Confused at a higher level

A professional journal: As a physicist, a teacher, and in a few other roles

Relativistic economics

Posted by arjendu on March 12, 2008

While posting the relativistic poems and songs, I was delighted to find Tyler Cowen’s blog post on the effects of including relativistic effects in economic analysis. Specifically, for example, you could deposit a little bit of money in a high-yield savings account, and then blast off for a round trip at high speeds and come back to find lots of money in there while you are still young enough to enjoy it (due to time-dilation effects). This means that the interest rates applicable cannot be such that it is profitable to do so.

A completely tongue-in-cheek hypothetical scenario, of course, but hey. If quantum mechanics could turn computer science on its head — in terms of setting limits (’information is physical’), there’s no reason why relativity couldn’t set some  limits for economics (’utility is physical ?’). Enjoy!

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Relativity poem

Posted by arjendu on March 11, 2008

Here’s a poem from one of my students, Meaghan Foster.
I stand upon this face of earth, this cliff.
You speed by sudden, slender, contracted
like the quintessential caterpillar, afraid
that my outstretched arms will catch you tight.
We fear different things; we both think they are true.
I see you as you see me: shrinking, dissolving into this relative world.

If you accelerate away from me now, if you find another orbit
someday years later when you return
you may find me old and gray, closer to death than you—
having measured my life by different increments,
obeyed the ticking of another clock.

And when you have stretched the taffy surface of space-time to extremes,
when you have twined it supple and compliant round your firmly fleshed finger,
will you then (although, what is ‘then’ to us?)
will you then stay on earth as I blast away,
to wait until we are brought back into alignment
so that we may again meet at a coordinated intersection of time and space?

The other shoe will drop, be it by gravity or acceleration.
It makes no difference; the outcome will be the same.
Light will move at speed c—more constant than love
and sharing a reference frame will be but a dream.

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Relativity songs

Posted by arjendu on March 9, 2008

Part of my ‘Revolutions in Physics’ class grade is given for a ‘creative’ project, where I’ve gotten all sorts of cool things over the years, some useful, some silly, some very thought provoking.

Last year Gaetan Damberg-Ott (an IR major) wrote a side-splitter of a relativistic noir (I wonder how many times those two words have appeared together before :-)) detective story he called The Case of the Missing Time which was picked up by APS News for their ‘Zero Gravity’ column. Gaetan had a blast annoying the graduating physics seniors with his claim that he was a published physicist.

Once in a while I get an original song. Here’s two for your listening pleasure: Dear Electron (Adam Fetcher) (from a few years ago) and Relativity (Tom Weishan) (from last week).

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Quantum jokes

Posted by arjendu on March 4, 2008

What’s your favorite quantum mechanics joke?

I got the following in early morning email:

How do you know you’re dealing with the physics mafia?
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.
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.
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.
.
.
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They make you an offer you can’t understand.

——

And my response:

How do you know you’re dealing with the quantum physics mafia?

.

.

.

.

Because you wake up with a horse on your bed that’s both dead and alive.

Oh come on, that’s half-decent. You smiled.

It’s clearly silly season at the end of the term here at Carleton College. Your contribution appreciated.

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Life at the Olin Outpost, or a whole new way of doing quantum mechanics …

Posted by arjendu on March 1, 2008

Carleton Physics majors are always studying in Olin. Don’t they ever do anything fun? Of course they do!

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Concept maps

Posted by arjendu on March 1, 2008

Towards the end of one of the comps presentations I’ve attended this year, the student said: ‘And now for a concept map, Arjendu-style’. And she laid out the ideas she’d talked about, with links showing which features of the system were crucial for which properties, and which were understood, and so on.

Once or twice a term, on one of those many occasions when I see students’ eyes beginning to glaze over in class, I call for a time-out. We take 10 - 15 mins during which the students stand at the various boards and put their heads together to sketch out the recent ideas they have encountered, while I circulate and chat with them. I do it because I think students get lost in the details and forget the big picture of what they are doing. But also to wake them up. I’ve been doing this in all sorts of classes, including quantum and stat mech. And I was pleased to see that it had at least become part of one student’s thinking style.

At the NSBP conference, Chandralekha’s presentation on cognitive issues and student learning in physics reminded me why I had started doing this. As she said, if you give the same problem to a novice and an expert and ask them to think out loud, you will see a completely different intellectual structure to the approach. For an introductory mechanics problem, for instance, a student will say things like “oh, it’s an inclined plane. I should think about which forces are involved. Wait, is there friction? What about the normal force? What axes should I choose? Oh no, this is a complicated one — there’s gravity and a spring as well.” And so on. An expert will say something like: ‘Hmm, that’s probably best done by a conservation of energy analysis. Ok, which potential energies do I have to track …” And so on. Neither approach misses the point, but the latter constrains you, and focuses you much faster. And you can see this in maps that you can get people to draw. So I figure anything I can do to help people to get from novice maps to expert maps is a good thing. And by making their conceptions explicit, I am able to do this to some extent: At the end of the exercise, I will quickly sketch my own version of the concept map which I hope helps with this transition.

