QFT is (not) hard

Yesterday was our faculty's postgrad symposium, where science students of all descriptions attempted (usually with some measure of success) to explain to science students of all other descriptions what their research is all about. This necessitates some creativity and has left me thinking (not for the first time) about whether or not QFT is indeed inexplicable. It seems worth writing up a few thoughts here.

QFT is hard.

There's a reason that nobody less than four years out of high school gets QFT (for an approximate value of nobody and allowing 'gets' to be ill-defined) and nobody with less than six years of tertiary education has actually used it in any practical way. (Again, generalisation, but I don't think it's far off the mark.) QFT is a very abstract, mathematical theory and divorcing it from the mathematics is like trying to explain swimming without water. If you want to understand QFT, come back when you have a degree's worth of mathematics. This is perhaps a little too depressing, so let's try another tack. 

QFT is not hard

Sure, the scientists who do QFT research need lots of training and deal with scary equations all day, every day, but that's not the heart of what they're doing. They're actually doing calculations on "god particles" and quarks, which are basically very small marbles glued to elastic bands which are other particles called gluons and the gluon is massless which means it's like a fish that can swim through the god particle molasses slickly, unlike the other particles, which are like whales because they have masses.

Now, I will admit that our building houses not just the physics department, but also the oceanography department and the Marine Research Institute, but we are separate departments. A quark or a Z boson is nothing at all like a whale. In fact, the work I do on a day-to-day basis involves talking about mathematical abstractions that can be experimentally tested using the ideas of such particles, but doesn't really talk about particles at all. So while I do think that non-specialists should be able to get an idea of what's going on in QFT, I'm not convinced that these analogies do much more than make people think they know what's going on. Which is perhaps worth something, but seems suboptimal.

QFT is (not) hard

QFT is an abstract theory based on abstract mathematics. If you want a genuine feeling for how it behaves, you need a genuine feeling for how maths behaves. To reuse an analogy (since I've decided they're not all bad), you can't understand swimming if you don't know what water is. QFT is related to abstract maths just as intimately and shying away from it doesn't help. But what I think we miss is that all you need is a "genuine feeling for how maths behaves". I say 'all', but of course such a feeling can be hard to come by. However, it's an awful lot easier to come by than a degree in mathematics. It almost has to be.

I don't think you need to be able to calculate a commutator to get a feel for what's going on in QFT. I do think you need to know that sometimes in maths, as in life, order matters. 2 + 3 = 3 + 2. I don't care whether you put on your hat and then scarf or you scarf and then hat. But pq is not the same as qp and you should put on your socks before you put on your shoes, unless perhaps you're going to a fancy dress party.*

For some reason we don't seem to want to explain QFT this way. Perhaps it's because we've all learned in school that maths is terrifying. Perhaps it feels like it takes us too far off topic. (I feel this every time I try to give a talk about QFT, but I find there's nothing to say if I take out the maths.) Perhaps we just haven't thought about it enough. (We almost certainly don't think about science communication enough.) Perhaps it is happening, but I'm not aware of it (and neither are my scientist friends, which would mean it needs way more publicity).

I'm still working out where  this leaves me. It means that when I talk about QFT for a general audience, I don't shy away from the maths. Maybe it means I need to write and/or talk about these ideas more often (she said, guiltily writing her first blog post in months). Maybe it's enough to be aware of it and to talk about. Maybe I need to pick fights about it. Maybe (definitely) it's not all a problem for me to solve, all on my own, today. But it's a topic that deserves some thought, in the midst of marking and debugging and trying to put in those six years you need to learn to use QFT. We'll see.

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* I feel like a cheat putting in mathematics without explaining the physical significance. The p and q here are representing the tools we use to measure the position and momentum (which gives us the speed) of a particle respectively. The maths tells us that the order in which me measure them matters, because pq ≠ qp. This means that making one measurement must somehow corrupt the other (it doesn't tell us how that happens, sadly). This in turn means that if we measure the position correctly, we can't measure the momentum and vice versa. This is Heisenberg's Uncertainty Principle (which is one of the most obvious and well known consequences of order mattering, although not the only one). You can talk about thought experiments, like the Heisenberg microscope, to make it seem more intuitive, but it comes from the fact that if we choose maths that gives us the right answers, order matters when you write down p and q.

