Limbo

Hong Kong airport has free wireless. I'm hanging round, arrived from Munich, leaving later for Auckland. I'm excited about going home, and I'm exhausted.

I don't know how I'll feel when I get home. Germany, with its delightful and demanding system of mathematical education, has taught me how to work -- or at least, one way of working -- and it's this: you simply clear your life of distractions, until there's nothing else to do. I'm looking forward to being back home in a land where I bother cooking properly, going for runs, seeing movies and concerts and talks, listening to schoolchildren debate, and a hundred other things. But will I be able to learn as much maths as I did in the last few months? I don't know, and at the moment I honestly don't care.

Germany's taught me other things too. I'm better at organising things -- travelling, and bureaucratic niceties, and random encounters with friends. It's taught me some German, unsurprisingly. I still don't speak or read it very well, but I can understand when people talk to me, and I can survive. It's taught me things about myself, or possibly just made me realise things I already knew:

• I like having, or at least find it easier to have, isolated friendships rather than big clumps of them.
• I like home comforts. Real travelling, where one wanders the desert with a passport and spare undies, I'd find difficult.
• I'm easily amused. I find most things interesting. (I think this is a good thing.)
  

It's been wonderful, and I'm grateful I went. But -- I think -- I'm also going to be grateful when I'm home.

The time has come

I've been saying goodbye to people.

I went cycling west the 20 km to the Rhine with my maths friend Clemens. It was a gloriously sunny day that looked like New Zealand February rather than German; the countryside was yellowed and very slightly rolling, with fields and apple orchards and vinyards and a couple of typically delicious villages. We hit the Rhine at the smallish old town of Breisach, puffed up a hill to its cathedral, and ate lunch looking out across the river to France. Then we lurched and bumped the steep cobblestoned way down.

I met my neighbour and fellow exchange student Alex on the trams, and elicited within moments both that she was sad to see me go and that she'd happily take all my furniture off my hands. So we spent much of the next day or so transferring carpet and curtains and chest of drawers and kitchen utensils down the stairs of my building and up the elevator of hers. My room's nearly emptied now.

I went out for lunch with my floormate Max. I went out for ice cream with my exchange student friends Alyssa and Vanessa. I ate cake with Elliot.

Emily I'm meeting for dinner now; her job is to keep me from dejection on my last night in Freiburg.

Through Bavaria

I went to Nuremberg for my second pilgrimage of the week. Five months was enough to enamour me with the German railway system, and I decided I simply had to trek to the Railway Museum in Nuremberg to see its baby pictures. I carpooled from Berlin to Nuremberg and crashed with a girl there, spending the evening chatting about organic groceries and quirky housekeeping neuroses. The next morning I went to see the former Nazi rally grounds south of the city -- they're enormous, they had a pastel mock-Colosseum, and lots of efficient historical plaques and photos, and were almost totally empty. Then I wandered the old town, which was impressive, because Nuremberg's the former semi-official capital of the Holy Roman Empire, and looks the part.

And then I went to the Railway Museum, and spent an hour in bliss. The best was the Hanover King Ernst August's early reaction: "I don't want any railways in the country! I don't want every cobbler and tailor to be able to travel as fast as I can!"

Later, I travelled south, and stayed some nights with Elisabeth and Hans, retired and living near Munich, random secondhand acquaintances turned friends. (And kind, and generous -- and I should mention that I've been continually amazed for the last few months at the welcomes I've received from friends of friends, and friends of friends of friends, all over Europe.) We spent two days rolling through Munich by subway reading train ads to "Learn Wall Street English Fast!", and speeding over southern Bavaria by car, on autobahn through yellowy moor past tiny red-roofed villages with the Alps always in the distance.

We fulfilled another dear romantic once-thwarted wish of mine, and visited a medieval abbey, possibly once complete with long, damp passages, narrow cells and ruined chapel, all however now nicely kept up. There were (photocopies of) books on display dating from the ninth-century founding, faded twelfth-century reddish floorstones in the chapel, and a map somewhere showing the sizeable 20 km or so chunk of Bavaria south of Munich that used to belong to the abbey. It was impressive.

