The Little Things

 That title was one of several that almost made it to this blog. The last few days have been filled with moments about which I really have wanted to write – and though each one in itself might not be enough for a full entry, all combined, they make a nice little montage of last week. Plus, like that, I can give them each the title they would have had, had they made it to full entry status.

Work for Lesser Minds, And the Ivory Tower of Mathematics

This week was the first one of our semester here in Germany. That means that after the weeks and weeks of feverishly studying for exams, the strange sad let-down that follows after the exam is over, and after the subsequent weeks of relaxing and visiting family, all of a sudden, I’m on that bus again, heading to the campus every morning.

I am one of those people who tends to work better within the confines of a schedule, so I’m not that upset about the semester starting again, but there are a few things that are intimidating me about this semester (see my other entry about TAing and writing a Bachelor’s thesis!). Also, another plan for this semester for me is to be more engaged in the math department – not just going to the lectures I’m supposed to attend, but also going to talks from visiting professors and seeing what other folks in that area are up to.

So, on Thursday, I went to my first colloquium given by a visiting professor from Smith College, no less. “A female mathematician from a liberal arts women’s college?”, I thought. I just had to go! It had been such a damn mathematical day, too. I had Projective Geometry starting at 8 in the morning, then worked on a Topology homework assignment for about three hours, then prepped my own Linear Algebra workshop for next Wednesday, and then had my “office hour” (I don’t have an office, but I’m available for students if they have math-y questions). In between I also had some food and plenty of coffee. And then it was 5 in the evening and I finally went to this colloquium.

Her talk was on an international quarterly called The Mathematical Intelligencer – which is very much unique. Not specific to one area of mathematics, the Intelligencer encourages experts in various fields to write about what is important and happening in their field – but to write it for other experts, not just ones in their field. (For people of high mathematical literacy, as she explained.) The Intelligencer also prints columns on things like the history of mathematics, looking at what was happening 50 or 100 years ago – and it even includes articles simply on the inherent beauty of certain mathematical concepts, such as space-filling curves (look here!), fractals, or other amazing constructions. They also print articles about math education –  a subject I care very strongly about.

However, this makes them a very strange quarterly. And from the perspective of their publisher, they aren’t doing well as a quarterly. How many times were they cited in mathematical papers in the last year? Not that many. How many new, young professors do they have writing for them? Also not many, since they all are worried that they need to print things in more traditional journals. So we have lots of metrics that don’t put the Intelligencer in the best light. But that doesn’t mean it’s not important. What do to? This was the main question the professor had for us and quite a lively discussion ensued, during which the following quote came up. I warn you, this quote contains the true epitome of mathematical and academic snobbery, from the heart of what I call the Ivory Tower of mathematics:

It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

G.H. Hardy, A Mathematician’s Apology

Oh, it’s quite a thing, that essay! It also contains such nuggets as: “Most people can do nothing at all well”. (I feel like I can just hear Saruman reading it. Okay, obviously in Christopher Lee’s voice.) A professor had brought the essay up to give some context to some of the critiques the Intelligencer has received within the mathematical community.

As soon as this quote came up, it was rebuffed by others. No one really admits to agreeing with that sentiment – and indeed, I think most do not. (Although some do.) At that point many things I have thought before were streaming through my mind:, about how well mathematics needs to be explained; how difficult and simultaneously crucial it is to be able to explain mathematics in prose, or hell, even poetry; to make it accessible and exciting and to make folks want to take part.. And as I heard some of the folks quoting Hardy and talking about the attitude within a lot of pure math circles, I remembered what I heard just a few days ago from a friend: “The trouble with exclusive communities is that they tend to die out over time.”

What was so very exciting is that I have had lots of thoughts about the teaching of mathematics, and about making it accessible – and I’ve held many a minor soap box lecture on this topic among my friends – but I’ve never really spoken to professors or graduate students about it or heard them speak on it – so to suddenly hear some of my own arguments coming from other people’s lips was so very exciting. And I spoke up, too. Sometimes it’s difficult to fathom doing anything except that which is expected of me in my classes, but I do think I might want to start being a bit more active in this whole field. Who knows. Maybe the local math department magazine needs another editor.

