Category Archives: University education

Group Theory, Information Theory, Quantum mechanics, University education

New Textbook

Copies of a textbook surrounded by Oaxacan carved wooden animals

B. C. Stacey, A First Course in the Sporadic SICs. SpringerBriefs in Mathematical Physics volume 41 (2021).

This book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of “sporadic SICs”. By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell’s theorem and the discovery that “hidden variables” cannot explain away quantum uncertainty.

While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.

ERRATA:

In the preface, on p. v, there is a puzzling appearance of “in references [77–80]”. This is due to an error in the process of splitting the book into chapters available for separate downloads. These references are arXiv:1301.3274, arXiv:1311.5253, arXiv:1612.07308 and arXiv:1705.03483.

Page 6: “5799” should be “5779” (76 squared plus 3), and M. Harrison should be added to the list of co-credited discoverers. The most current list of known solutions, exact and numerical, is to my knowledge this presentation by Grassl.

Page 58: “Then there are 56 octavians” should be “Then there are 112 octavians”.

University education

On the Writing Process

The problem I typically have when writing about technical topics is trying to include everything and to answer objections that seem vitally important to me but which don’t make much sense unless you’ve heard the debates inside my head. Removing that stuff has by now become a standard part of my revision process. My colleagues point it out, I feel a little hurt, then I grudgingly agree, and in a week or so I re-read my work and I don’t get why I thought that extra stuff was so important in the first place.

I’ve also noticed that the parts of an argument that people object to are often the bits that I thought were almost incidental, or that exist mostly in their head — they want to keep having the argument they’ve been having before. Trying to foresee how this will play out is hard, and it always helps to have input on that.

I count myself lucky to work with people who care about this kind of thing. I wish I’d had more training in my early years of physicist school — some harried lab reports and a single term paper don’t add up to much, honestly, given how much of our professional output is the written word.

Bibliophilia, Software, Transparency, University education

What Would I Buy With $3 Million for Math[s]?

Leading off the topic of my previous post, I think it’s a good time to ask what we can do with resources that are already allocated. How can we fine-tune the application of resources already set aside for a certain purpose, and so achieve the best outcome in the current Situation?

This post will be a gentle fantasy, because sometimes, in the Situation, we need that, or because that’s all I can do today.

Last month, Evelyn Lamb asked, how should we revamp the Breakthrough Prize for mathematics? This is an award with $3 million attached, supported by tech billionaires. A common sentiment about such awards, a feeling that I happen to share, is that they go to people who have indeed accomplished good things, but on the whole it isn’t a good way to spend money. Picking one person out of a pool of roughly comparable candidates and elevating them above their peers doesn’t really advance the cause of mathematics, particularly when the winner already has a stable position. Lamb comments,

$\$3$ million a year could generously fund 30 postdoc years (or provide 10 3-year postdocs). I still think that wouldn’t be a terrible idea, especially as jobs in math are hard to come by for fresh PhD graduates. But […] more postdoc funding could just postpone the inevitable. Tenure track jobs are hard to come by in mathematics, and without more of them, the job crunch will still exist. Helping to create permanent tenured or tenure-track positions in math would ease up on the job crisis in math and, ideally, make more space for the many deserving people who want to do math in academia. […] from going to the websites of a few major public universities, it looks like it’s around $2.5 million to permanently endow a chair at that kind of institution.

I like the sound of this, but let’s not forget: If we have $3 million per year, then we don’t have to do the same thing every year! My own first thought was that if you can fund 10 postdocs for three years apiece, you can easily pay for 10 new open-source math textbooks. In rough figures, let us say that it takes about a year to write a textbook on material you know well. Then, the book has to be field-tested for at least a semester. To find errors in technical prose, you need to find people who don’t already know what it’s supposed to say, and have them work through the whole thing.