Theme Thursday: Sport?

Boogie at the UCT Ballroom and Latin Dancing Society

Cari at Clan Donaldson runs the Theme Thursday linkup, and since she says there are no rules, I will persist in joining in erratically, even when I'm not really in the target audience. Also I will post-process the heck out of mediocre pictures until I can convince myself that they're arty. And claim that the social dancing when Ballroom lessons are cancelled for the holiday is a sport. (Actually, looking at what other people have linked, this last might be on-trend.)

Straight off the camera cellphone

 If I go to black and white, I can convert the motion blur to graininess (yay, unsharp mask) and call it a feature, yes? It was fun to play with, at any rate; and a fun evening to remember. So perhaps I can file this under "further perks of [still] being a student". It fits somewhere below "Science is cooool" and above "No, actually, I don't get to take the university holiday off. I need to learn everything about everything before my funding runs out."

 
Savo 'lass a lalaith.

I should be debugging

, but the server's down and sometimes it's good to step off the hamster wheel. I think. Maybe. It's okay to step off the hamster wheel, right? Are we allowed to admit that there is a hamster wheel?

I'm not complaining, mind you. I love my work. Really, laugh-out-loud, love theoretical physics and seeing how ridiculously, beautifully abstract mathematics can describe the real world and how things actually happen. I love C++ debugging somewhat less, but I can accept that it's part of the package. Which isn't to say it's not a bit of a hamster wheel.

On Saturday at a workshop on science communication I told an auditoriumful of people that I was infatuated with Grassman algebras. That isn't a hamster wheel. It's something to remember and savour. It's a reason to get on the hamster wheel when the wheel needs to be turned, even if I don't seem to be going anywhere.

Grassman algebras are very neat. See, ordinary numbers commute. That means you get equations like

ab - ba = 0

which is to say

ab = ba.

Five times three is the same as three times five, and for most of the things we want to use maths for, that's awfully convenient. If I switch the length and breadth of a room, I don't want the area to change! But sometimes switching things around does change things. Putting on my shoes and then my socks is not the same as putting on my socks and then my shoes.

It turns out that in particle physics there's a family of particles -- called fermions -- that behave like this. If fermion the first and fermion the second are identical (for instance, they might both be electrons), it still matters which order I put them in. No, that's not intuitive, but it does seem to be the way nature works. If I switch fermion one and fermion two, so that instead I'm looking at fermion two and fermion one, the mathematics I'm using needs to have a minus sign attached. And that's where Grassman numbers (the things you use in Grassman algebras) come in. Grassman numbers don't commute, they anticommute:

ab + ba = 0 

which is to say

ab = -ba.

In fact, Grassman numbers behave just the way fermions seem to. That means that while I might describe the length and breadth of a room using ordinary ("real") numbers, it's more convenient to describe fermions using Grassman numbers. I have to modify the rules of maths slightly to make sure that they anticommute, but otherwise I can carry on just as before. The kind of number I'm using does most of the work and I don't have to keep accounting for the odd behaviour of fermions. The fact that they do strange things when you swap them around is built in.

 I think that's pretty. Just about pretty enough that I might muster the willpower to go and ask C++ why it insists that the solution to my equation is infinity. (The solution is not infinity. Unless I've given it the wrong equation. Or the wrong method for solving the equation. Or I accidentally typed +∞ before printing the answer. Maybe I'll go check that last one.)
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Savo 'lass a lalaith.

Patterns

 Some correlations without much thought on the mechanisms behind them. Things I've noticed. 


Three participants at the Cape Town heats of the FameLab science communication competition prepared their talks for both regional rounds before the day. (The others prepared the second talk during lunch break.)
//
The same three participants were the three sent through to the national stages.

(Did they [we] do better because they [we] were more prepared, is there something that affects both or is it just chance?)


