while, sometimes not since those days, or they are people I met back then, and with whom I have a pool of shared memories from those days. So it has put me in mind of those times somewhat.

A quick example. Soon after I arrived last week, I was walking along, chatting with Petr HoÅ™ava (Berkeley) about various things, and we got on to reminiscing a bit about our time together as postdocs in Princeton. And then minutes later, as though conjured from the very substance of our conversation, who should walk by but one of the Gods/Legends of the field (then and now), Princeton’s Alexander Polyakov. He walked by in exactly the same sort of way he would back then, either coming from or going to a walk along the river or canal, perhaps to give us a lecture. Petr and I looked at each other, and continued our walk and talk.

The great news for me last week was that Polyakov then gave a talk. I’ll admit to being a big fan of his physics. When he gives a talk nearby, I show up, no matter how confused I might end up at the end. There’s going to be good stuff in there – it’s only a matter of time before it sorts itself out in your head. Often years. Decades. Several of us sat in on his graduate class back in Princeton in the early 90s just to try to catch the pearls of wisdom which we’d pick up as he lectured on….. Well, I’ve no idea to this day what the class was really about. He would show up (probably fresh from a walk), with no notes or anything, and just pick up a piece of chalk, stare out the window for a few seconds, and then start writing stuff. Essentially, he was randomly jumping around the subject matter in his widely under-read book “Gauge Fields and Strings”. He was all over the book. It was not always a simple and coherent path through the subject matter, and it seemed that he was largely exploring whatever took his mood in the moment, but I suspect that was largely my ignorant young mind’s impression.

Polyakov in Aspen
A. M. Polyakov in the middle of giving what for me was an excellent and intriguing seminar at the Aspen Center for Physics. Click for larger view.

Sadly, it is the type of course that these days would score close to zero in most universities in (especially undergraduate) teaching evaluations, but in which -if you cared about the physics and took the time to think through what he said after and let the seeds that were planted grow in time- you could learn more physics in one or two lectures than from an entire semester’s course given by someone teaching a highly structured user-friendly course that required no effort on the part of the audience. Not surprisingly it is the latter sort of lecture that we are expected to give these days at all levels -forcing out this unstructured sort of style- because today’s students (undergraduate and increasingly graduate) seem to have much less of the patience, time, (or whatever) to fill in the gaps themselves, do voluntary extra reading, or to take the long view of some of the things they’ll hear and not immediately understand. We really seem to have to spoon-feed the material and baby-sit more than ever. I do not mean to offend here. In my opinion, this is nothing to do with how smart the students are (they are as smart as they ever were, I’m sure), but more with how the system has become more tilted toward the expectation on the part of the students that the spoon-feeding and baby-sitting will be there. So give open-ended or loosely structured lectures (where you hope students will make connections and explore more on their own) at your peril. On the other hand, for every Polyakov there’s several hundred people who, if they lectured in his style, the content would simply be zero (or less)…. They simply don’t have his knowledge or insight into the material. So while I believe more structure by default is the way to go, we must leave room for the Polyakovs of this world.

Ok, back to Aspen. My ignorant older mind of last week found him much more understandable, partly as a result of having learned more about how to listen to him from back then, and partly because I know a trifle more about things than I did back then. It was my highlight of the visit to Aspen so far this year, in terms of talks that were given. Some of the reason for this is nostalgia, I will grant. I was sitting there like a kid in a candy store just enjoying the style of physics, his turns of phrase (he’s got a funny but understated sense of humour – his curious ways of saying things are not accidental, I think), and the feeling that I’d been transported back in time 14 years.

