Confused at a higher level

The view from Carleton College's physics department

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Quantum video games in class

Posted by Arjendu on February 6, 2016

I am teaching our junior quantum mechanics out of Townsend’s book, which starts with Dirac notation and spin states, and when it lands in the position representation the students still haven’t made the full connection to the material they learned in their ‘modern physics’ course.

Here they are re-introduced to things like bound states (particle in a box so far mainly) and we read but did not discuss in detail a derivation of the tunneling coefficients. Yesterday was my designated ‘wrap-up the reintroduction/transition from Dirac notation to position space’ day. I chose to spend the class meeting time 1/2 on doing in-class simulations and 1/2 getting started or finishing the quantitative problems I had assigned. I found myself spending a big part of the afternoon discussing one particular problem with the students, which would perhaps have gone differently if I hadn’t (a) assigned it as a ‘mini-test’ (which meant that they couldn’t consult with anyone but me about it) or (b) gone over some material in class instead of the simulation. I am still a little puzzled about the number of visits I had, since things have gone differently with this section of the course with previous classes, but difference from previous years is a given, so I am just noting this and moving on. About the only thing I intend to change if I assign it in the same way in the future is to remember to ask everyone to look at the problems and make sure they knew how to start every one of them before they came to class.

I have assigned some version of the simulations as take-home assignment before, but we never got to discuss things together as a class, and I wasn’t available to guide their explorations. This time, by the end of the class I saw and heard some sense of understanding for some or many of my students about the qualitative and conceptual sense of time-dependent quantum mechanics at this level: How wave packets spread, in what sense they are superpositions of states and how you might move back and forth between the position and momentum representation, and how uncertainty connected with that, some sense of how different choices of superpositions of states affects the dynamics, how properties of time-evolving states are such that some expectation values are ‘stationary’ while others not, how even things like tunneling were built into the initial condition. We also discussed — very quickly, but more than once — other interesting notions like how symmetry affects things like energy eigenfunctions and eigenvalues, how tunneling splitting between states for a 2-well problem works, and how when generalized leads to band structure. It was possibly ambitious and maybe none of this landed or will stay or be useful but we shall see. I certainly walked away reminded of the importance of the transition — from introduction to the math to ‘understanding’ -in my grasp of most of these ideas. I do know that the difficulty of the transition was because the math was new and it took some time to translate into intuition. I learned all this in the world before computer simulations/movies/visualizations existed, and I am *sure* it would have gone better and faster for me by far if I had had access to such tools. Perhaps all of us teach the course we wish we had had.

Below is an adapted version of what I said in my pre-class note for my quantum mechanics class.

Tomorrow in class I’d like us to start with numerical experiments (quantum video games) on the position-representation quantum mechanics that we’ve just revisited. We will work on HW for the second 1/2 of the class.

We will play with some jnlp apps to improve our intuition.

If you spend 20 minutes or so tonight (or before class tomorrow) looking at the apps (links below), it would save an enormous amount of start-up time in class tomorrow. Just try to get a sense of what the various knobs and buttons on the apps do, and play around a bit with the settings. These apps should work with lab computers, and/or with your laptops. I just installed it on my office laptop.

Here are the basic ideas to explore

(a) Tunneling: This jnlp app allows you to ask all sorts of questions about tunneling: http://phet.colorado.edu/en/simulation/quantum-tunneling

(b) Bound states: http://phet.colorado.edu/en/simulation/bound-states; make sure you click over to the two-well and multi-well bound states; both to to get a sense of more complicated problems and also how band structure arises in quantum mechanics.

When they walked in to class, they found 10 questions that I thought they could explore and were free to choose what they wanted and how many they wanted as long as they kept working at the questions. We spent 20-25 minutes exploring these questions (I had checked that we had enough laptops in the class and they landed up being in pairs or threes), and then we talked for 10 minutes together as a class. We finished with them working on the problems assigned.

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Two visiting positions (possibly 2 years each)

Posted by Arjendu on December 26, 2015

Here’s the link with more information: https://jobs.carleton.edu/postings/2560

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Student site on constraining sci-fi with thermo

Posted by Arjendu on November 18, 2015

As part of their thermal and statistical physics class, a group of students has decided to create a resource “to help writers and producers of fiction[] make their stories consistent with [] thermodynamics.” Enjoy! (And comment and jump in as you like).