I talked with a colleague about this, and a couple of days later, his wife, who actually leads workshops around the world on teaching techniques sent me an email that I thought worth sharing with the world:

‘[I heard about your conversation about] concept maps - quite a coincidence because just today I was putting together my handouts on concept maps for my upcoming faculty workshops in Taiwan. It is one of the most versatile, useful but seldom used teaching techniques.

I’ve trained faculty in active teaching techniques in Ukraine, Uganda, Oman, Cambodia and now Taiwan - it works in all cultures. I’ve trained only in schools of education and business but in Taiwan I will also be dealing with engineers. Interestingly enough, it was “invented” by a science faculty member at Cornell.

One of the business faculty I worked with in the Ukraine did a great job in combining it with collaborative learning. She had 3 groups of students create a concept map for something in business (I can’t remember what), had them put it on sheets on the walls and then present it to the rest of the class who questioned them about their concepts and they had to explain or revise. There was SO MUCH learning going on …’

And she also sent me a link:
http://cmap.ihmc.us/Publications/ResearchPapers/TheoryCmaps/TheoryUnderlyingConceptMaps.htm

So this post is mostly a reminder to myself to keep using this technique — it’s not just a fun way to wake up students, it seems to have some sound pedagogical theory to back it up!

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How quantum is a given state?

Posted by arjendu on February 26, 2008

One of the puzzles I have been thinking about for a little bit (triggered by trying to explain to Referees that we were definitely seeing a quantum phenomenon) is trying to answer the question: Given a certain quantum state, can you quantify how quantum it is?

I have a sharp senior working on it (whenever he can not manufacture sufficient number of excuses relating to his two comps exercises in Math and Physics, his robotics projects, and general life excitement, sigh) right now. The starting point of our analysis is the idea that you can take the Wigner function corresponding to your quantum state, find out how much ‘negativity’ there is in that Wigner function and call the amount of negativity a measure of the quantum-ness of the state.

This seems fundamentally fair: Classical probability distributions in phase-space are positive-definite, and it is clear that Wigner function negativity comes from interference effects, so quantifying this should be a pretty good measure of quantum-ness. It is, except in a handful of cases, a numerical exercise, which is a bit of a pain, but that’s fine.

However, there is something counter-intuitive about what emerges from this calculation, and my instinct is that this should be a resolvable issue. Our project figuring this out is moving slowly however, and I’m not completely comfortable revealing all of our thinking so far on this particular project. So I’ll leave it as an exercise to the reader — take a look at that paper by Kenfack and Zycskowski (which has since been published in J. Phys. A) and see if you can find what’s weird about the one (semi-)analytic result they have on the harmonic oscillator.

And if you want to talk about it with us — and in particular about resolutions of the weirdness –  that would be great; as I’ve said before, I’m always open to fresh collaborations/conversations.

What I like about this project is that it has all the hallmarks of a classic liberal-arts-college theorist project: Deep enough to be very provocative, but simple enough for an undergrad to make progress. Of course, I could just be completely out of the loop on some critical literature. We shall see.

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National Society of Black Physicists/National Society of Hispanic Physicists Joint Annual Meeting 2008

Posted by arjendu on February 23, 2008

I am at the National Society of Black Physicists/National Society of Hispanic Physicists annual meeting for the 3rd year in a row, this time in Washington, D.C. The first time I went it was because I wanted to find out what was behind the much bemoaned lack of minority Ph.Ds in physics — I was tired of arguing about numbers, and as with everything else in life, wanted to understand the human side of the issue. That visit, to San Jose, was a revelation. To sit in a ballroom-full of physicists listening to great talks is always a great experience for me — I am a physics geek, cool physics ideas turn me on, and it’s like going to a live rock concert to hear and discuss these ideas along with so many other aficionados. But to sit in a ballroom-full of minority physicists was novel, and it affected me in a deep emotional way.

I managed to connect with a member of the board for the conference program, Wendell Hill, and the next year, in Boston, Carleton, Bowdoin, and Morehouse faculty and deans put together a panel on careers at ‘elite’ liberal arts colleges. When I am feeling particularly blunt, I like to contrast places like Carleton and Bowdoin with the HBCUs (the Historically Black Colleges and Universities) by calling Carleton a Historically White College — and in physics it certainly is. So careers at such places honestly don’t appear on the radar for most of the smart young students out there — it would be like teaching in a foreign country for many. And elite colleges and the minority physicists community has so much to gain from that not being the case. Wendell suggested to me this year that it might be time to come back next year for another pitch, and even if we are not in the hiring cycle next year, I think I might give it a whirl.