Researchers are evaluated not by what they understand (which is hardly measurable), but by "research output" or publications.
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Students are told that it's more important to understand the topic than to worry about the grades.

(This is partly to do with what we can measure and partly to do with how we look at things and definitely a question that goes much deeper than what I've written here.)





If I get to  bed early, I'm much more capable of being productive in my work the next day.
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A lot of fun-sounding events are run in the late evening.
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There's a stereotype about scientists not having social lives.

(Even the most obvious way of linking these doesn't involve social awkwardness. One might argue that it implies it, I suppose.)


Mathematica is probably* the most expensive and widely-used symbolic programming language out there.
//
It also has the best pattern matching capabilities.*

(My supervisor likes to point out that, even so, it's a terrible stand-in for your brain.)



*I've heard so and it sounds plausible, but I haven't looked it up for myself.

What exactly counts as open?

I'm currently writing a paper for a journal that accepts submissions only in .doc format. That doesn't sound like a problem – everyone uses Microsoft office anyway, right? Well, no, I don't. Because MS Office doesn't run under Linux, which I'm using. And even if it did, there are places I'd prefer to throw my resources, given a choice. But aren't there open source alternatives that can produce those files? Well – kind of. LibreOffice will produce a .doc file alright. And if it contains straightforwardly formatted text with the occasional picture, MS Word would handle that file fine. However. I need equations. And while both LibreOffice and MS Word have equation editor functions, they're not entirely compatible. Nor are they particularly fun to use. Why can't I just use LaTeX?

Well, okay, I know why I can't. It's a general science journal, and unless you're doing fairly mathematical science, the LaTeX learning curve may not seem or be worth the (relative) ease of use. (And, I suppose, not allowing LaTeX forces me to consider if I really need to include that obscure equation in the paper.) LaTeX documents are not, for most people, as easy to read and edit as is a .doc file. It is free, though. Which MS Word is not.

It raises an interesting question about which method is really more "open". Requiring Microsoft formats means I need to buy – or, more realistically, borrow – an expensive piece of software to contribute to the journal. Requiring LaTeX formats forces contributors to pick up a non-trivial skill set before submitting. Neither of these is really entirely open. Perhaps simply offering a choice of format would be a reasonable workaround, although it does still feel like a workaround. Improving the compatibility of LibreOffice (or other open source office suites) with MS Office, while far beyond the reach of the journal, might be a slightly better fix. I think that will happen, but not until long after I've written this paper!

In the meantime, I'll be sulking in the corner because a side effect of using an office suite format is that I can't work in vi.

Friday Five

1. It's Sir-Laughs-a-Lots' birthday tomorrow. (Happy birthday!) We're going to do silly celebratory student things. No, not that kind. The kind where you realise you have the reading comprehension of a grad student and a pile of children's books and what are you waiting for? Yay.

2. Today I wrote my last test of semester, and our lectures are finished. Exams are looming only in a manageable couple of weeks, so tomorrow we're going to do silly celebratory student things . . .

3. The test I wrote today may be the last maths test I ever write. (I take all my courses from the physics department next semester, and if I'm lucky that could be the end of coursework.) It's kinda weird.

4. Do I sound like Hermione Granger if I say I want an analysis textbook for bedtime reading? We've touched on functional analysis in this PDE course and while I don't feel much need to do the proofs myself (though it would be fuuuuuun), but I think it's be interesting, useful and, relevantly, doable to get a sense of the terminology and what the results actually are. Maybe I could find an analysis for physicists book. Hmm.

5. Although while I don't want a full-of-detailed-proofs book, I kind of want a rigourous one. We can pretend that makes sense, right? It's like, I was talking to one of my lecturers about an applied physics course and he said "Well, for a pure mathematician like yourself [. . .]" Now, I'm certainly not much of a pure mathematician if I haven't even read much analysis (I do know a very little), but I guess I'm pickier than most about maths being done properly. As it should be.

And there's today's allocation of nerdery. If you know of a readable introductory source on analysis, I'd love to know, though I don't promise I'll actually get to reading it.