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Ramanujan (redux)

Posted by Arjendu on November 7, 2015

At one point in the past, I used to write for an Indian-American print magazine, which later found my ramblings to be ‘not the right fit’ and I haven’t done that for a while. But while I was writing for that magazine, I would occasionally produce longer pieces on things of interest to that community. I frankly don’t remember if this piece on Ramanujan was ever published. It is somewhat dated, but still I thought it worth sharing (or at least, like a good stingy academic, worth not throwing away).
—-
Ramanujan

All of a sudden there is what feels like a Ramanujan celebration going on. There is very recently released historical fiction book about him and his mentor G.H. Hardy, called ‘The Indian Clerk’ (despite the title, mostly about Hardy) by the popular and renowned writer David Leavitt that has received glowing reviews in the New York Times, and the Los Angeles Weekly among other places. I should note that Margaret Wertheim’s review in the LA Weekly is a work of art in itself, and still easily accessible online.

The release of this book follows on the heels of an off-off-Broadway production of the play ‘First Class Man’ by David Freeman, which has Ramanujan as one of the primary characters, again considering his relationship with Hardy. More recently, the play ‘A Disappearing Number’ where Ramanujan’s character has a prominent part, was a sold-out production in October 2007 at the Barbican in London. As of this date, there are in the works two films on Ramanujan’s life, one co-directed by Stephen Fry and Dev Benegal. It’s clear that Ramanujan’s life is of relevance to the present, and in an era where the Minneapolis Star Tribune sees fit to run the Los Angeles Times review of Bollywood pop releases, it makes sense that this interest in one of India’s intellectual greats is not confined to India. But this isn’t a particularly special anniversary nor are there particularly wonderful new mathematical developments based on his work. Then what, apart from Ramanujan’s sheer brilliance makes his life such a compelling story today?

Srinivas Ramanujan Iyengar was born a hundred and twenty years ago in Erode, Tamil Nadu. This was a special time in subcontinental scientific history: Chandrashekhara Venkata Raman, Satyendra Nath Bose, and Meghnad Saha are of the same era. All of those scientists produced work of the absolutely highest quality, which depended on their access to the best education possible. Ramanujan stands out in this respect — unlike the others, he was not from a particularly technologically inclined or distinguished family. His father was a clerk in a sari shop in Kumbakonam, as was his paternal grandfather. His mother was descended from a slightly more educated family, but at the time of Ramanujan’s birth, was a manager for a temple complex. He showed an early aptitude for mathematical thinking, and was acknowledged by teachers and friends as being ‘off-scale’: smart at a level not seen before by them. He did not manage to go through the standard march of academic success despite this, failing his non-mathematics courses and losing his college scholarship. He landed up as a clerk in a colonial accounts office, indulging his passion for mathematics on his own time.

During this time, however, as an impoverished, somewhat ailing young man outside the academic mainstream, Ramanujan produced some results in the abstract area of mathematics known as number theory. All those who saw glimpses of his work knew they were seeing something special, and in keeping with the standard practice, encouraged him to find a mentor in Britain. He sent some of his results to a few mathematicians there, but did not get a truly useful response until he wrote to G.H. Hardy. Hardy looked at the nine pages of results he was sent, and was quick to recognize the brilliance of the work, but was initially certain that these could not possibly those of an ‘untrained’ person. He soon got past this — he is said to have commented that these “[theorems] defeated me completely; I had never seen anything in the least like them before …[but they] must be true, because, if they were not true, no one would have the imagination to invent them.” He then managed to persuade Ramanujan to get over his Brahmanical constraint against traveling overseas and come to Cambridge for five years, where he collaborated extremely fruitfully with Hardy and Littlewood. In his time in England, he earned the equivalent of a Ph.D., was elected to the London Mathematical Society, and became one of the youngest Fellows in the entire history of the Royal Society. Ramanujan was never the healthiest of men, and living in cold, damp Blighty, with not the greatest access to comfortable and familiar food or living conditions was not very good for him. He was diagnosed with tuberculosis, and sent to a sanatorium for a while before returning home and dying at the tragically young age of 32.

Ramanujan’s mathematical results have continued to astonish and challenge mathematicians since, and his work has since found unexpected applications in cancer research, string theory, and crystallography, to give some random examples. There have been several interesting biographies on him, of which I would particularly recommend ‘The Man Who Knew Infinity’ by Robert Kanigel, apart from the above which, you might have noticed, are increasingly about fictional explorations of Ramanujan — his life and his work. As with Einstein, and more recently as with the relationship between quantum physicists Bohr and Heisenberg explored so brilliantly by Michael Fraym in the play `Copenhagen’, Ramanujan has become part of the popular culture, part of the mythology of humanity. Here elements to his life that point to why this is true.

