What You Will

You can't see that Malvolio's cross-gartered stockings are bright yellow.

I have been lucky enough to recently come into possession of an Android phone. One of my favourite things about having such a clever phone is the Kindle app. I can put so many beautiful books in my pocket and there are many many many of them for which I don't even have to pay. A consequence of this is that this morning I (re)read Twelfth Night. I first read it in high school, inspired, I think, by Shakespeare in Love, which was our grade twelve English film study. (I know I wrote an essay comparing the film and the play, but I don't remember exactly why I chose that topic or if I read the play specifically for the essay.) I realised recently that I haven't touched Shakespeare since starting university and today I remembered just why that really is a pity.

Plays are fun to read and Shakespeare is just plain clever. I can fly from my cosy curled-up armchair spot to the Globe theatre; to the private showing at Candlemas 1602; to a performance in a modern theatre; to the director's chair at rehearsals; to the tech crew's  scaffolding and lighting board; to that half-enchanted land of Illyria where, ghost-like, I anxiously watch Viola extract herself from the horrible mess that Sir Toby and Fabian have taken it upon themselves to create. It's quite glorious. I daresay I miss some things and misinterpret others; but the stuff wasn't written, I don't think, so much to be analysed as to be enjoyed. Analysis will inevitably proceed from the enjoyment and some folk will carry that out in great detail. That is one good thing. Also a good thing is those of us left feeling awfully lucky that there's another play and another and another to be downloaded at the click of a button.

Learning/Understanding

(Two sides of the same coin)

Abstract

Mathematics, like poetry,
half-conceals truths
so abstract that,
were they made explicit,
the very substance of the universe
would burn.

You must learn what they
can express
to understand
what they can't.

 Lauren (aka SilverInkblot) of Autumn Brontide has been writing poetry in a series she calls "A Poetic Education". (The poemish thing above is part of my attempt at a response.)  My favourite so far is Half. The series is, I think, an interesting exploration of learning and schooling and education and how the three get tangled up together or end up (very sadly) excluding each other. I muddled around what she'd written a little, and she responded and expanded on her thoughts here. In consequence, I am thinking about education.

I read a few blogs about homeschooling, higher education and occasionally both. They're interesting, but I don't often do anything about them. I'm not a homeschooler. I'm not  a university professor. I guess I do a little bit of TA-ish work, but I've yet to discover a blog about those sorts of things! Despite that, I think it's worth reading those blogs.

Partly, they're just interesting. If something's interesting, I like to learn more about it. (Perhaps this is because I'm lucky in having received an education that by and large nurtured my love of learning, rather than crushing it.) Partly, I think they're useful even when I don't immediately act on them. Becoming aware of how education and learning work means that if I do end up making a decision about them, I have data to work with. And I'm sure I make minute day-to-day choices slightly differently when I make them against a broader background.

That is, I think awareness makes a difference and I think that an education -- even an education on education -- has to be built up over time. Which is why I think that saying something about it will almost always be better than saying nothing, even if the something has to be accompanied by and admission that it's a long way from being everything. I don't think the difficulties education has to overcome can go away overnight. But by engaging with them and thinking about them, we make change possible.

Trends and Community

Exams are finished! I'm not sure it's possible to adequately express my glee about this in writing. I am not an exam person. (Lest you think that redundant, let me assure you that I have on occasion met people who do handle exams with poise and grace.) Presently I will go home, see my family and laze around reading analysis textbooks. In the meantime, I am working at university, which is quite* cool.

The work I'm doing involves going way back through the archives of academic journals and sorting out which papers are relevant for one of my lecturer's projects. One of the side-effects is that I get to see a little bit of the flow of physics research over time.

It's weird to see the papers people were writing when I was still learning to read, all put together in a sort of conversation. It's no surprise that people were doing physics when I was a kid (I've certainly used papers from way before I was born before), but it is a little odd to find this community that I can never really know preserved in the pages (or pdf files) of the Am. J. Phys.

It's also interesting to see how different topics go in and out of vogue. There's always a certain amount of mechanics, quantum physics, electromagnetism and so on, but there are time periods when certain things crop up repeatedly and quite frequently. For instance there were a couple of years that saw a cluster of papers about the charge on a magnetised needle; during another phase it seemed quite fashionable to deal with surface tension problems. I think it's fascinating that such trends exist.

I'm not sure if these patterns have much direct practical application, but I do think they're useful in getting know physics. I recall once reading somewhere that before trying to participate in an internet forum, it can be helpful to 'lurk' and see how things are done there. I guess the academic equivalent is reading all the way back through the journal archives.
_____________________
*Where 'quite' means 'extraordinarily, but that seems potentially like an over-the-top response, so I'll just say quite,'

Thinking like a physicist

@mathematicsprof on Twitter recently tweeted a link to a page asking what it's like to understand advanced mathematics. There are a number of very interesting answers there, but one interested me particularly. I can't figure out if there's a way to link to it directly, but I'll quote it here:

From Jack Miller:

 

A two part question to determine if you "think like a mathematician," from Prof. Eugene Luks, Bucknell University, circa 1979.