This year I am here (along with a colleague, who I persuaded at the Boston conference to come to Carleton last year for a short-term gig while postponing her post-doc — we brought along three students, too) with the primary goal to recruit faculty for a visiting position for next year — and since we will be conducting a tenure-track search the year after, this is in some sense for that tenure-track position, but with less pressure on both sides. And I’ve found some great candidates. What I’ve enjoyed greatly in the process is getting to know the younger students, and to talk to them about the future, and how they might think of teaching at one of these colleges.

I know there’s little chance we’ll be hiring when these kids hit the market, so it might look a little unfocused to talk to them, but I see this as being of general benefit to the physics community, and thence of specific benefit to Carleton. It’s in keeping with a broader philosophy I have of focusing on the long term, and on statistics where possible. It takes a damn sight more effort, and is far more chancy, for me to try to attract a specific person to Carleton. But if I keep talking up liberal arts colleges — and it comes easy to me, I love my job — and if every liberal arts college faculty member keeps talking up liberal arts colleges when possible, in the long term we all benefit from the increased talent pool, whether minority or otherwise.

I’ve also heard some great talks here: For example, one from an undergrad, Cacey Stevens, who worked during an REU with Sid Nagel at Chicago studying the physics of splashing. Totally fundamental, beautiful experiments, puzzling, very cool. John Mathers (Nobel 2006) gave a plenary talk on the state of our understanding of the Universe, and the next generation of telescopes, and I got to puzzle some more about dark energy, the notion that everything we think of as matter is essentially ‘noise’ on the scale of ’stuff’ in the Universe. I really enjoyed the atomic physics talks, including a very gracefully pedagogical one from Luiz Orozco about Francium, and a sweet description of some beautiful cold-atom Bose condensate and degenerate Fermi gas work by Marcius Extavour of Joe Thywissen’s lab in Toronto. Jun Kono’s lab from Rice University was well represented by a couple of excellent poster presentation on device physics — one student working with quantum dots and another with carbon nanotubes.

There were also intriguing talks from physics education researchers, including one from a friend of mine, Chandralekha Singh (I hadn’t met her in about 10 years, so it was great to reconnect) about the connection between cognitive science theory and teaching techniques. I sat with Chandralekha at a couple of meals and got to argue furiously with her about the benefits of teaching students quantum mechanics from the Stern-Gerlach experiments, a finite dimensional Hilbert space, and Dirac notation perspective first (I do this, and love it!) versus the traditional Schrodinger equation and partial differential equation method, which I have to say frustrates me tremendously. Given Chandralekha’s background, the conversation was appropriately meta, and hence very valuable.

I also got to make some new friends and reconnect with old friends, including the always remarkable Philip Phillips. My first memory of Philip is from when I was a young grad student at a conference in Los Alamos. I walked by him arguing with someone in a corner, and I heard him saying with what I now know is his characteristic forthrightness: ‘It’s so much better to solve the exact problem approximately than the approximate problem exactly.’ I was very struck by that and have repeated it to myself as a mantra for a guiding principle for my work (of course my math colleague told me that it exactly the opposite in math, but hey, that’s how you can tell us apart). I reminded Philip of that phrase when I saw him next, and he said: ‘Hmm, I don’t remember saying that, but it sounds like me.’

As always, when I travel during the teaching year, I landed up at this conference edgy from the stress of getting things organized enough to get away for a few days, and unclear about the benefits of doing this. And as always, I am going to leave happy I came.

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Advising, advising, advising

Posted by arjendu on February 19, 2008

This is advising week — because of travel plans later this week, it is advising 1/2 week for me, so there is a flood of students in here walking in and out. As with everything else I do at Carleton (perhaps grading excepted), I value these conversations, and enjoy them — but the number can get a little overwhelming.

I taught a Cross-Cultural Studies Seminar last term, and incoming students often get assigned to Profs from their first term seminar. So for a change I have many kids with interests clearly on the other side of campus. Not that all my advisees land up in the sciences typically, but since I’ve usually met them through a physics course, I know they aren’t antipathetic to science. Not this year!

Some conversations with first-years are interesting, about why one might choose an Asian Studies major, for example, and how to make choices within the broad range that Carleton offers, with the minimal constraints it imposes.

There’s one student who wants to spend a long time away from campus, and I’ve asked him to convince me that he can do this by mapping out a course of study over the next few years. I tell him that he can argue all he likes that it should be possible to do this, but one example, which would take him a couple of hours at most, would make me happy, and constitute empirical proof that it is possible to do the major he wants even with all that time away from Carleton. It would make sure that there are no ‘oops’-es to address later. But there’s something about this exercise that he simply doesn’t want to do — not a particularly empirical thinker, perhaps?