For instance, I don’t know if you’ve every thought about something mathematicians wonder about: Are mathematical truths ‘out there’, like a mountain or a planet, and are all the methods and training used by mathematicians just tools to help us get to these new intellectual places? Or are mathematical truths ‘constructed’ from the tools and training imparted to mathematicians? Ramanujan’s astonishing life is actually used often as anecdotal evidence in this debate on whether mathematics is ‘discovered’ or ‘invented’. It is argued that the fact that he ‘saw’ so many of these amazing truths with such little training, which far more trained people had to struggle to see, is evidence that mathematics must be an absolute truth, to be discovered. The counter argument, a little thinner and harder to justify, is that this is sheer prejudice against people who do not grow up in the intellectual mainstream — that Ramanujan was simply able to ‘invent’ with a few tools what others needed a whole workshop to do.

Or consider why it was that it was Hardy that mentored and collaborated with Ramanujan so successfully. Hardy, a tremendous mathematician, was a member of Cambridge Apostles, a secret society that included Bertrand Russell, John Maynard Keynes, G.E. Moore, and Lytton Strachey among the members, and had many closeted gay members. More to the point, Hardy was gay himself. An easy enough hypothesis therefore is that was that it was because as an ‘outsider’ himself, he was more inclined to be sympathetic to outsiders, in some respects. Hardy had a strange perspective on India, gleaned from pageants and passing images from when he was a child. As a result he had a almost filmic notion of what it was like to be Indian, that was ridiculously off-base: Leavitt’s book has him talking about “the vision he has conjured up, in spite of himself, of Ramanujan: a young Gurkha, brandishing a sword.” He couldn’t have chosen an image further from that of Ramanujan’s reality if scripted by a comedian. And what’s interesting is that the New York Times Review of Leavitt’s book seems not to recognize that this is not just a romantic image, it is utterly absurd, so perhaps things haven’t changed much in the hundred years since. The thrill of mentoring an amazing mind like this was an intense experience for Hardy, and he called his association with Ramanujan “the one romantic incident in my life”. It included a struggle between Hardy’s belief that religion of course had nothing to do with Mathematics, and Ramanujan’s contention that his theorems came to him from the goddess Namagiri, for example. This was certainly an intense and complicated partnership.

Perhaps some of you have encountered the equivalent of this. When I was in graduate school in Austin, for example, my social world, as opposed to my intellectual world, included many well outside the mainstream. They helped me negotiate the cultural transition in a way that mainstream Americans never quite managed. It brought a different appreciation to me of the way societies include and disinclude people as those whose words and actions are automatically given respect. It was equally interesting, raised to be intellectually secular, and culturally — well, typical of many in my generation, I did all the rituals my mother asked me to do without thinking about their meaning — to see orthodox Jews, for example, in the Physics and Mathematics community working hard to intellectually reconcile their science and their faith. This tension between faith and science, and between being an outsider and attempting to assimilate will remain true, I reckon, for a long time in the West for desis.

Even beyond that, Ramanujan’s life is echoed in the lives of so many in the United States in particular, and across the West in general. Sheer technical ability is throwing up into prominent and well-rewarded roles desis who are not necessarily from families with a lot of education themselves. And these smart young men and women continue to struggle with many of the same issues: The weather, the cuisine, and the cultural isolation, for example. A good mentor is invaluable in these situations, and how many times does such a person surface?

All good stories — whether real or fictional — have emotional resonances beyond the sheer importance of their actors actions. The tragically short arc of Ramanujan’s life, the improbability of his work, the strangeness of his ‘discovery’ by Hardy, the sense of a repeated immigrant experience, and the first spark of desi technical brilliance visible to the West, ensures that this story is one that will live on for a long time.

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We’re hiring: Theory or Computation tenure-track Sept 1 2016

Posted by Arjendu on July 20, 2015

We’re hiring a theorist for the first time since we hired me, if you get what I mean. It’s a great gig, in case my ramblings over the years haven’t made that clear. Come join us! Happy to field questions etc.

https://jobs.carleton.edu/postings/2428

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Energy Games People Play

Posted by Arjendu on June 5, 2015

Over the past year and a half, when I’ve taught about energy (during the month-long visit to Ashoka’s Young India Fellowship last year, the first year seminar this fall, and now the Environmental Physics class this spring), I’ve given students the option of doing a final project that included a ‘creating educational materials’ option. In this category, some students have chosen to work on an ‘energy game’ (this term 3 board games were created).