Part I: You're in a room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on the floor.  How do you make hot water for tea?
Answer to Part I: Put tea kettle on stove, turn on burner, heat until water boils.

Part II: Next, you're in another room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on a table.  How do you make hot water for tea?
Non-mathematician's answer to Part II: Put tea kettle on stove, turn on burner, heat until water boils.
Mathematician's answer to Part II: Put the tea kettle on the floor. 

Why?  Because a solution to any new problem is elegantly complete when it can be reduced to a previously demonstrated case.

 This might be why I'm studying physics more than maths. I can see why putting the kettle on the floor solves the problem rather elegantly - I think it's a nicer solution than the "non-mathematician's answer" up there - but it's not how I would solve the problem. Isn't it obvious that the table is negligible in this situation, so that Part II is reduced to Part I?

Mathematicians aren't, I think, supposed to say things are negligible. Assuming that the table is negligible isn't rigourous. It does, however, get to the right solution without (explicitly, at least) going via the floor. It's still elegant (if you can get over the idea of neglecting the table) and it takes less effort.

Perhaps it's related to the idea that physics is not so much about working out how to describe some given bit of the universe as it is about working out which bits of the universe we can describe and doing so. This is usually expressed in terms of finding symmetries, from what I've seen and heard. Here, I think the system is invariant under the introduction of the table, which is a symmetry.

There are probably other ways of solving the problem, too. I think it's a very interesting exercise in how people think!

With Recurring Kittens

One.

I wrote my first exam for this semester yesterday. I think it went reasonably well; it was oddly satisfying to throw out the thirty-plus pages of notes I'd generated over the last few days. (Not the actual notes I made in class - I keep those. But I tossed the duplicates that ensured the class notes did actually (mostly) transfer to my memory.) There is now some danger that I begin to feel that having worked so hard for that course, I needn't worry about the others. Which would be foolish. To combat this assumption, I'm going to try to finish a section of Quantum Mechanics between writing each take here. (I'm stealing the general idea from here.)

Two.

I came across this writing competition yesterday, which asks for writing inspired by Benjamin Franklin's quote "If you would persuade you must appeal to interest rather than intellect." Now, physics is indubitably awesome because it allows us to harness the power of mathematics to understand the nature of the universe. It's pretty cool that way. But part of the fun - especially, perhaps, when it comes to revision - is things like my Q.M. lecturer's comment that there are physics-loving kittens who cry every time students try to explain the uncertainty principle without explicitly stating that it's fundamental. Doesn't sound plausible, you say? Well neither does quantum mechanics.

I don't think those two ideas are properly linked up there. If I figure out how to link them properly, I might have a competition entry.

Three.

I am going to use part three to write about the idea of determinism in classical mechanics so that I can refer to that idea in part four. It's pretty interesting for it's own sake too, though. Determinism starts with the sort of idea that if I know that a train leaves the station at two o'clock and travels at a constant speed of 60 km/h (I have no idea how fast trains actually travel) in a constant direction, I can tell you exactly where it will be at three o'clock. Of course, the train needn't travel at a constant speed in a constant direction, so I could  be quite wrong. When it comes to Newton's laws of mechanics, however, the only thing that can cause a particle to change its state of motion is some kind of external force (that's basically Newton's first law). So if I know all the particles and all the forces they can exert, I can work out everything that will happen. This raises some rather interesting questions about free will, since although practically nobody could know what every single particle in the universe is doing, the idea that it's theoretically possible is rather creepy. Quantum mechanics saves the day here, though: it turns out that even theoretically it's not possible to know everything about even one particle. Of course, that's rather weird in its own right.

Four.

This painting is awesome.

Il castello di Bentheim (Jacob Van Ruisdael)

I don't think you can explain why a painting is awesome by describing particles that fly around colliding and absorbing one another. They can be deterministic classical particles or random quantum particles, but they don't explain things like beauty. Or truth. (You can talk about my perception of truth in terms of particles in my brain, perhaps, but not about truth itself.) And they're not supposed to. That's why physics isn't metaphysics. It's kind of obvious in some ways and awfully hard to hold onto in others. Part of the appeal of physics (apart from the kittens) is trying to understand things. We understand more and more stuff, at a more and more fundamental level, as we go on, but at some point, in some directions, it has to stop working. Which is just as well, on the whole, but can be a little disappointing in the moment.

Five.

 It is a mark of something, I'm sure, that I've quite lost track of my reading list. Probably the amount of work involved in a final year maths/physics course. I don't actually know if I've read (well, finished) anything (that's a book) since Silver on the Tree, although I suspect I haven't. And I don't remember exactly when I read that, so that it's an altogether sorry state of affairs. However, in my efforts to do something meaningful and productive that does not involve calculating the probability amplitude function for a particle on a ring for the umpteenth time, I realised that my average reading rate for the year is still a book a week. And I definitely read more academic papers than I used to, which ought to count for something. Perhaps not altogether a sorry state of affairs, then. But it's rather odd to say that I can't remember the last time I finished reading a book.