This is Why

This story comes right at the end of the one I just told. After the colloquium I was heading into town to meet up with some friends for Pub Quiz, our weekly tradition. And as I was in the bus, I was standing there, holding on to the rail to keep from falling over and all of a sudden, I felt like I had a very specific type of x-ray sense. I looked at my feet on the floor, shifting to keep me from falling over as the bus turned, and I felt like I could see through to the wheel and axles and mechanics of the whole bus – I saw signs flashing past on the road and thought about the machines that made them – my music came through my headphones and I saw the chords in my mind like graphs, the harmonies corresponding with beautiful visual symmetry. And I just thought – this is why I study math. Because the world is math. The language of the universe. Yes, I felt like a nerd – but I also felt like I was flying. I’ll take the one to have the other.

That Small Town Feel

At Pub Quiz, one of the waitresses who usually works Thursday nights came over to our table and was taking our order – and as she brought our food and drinks a bit later, she said to me, “Did you cut your hair?” – I was so surprised I couldn’t stop smiling! I’d been recognized, without ever realizing that I’d been noticed in the first place. And then the next morning, I went to the bouldering hall where I’ve been going climbing for the past several months – and the woman who checked me in said, “You DID cut your hair! I saw you in the bus yesterday but I wasn’t sure if it was you, so I didn’t say anything! It looks great!” I never realized . And it’s not that I think I’m incredibly important – or indeed at all important – to any of these people. But it just enhances the feeling of belonging in a place that is just so, so lovely.

"You're not doing it right!"

One of my favorite comedians for the past few years has been a woman named Maria Bamford. I'm not sure if I've written about her here before or if you already know who she is - but I highly recommend her. The kind of off-the-wall, makes-you-cringe-while-you-are-crying-from-laughter comedy of hers is, I think, simply brilliant. I've rarely seen something so original that not only makes me laugh so much that I can't breathe and also touches on subjects that so desperately need it.

One of my favorite sketches of hers is from a particular show, the 'Maria Bamford's One-Hour Homemade Christmas Stand-Up Special' (in which she is in fact sitting down on a couch with her two pugs). One of the main topics she discusses in her sketches is mental illness – something she's struggled with a lot and thinks deserves some more attention – even comedic attention! n this particular sketch, she discusses some of the woes of going to a therapist. This particular therapist of hers insists on getting Maria to follow her rather irrational worries to their rather crazy conclusions – just to prove a point, to make Maria 'face her fears'. For example, Maria says she is worried about making eye contact with people, so her therapist asks the following questions and Maria responds:

(Keep in mind, everyone, that she is doing both voices – and spectacularly so.)

"Maria, what would happen if you made eye contact with someone?"
--"I dunno, probably genocide 'em."
"And then what would happen?"
--"Uhm...I'd go to genocide jail."
"And then what would happen?"
--"Pff...probably genocide everyone in the jail."
"And then what would happen?"
--"...they'd have to find a super-strong jail..."
"And then what would happen?"
--"I DON'T KNOW- you're not doing it right!"

So, I have to write a bachelor's thesis this semester. I'm writing about a topic that is, at best, just barely barely within my grasp as far as understanding goes. Like, I can feel it brushing the tips of my fingers. But I have not grasped it yet. Not even close. I'm also going to be a teaching assistant for a course this semester -something I did and loved at Mills but am a little nervous about doing in Mainz.  Also I have normal classes to attend. Plus, you know, run-of-the-mill "what am I going to do with my life" thoughts. So, as might be expected, I sometimes catch myself freaking out and spiraling into paralysis about all the things I need to do. And sometimes, when I catch myself going into this, I have to ask myself the same questions – or just, that one particular question over and over.

"And then what would happen?"

And luckily, this merry-go-round of questions, me pestering myself about just what would happen if everything I feared happened–- it usually ends with me realizing that the paper is after all, just a paper – the T.A.-ing job just a semester-long job, and in fact, the classes are just classes and people fail classes and are okay -- and after all, I have a family and friends who would greet me with cookies and hugs no matter what happens. So, I suppose things will be alright. Now, I just need to get started!

P.S.: If you feel like seeing some of her stuff, check out this link right here.

All Shapes and Sizes

Let's try not to be so linear. We tend to think in a very Euclidean sense (and why shouldn't we?) when we think about measuring space and objects – and not only that, we also tend to think rather continuously, as opposed to discretely. However, measuring things can actually be done in a variety of ways. Let me explain what I mean.

First of all, I'm currently studying for a measure theory final, which might explain why any of these things are in my head in the first place.

What is measure theory anyway? Basically, a lot of measure theory deals with the measurement of objects – some of which we already how to measure. I can ask you to find the length of a line (or an interval, like [1,5]) or the area of a square or even the surface of a sphere (though I recently completely forgot the formula for exactly that calculation at a pub quiz a few weeks ago – quite embarrassing). If you've had some calculus, you also know how to measure the area under a curve by using an integral. And we also know how to calculate the volume of things like spheres, cubes, or other shapes.