Most of all, however, it was just great to hear from one of the old masters on a subject of great interest to me – He was talking about aspects of doing quantum theory in de Sitter spacetimes, presenting a new proposal for how to do this, and exploring some of the consequences. For those of you who don’t know what that means, don’t worry. Briefly, de Sitter spacetime is one of the prototype spaces you study as a model of positive cosmological constant. A cosmological constant can be thought of as an intrinsic energy density that space itself has. A positive energy density turns out to mean that it is energetically favourable to increase the volume of space (more volume, more energy…. its a density you see), the space obligingly expands as a result of this positive energy density. So in physics terms, you’d say this was an outward or “negative” pressure of the vacuum. It is believed (after the spectacular supernova observations announced in 1998 that show that our universe’s expansion is accelerating) that our universe may have a positive cosmological constant (it is one of the simplest effects consistent with the observations). This is the “Dark Energy” issue that you hear a lot about from time to time. (Search the archive of posts for earlier discussions.) One of the biggest problems in physics is that nobody has a good theory of how to do quantum physics completely reliably in the context of positive cosmological constant. So people spend time studying model spacetimes that allow you to focus on the technical issues. de Sitter is one of them, and this is what Polyakov was doing, although much of what he was saying pertained to other issues as well, such as (technical aside:) defining propagators in the quantum theory, á la Feynman, in various kinds of spacetimes you can put into two categories, “eternal” or “non-eternal”. His working definition of “eternal” was that there were no instabilities that would arise that would destroy the background metric. “It is a very limited definition of eternity”, he remarked, not without humour and irony. I was in theoretical physics heaven.

Well, I’ll end with an amusing (to me story). I suspect that only people working in the field will really get it, so I apologize. Near the end of the talk, Polyakov was talking about the implications of some of the things he’d presented, and he prefaced his main point (which he never got to – I took it upon myself to organize an informal follow-up presentation from him so that he could tell his main point to those who wanted to hear it) with a preamble. The gist of the preamble was that he keeps being surprised to hear from people to day that the AdS/CFT correspondence is the realization of ‘t Hooft’s original idea from the 70’s. The AdS/CFT correspondence, I remind you, tells you that the physics of a large class of four dimensional gauge theories (the theories at the foundations of particle physics) in a certain limit called the “large N” limit, is the same as the physics of string theories and the quantum gravity they contain, in higher dimensions. This is a central piece of the physics many of us work on in one way or another, whether it be in applications to cosmology and higher energy particle physics, or to understanding aspects of the nuclear interactions. It was ‘t Hooft who pointed out a long time ago that gauge theories may well be re-written as string theories in certain limits, which might be extremely useful for computations, but the idea never really took hold fully in all its glory (for four dimensional gauge theories you might want to think about since we know that the real world uses them) until the AdS/CFT came along (proposed in its simplest form by Maldacena) in 1997. “I remember t’Hooft’s idea well”, Polyakov said (which is sort of funny, of course), and he went on to say that what people are saying is wrong. AdS/CFT is not what ‘t Hooft was saying back then1.

Murmurs and a bit of in-seat-shifting from the audience, since the connection of this new and marvellous piece of physics with what ‘t Hooft was saying long ago is one of the things we love to point to. I suspect ‘t Hooft does too. (1999 Physics Nobel Prize winner Gerardus ‘t Hooft is another God/Legend of the field who still walks the earth, but more about him some other time).

Well, before he could explain what he meant, his mobile phone rang. Of course, the joke sat up and begged and so I had to feed it: “It’s ‘t Hooft!”, I called out.



  1. Ok. Semi-technical words follow: For those of you who work on this stuff and whose world is shattered by Polyakov’s remarks, don’t worry. I understand what he is saying and it is rather nice, and strictly it is true in a sense. Taking N large in an SU(N) gauge theory is not by itself enough to ensure that the diagrams that are dual to the resulting Feynman diagrams actually fill up densely enough to become the smooth string world sheets of the dual string theory. This is not really what happens in AdS/CFT at all. The string world sheets are swept out by flux tubes. They don’t really arise as dual Feynman diagrams, as suggested by ‘t Hooft. This is Polyakov’s point. To get ‘t Hooft to work, you need to also tune the theory to a point where while N goes large, the diagrams fill out the world sheets. How? You tune a coupling in the theory too. This is familiar from the “double scaling limit” of the late 80s and early 90s, in the context of matrix models of string theory, but that was for zero and one dimensional gauge theories, which gave rise to one and two dimensional dual strings (which we now think of as early examples of holography too). So AdS/CFT is strictly not ‘t Hooft, while matrix models are. He was saying all this for a reason to do with his new work, but I think I’ll leave it there.[return]


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18 Responses to More Than A Hint Of The Old Days, II

  1. Tommy says:

    Ah, I also have fond memories of hearing Polyakov lecture one summer in Princeton, and also not fully understanding what he was saying, yet nevertheless being very impressed. How’s Aspen treating you this year?

  2. Clifford says:

    It has been good, thanks. Lots of quality thoughts have been had, good computations done, and so forth… and hopefully more to come.