The projects and results have been pretty striking. I’m starting to realize that there is a lot more value to creating such games than I had assumed. A little more tweaking, and this is should be a permanent part of my repertoire for certain kind of courses.

Here is an attempt to summarize why: These are typically based off some standard commercial board game like Monopoly or ‘Game of Life’ or other such games. There are games where players are trying to maximize energy production given finite resources (the person who gets to 15 energy points wins in one game), other games where they are developers for a new habitation area and trying to figure out how they should source energy while paying fines for ‘pollution’ and trying to maximize their financial profit, etc, etc.

There are many cool things I am getting from the exercises, not the least of which are some fun energy games to play (for the public or elementary/middle school children). A (retrospectively obvious) effect is that the students go through a fairly sophisticated discussion of *what* the objective of the game should be (more energy, more green, more money), learn how to put numbers (at least relative to each other) on the various energy sources according to cost, productivity, emissions, and see how the rules they create (and the values they put in) affect outcomes. What’s also entertaining is seeing how uncertainty in chance events that happen as the game develops affects the story.

For example, teams have used the games to learn that certain strategies help more than others (diversifying your energy production portfolio so that you don’t get trapped by chance events or political shifts for example; or that you should probably buy cheap and dirty first and then buy ‘expensive and clean’ if cost and profit maximization is prioritized, etc, etc) . That is, they are learning to think about the economics and policy issues from the energy landscape and are able to *model* it without using complicated differential equations etc (creating an agent-based/game-non-theoretic-but-fun model, in short) but all the while it’s a board game that people can play with. This sloppy thinking about models etc is probably going to annoy the heck out of my social science friends and family, but it will have to suffice for now.

I am excited about this. Students have suggested creating an app version of their games as part of their ‘future plans’. That’s one of the many directions to go with this …

And now, back to grading.

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Like a newbie

Posted by Arjendu on June 2, 2015

This year back in the classroom has been like being a newbie again. I was nervous about the content of the various courses (it really felt like almost 5 new preps for me). And being able to tell a coherent story, of course. The logistics of staying on top of assignments and assessments: the tests, exams, homework, projects, writing, labs — their creation and their grading — in Carleton’s notoriously fast-paced 10-week terms, and the physics department’s ultra-compact 5-week courses are also not trivial. My colleagues set a high bar for teaching performance, and I had to re-learn how to join the troupe.

My in-front-of-class teaching is done for the year. I just got through the last lab, and there are yet final project presentations left, and project reports to collect and grade. It’s as good a time as any to collect my thoughts for the year.

Short version: It was hard, I got to re-learn things I like to learn about, and re-think them, and to work on understanding new areas better, and old things from different perspectives, and to confront things I don’t like doing, and do them anyway because it’s needed for the course, etc, etc. In short, while it was very challenging, it was equally rewarding, and fun (that’s how I know I am happy with my gig).

Overall assessment of the teaching year: I’d give my performance a B+/A- average between the content mastery, excitement, engagement bit (pretty good) and the organizational/logistical side (could do better but not terrible). That’s consistent with the student evaluations I’ve had over the year. I feel qualified to grant my self enough self-assessment independence to call it not bad for someone feeling rusty and definitely aware of the cost of re-entry after 4 years away.

I can see ways of re-doing these classes next time through, of course. Next year, I have three repeat course: (1) Thermal and statistical physics in the fall [junior and senior majors and two curious chemists], (2) quantum mechanics [should be mostly junior majors, though I occasionally get seniors and math majors] in the winter, and (3) environmental (mostly energy) physics for the 2nd half of spring term [typically non-majors, mostly from the other sciences]. I also have scheduled two different variations on the introductory physics I taught for the the 1st half of the spring term, so overall, it’s almost entirely a chance to go back over everything. I’ve usually really enjoyed my second or third consecutive time through a particular course, so I am not half as worried about teaching next year as I was about this year.

An unexpected thing this year was discovering that I need a new teaching persona and voice. It’s quite possible the curmudgeonly absent-minded professor shtick present on Facebook is more real than I thought. But I’m trying to re-learn by re-starting my old habits. My teaching journal has been restarted. I have started writing a new list of ‘things I should be doing that I should probably confess I already know I should be doing but haven’t been doing quite as often as I now think I should have’ (For example: a periodic five-minute check in to see what people have understood that week and what’s missing, a five-minute map of the week ahead and the schedule, even it’s all on the syllabus, just as a reminder and to note the inevitable modifications/adaptations/scheduling things; I’ve tinkered the assignment prompts already where I saw incomplete communication — all this now because I know I’ll have forgotten my insights by this time next year.)