And we took a train up the highest mountain in Germany, saw a little Bavarian palace and a big Bavarian palace, watched the mechanical Munich town square clock strike, and visited the former concentration camp at Dachau, where political opponents of the Nazis and other inconvenient people were kept until 1945. This was also impressive, in a way -- huge and bleak. I read about horrible things in the museum until my mind was numb, and felt lost and couldn't form any coherent impression. As we left, I kept seeing the faces from the photographs on the people in the parking lot.

I heard about fifties Dachau from Hans, who went to school there. The place had disintegrated during the war; early on there was essentially no school building, and classes were held in local pubs.

I left on Sunday morning, and now I'm back in Freiburg, running errands and packing.

The world smiles with you

I eat my words. Or possibly my hat. Berlin's a much nicer place, in sunshine, than I gave it credit for. It has lots of glassy shiny colourful buildings, and it's that rare thing, a big city that's managed to create open spaces without having them look as if they were bulldozed clear yesterday in preparation for a parking lot to be built tomorrow. I slept in late this morning, then went undirectedly wandering, and saw all this and more.

It also has lots of neo-classical Victorian official buildings with svelte nymph-columns and Latin inscriptions along the lines of "Erected by King Frederick to the honour of Apollo and the Nine Muses". Berlin's the capital of the former Kingdom of Prussia, which meandered along in backwater obscurity for hundreds of years before becoming big in the eighteenth century. So its building burst was late compared to most German cities. Most oldey-buildings are erbaut 17- or 18-something, by the time when mischmasches of ancient religions were retro or appropriately regal rather than blasphemous.

Everywhere in Berlin -- particularly the centre of the former East Berlin -- is under construction. Some of the construction defies belief -- they want to build a new main-Berlin-Palace! To mimic the glorious old eighteenth-century one! Which was bulldozed by the DDR fifty years ago while perfectly intact to make space for some sort of government building, which was itself bulldozed a few years ago to erase all memory of the deed! And they're repainting the inside of the Marienkirche (the oldest still-used church in Berlin)! but when I was there today, the whitewashed-but-unpainted walls were being rehung with pictures! I don't understand much, but the sheer energy's nice.

I forgot to mention that yesterday I went to inspect our men in Berlin, otherwise known as the New Zealand Embassy. It's a carpeted office on the third floor of an office building somewhere south of the centre. It's staffed largely by enthusiastic Germans, it has two pictures of Helen Clark on the wall, it has multi-month-old North and Souths and a view out to Checkpoint Charlie. And I went to see the archaeological remnants of Troy, dug up in Turkey a hundred years ago by a German businessman and smuggled to Berlin before their discovery was announced. This was clearly either the source of, or a successful application of, the principle that possession is the fastest nine-tenths of the law. Troy consisted mostly of clay pots, it seems. Now we know what was in Helen's dowry.

To Nuremberg this afternoon, and Munich tomorrow.

Ich bin kein Berliner

In accordance with my newly-ratified policy on foreign travel, I checked in at the youth hostel on arrival in Göttingen, then headed out into the nearby woods to go hiking.

The newly-ratified policy has developed gradually over the last few months, starting when I realised on one of my weekend trips that despite my continuing Europe-seeing excitement, I was starting to have gorgeous-old-building-ennui. It's just not possible to keep finding everything wonderful for six straight months, especially when you're as ignorant of historical and technical details as I am. So, to properly enjoy my last week of travels, I've issued to myself the following proclamation:

• first, that I'm here to enjoy myself, and needn't Make The Most Of Every Moment or see uncongenial sights -- so I can go on pretty but insignificant backhill hikes, curl up early at night with a novel, and avoid Museums of Natural History without guilt
  
• second, that I'm here to educate myself -- so I can follow what Lonely Planet calls "the lemming routine" without shame, and go on tours or take the audioguide rather than always relying on imagination or intuition or independent thought

When I go home, I promise I'll never again sneer at tourists who are clueless or ignorant or can't speak the language. Really, perhaps it's best to go travelling to a place of which you know absolutely nothing beforehand. At any rate your net gain in knowledge is certainly thereby maximised.

Anway, the policy's working well. The hills in Göttingen are very nice -- gently sloping, and with mini-farms on the nearer edges rented by eco-keen city-slickers -- and the old earth fortifications round the town, where I wandered later that night, are pretty cool. I got home, and went to bed, and slept for a very long time.


The next day, yesterday, I took the train to Berlin, where I've been since. It's exciting; it really does feel like a big city; but it feels drab enough that I wouldn't want to live here. Perhaps it's inevitable for a town famous for wars and workaholic princes, totalitarianism and techno. I don't know. Maybe it's just the winter rain.