Savo 'lass a lalaith.

End of Semester

I sat down to study today. I cleared my desk properly for once, and finally actually handwashed the tie-dye shirt that's been sitting there (now it can go into the laundry with everything else). I gave my hopefully-not-dead-yet pot plants some attention that they probably needed quite a while ago, and got mud all over my notes and the carpet. So while I was cleaning that up I gave the rest of my room a quick going over too.

It's almost procrastination, but the tidy, organised environment did seem more conducive to sitting down for two hours and making maths notes. Besides, it all needed to be done, right? It's nice to revel in the straight lines and neat corners that come with exam season before it really gets going.

Once exams are actually upon me I know those corners will seem poky, but a (relatively) clear schedule and a clear desk look quite inviting right now. There's space to breathe.

Not-Friday Five

1. We cooked spaghetti and meatballs for supper Friday night and it turned into a fancier meal than I expected. I'm not sure if it was because making meatballs is a little more effort than I usually go to or just Friday night fanciness or some happy serendipity, but it reminded me that cooking can actually be fun. I need to find more time and energy for that on a regular basis.

2. Quantum physics is weird. Niels Bohr (one of the founders of the subject) once (somewhat) famously said that "Anyone who is not confused by quantum mechanics has not understood it." This makes for some really cool stuff, but also makes it tricky to tell whether there's a typo in your notes or things really are just that weird.

3. I spent quite a while persuding the campus bookstore to source books from the suppliers for me. The online people would do it happily, but they couldn't process the gift card I'm using to finance the purchases. However, I now have a couple of books I've been wanting to read - that weren't even on special - on the way. This is exciting!

4. My siblings have all attended schools that presented book vouchers with academic awards, but I never did. I feel like part of the club now that university's doing it too.

5. Wednesday was a public holiday. It was wonderful to have a day off from classes, and while chunks of it were filled with homework, other chunks were filled with a tie-dye project It was fun! I could get addicted to this stuff.

Work and Play

I downloaded photographs for the first time in ages, and these seemed to more-or-less cover the spectrum of stuff I've been doing.

First year labs - taken during a lull in the questions. Using a torsion balance to determine relative densities. Demonstrating is actually a pretty cool job; and it makes for more interesting pictures than most of my "real" work (the stuff I'll hopefully get a degree for). You can just picture me moving between the computer and my notebook for that.

Afternoon tea - just off from the middle-of-town traffic is a lovely Victorian garden with hedges and archways and benches and grottos, which I was too busy exploring to photograph - maybe another time! After that it was time for tea. We try to do something exciting most weekends, although that sometimes means making tea and drinking it without doing work at the same time. Those times are slightly less photogenic, but they're good too!

Book Logs

I've finished a handful of books in the last couple of weeks (mostly the last week, which was a holiday from lectures, if not university work) and since it seemed unlikely I'd write posts for all of them, I'm going to put a snippet about each here.

The Lord of the Rings
J.R.R. Tolkien

I am always impressed by the immensity and grandness of this story by the time I finish it. It starts out merely cheerful and exciting - by the end it makes me wonder if I could ever do anything so worthwhile. Then I remember Frodo telling Gandalf that he wished he needn't have lived in such a time, and Gandalf's response about having to live through the time we are born into (although I've a feeling he phrases it more eloquently). I can thus convince myself that I don't need to be a Frodo or a Samwise or an Aragorn or an Eowyn.

It's harder to justify why I shouldn't strive to create as magnificently as Tolkien did. Exactly what that means is a little fuzzy, but I come away feeling inspired; like it's no good if all the book does is make me sad and happy and incredulous and awestruck. One needs to do something, whether it's a trip to Mount Doom, making sure Gaffer Gamgee has enough to eat, creating something to reflect the glory of our world, devouring knowledge like it's gong out of fashion or - just something. It doesn't seem enough to let life happen to one, after that account. One must do something.

