Königssee

This past Samstag I went to Berchtesgaden, the city, which is just outside of the Berchtesgadener National Park, located in the Alps in the southeast corner of Germany near Salzburg. It was a four hour train ride to Berchtesgaden, then a short bus up to Königssee, a deep glacial lake. Finally, a boat ride across the lake to St Bartholomä, which is where I'm standing below.

The snow on the ground was fresh - last week was cold and the Alps got their first snowfall. I'm sure the snow in the mountains was not fresh. In fact, in the notch in the mountains behind me, is a glacier, which you can't see.  The peak behind me to my left is Watzmann (2713 m), and the glacier is called the Eiskapelle. But we went for a hike up that valley - didn't get to the glacier, but saw some pretty scenery. "We" is Jack and I. Jack is another engineering professor in the same fellowship program as I am. He's teaching in the Mechanical Engineering department, and is from Taiwan.

It was very nice to be hiking on hills, and the smell in the air was wonderful - trees, snow.  It reminded me quite a bit of Glacier National Park. As far as I could tell from the German brochures, much of the geology was similar, too.

The only bad part was the long train ride, which, on the way there was made even longer. Just outside of Munich the train stopped because of some blockage on the track ahead. We had to go back to Munich and wait for the next train - two hours later. So a 4-hour trip took 6 hours. But, the did give everyone a coupon for a free coffee and "Butterbreze", which is a pretzel sliced in half and spread with lots of butter. Pretty decadent.

Munich impressions (3)

Tipping is not as prevalent as it is in the US. And when tipping does occur, it is at lower levels and is much more relaxed. For example, if you eat a meal at a restaurant, you would tip only 1-2 EUR rather than a fixed percentage (and a rather high percentage) of the bill, as in the US. Also, the way you tip is more casual. This evening I ate with a friend and the bill (which was simply written on a piece of paper) was 13,80 EUR. I gave the waitress a 50 EUR note and said "fünfzehn" (fifteen) indicating that I wanted to pay 15 EUR (i.e., a 1,20 EUR tip). She gave me back 35 EUR in change. It's all very above board, rather than the somewhat secretive way we tip in the US, leaving an amount on the table  and then leaving.

They put mayonnaise on French Fries (or Pommes). Just like John Travolta learned in Pulp Fiction. And there are many things that are 'finger foods' in the US, but here they use a fork and knife. French Fries, for example. With mayonnaise. And burritos. In order to not stick our like a sore thumb, I have to eat my burritos with a fork and knife. It's important for me to watch people around me to make sure I'm not committing a blunder.

One thing that's not so different. As I rode my bike around central Munich today, I saw quite a few people who I assume are homeless. I guess it's a problem everywhere.

Around Munich

On Saturday, I went for a bike ride around Munich, led by my knowledgeable host. We visited the famous Chinese Tower in the Englischer Garten, and of course, saw the surfers on the stationary wave in the tributary of the Isar river.

Of course, we had to stop at the Biergarten near the tower. The weather is so beautiful - unusually warm for October, that it's almost sacrilegious to not stop. I had a Schweinschnitzel and pommes, with, of course, ein Maß.

Then we moved on and found a piece of the Berlin wall by the US Consulate building...

... and a piece of the Universität München (now called LMU, or the Ludwig Maximilian University) whose wall still showed signs of the fighting in WWII. Or so my host claimed.

All in all, a pleasant day.

Pullach im Isartal

This is my current residence, and it means something like "Pullach-on-Isar" because it's situated next to the Isar river. 'Tal' means valley, so more correctly it would be "Pullach on the Isar valley". Here's a nice shot of the Isar river.

If you look closely, you can see the Alps in the distance (the picture is taken toward the south). Also if you look closely, the river is on the left, and there's a canal (a diverted part of the river) on the right. The canal appears to be used to run some power stations. In between these two is a raised berm with a running path on it. That's one of the places where I (and many others) run.

And here is my house. Well, it's Karl's house.  We'll, 1/4 of it is Karl's house. It's a 'quadplex' in which four different 'apartments' have been made. We are in the front left.

I actually live in the Großhesselohe section of Pullach. Großhesselohe and Pullach used to be two separate cities, but recently they merged and have one Mayor. In addition, it's a separate city, not a part of Munich. This meant that to get my 'residence permit', I had to go to the office specifically for the outlying regions, not for those who wish to be a resident in Munich. But the good news is that I think I'm done with the German bureaucracy....for now.

Munich impressions (2)

As in my last post, here are a few things that have struck me about the differences between Germany and the US.

Pizza: what looks like a pepperoni pizza really has salami on it (the slices are larger than pepperoni usually is in the US). If you ask for a 'pepperoni pizza' you get a pizza with chopped up pepperoncinis. So you must beware!

Children travel on their own much more than in the US. For example, on the S-bahn and U-bahn trains, there are many young students going to school. Many look like they're 10 years old, or even less. Even though it's perfectly safe, it's not something that you would see any more in the US. Perhaps 30 years ago, but not any more.

When someone sneezes in public, there is no "God Bless You" or "Gesundheit" response. That just doesn't seem to be the custom here.