As you might have noticed (though we don't always say it so directly) all of these measurements have an inherent dimension. 'Length' is always one-dimensional, 'area' two-dimensional etc.  Obviously. We just say 'length of a line' instead of saying 'the default one-dimensional measure of a line' because, since it is the default, we don't think that there could be other ways to measure such a thing. Measure theory looks at some of these other ways. But I'm getting a little ahead of myself.

I mentioned earlier that we also tend to think continuously as opposed to discretely. Things that are discrete are a little bit different. For example, if we consider the interval [0,1], which includes all numbers between zero and one, that's a continuous chunk of numbers. If you were to draw it, intuitively, you would not pick up your pencil or pen – you would just trace along a number line from zero to one, hitting all the elements in that interval. However, if we think about the set {0,1} (notation is very important in math – [0,1], (0,1) and {0,1} all mean different things!) – then, the only things in that set are the number zero and the number one, nothing in between. Two unconnected dots on a number line. A discrete set.

And what measure theory tries to do is to measure things like these sets. But imagine trying to use that intuitive 'length' notion to measure something that is discrete – something whose elements are separated by space, even if it's a very small amount of space. How does that even work? Does it even make sense to try to apply that definition? Not really.

We need a new idea of measurement.

So, that's some of the fun stuff we've been getting up to in the lecture this semester. If you'll let me use as a premise that we do have a tool (several, in fact) that can handle discrete inputs and measure them – then we can come back to the idea of dimension. What if you're trotting down a road in the mathematical world and you come upon a set Ω. Very startled, you want to know some things about it – its measure, for instance. But we know nothing about its contents. They could be related to a function or an algorithm. They could be points, vectors, or even  – gasp! – nxn-dimensional matrices. We really don't know much. So, how do we find out what dimension it has? 

What are some things that could go wrong here? I claim there are several ways to get the wrong impression. What if this set you happen to meet is actually just a kind little square, but you don't know that, and mistakenly, you try to measure it with a three-dimensional measure, like volume. What happens if you try to figure out the volume of a square? Well, you get zero. Just like if I tried to measure the length of a single point. If my object is n-dimensional and I try to measure it with a measure any bigger than n (in this example, n+1), then I get zero.

And what if I make a mistake the other way around. What if the set I encounter happens to actually be a cube and I try to calculate its area. I don't just mean the surface area – the surface is two-dimensional, that wouldn't give us any trouble. But the area of the entire cube? That would have to be infinite.

So, let's get back to that road in the mathematical world and back to Ω. You want to figure out what its measure is – but in order to do that accurately, you have to figure out what dimension it has.

I'm skating over a few technical details here, but basically, in one area of measure theory, we talk about something called the Hausdorff measure. (Hausdorff was, as you may have guessed, some old math guy. He actually did quite a lot of cool things.) The definition of the Hausdorff measure is pretty hairy – it looks a bit like this:

(If I have any math critics reading this, I realize this is the delta-approximative, s-dimensional Hausdorff measure – I thought it was the prettiest formula to show here. The actual formula for the Hausdorff measure hides all the details by taking the limit.)

And just like with our intuitive standard ways of measuring things – like length and area and volume – there are different versions of this measure in different dimensions. And there is also something called the Hausdorff dimension. The Hausdorff dimension of a set is simply the dimension that is 'correct' – which is to say, if I try to measure that set with a dimension that is higher than the Hausdorff dimension, I'll get zero for the measure (like measuring a square's volume) and if I measure it with one that is lower than the Hausdorff dimension, I get infinity (like the area of a cube). So, to figure out what dimension that set has that you see walking towards you on a lonely road, simply measure it with a few different dimensions and see where the jump occurs. That's it's Hausdorff dimension.

Many of you will say: "But when will I ever be walking down a lonely mathematical road? When will I ever need any of this?" My answer: "Yes. But... isn't it cool?"

Ponderings from the Internet Age

I'm not sure whether the thought I am thinking now is well formed enough for me to explain it, but I'm going to give it a try. I just sat down with a nice cup of jasmine tea and was about to do some proofreading for work when, as is so oft the case, I decided to briefly take a glance at my Facebook.