OpenIntro Statistics
openintro.org

It's been a while since I read a textbook from cover to cover. It's nice having work that's focussed enough to make it worth the investment. This was very accessible, but covered a fair amount of ground (at least it felt that way to me - I don't have much to compare). It was, at least, enough to springboard me from high schoolish level into a more specialised textbook with a fair degree of confidence. (I'm currently reading Christopher Chatfield's The Analysis of Time Series: An Introduction)

The Four Loves
C. S. Lewis

I read this and thought "Hmm, that's interesting, but there's nothing particularly mindblowing about it." But since then I've been remembering this quote or that idea in a bunch of different contexts. I'm not sure there's an exciting core message that the whole book works to convey - although it's all thematically consistent - but there are fascinating insights scattered throughout. I was a little disappointed that so much of the book seemed to address men only. I see Lewis's point that he doesn't have any other experience, but I still didn't like it. Nonetheless, this was an enjoyable and thought-provoking read.

A Skull in Shadows Lane
Robert Swindells

From the title, the back cover blurb, and what I've previously read from Swindells, I was expecting this to be a light-hearted five-find-outers-style mystery story. Instead it was a rather thoughtful look at post-WWII life through the eyes of eleven year old Jinty Linton, her brother Josh and their cohort, in a little English village where "nothing ever happens". I think Swindells exploits that ordinariness very well - this connected with me in a way that war stories generally don't. It felt like a children's book (which it is), but I still enjoyed it and have found a new way of seeing that time period.

Monday Miscellany

1. I posted recentlyish about knowing "nothing", largely prompted by the fact that some of the papers I'm reading for my honours project go way over my head. I also ended up emailing my supervisor to say "Wah! I don't know any stats!" (But in more grown up language, 'cause I'm boring like that.) He helpfully sent me an open source stats textbook. After reading about half of it, I was thinking "No, I know all of this. I meant the other stats." Oops. The second half of the book has been more helpful/new, but I suspect I'll need yet another book after that. So many things to know!

2. Easter was awesome. Easter is awesome. Something like that. And Easter hymns are amazing. Something in the music and the physicalness of really singing it out captures the wonder and excitement that is so hard to maintain through the year, but so much what Easter is about. He is risen! We are forgiven! He is risen!

3. In the sermon on Good Friday, our minister pointed out that Jesus was hated - and crucified - for showing love. I'm not sure how often I want to be liked more than I want to show love (and act on that). More often than I should. But at the same time it's definitely not right to alienate people. It's a tricksy topic, but one worth thinking about, I think.

4. I discovered that Google Reader was shutting down from my sister, who actually spends enough time on a computer (with internet) to use it regularly. I also discovered from her that there's a Feedly mobile app which works quite well. And now I have a feedreader on my phone (which, in fact, I really like). I haven't been so informed in months.

So Very Little

I have been very busy lately, with the masses of stuff I'm trying to cram into my head. Formalisms quantum mechanics and principles of thermodynamics and methods of solution of partial differential equations are all buzzing around, needing to be learned before I write tests and just because they're useful.

Then I move to reading for my project and there are all sorts of more specialised things I need to know - everything buzzing around my head is not very much at all.

Marking first year undergrad work reminds me of how much I do know, though. More than the owners of the scripts now covered in red ink (at least when it comes to physics - there are other spheres of knowledge, I know). But the difference between what we know is so very very much less than the masses of things we don't (even just in the realm of physics). None of us know very much at all.

There's a continual tension between ignorance and opportunity. We would never have the joy and excitement of discovery if we knew everything - but there's enough we don't know to go on discovering as long as we care. On the other hand, ignorance in its own right doesn't seem awfully lovely. Somehow, though, I need to love my ignorance at least inasmuch as it gives me the opportunity to abolish it. It's an odd kind of not-quite-dichotomy.

Game Mechanics

In a roleplaying game that I'm currently running/playing/somethinging, there's a mechanic built around an attribute called will. Roughly speaking, fighting monsters and making arduous journeys depletes will. Sleeping or relaxing in a safe place replenishes it. Will is also regained after achieving success in some way, which is a more complicated/interesting mechanic.