Six.

Do you still remember the physics-loving kittens? I suggested that such a thing might be implausible, but through the wonders of Google image search and The Particle Zoo, I have now found such kittens. Behold:

You can click the image for more quarky quirky physics humour with kittens.

If you have not encountered The Particle Zoo before, it's where you go to buy a universe in a box. No, seriously.

Seven.

And that's that. I did not study a section of quantum mechanics between each post, because I couldn't make up my mind about how to define a section. So I did some studying and some writing and it all got mixed up together. As long as I don't start drawing kittens in my exam paper, I think that's okay. I missed the boat for keeping quantum mechanics off the blog a while ago.

Feminine(?) Role Models

Preface: Apparently the people at The Aperiodical are not as great as I think they are. You should make your own judgement, though. (In my undenied naivete, I think it's cool that somebody mentioned me on a podcast. Two, actually.)

 So recently some people at Michigan university did some research finding that feminine maths and science role models are not inspiring. I've been wondering for a little while why the article bothers me. Perhaps it's because I exhibit most of the characteristics that they say put girls off studying STEM (science, technology, engineering, mathematics, if I recall correctly) subjects. Which is, you know, kind of sad. I would not like to think that by wearing pretty skirts and getting good marks I send out a message that other people can't . . . can't what? Do mathematics? Understand physics? That sounds plain ridiculous.


Part of it is that the study was actually fairly limited -- it only looked a middle school girls. More significantly, from what I understand, 'feminine' here means something more like 'glamourous' than, say, 'womanly'. (The introduction to the paper proper refers to "pink-laptop-toting ‘‘Computer Engineer Barbie,’’" for instance.) That's not my immediate interpretation of feminine, but perhaps it's other people's. (If you're reading this, I'd love to know what you think.) I can believe that most girls don't think they have the potential to be the real-life version of Computer Engineer Barbie. I for one don't even want to. Does that make me unfeminine?

I like pretty dresses and I have a formidable collection of hair ribbons, but I can't be bothered to go through a fifteen minute make-up routine every morning. I own pretty high heeled sandals, but I don't wear them often. For one thing they're impractical for running up to the Physics department on the second (I think that's third in the USA, where people count funny) floor of Science block. For another, I'd feel overdressed when I arrived amidst the rest of the jeans-and-sneaker-clad students. If that's unfeminine, then I guess all those conclusions about STEM-successful women being unfeminine are probably true. Only I'd be inclined to think that most women are rather unfeminine then. (In fact this is semi-almost-implied in both the press release above and the paper proper.) Motherhood certainly doesn't sound feminine by this metric, which strikes me as rather odd.

If feminine means putting a fair amount of time and effort into satisfying certain perceptions of beauty, then being feminine means having less time to be good at anything else. It also means that anyone with a different idea of what beauty is will rather dislike being labelled as feminine. It wouldn't surprise me that many women who are successful in any number of other fields qualify as 'unfeminine'. On the other hand if being feminine is simply being typically female, I don't think it's nearly as likely to scare girls away from maths and science. (Of course STEM-successful women may still be perceived as unfeminine, which is not cool, but not something I really want to get into here.)

I do think the study is interesting and even useful, but I don't like the lack of definition of 'feminine'. It seems to mean something different every time I see it, until I find myself wondering how I've ended up in a world where it's referred to as counter-stereotypical for a woman to be feminine.

Perhaps I'm overthinking things, but that does strike me as a little odd.

Redefining Survival Mode

Every once in a while one is forced to go into survival mode, I think. It's simply not possible to do everything that one would like to, or even to do most of it altogether properly. So one ends up doing an okay job of the critical stuff until things improve. For instance, I may or may not have recently been heard to say 'I don't understand that, but it doesn't matter -- it's not in the exam.' It's not that I don't care about understanding things. It's that I have a fairly good argument for understanding the things that are in the exam first.

However, I've noticed that my definition of what exactly constitutes this survival mode seems to be changing. Survival mode used to mean sitting and staring tiredly at my cup of tea instead of getting on with my work. Now I sit and stare tiredly at my cup of tea, contemplating the curl of the tea velocity field and wondering if heat transfer would affect that velocity field. And what would the scalar heat field superimposed (as a colour map, say) on the velocity field look like? And if heat flow was treated as a vector? I may even pull up something like Mathematica or Gnuplot to get an idea of what those things would look like. All this still instead of the work I'm supposed to do, although I won't take it any further than that.

It still feels like survival mode, but it seems qualitatively different from the other kind of survival mode. I'm not quite sure where it comes from. Perhaps it's the increased 'mental fitness' after a couple of years of university maths and science; a gradual change in the way I think about things that's just highlighted by the fact that I'm survival mode-ing. Perhaps half a dozen things. I'd need to create an ensemble of identical systems and observe their evolution over time to be sure.

Whatever the cause, I think it's a kind of interesting phenomenon. I should probably stop staring tiredly at the computer screen and go figure out how to use a Cornu spiral, though.

This describes Fresnel diffraction. I'm still figuring out how.