If we look at, say, what MIT expects of undergrad math majors, we can work up a list of courses:
Continue reading What Would I Buy With $3 Million for Math[s]? →

Pseudoscience, University education

Reaction GIFs are Useful

It’s pretty darn remarkable, really. Every time—every! smegging! time!—that Steven Pinker opens his yap and opines on something I know about, he comes across as a transparent buffoon. The topic could be modern research on evolutionary dynamics, or it could be fanfiction. Today, thanks to his participation in the annual Edge essay shindig, it’s the Second Law of Thermodynamics. Pinker’s essay is of the kind that starts semi-competently before going off the rails. He takes a valid and important scientific principle, oversimplifies painfully, discards all the actual content and ends up with a vacuous statement that shades into ethical irresponsibility.
Continue reading Reaction GIFs are Useful →

Bibliophilia, Science history, Statistical mechanics, University education

Less Heteronormative Homework

A few weeks ago, I found an old physics book on a colleague’s “miscellaneous” shelf: University of Chicago Graduate Problems in Physics, by Cronin, Greenberg and Telegdi (Addison-Wesley, 1967). It looked like fun, so I started working through some of it.

Physics problems age irregularly. Topics fall out of vogue as the frontier of knowledge moves on, and sometimes, the cultural milieu of the time when the problem was written pokes through. Take the first problem in the “statistical physics” chapter. It begins, “A young man, who lives at location $A$ of the city street plan shown in the figure, walks daily to the home of his fiancee…”

No, no, no, that just won’t do any more. Let us set up the problem properly:

Asami is meeting Korra for lunch downtown. Korra is $E$ blocks east and $N$ blocks north of Asami, on the rectangular street grid of downtown Republic City. Because Asami is eager to meet Korra, her path never doubles back. That is, each move Asami takes must bring her closer to Korra on the street grid. How many different routes can Asami take to meet Korra?

Solution below the fold.
Continue reading Less Heteronormative Homework →

Bibliophilia, Popularization, Science history, University education

Concerning “Great Books”

Shimer College: the worst school in America?

Subhead: This tiny, eccentric institution in Chicago was just voted the worst place to study in America. But does Shimer, which shuns lectures and has no societies or clubs, deserve such an accolade? Jon Ronson went there to investigate.

In the body, we have a bit more detail:

This is a ‘great books’ college. The great books of the western tradition, not the professors, are the teachers: Da Vinci’s Notebooks and Aristotle’s Poetics and Homer’s Odyssey and de Beauvoir’s Ethics of Ambiguity and Kafka and Derrida and Nietzsche and Freud and Marx and Machiavelli and Shakespeare and the Bible.

And:
Continue reading Concerning “Great Books” →

University education

Adventures in the Sophomoric

Yesternight, I went memory-road-tripping through my blog archives. One of the things I realized, apart from how amazingly enthusiastic I was for the blogging form back in 2007, was how much I reviled my sophomore-year university physics classes. At the time, they were unpleasant; in retrospect, they were deleterious.

The worst was the relativity class, which had most of the interesting stuff dug out, and hot air pumped in to fill it out to a semester. Also a waste of time was the first semester of quantum mechanics—we had three, and the latter two were great. That is actually a topic where a three-fold division could make sense. One could have, for example, a semester on the basic formalism, a semester on symmetries and exactly solvable systems and then a term covering approximation methods. But that’s not what we did. Instead, the first term was “intuition building,” which translates to “let’s plod through differential equations over and over and over again, because learning any oh-so-much-harder math would be too much for your young brains.” Mixed in with that was a rather bog-standard “physicist’s history of physics,” which was as usual too inevitably misleading to be worth bothering with. The time period in question is fascinating to me, as is our professional mythologizing about it. The textbook cardboard we got couldn’t do the subject justice.

And another thing: ditch the requirement of going to the Math Dept for a differential equations class. That class sucked. Again, pretty much inevitably. I’d say it was doomed from the get-go, i.e., failure was ensured by the choice of topics and level of coverage. (All I remember from that semester was the professor’s claim that the Laplace transform takes you into a world where everything is yellow. I still don’t know what that means. Everything I was supposed to learn in that class, I picked up elsewhere and elsewhen.) A much better alternative would be an in-house class on mathematical methods. It’d slot neatly into the same place in the curriculum, even. And there are good books to teach out of! Also, for the love of Gauss, don’t rely on Matlab. Real programming languages exist and are at least as easy to introduce. If you’re going to be gung-ho about Technologically Enhancing the Active Learning in your classrooms, you might as well teach some skills which physicists could actually use.

(Said in a tone of voice suggesting that one might eventually have dinosaurs on one’s dinosaur tour.)