Now, I have had an off-and-on relationship with Facebook for years. I was one of the first people in my age group back in middle school to get a Facebook account, at a time when nearly all of the people on the site were in college -- but back then, I was taking a lot of dance classes and performances with the Allegheny College Dance Department, so many of my friends were that age. Then, when I did my year abroad in high school, it was a great way to keep in touch with folks, and to share parts of my experience with large groups of my friends or acquaintances at once. Then, after I got back, there was about a year in college when I simply deactivated my account, not liking the "timesuck" that it was.

But now, after this and that and oh so many awkward moments of "You don't have a Facebook? I guess I can email you, but I never check my email..." and simply wanting to see the pictures of my friends on vacation and the children of extended family - well, I'm back on it again. But I've noticed a new trend in my news feed of late (that is to say, the past year or so) that I find troubling.

First off, a few caveats. 1. The things I am about to list may be specific to those people I happen to be "friends" with on Facebook. 2. I may be extremely sensitive and pick up on things no one else would think were an issue. 3. Well, I'm sure there are more. I'm just going to tell you what I think anyway.

There seems to be a big wave of negativity these days. I don't just mean that bad things are happening in the world and people are upset about them, but rather there is a desire to post about things that make people upset, hoping to have their outrage validated by others. For example, there are often internet articles that are fads; they go viral and zoom around from one person to another over the course of a few days and get a lot of "buzz". Now, most mainstream "click me" articles, even if they're supposed to "make you cry" or assure you "you won't believe what happens next" -  well, they are frequently problematic. Whether it's racist, sexist, classist, whichever-ist - there are usually some problematic undertones. Sometimes they are obvious, sometimes you really have to dig for them -- and someone will. And I think there's a difference between commenting when someone else posts said article and saying (KINDLY) "I think this article has a few issues because...." and between posting that article (as many of my Facebook seem to acquaintances do) simply out of bile. Just so they can say "Take a look at this disgusting exhibit of the patriarchy" - or whichever the enemy du jour is.

I don't know why this bothers me so much - but I find that every time I read over my news feed, I end up unhappy. And I feel there's a difference between responding truthfully and critically to other people and the world, and bringing up something you are angry about merely out of spite, encouraging more anger, hoping for that validation... I just feel it multiplies. It makes me not want to look at Facebook anymore, but maybe that's not such a bad thing.

A few more caveats at the end - I am not advocating pretending everything is jolly and ignoring all the bad things in the world - absolutely not. Also, it's quite possible that after having attended an extremely liberal women's college in the Bay Area, I have an above average number of vocal, angry activists on my news feed.

If you are at all interested in a discussion of similar topics in the form of a podcast, I highly recommend going to this webpage and clicking on the podcast called 'Our Computers, Ourselves'.  It's a great listen - talks of technology and how we feel about it and what we do to it vs. what it does to us. Go for it. :)

Spring 2015

Here are a few pictures of the lovely spring week we've been having here - taken in downtown Mainz as well as the University's botanic garden.

Shadow of Habits Past

I made it through finals for this semester and through the orientation for a new part-time job I have for the next semester. Whew!

And recently, I've been thinking a lot about routines and habits. I've been thinking about the positives and the negatives of each. Habits can be so small and also so big. I mean, there's the habit of checking Facebook every morning or your email, or it could also be the "habit" or tradition of celebrating birthdays and the new year. (More about this thought in a later post!)

Routines and habits have a lot of good aspects. When I'm studying or have a project to work on, nothing makes me productive like a good schedule or routine. For me, that particular set of circumstances is a cup of a particular kind of tea, classical music, and the ritual of lighting a small candle on my desk (if I'm working at home). But then again, nothing makes me feel that distinct kind of hollowness inside like being in the rut of habits and feeling powerless to get out of them.

Just these past few days have introduced me to some habits that I thought were lost. There's that pesky old foe of nail-biting, which I have battled for years, but where it only takes the pressure of an exam or a particularly difficult piece of work to dismantle my resolve. But another habit surfaced that I hadn't witnessed in a while – but I still call it a habit because it is my reaction to a specific set of circumstances.

The circumstances: excitement/stress about an activity (frequently, but not always, travel) very early the next day, for which my presence is absolutely necessary. Now, this doesn't include early morning classes or things of that nature. It's more like transatlantic flights or, in this circumstance, picking up my sister from the airport! In these situations, I wake up at some ungodly hour, am thoroughly convinced that every clock in my apartment/room is showing the incorrect time, and proceed to try to begin that activity that is supposed to happen. This happened most memorably during my first month of Freshman year, when I was a newbie on the crew team and we had practice every day at 5 a.m. and on the eve of one particularly important practice (I believe choosing who would be able to row in an upcoming race) I attempted to go to practice at 2 in the morning (fully dressed in my workout clothes, etc.) and was only stopped by someone who lived in my hall who happened to be coming back from a party while I stumbled sleepily out of my room. She managed to convince me to go back to bed and I remembered nothing of the incident until our eyes met at dinner the next day and it all came rushing back.