  3. candace says:

    Hmmm…I have never had the honour of sitting a course where the lectures required no effort from the audience. Maybe I am just thick, or maybe I am just grasping at straws trying to get the barest inkling of what is going on because our syllabi are jam-packed and with a stonking exam lurking at the end. We, as students, would absolutely love and adore having more expository lectures, but as you and I both know, the course outlines form the dictats of our respective terms — we have had literally no time to talk about anything that isn’t covered on the exam, and sadly no time to ‘let the seeds that were planted grow.’ My class has been frustrated with this state of affairs and even asked one of our lecturers to schedule an extra class just to tell us about his research — but most of the time we are grasping at straws under serious time pressure. We have also lobbied (successfully) to have some course outlines reduced a bit to allow the lecturer to cover things more in depth.

    In my experience, it’s not baby sitting we expect: we’re just trying to survive any way we can against a fairly hostile and rigid examination system.

    Polyakov’s lecture sounded really fantastic. I only hope that one day I’ll understand even a small fraction, but it sounds like it pertained to issues that I am keen on learning about.

  4. Clifford says:

    Thanks Candace,

    Time. Thats the part that always gets me, and is presumably the key to all of this. Again and again I hear from the students just they don’t have time to explore more, or do the extra reading, etc., and I find myself wondering what on earth they are doing that I was not doing when I was a student. I cannot find the answer. Not a convincing one, anyway, such as “reading blogs”. So what is it? Is it the way we structure syllabi now? The way we structure exams (which seem to test and require less and less creativity and actual knowledge of the subject, as far as I can see…) I should stop now because I’m sounding like an old man complaining about “kids today”, but that’s not really what I am getting at.

    I admit to being very confused about this.


  5. agm says:

    Possibly, expecting more of a real life as an adult rather than scavenging and hoarding precious little scraps of time, as many did in earlier generations?

  6. Clifford says:

    Not sure I understand. You’re saying that current generations no longer think it is worth finding the (precious little scraps of) time to explore material and learn more about their chosen subject? How are you defining “real life” exactly? Is studying not part of real life? I’m more confused.



  7. Yvette says:


    Speaking as someone who’s experienced the way the “spoonfed” system in the US and the “go the extra mile yourself” one in New Zealand, I will say that the American system really does take a lot more work and time, or at least seems to. The reason for this is because you will usually have one homework assignment a week and two (perhaps three) tests, and the final exam to boot. If you have three or four challenging classes done like this, and know that you can’t mess up because every grade counts just enough to hurt you, I trust you that you won’t find much spare time either!

    I already know I will miss the more loose system when next semester starts. Under it I might have not done as well because there was a bit of inevitable slackerage, but I got to take a lot of time to do calculations on my own or think a bit about interesting things for the fun of it. Being forced to do so much on a strict schedule on the other hand leads to a lot more burnout, and I won’t have half as good thoughts even if I do have the time to pursue them.

  8. Clifford says:


    So there’s just way too much scheduled during the week. It goes back to the “too much structure” aspect I was talking about in the post perhaps. I think that’s worth knowing, as I just heard I’m on a curriculum reform committee, starting in the Fall, for my sins….

    Any other thoughts on this welcome, by the way.



  9. Moshe says:

    Let me echo the “too much structure” impression; as I did BSc in Israel and grad school in the US (and now teach in Canada), I can compare. It is also my impression that there is a lot more day to day monitoring and hand-holding and testing and generally make-busy work in north America. In contrast, in most cases as an UG I simply had to write a final exam which accounted for 100% of the grade, and nobody was interested in how I got there (maybe sometime homework would count as well). In fact in a couple of extreme cases I never laid eyes on the instructor of the course or my classmates… Granted, this is maybe too little structure, but there can be probably some kind of reasonable compromise.

    (Polyakov’s comment is intriguing, but I am not sure I understand completely- the fat graph turning into continuous surface depends intuitively on amplitudes being dominated by very complicated graphs. Is that intuition made more precise for the double scaled matrix models? otherwise as far as vague intuition goes, perhaps taking \lambda large does the same thing…)

    (p.s., it is late, so not sure that comment makes sense, will try to read in the morning).

  10. candace says:

    “I find myself wondering what on earth they are doing that I was not doing when I was a student.”