I think it has interesting consequences for how much attention one pays in lectures. See suppose the characters in the game had to sit through a quantum mechanics lecture (if you're playing the game: ooh, foreshadowing). One character pays attention, takes complete notes and asks questions. She loses a will point for all the effort, but regains it when, at the end of the lecture, she understands operator methods better and can consider her time well spent. Another character disagrees with the lecturer's interpretation of quantum mechanics, but thinks better of starting a philosophical debate in class. Rather than spending a will point stewing over it, she starts doodling in the margins between taking down the most salient points of the lecture. Her understanding of operator methods improves, but she's not satisfied enough to gain a will point. Nonetheless, between taking some notes and worrying about philosophy and doodling, she's lost a will point. She'll be more tired than the character who paid attention. (The character who bunked the lecture is also doing better, but only until exam time.)

Now, if only real life could be modelled by such simple mechanics. Quantisation of willpower, at least, sounds like a viable physical mechanism.

(This picture is mostly just because I like it. It has to do with lectures (phase space representations, not operator methods) and end-of-long-day/weekness. That's all.)

These Are a Few of My Favourite Things

Or at any rate, things that have made me happy recently, even if they aren't absolute all time top favourites.

Pausing to stand under a cascade of pink blossoms spilling over a fence on the way back from the supermarket.

Finding that an example I made to help some students has osmosed into nearly every workbook in the group.

Eating a perfectly ripe plum after a long afternoon.

Having my own keys to [parts of] the Physics department.

Lying on my bed with a supersized mug of milky tea.

Working out a proof until it suddenly blossoms into understanding of the general case.

Finding a skirt that hits at the ankle even if you're tall and high-waisted, marked down from the markdown price.

Watching and helping a student 'get' a new concept.

Scheming to make homemade hamburgers and chips on Friday night.

Drawing Koch snowflakes until the iterations get smaller than my pen strokes.

There are moments on the other end of the scale too, of course, but life is good.

Wordless Wednesday: Before the Lecture

Research

Today while I was talking to Sir Laughs-a-lot, because this is apparently what grad students do, we formulated an algorithm for research. I, uh, decided the world would be a better place for my putting on the internet. So here goes.

1. Get confused. (We totally have this one nailed. But as Sir L says, it can be fun.)

2. Get unconfused. (Easy, right?)

3. Write a paper. "Look! I'm unconfused, look at me! You can be unconfused too."

4. Win Nobel prize; become rich and famous (optional).

We were doing step two for a thermodynamics problem which has technically already been solved, but only by other people and we ended up with a (hypothetical) balloon that filled the whole universe. This is why I'm studying physics.

Friday Five

1. Lectures started this week! It's a bit odd only having nine hours of class time in a week, but there still seems to be plenty to do. I wonder how many of us are realistically putting in the other 3+ hours a week on project work.

2. Most of my project time this week has gone to watching video lectures on machine learning (via Coursera). One of the neatest techniques is an algorithm called gradient descent. For each iteration it considers each parameter A and a function J to minimise. Then it sets A to be A - c(dJ/dA) for a learning rate constant c. This means that at the top of a hollow, you move down the steep sides rapidly. As things shallow out towards the minimum, the steps get increasingly smaller. Awesome. (If you think of a derivative as the slope at a point, you can see this, as well as why the algorithm always moves towards the lowest point.)

3. Next week is going to be a toss up between machine learning videos and reading papers on things like Kalman filtering. Both are interesting and a little zombie-ish in that they tend to steal my brains.

4. I think students might be anti-zombies, since Statistical Physics, Quantum Mechanics and Partial Differential equations somehow have similar effects. Considering how many things are like that, it must be me, right? They can't all be zombie subjects.

5. Despite a bit of grumbling, this is totally what I signed up for and it's really great. Now I just need to get my brain into gear so I can stop confusing scalar products with scalar multiplication, which, despite the names, are not the same thing at all. Oops! I blame the zombies.