It's very good for me, though. I've seen a dozen classes of German schoolchildren, presumably on educational trips to the capital. I feel exactly the same. And really, after five months of bluffing my way through conversations with Germans on history and politics (which happen often, because Germans really like talking about history and politics), I'm grateful for an excuse to find out things like what the German parliament does, how so many Jews ended up in Germany, why the Berlin Wall was put up in the first place. I'm particularly ignorant of the Cold War -- I suspect, somehow, that this is standard for New Zealanders my age -- and it's been nice filling in whole "here be dragons" segments of my mental historical map.


My mathematical tour of Europe continues. In Göttingen -- whose main, perhaps only, claim to fame is as the home of a university that for a long time housed all the best mathematicians in Europe -- I saw a plaque to Riemann's former lodgements, in a boxy apartment overhanging a cut-price clothing store. Later I made a little pilgrimage out to the grave of Carl Friedrich Gauss. In Berlin this afternoon, in a spectacular Hohenzollern palace, I saw a picture of Bessel. He was labelled as an astronomer, and carrying a clock. Clearly the assumption that mathematicians are "er, those guys that deal with numbers" is of very long standing.

For a final news-tidbit -- I, too, have a hat! It was sourced on the weekend in a secondhand shop in the Freiburg old town. It's tweed and buckety, a little silly-looking . . . but of course nonetheless rather fetching.

Good cop, bad cop

Before I left for Germany, somebody warned me that the professors would be distant and scary and never speak a word. I heard the story of Albert Einstein, who made a lifelong enemy of his one by addressing him as "Herr Weber" rather than "Herr Professor Weber". And to some extent it's true. But there's a hidden counterbalance, to which I shall pay tribute today:

every course comes equipped with a tutor.

And this is not the nonentity sort of tutor that I myself have been in Auckland, who from the grand heights of one-semester-further-along-the-mathematical-spectrum gets paid small wages to grade calculus exercises and deflect some of the silly questions away from the lecturers.

Nah, these are gold-hearted black-belted mathematical ninjas.In their other incarnation as students, they're usually occupied writing a thesis for their Diplom or Doktorat. They know their stuff, and they're beautiful, beautiful people. They call us "du" rather than "Sie". They organise field trips, they take whole classes out to end-of-semester afternoon teas. Their eyes fill with tears when there's something we don't understand.

(In case you ever read this, dear representation theory tutor, maybe I'll just mention that . . . well, the exam I wrote this morning . . . er . . . well, it'd benefit from your characteristic generosity.)

Silly questions

I'm a little tired. Stupid things I've asked today:

[to a tutor] "How many pages should we write on the exam?"

[to a guy from China] "So, do you have any brothers or sisters?"

[to myself] "Hey, where am I?" (Germany? Reeeally?)


(later, addendum) Oh, and I got told my first German dirty joke! Though, characteristically I guess, it was neither particularly dirty nor much of a joke. Details on request.

Pullbacks and frozen peas

I've spent this weekend studying for a differential geometry exam.

Differential geometry's the mathematical equivalent of the TV dinner. It was invented one afternoon by some disillusioned engineer or physicist, who got bored doing her 47th messy multivariable calculus computation of the week, and told herself that there had to be a better way of doing things. So she rewrote all the calculus into lots and lots of meaningless abstract symbols, and spent ten years doing every conceivable convoluted computation on the meaningless symbols for once and for all. Then she settled down happily on the couch, knowing that for the rest of her life she'd only have to defrost her pre-computed meaningless-symbol solutions and not actually cook new ones herself.

(There is a problem with this approach, though. The engineer realised it a few years later, prematurely aged and trying unsuccessfully one day to get her mental microwave to do its reheating stuff. All this high-falutin' time-saving mathematical technology is kind of complicated, and once you forget how the meaningless symbols work, you're back to the chopping board again.)

Anyway, my exam tomorrow is on the convoluted mechanics of differential geometry -- the 129 pages just before the engineer sits down to her first TV dinner -- and may well be both difficult and dull. But every computation I do tomorrow is another 388 that no one else will ever have to. And for this, you should all be very grateful.