Sophomores are facing a more dramatic moment: Choosing a major. For them, the world is seemingly narrowing suddenly and I see some students thrash around at this point of decision. How does one choose with confidence that one path through life and expect it to bring happiness? How can one minimize regret? I look back on my choices, and boy did I make it early. I knew when I was a very young kid that I wanted to be a physicist, and the way the Indian system works, my early choice committed me kind of definitively. Given that I hung out with economists all my college life, I am sure I would’ve landed up drifting towards economics if it hadn’t been for that early commitment. Some of my sophomores are still drifting, but most are trying to choose carefully between related fields, or trying to figure out how to double-major, and so on. These conversations end on a slightly nostalgic note, since this is our last advising meeting. After this, they get advisers in their major.

Talking to the seniors, some of their excitement rubs off — they’re getting the grad school acceptances back and the future looks so inviting. There’s a certain amount of reeling back in shock, I have to say, at the fellowships schools are offering nowadays ($25K, wow!) and I am thrilled for them. But they do have to choose. Somewhere in the mists of memory is lost a description of the feeling of choosing a grad adviser at the end of your first year. As a a physicist, one minute you had all the options in the Universe, literally — from studying the cosmos to studying tiny particles, to everything in between. The next, you have committed to one area, and a few months later, to one problem, and very soon after that, you have an incredibly narrow focus. You are the only person in the world who knows your particular research problem as well as you do, and cares about that minus sign with the same intensity that you do.

Boy these kids have a lot of trust in me, asking me to hold their hands through some of this process! The trick of advising, or choosing in general is, as I said in an earlier post, the dichotomy between global statistics and individual chaos: We can reason statistically, make educated guesses about what’s typical or not, but to know what the future will be like for the one contingent case about which we care (that is, ourselves) is impossible. You never can tell the consequences of your choices. And if you did, it would be boring.

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The things you learn

Posted by arjendu on February 12, 2008

Yesterday was exciting: The first physics comps of the season for me (I don’t go unless I am invited or am on the committee) and the unveiling of the new curricular proposals.

So this was definitely one of those kick-ass comps presentations I was talking about earlier. She talked about biomimetic adhesives, that is, the attempt to reproduce the ’stickiness’ of gecko feet.

The facts are amazing: a Tokay gecko can theoretically hold up 2 human beings with the adhesive forces of its feet, with a surface area slightly less than two dimes. And geckos do it without suction, and without exuding any sticky substance whatsoever, with the ability to go from adhesion to ‘running’ on demand. Move over Spiderman, I want to see Geckoman in action!

And the physics (at least, as understood so far) is that it involves van der Waals forces (for the non-physicists, the fact that neutral atoms can separate into positive and negative parts, induce neighboring atoms to separate as well, and therefore attract each other) and some interesting geometry. van der Waals forces only act at the nanometer scale and it turns out that the feet of the gecko are very very branched, such that it can offer this kind of close contact (and facilitate other good properties as well).

It was a great talk, everyone learned a lot, and she even finished with a report on results that came out 2 weeks ago, where a Stanford group has managed to get to approximately half the strength of gecko feet. Man. I can’t wait to read her paper — she promises, in addition, an equivalent discussion of certain butterfly wings that are structured so that they only let certain kinds of light through, so that the color comes from the structure, rather than the ingredients of the wings. Cool.

Right after this talk was the college-wide Faculty meeting, starring the unveiling of new curricular proposals — for graduation requirements, not fiddling with the major — from the team-leads. Things were a little more firmed up than the last look we had at the ECC, and despite the nervousness, all three did a good job (they were standing up there, telling us what *our* vision of liberal education was, and how to implement it. Tough audience!).

Gut reaction(s):

(1) Some of the new requirements are very prescriptive (as are some current ones) ; these will meet with the most resistance or alternatively will be hardest to implement.

(2) All the proposals shift resources around. For example, more first-year seminars might have to be offered, or different kinds of ‘distribution courses’ will be imagined by each Department and so on.

(3) All the proposals ease the weight on physics — yay (assuming we actually accept some version of these proposals)! That is, our Department is the only science that offers 3 or 4 large-enrollment courses a year that people typically take for distribution requirements. The science requirement in all three proposals is definitely decreased, whence …

(4) The pressure on the Arts and some other department is going to increase.

(5) As a member of the ECC, I will be consulted — that is, we get to do some slight nudging and questioning as the next stage evolves (discussion, modification, etc, until we have proposals that can be subjected to an up-or-down vote). But at this point, any faculty member has just as much of a say as any other. Let the discussions begin!

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Now playing: Nusrat Fateh Ali Khan - Zindagi Jhoom Kar
via FoxyTunes

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