Okay, so maybe that's more of a quirk than a habit – but it is a repeated set of behavior. Sometimes habits make us keep to our plans, make us productive and comfortable in our environment. But sometimes routines make us blind to everything that isn't in our sights for the day, or make us forget the individual importance of the parts of our routine – like how good that cup of coffee tastes, instead of just drinking it without thinking.

But every now and then, I feel like the wires in our heads just cross somehow and we get that breach of routine, the breaking of a pattern, and it's like a packet of potential energy gets released when something unexpected happens. Usually, it results in surprise (meeting your friend on the subway you always take to work in the morning, for example). But sometimes, when you accidentally mess up a routine, the only reaction is hilarity. Such as yesterday, when I came home from picking up Rachel from the airport, came into the apartment and put my keys down on the counter. We greeted C and made some tea, hung around and were about to go out for a walk later, and my keys were nowhere to be found, least of all on the small nail in the wall near the door where they generally hang. Since then, we have been through every coat pocket, every shoe (they sit under the coats), and every trash can. We've searched under the couch, desk, kitchen table, behind the oven – everywhere. We looked and looked and found nothing. Now today, while we were making an apple rhubarb crumble, C and I were discussing making copies of all my keys since they were nowhere to be found, and I reached up to grab an oven mitt from the small nail that protrudes from the side of our cupboard  – and lo and behold, there are my keys. The action of hanging the keys on a small nail in the vicinity of the front door was carried out, but it cracks me up. Putting phones in the refrigerator or losing your glasses while they are on your face – or pushing your "glasses" up your nose while you are, in fact, wearing contact lenses. We are so evolved, and yet sometimes, so thoughtless. Or maybe it's just me. But I don't think so.

Also, it's so lovely to have my sister here.

Walking across the campus.

As I mentioned in my last post, this is the "Lernphase". There are only a few courses offered at this University of 30,000 students that actually have exams during the first part of the semester. The vast majority just have a final exam or a final paper due during the semester break (it's a joke, of course, that it's called a break). But because attendance is not required in most lectures (seminars and other smaller courses, sure, but not most lectures), there's at least as many students on campus during the Lernphase if not more than in the regular semester, as all are making the pilgrimage to one of the several libraries or cafés on campus.

Everyone is in a haze of exams. Studying habits like constant tea consumption and the listening of dramatic instrumental music are contagious. Diagrams like this one are flying around Facebook:

And I'm part of the craziness. However, with only one final this time, I have a relatively calm few weeks ahead of me - just a bunch of algebra, which I'm alright with.

There are two non-exam-related things I wanted to mention today. First of all, as I got to campus today I worked for a while on the other side of the University from the math building (a more cozy library than the math one, and since I was only there for the atmosphere and not for the books, it didn't matter that there weren't any math books around). Then after lunch, I made the trek to the back of the campus and as I went, I heard snippets of different conversations, since I (for once) didn't have my headphones on:

In front of the building where most foreign language classes are held:
"Yeah, there's a lot of exchange students in that lecture..."
-
In front of the main library:
"Really? Sub-saharan? I thought that was..."
-
In the absolute center of campus near the music building:
"I have my first exam tomorrow..."

Then a trend starts:
-
In front of the main cafeteria, on the other side of which is the math building:
"Yeah, that's what I said - positiv-definit and symmetric..."
-
On the other side of that cafeteria:
"And we have to calculate Eigenvalues too, right?"
-
And finally, in the elevator of the math building.
"Of course it's obvious if you are considering it over the complex numbers. But as soon as you move to a more general ring, then...."

I just couldn't help grinning to myself. That last conversation was actually happening in English (the others I translated), with heavy non-German accents on either side (grad students, I'm assuming) and it went on to name a bunch more terms that I know vaguely from hear-say but have no real clue what they are mathematically, and just the fact that that kind of research is going on down the hall from where I'm prepping for my one little Algebra exam makes me so happy.