Friday Five

1. I made substantial progress in sorting out the direction of my honours project this week. It's really nice to have something worthwhile to direct my energy at, instead of worritting about admin. And the admin is slowly diminishing. Hurrah!

2. We played Settlers of Catan for the first time (except for one of the group) tonight. It was pretty awesome. I suspect some of the appeal is just in the newness of the system, but there's quite a bit of scope. I really enjoyed playing a strategy game that doesn't require attacking people. (Although the cutting off of other people's roads can get surprisingly intense.)

3. I think board games like Catan can be considered kind of nerdy, but do you know what would be even nerdier? Getting really frustrated that nine gets rolled more often than seven, which is not what the maths says should happen. Not that anyone I know did this. And it certainly didn't cause more upset than pretty much anything else in the whole game. Because we're not that nerdy. Oh, no!

4. My lectures start on Monday, except they don't, which is confusing. Depending on electives, we can end up with whole days free for project work (if you're disciplined) and other things (probably regardless). I don't have a timetable for my elective yet, so my actual first lecture is currently set for Wednesday. I'm finding that kind of weird.

5. The varsity notices today included a FameLab flyer. Now I'm wondering if coming up with a three minute talky thing about physics for the general public (and videoing it or driving a fair bit to actually speak in front of people) constitutes unnecessary stress. I think it's probably worth a shot, because it seems like there should be more fun than complicated, if there's some of both.

Savo 'lass a lalaith.

Friday Five

1. It turns out that running around varsity trying to perform multitudinous administrative tasks is more tiring than sitting at home doing interesting projects. In consequence I'm going to borrow some things other people have said (as well as I remember them) to make five.

2. While discussing shapes of trees that are good to climb: "a melting candle, which is like a squid."

3. Talking (initially) about time zones:
"I always get my pluses and minuses mixed up."
"Always? What's three minus four?"
"Seven."
"And four minus three?"
"Seven."
"So subtraction commutes! Is addition distributive then?"
"Yes."
"And multiplication."
"Yes, it's normal."
"Wait, the integers aren't a ring then."
"Nope, they're a helix."

4. Trying to work out if I can take PDEs as an elective:
"The lectures aren't timetabled; the students and lecturers will negotiate the times."
"Clashes shouldn't be a problem then."
"Well, that depends on your negotiating skills."

5. "Can I quote you on that?"
"Yes. In or out of context."

Friday Five

1. I made a thing! A highly age-appropriate book bag that clearly indicates my new and august status as a postgraduate student of computational space physics. I'm kinda pleased that I managed to do it without an actual pattern and pretty much for free, since I found all the fabric in my mom's scrap box. (I'm totally enjoying this dependency thing while I have it.) And then I took an awkward photo with it.

2. I may or may not have taken a photo in the mirror, seen that the letters on the bag were reversed and panicked for a moment that I'd somehow left everything inside out. Then I flipped the photo and my brain was much happier. The End.

3. I sent my acceptance forms to the university this morning and I'm in the process of sorting out funding admin (and mostly being grateful that I have funding to which all the paperwork applies) and I'm going back to Maritzburg in less than a week and whoa, how did everything start happening again?

4. Part of me wants to squeeze another sewing project into the last few days before I go and part of me thinks I should make sure I remember handy things like Schrödinger's equation before starting Quantum Mechanics N (where N is an integer greater than 1, the exact value of which I'm not sure how to determine.) The part of me that wants to take advantage of WiFi and exotic foods like tomato sauce from a bottle while I still have them is probably going to win in the aftermath of the stalemate. Oh well.

5. I have this scheme about not over-committing this year, so that I can do fun projects even during semester. Also this scheme about maybe dropping one of the easier/less critical physics courses so I can pick  up Advanced Differential Equations from the Maths department. And a few other schemes which are probably definitely not all compatible. It's just as well I don't have to do everything, because I can't do everything. Now to remember that.

In honour of rereading The Lord of the Rings for the umpteenth time, may I sign off in Elvish (Sindarin, to be precise)? Thanks.

Savo 'lass a lalaith.
Have joy and laughter.