During this year I found that figuring out the extent of my post-Deanery service role to the college was important to my identity as well, of course. The ‘Future of Liberal Arts in India’ conference I helped put together was the major time-and-attention needing activity over the year, but I also served on at least one steering board for an interdisciplinary initiative, did some language testing, and served on an emotionally heavy but medium work-load college committee as part of my broader role at Carleton.

All this while try to re-orient and advance my research, the broader direction of which seems to continue to be on the right track, with promising and interesting results (assuming colleagues’ feedback on talks, posters, and other presentations isn’t only politeness), but is only limping along when it comes to finished products. In about a week’s time, it will be my highest priority again.

Ok, this is enough navel-gazing for now. To summarize this end of year teaching report to self: Survived the re-entry to the Carleton classroom, and happy for it.

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Some energy links as posted on facebook

Posted by Arjendu on May 19, 2015

I post links regularly on facebook to articles of interest; I tend not to do that on this blog, but I thought I’d try it for a change.

Here’s a collection of recent energy-related links as posted on facebook:

http://www.economist.com/news/finance-economics/21651671-energy-subsidies-do-not-just-gobble-money-they-help-cook-planet-too-costly-mistake

http://qz.com/405059

http://www.theguardian.com/environment/2015/may/08/community-energy-model-is-speeding-us-move-to-renewables

Enjoy!

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Grad students and undergrad students

Posted by Arjendu on May 7, 2015

Musings:

An undergrad student doing research with me goes away and comes back a week later with a result. I say ‘nice, let’s do the following with it’. And (s)he goes away and does that and comes back a week later, and we talk again, etc. And things move slowly towards a result and more slowly towards manuscript writing and even more slowly towards publication.

If this was a graduate student, then about the same progress happens in about a day rather than a week. That is, since undergraduate students do research as something squeezed in beyond the classes they are taking, etc (rather than being the central thing they do, like for graduate students), 4-6 hours a week of effort is about standard for an undergrad, and about 4-6 hours of effort a day should be standard from a graduate student.

Whence we conclude that a day in grad student time == a week in undergraduate student time (independent of technical preparation, expertise, length of time a student stays with you compared to start-up time to understand what the project is about, etc); and hence the two years the undergraduate spends (about how much most of them spend with me) is about a semester or so of graduate student time.

This makes me a lot happier about the kind of progress my students have made over the years.

No happier about my own pace of production, though.

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Intro to Newtonian Physics

Posted by Arjendu on March 31, 2015

Yesterday was the first day of Spring Term at Carleton. This is what my teaching journal entry (aka Facebook wall) read:

“What I am teaching: Intro to Newtonian Physics. It’s my first time through since Spring 2008, though I’ve taught some variation about 9 times, including the giant classes at Rice, and the Matter and Interactions versions here. Syllabi are written but not yet printed, the structure of tests, assignments, etc semi-decided, labs are lined up (borrowing furiously from colleagues here), student assistants contacted. The administrative questions from students have already begun. Writing my first lecture, and feeling the butterflies as always.”

The last time I taught it, I went extreme: ‘No lecturing’. This was in 2008, just slightly before the term ‘flipped classroom’ came into vogue, else that’s what I would have called it. It was documented on camera (I still can’t bear to watch the video) by Carleton; you can watch it here if you like: http://serc.carleton.edu/carl_cam/courses/physics131.htm .

I also blogged about it then, and that’s proving useful notes for me this time:
Spring Break and new experiences
So far so good
Stable and unstable lectures
Refusing to throw stones
and
Almost done.

I am not being that extreme this time, though I think it went well enough. It takes a certain deep familiarity with the material to do things that way and seven years later, I can’t legitimately claim that. So the students are going to get a more lecture + conceptual tests + problem solving version that resembles how I taught it at Rice (I believe they still do things that way there) and also how I taught it at Carleton my first 2 years.

For all sorts of reasons, this Spring Term group of students is very similar to those that I had that Spring Term. It is also a very different group than the majors and first-year seminar students I have had so far this year. There are essentially zero majors or potential majors and many seniors. Almost all the students are taking this course because it fulfills a major or other requirement. Most of them haven’t taken physics in a while if ever, and some of them have expressed anxiety about the physics as well as the math on my first-day survey.

I’ll report back as possible on how this iteration works out.

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