Bad Math, Popularization, Pseudoscience, University education

Reflections

Prompted by this review of Colin McGinn’s Basic Structures of Reality (2011), I read a chapter, courtesy the uni library. It was endumbening. To the extent that he ever has a point, he says in many words what others have said more clearly in few. He confuses the pedagogy of a particular introductory book with the mature understanding of a subject, displays total ignorance of deeper treatments of his chosen topic, blunders into fallacies, and generally leaves one with the impression that he has never done a calculation in all the time he spent “studying physics”. Truly an amazing achievement.

A few years ago, I might have blogged my way through the whole darn book. I must be getting old (“REALLY? NO WAY!” declares my weak knee). But is it a healthy and mature sense of priorities, or a senescent academic crustiness? Have I become one of those people, concerned with my vita to the exclusion of all else? Dark thoughts for this cold autumn evening, dark as our current season of superhero movies—Fimbulwinter 3: Flame of Despair….

Bad Math, Science history, University education

“Is Algebra Necessary?” Are You High?

“This room smells of mathematics!
Go out and fetch a disinfectant spray!”
—A.H. Trelawney Ross, Alan Turing’s form master

It’s been a while since I’ve felt riled enough to blog. But now, the spirit moves within me once more.

First, I encourage you to read Andrew Hacker’s op-ed in The New York Times, “Is Algebra Necessary?” Then, sample a few reactions:
Continue reading “Is Algebra Necessary?” Are You High? →

Popularization, Pseudoscience, Transparency, University education

The Transparent Academy

You know what I’d like to see? I’d like to have all the course materials necessary for a good, solid undergraduate physics degree available online, free to access and licensed in a way which permits reuse and remixing. I’d like it all in one place, curated, with paths through it mapped out to define a curriculum. When I say all the course materials, I mean that this webzone should have online textbooks; copies of, or at least pointers to, relevant primary literature; video lectures; simulation codes; sample datasets on which to practice analysis; homework and exam problems with worked-out solutions; interactive quizzes, so we can be trendy; and ways to order affordable experimental equipment where that is possible, e.g., yes on diffraction gratings, but probably no on radioactive sources. I’m talking about physics, because that’s what I nominally know about, but I’d like this to encompass the topics which I got sent to other departments to learn about, like the Mathematics Department’s courses in single- and multivariable calculus, differential equations, linear algebra, group theory, etc.

One way to think about it is this: suppose you had to teach a physics class to first- or second-year undergraduates. Could you get all the textual materials you need from Open-Access sources on the Web? Would you know where to look?

What with Wikipedia, OpenCourseWare, review articles on the arXiv, science blogs, the Khaaaaaan! Academy and so forth, we probably already have a fair portion of this in various places. But the operative word there is various. I, at least, would like it gathered together so we can know what’s yet to be done. With a project like, say, Wikipedia, stuff gets filled in based on what people feel like writing about in their free time. So articles grow by the cumulative addition of small bits, and “boring” content — parts of the curriculum which need to be covered, but are seldom if ever “topical” — doesn’t get much attention.

I honestly don’t know how close we are to this ideal. And, I don’t know what would be the best infrastructure for bringing it about and maintaining it. Idle fantasies and pipe dreams!

I’d like to have this kind of resource, not just for the obvious practical reasons, but also because it would soothe my conscience. I’d like to be able to tell people, “Yes, physics and mathematics are difficult, technical subjects. The stuff we say often sounds like mystical arcana. But, if you want to know what we know, all we ask is time and thinking — we’ve removed every obstacle to your understanding which we possibly can.”

I don’t think this would really impact the physics cranks and crackpots that much, but that’s not the problem I’m aiming to (dreaming that we will) solve. Disdain for mathematics is one warning sign of a fractured ceramic, yes: I’ve lost count of the number of times I’ve seen websites claiming to debunk Einstein “using only high-school algebra!” We could make learning the mathematical meat of physics easier, but that won’t significantly affect the people whose crankishness is due to personality and temperament. Free calculus lessons, no matter how engaging, won’t help those who’ve dedicated themselves to fighting under the banner of Douche Physik.

Alchemists work for the people. —Edward Elric

Bibliophilia, Electromagnetism, Science history, University education

Gbur’s Mathematical Methods

REVIEW: Gregory J. Gbur (2011), Mathematical Methods for Optical Physics and Engineering. Cambridge University Press. [Post also available in PDF.]

By golly, I wish I’d had this book as an undergrad.