Conversations IV (Special Waitangi Day Edition)

The day before yesterday, I started musing: on Wednesday it would be February 6, and I would be all aloooooone. And a little bit homesick, and yet what could I do? I couldn't have a cricket match, because no one here knew how to play. I couldn't eat pavlova, because it'd start arguments with Australians. I couldn't throw mud at the Prime Minister, because it wouldn't be very nice.

And then inspiration came.

And so I collected together some floormates, and we made chocolate fish.


They were pink and sweet and very sticky. As confectionery went, there was certainly room for improvement -- but as exotica, they were excellent. I left some at home, took some to uni, and fielded questions.

Hans: Does one wish someone a "Happy Waitangi Day"? "Merry"? "Congratulations on the occasion of"?

My floormate Lena: What are your exciting New Zealand Day traditions?

My classmate Clemens: What are we celebrating? The signing of a humane and revolutionarily civilised colonisation treaty that was later repeatedly broken? why, how very interesting.

My classmate Leander: What are your national songs like? Can you sing one? Please?

Unidentified model theory classmate: So, how do you spell this . . . er . . . Vy-tay-ni?

Emily: What is this pink thing you're giving me made of? Oh -- marshmallow, really? . . . I'd never have guessed.

It was fun while it lasted.


But now the chocolate fish are all gone.

Rosenmontag

"What's the German word for 'parade'?" I asked my floormate Max.


"Parade," he replied.

Witch Sabbath

The guy across the aisle from me last night on the train was wearing a bear costume. It was brown, and fuzzy all over; he was eating a pretzel, and his friend next to him was just wearing normal army-corps uniform. 'Twould have felt surreal, except that the train was packed full, and half the other people on it were dressed as eighteenth-century sailors or fleecy goggly-eyed pink things. It was Hexensabbat ("Witch-Sabbath"), and we were heading into the Black Forest to celebrate.

"Carnival"'s got quite a precise meaning in Germany: it's the few weeks and days just before Lent starts when people do silly things in an organised fashion to let off steam before the forty days of boredom. It's highly regional; round here it's called "Fasnacht" and I'm told the highlight in Freiburg is a parade tomorrow which I'll be making certain to attend. Twenty minutes away by train, in 20,000-inhabitant Waldkirch, where I was yesterday, people spend the nicht of February 2 costumed and drinking and burning a straw witch in the town square. German Wikipedia claims it's the local version of a Celtic festival called Imbolc. (The American version is Groundhog Day.)

At any rate, it sure beat Halloween. Well, New Zealand Halloween, at least. It was nice to see a crowd-together-and-make-merry festival that attracted equal parts families, elderly couples and packs of drunk students.

I missed the witch-burning, but the place was still crowded by the time I got there. I felt a little left out costumeless, though I've no idea where they all came from (does every German have a Carnival costume somewhere in his wardrobe for annual use?) It seemed to be a matter of pride to be part of as big a group as possible of people all costumed identically -- a group of friends would all be dressed as bumblebees, or New York policemen, or the aforementioned fleecy goggle-eyed pink things (the girls in that group also had yellow miniskirts with bright blue flowers). Default costume (that adopted by the middle-aged men) was devil ears and a pitchfork.

Admittedly, lots of that pulsing carnival atmosphere was thanks to German power-pop boomboxed all through the square. Every booze-selling stall, of course, had a vested interest in making people feel as festive as possible while in its immediate vicinity, and so each one was blasting its own noise; sometimes in between two stalls I'd get the weird wavy effect of hearing both. Sample track: this song, known as "Reiß die Hütte Ab" ("Smash Down the Cabin"), which I've since discovered has a cult following of German teenagers who post montages of collapsing structures (Galloping Gertie, the World Trade Centre) to the internet with it as soundtrack.

I came home and learned about Weyl groups for a while before going to bed. I've been speed-learning Lie theory for a little while, and though it's very beautiful I'm frustrated by the need to go faster and faster. This is the course I decided to take out of optimism, despite being woefully underprepared; the unwritten soundtrack of this blog of exciting European adventures has been Lie theory steadily and mercilessly leaving me behind. (That, and me mixing my metaphors, of course.) To catch up, I've read fifty pages of the stuff in the last week. Progress sounds great, until you realise that I've another eighty, plus other material, to cover before the exam ("Klausur") Friday after this.

Wish me luck! And, sometime when I get home, ask me to tell you about maximal tori. You'll like them.