And finally, C and I have started a new project with our fantastic neighbor. We've decided to watch all the movies on the American Film Institute's Top 100 list. Actually, we decided to do this a while ago but we haven't managed to start until last weekend. Let me just say - 100 films is a lot of movies. A few I've seen on the list, but not all. We're starting at the bottom, so theoretically, they'll just get better and better. The list was apparently constructed based on criteria such as: awards won (i.e. Oscars or similar), popularity over time (including DVD/VHS sales as well as box office), critical recognition, historical significance, and cultural impact.

In any case, we began on Saturday night with Ben Hur, Film No. 100, and Toy Story (No. 99) on Monday. We decided to keep certain tallies with each of the films, though the same things might not be counted - for example, for Ben Hur we counted the number of beers drunk during the 3.5 hour spectacle (5) but for Toy Story, we counted cups of coffee (4). Ben Hur also got +3 Jesus points, since none of us expected to see Jesus because all we knew about the film was that there was a chariot race. I shall be sure to keep you posted about our progress there! We'll have to make hay while the sun shines, or rather watch films during our semester break, since if we watched only one every week it would take us at least a two years to get through all of this. We shall see!

Forgot to mention!

I realize that the article to which I will be linking in just a few sentences is already taking the internet and podcast discussions by storm, but I want to make sure that I also say a few words about it. I'm talking about the article "Not a Very P.C. Thing to Say" by Jonathan Chait. This article discusses a phenomenon that I frequently find hard to explain to folks who didn't go to a liberal women's college in the Bay Area. It's about the phenomenon of P.C. culture, particularly in academia in the US currently.

Please do read this article if you haven't already, but while you do, keep in mind one important thing: Chait is a white man (he says as much in the article). In addition, I have read several criticisms of the article as well, all mostly focusing on the lack of research into the claims Chait makes, instead covering ground mostly based on anecdotes that illustrate his point. Take all of this with a grain of salt, maybe a tasty grain of salt since it's the first time I've ever heard anything written about the phenomenon. My head has been reeling with arguments for and against the article ever since I read it and I'm about to Skype with a dear, dear friend and fellow Mills graduate tonight to talk about it some more. If you feel particularly flummoxed afterwards and want a little more discussion of it, I also encourage you to listen to a podcast from Slate.com about it. Slate (yes, notoriously liberal-slanted, bear this in mind as well as you listen) offers a great deal of interesting (and free) podcasts and the one to which I regularly listen is called the Political Gabfest. Last week's issue (the podcast title is "The 'Can You Buy a President for $889 Million?' Edition") has the three correspondents discussing three topics - the Koch brothers' enormous financial commitment to the 2016 election, the supreme court facing an upcoming decision on the death penalty as well as Chait's article. You can skip to the end to just hear the latter, but if you feel like giving the podcast a chance, I encourage you to listen to the whole thing. I've linked to the page where you can stream the podcast, or you can find it in iTunes. If you feel like pulling an Emily, put it on while you do the dishes and then forget that you are doing the dishes and stare into space while you listen. :)

If you have any thoughts about it and feel like sharing, please do.

So, February.

“It was a Tuesday in February. Many of my life's most awful moments have taken place on Tuesdays. And what is February if not the Tuesday of the year?” -Stephen Fry, in Moab is my Washpot

Okay, so don't get me wrong - nothing terrible has happened to me in February, but it is a Tuesday in February as I write, and I always have to think of that quote on such occasions.

No, so far, my February has been fairly reasonable. I have two more weeks (including this one) of classes and then the "Lernphase" (studying phase) begins before exams. As I have explained in earlier posts, the German university system (at least in Math) is based on one grade from the final exam, so it's around this time of the semester that a little ripple of panic goes through the lecture halls and study rooms as students realize that the are soon to be responsible for every lecture and piece of homework that has passed through their ears and eyes since the beginning of October. Due to a complicated set of circumstances induced from the switch of University systems, though I was in five courses this semester, I am only required to take one exam, and that's possibly in the very class that I feel most confident. So as I said, February's not been so bad.

We've been enjoying a mixture of Fall, Winter, and Spring weather here, including sudden flurries with the biggest snowflakes I've ever seen:

A ten minute flurry, photo taken just outside the Mainz train station.

 We've also had singing birds and falling leaves and sudden gifts like this one next to a Wiesbaden sidewalk:

The happiest leaf I have ever seen.

And now, my desk is properly set up for a preliminary stage of the Lernphase - pot of tea, candle burning, pencils, erasers, rulers and pens (Yes, rulers - I like my underlining to be quite straight). Better get to it while the tea's still hot.