As it was, I had to wait until this past January, at the ScienceOnline 2011 conference. These annual meetings in Durham, North Carolina feature scientists, journalists, teachers and students, all blurring the lines between one specialization and another, trying to figure out how the Internet can help us do and talk science. Lots of the attendees had books recently published or soon forthcoming, and the organizers arranged a drawing. We could each pick a book from the table, with all the books anonymized in brown paper wrapping. Greg “Dr. Skyskull” Gbur had brought fresh review copies of his textbook. Talking it over, we realized that if somebody who wasn’t a physics person got a mathematical methods textbook, they’d probably be sad. So, we went to the table and hefted the offerings until we found one which weighed enough to be full of equations, and everyone walked away happy.

MMfOPE is, as the kids say, exactly what it says on the tin. It begins with vector calculus and concludes with asymptotic analysis, passing through matrices, infinite series, complex analysis, Fourierology and ordinary and partial differential equations along the way. Each subject is treated in a way which physicists will appreciate: mathematical rigour mortis is not stressed, but when more careful or Philadelphia-lawyerly treatments are possible, they are indicated, and the ways in which their subtleties can become relevant are pointed out. In addition, issues like the running time and convergence of numerical algorithms are, where appropriate, addressed.
Continue reading Gbur’s Mathematical Methods →

Classical Mechanics, Popularization, Science history, Statistical mechanics, University education

“More Decimal Digits”

On occasion, somebody voices the idea that in year $N$, physicists thought they had everything basically figured out, and that all they had to do was compute more decimal digits. I won’t pretend to know whether this is actually true for any values of $N$ — when did one old man’s grumpiness become the definitive statement about a scientific age? — but it’s interesting that not every physicist with an interest in history has supported the claim.

One classic illustration of how the old guys with the beards knew their understanding of physics was incomplete involves the specific heats of gases. How much does a gas warm up when a given amount of energy is poured into it? The physics of the 1890s was unable to resolve this problem. The solution, achieved in the next century, required quantum mechanics, but the problem was far from unknown in the years before 1900. Quoting Richard Feynman’s Lectures on Physics (1964), volume 1, chapter 40, with hyperlinks added by me:
Continue reading “More Decimal Digits” →

Software, University education

Interactivelearn

A few complaints about the place of computers in physics classrooms.

Every once in a while, I see an enthusiastic discussion somewhere on the Intertubes about bringing new technological toys into physics classrooms. Instead of having one professor lecture at a room of unengaged, unresponsive bodies, why not put tools into the students’ hands and create a new environment full of interactivity and feedback? Put generically like that, it does sound intriguing, and new digital toys are always shiny, aren’t they?

Prototypical among these schemes is MIT’s “Technology Enabled Active Learning” (traditionally and henceforth TEAL), which, again, you’d think I’d love for the whole alma mater patriotism thing. (“Bright college days, O carefree days that fly…”) I went through introductory physics at MIT a few years too early to get the TEAL deal (I didn’t have Walter Lewin as a professor, either, as it happens). For myself, I couldn’t see the point of buying all those computers and then using them in ways which did not reflect the ways working physicists actually use computers. Watching animations? Answering multiple-choice questions? Where was the model-building, the hypothesis-testing through numerical investigation? In 1963, Feynman was able to explain to Caltech undergraduates how one used a numerical simulation to get predictions out of a hypothesis when one didn’t know the advanced mathematics necessary to do so by hand, or if nobody had yet developed the mathematics in question. Surely, forty years and umpteen revolutions in computer technology later, we wouldn’t be moving backward, would we?

Everything I heard about TEAL from the students younger than I — every statement without exception, mind — was that it was a dreadful experience, technological glitz with no substance. Now, I’ll freely admit there was probably a heckuva sampling bias involved here: the people I had a chance to speak with about TEAL were, by and large, other physics majors. That is, they were the ones who survived the first-year classes and dove on in to the rest of the programme. So, (a) one would expect they had a more solid grasp of the essential concepts covered in the first year, all else being equal, and (b) they may have had more prior interest and experience with physics than students who declared other majors. But, if the students who liked physics the most and were the best at it couldn’t find a single good thing to say about TEAL, then TEAL needed work.

If your wonderful new education scheme makes things somewhat better for an “average” student but also makes them significantly worse for a sizeable fraction of students, you’re doing something wrong. The map is not the territory, and the average is not the population.