    Working? I think every physics student I know directly has a job of some sort, at least on the weekends. Up until 6 months ago, I was holding down a full time job, which has now been drastically reduced to part time. Next year will be an interesting experiment to see if I still feel like I don’t have enough time, but I suspect that the physics will expand like a gas to fill whatever time is available. I will be picking up an extra class in spring, for example, so I’ll be one class short of a full time courseload and will probably stop working altogether.

    When I did my English degree, I remember many afternoons just sitting around talking with my friends. That is not a luxury I would have doing this degree, whether I had a job or not, because the studying is never done.

    Anyway, enough spilling my guts about this. I only hope to survive the next two years, and that the end result will be worth it, because I have worked so very hard for it.

  11. Blake Stacey says:

    My great-uncle, Benson Snyder, was the head of psychiatric services at MIT in the late 1960s. Based on his experiences there and at Wellesley, and upon various surveys the psychology people had conducted on the student population, he wrote a book called The Hidden Curriculum (1970). One of its points was that the sheer amount of work required from students forces them to become masters of “gamesmanship” — knowing what to skip and when to leave work undone, just to get by — while also choking off any chance for less structured types of exploration.

    I told friends about this book while I was there, and to a person, the reaction was “Nothing’s changed!”

  12. Mary Cole says:

    I agree with your sentiments about the expectation of students to be ‘spoon fed’. I have found this to be increasingly the case in recent years, but as Candace says, it is linked to some extent to the exam system. It would be great to structure curriculi which leave room for the Polyakovs!

  13. Yvette says:

    Clifford: my biggest suggestion is to consider introducing plussage (the option of having either your overall average or having the exam count for 100%, depending on what’s better) to the more advanced classes at least. What I hate, hate, hate most about the current system is the fact that with so much else factored in your final exam is often a relatively small fraction of the grade- just enough to hurt you, but unlikely to aid your final grade even if you were to ace it. This seems rather terrible because it leads to a system where you can never really have a bad day and no real consideration is given to those who might have taken a little longer to master a topic. And honestly, what does that matter if you show you figured it out in time for the final?

    The reason this one’s a little close to my heart, by the way, is because one of my friends just graduated without any graduate school prospects because he was brilliant enough to get As on all his exams without bothering to do homework, so his grades suffered as a result. (This student was already published and everything, mind, just knew the busywork wouldn’t help him so he didn’t bother.) In my opinion, something is seriously wrong with a system where brilliant people with lots to contribute are completely shut out like this, and I’ve seen it happen more than once.

  14. candace says:

    Yvette: Here in the UK, at least in my school, the exam (there is only a final, and finals are only given at the end of the year, even if you are being examined on classes taken in the autumn term) counts 90% of our course grade. I can’t say that I like this system, because it means that I can have one bad day on an exam and my entire average is blown (from the It Happened to Me dept.). I feel a terrible amount of pressure on me during the exam period.

    Also, I spend so much time and effort on my coursework getting good marks on it that I feel robbed for it only to count 10% of my grade. From now on, I have learned not to bother with coursework, which I think is a shame as it is much more indicative of my average ability and rewards my constant level of effort versus getting lucky with an ‘easy’ exam question. The biggest downside to the exam culture is the fact that we have to be taught to the exam, which goes a long way towards explaining my previously mentioned woes.

    I have experienced both US and UK systems firsthand, and for me they each have their pros and cons. In my ideal system, the exam would count about 70-75% of the grade, and coursework 25-30%, no midterms — a hybrid of both. Everyone is different, though.

  15. Moshe says:

    To soften the effect of the exam counting so much, as an UG we had two chances for each course, if you don’t like your first grade you can take the exam again (then the second one counts, even if it lower). Sometime HW will count as a small fraction of the grade also. Midterms, quizzes and attendance checks are all new world phenomena I think.

  16. Tommy says:

    One thing I have noticed is that in the NA system there is a large difference in the jump from UG to graduate school, at least in the theory side of the PhD. Grad students are expected to “fill in the blanks” a lot more, and often times there aren’t courses taught in subjects they need to know (e.g. string theory, SUSY field theory, various math courses). While on the whole I think this is good, since a practicing scientist has to learn these skills at some point, I think it would be better to sort of ease people into this change. Perhaps the upper level UG courses can be less spoon-fed, but not entirely free form. Otherwise, graduate school can often be a huge shock to people, and I’ve seen otherwise well qualified and brilliant friends drop out as they get hammered by this change.

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  18. Reno says:

    Back in school, I’m doing so much laerinng.