It’s easy to dismiss such complaints. Here, let me give you a running start: “Those kids are just too accustomed to lectures. They find lecture classes fun, so fun they’re fooled into thinking they’re learning.” (We knew dull lecturers when we had them.) “Look at the improvement in attendance rates!” (Not the most controlled of experiments. At a university where everyone has far too many demands made of their time and absolutely no one can fit everything they ought to do into a day, you learn to slack where you can. If attendance is mandated in one spot, it’ll suffer elsewhere.)

Or, perhaps, one could take the fact that physics majors at MIT loathed the entire TEAL experience as a sign that what TEAL did was not the best for every student involved. If interactivity within the classroom is such a wonderful thing, then is it so hard to wonder if interactivity at a larger scale, at the curricular level, might be advisable, too?

It’s not just a matter of doing one thing for the serious physics enthusiasts and another for the non-majors (to use a scandalously pejorative term).

What I had expected the Technological Enabling of Active Learning to look like is actually more like another project from MIT, StarLogo. Unfortunately, the efforts to build science curricula with StarLogo have been going on mostly at the middle- and high-school level. Their accomplishments and philosophy have not been applied to filling the gaps or shoring up the weak spots in MIT’s own curricula. For example, statistical techniques for data analysis aren’t taught to physics majors until junior year, and then they’re stuffed into Junior Lab, one of the most demanding courses offered at the Institute. To recycle part of an earlier rant:

Now, there’s a great deal to be said for stress-testing your students (putting them through Degree Absolute, as it were). The real problem was that it was hard for all the wrong reasons. Not only were the experiments tricky and the concepts on which they were based abstruse, but also we students had to pick up a variety of skills we’d never needed before, none of them connected to any particular experiment but all of them necessary to get the overall job done. What’s more, all these skills required becoming competent and comfortable with one or more technological tools, mostly of the software persuasion. For example: we had to pick up statistical data analysis, curve fitting and all that pretty much by osmosis: “Here’s a MATLAB script, kids — have at it!” This is the sort of poor training which leads to sinful behaviour on log-log plots in later life. Likewise, we’d never had to write up an experiment in formal journal style, or give a technical presentation. (The few experiences with laboratory work provided in freshman and sophomore years were, to put it simply, a joke.) All this on top of the scientific theory and experimental methods we were ostensibly learning!

Sure, it’s great to throw the kids in the pool to force them to swim, but the water is deep enough already! To my way of thinking, it would make more sense to offload those accessory skills like data description, simulation-building, technical writing and oral presentation to an earlier class, where the scientific content being presented is easier. Own up to the fact that you’re the most intimidating major at an elite technical university: make the sophomore-year classes a little tougher, and junior year can remain just as rough, but be so in a more useful way. We might as well go insane and start hallucinating for the right reason.

Better yet, we might end up teaching these skills to a larger fraction of the students who need them. Why should education from which all scientists could benefit be the exclusive province of experimental physicists? I haven’t the foggiest idea. We have all these topics which ought to go into first- or second-year classes — everyone needs them, they don’t require advanced knowledge in physics itself — but the ways we’ve chosen to rework those introductory classes aren’t helping.

To put it another way: if you’re taking “freshman physics for non-majors,” which will you use more often in life: Lenz’s Law or the concept of an error bar?

Bibliophilia, Chaos Theory, Plectics, Popularization, Software, Statistical mechanics, University education

Updates

In the wake of ScienceOnline2011, at which the two sessions I co-moderated went pleasingly well, my Blogohedron-related time and energy has largely gone to doing the LaTeXnical work for this year’s Open Laboratory anthology. I have also made a few small contributions to the Azimuth Project, including a Python implementation of a stochastic Hopf bifurcation model.

I continue to fall behind in writing the book reviews I have promised (to myself, if to nobody else). At ScienceOnline, I scored a free copy of Greg Gbur’s new textbook, Mathematical Methods for Optical Physics and Engineering. Truth be told, at the book-and-author shindig where they had the books written by people attending the conference all laid out and wrapped in anonymizing brown paper, I gauged which one had the proper size and weight for a mathematical-methods textbook and snarfed that. On the logic, you see, that if anyone who was not a physics person drew that book from the pile, they’d probably be sad. (The textbook author was somewhat complicit in this plan.) I am happy to report that I’ve found it a good textbook; it should be useful for advanced undergraduates, procrastinating graduate students and those seeking a clear introduction to techniques used in optics but not commonly addressed in broad-spectrum mathematical-methods books.