There is no prohibition on "open containers" in public. In fact, people drink on the S-bahn trains, especially the youth heading to Oktoberfest. Since the beer is expensive at "the Wiesn", they drink beforehand. And there are breweries everywhere. There's a small brewery and restaurant about a 5-minute walk from where I live (it's in the "platz" right next to the train station) so tonight my host Karl gave me a 2-L jug and told me to go to the brewery and get it filled. Which I did, for about 7,50 EUR. And I walked back. Now this jug just has a cork in it, so in the US it would be considered an open container, but no problem in Munich, where beer is king. Anyway, so we each had some beer with our dinner of homemade buffalo wings. Did I mention that Karl is a lover of spicy American food?

Addendum: The train drivers went on strike last night, but only for 9 hours. So, while the morning commute was disrupted (my S-bahn train into Munich was 20 minutes late) nothing serious happened. The worker-manager relationship seems to be different here, too, although I don't know enough about it to say in what way.

Munich impressions

Now that I've been here almost two weeks (!!!) I seem to have some time to write about it. I've got lots of pictures saved up (Oktoberfest and all) but I have noticed several things that are distinctly different than in the US. Not better or worse, just different, and sometimes surprisingly different. So here goes, a random list.

People are very nice. If you're introduced to them, almost all speak English, and if they don't, they'll still try (since they know more English than I know German). But, walking by someone on the street, there is almost never a greeting. I understand this in the big city, but in the tiny suburb of Pullach, where there's not too many people that you pass while walking, it is uncommon to even make eye contact.

At the end of a lecture - or class - the students show their appreciation by knocking on the tables. Instead of clapping. Not that my students usually clap at the end of each class. But here they do. I kind of like it. Now, in one of my classes, most of the students are international, so they have to learn this custom, too.

You get a lot of coins in change. This is because there are 5 € bills, but 2 € and 1 € coins. Of course, there are also 0,50 and 0,20 and 0,10 and 0,05 and 0,01 'euro cent' coins. So basically my pockets are always bulging with coins after I go into a store.

I mentioned this yesterday, that Germans love bank transfers. I'm going to become an expert in online banking in German! And another funny thing about banks. My bank is Kreissparkasse. There is another bank, with exactly the same logo (a red S with a dot over it) called Stadtsparkasse. You might think they are the same bank, but they're not. They are related, I've been told, and I can withdraw money out of either ATM system with no fees. But they're not the same.

Finally, I had Leberkäsesemmel for lunch. Leberkäse literally means 'liver' and 'cheese', but it is a meat similar to bologna that has neither liver nor cheese. In fact only products called 'Bavarian Leberkäse' are allowed to not have liver in them. All others, such as 'Stuttgarte Leberkäse', must have at least 5% liver. Go figure. And the semmel is the roll, on which you also put some sweet mustard, which I did. Very delicious.

Das Deutsche Museum

I went with my friend Wayne to the Deutsches Museum yesterday. It is a huge museum that has exhibits ranging from 'the history of calculators' to 'musical instruments'. We happened to be in the musical instrument room when a docent was playing several of the instruments, one of which was a harpsichord from the 1500s!  It sounded very cool.

My favorite spot (so far) was the roof, on which there was a sundial garden. There were about 20 different sundials, even one on the ground (look for the figure 8 - it's called an 'analemma').

However, one of the neatest was a polyhedron sundial, with a different sundial on each face.

I plan to go back because I became an annual member of the museum. Well...kind of. I haven't paid yet. In Germany, their preferred method of payment is the bank transfer. So, while you could pay cash for the 8,50 € single entry fee, you could not pay cash for the 52 € annual membership. I filled out a form, they gave me a temporary membership card, and I promised to transfer 52 € into their bank account. Very different from the U.S., where they wouldn't let you set foot in the place until you had paid.

Such are the lessons that I'm learning.

Fibonacci numbers

You've all heard of Fibonacci numbers, written down in 1202 by Leonardo of Pisa when investigating the number of rabbits in a group after successive generations. He assumed that in each cycle (about a month), each adult rabbit A would have one baby rabbit B. Also, each baby rabbit would turn into an adult rabbit. The transformations at each generation therefore are A→AB and B→A. So if we start off with one baby rabbit, the population in successive generations becomes

B
A
AB
ABA
ABAAB
ABAABABA
ABAABABAABAAB
ABAABABAABAABABAABABA
ABAABABAABAABABAABABAABAABABAABAAB
...

and the number of rabbits is the Fibonacci sequence, 1 1 2 3 5 8 13 21 34..., where each number is the sum of the preceding two numbers.

There are tons of interesting mathematical properties related to this sequence, my favorite of which is the golden ratio Φ. That is, if you take the ratio of successive entries in the sequence, you get better and better approximations to Φ as you use larger and larger entries in the Fibonacci sequence. For example, 3/2 = 1.5, 5/3 = 1.66666..., 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.61538. As you can see, these are getting closer and closer to Φ = 1.6180339887499..., which is the golden ration (or golden mean). A neat property of this number is if you take its inverse, it is 0.6180339887499..., which is the same number minus 1. For you math geeks, this simply means that Φ is the solution to the quadratic equation Φ² - Φ - 1 = 0.

But that's not the property of the Fibonacci sequence that I want to talk about. I want to show how it is related to quasicrystals, a topic that I've discussed recently. First, notice that in the AB sequences above, each sequence is simply the concatenation of the preceding two sequences. This is something you might not expect, since each is generated by making the replacements A→AB and B→A from the previous sequence, and, in principle, is not related to the sequence before that.

If you look at all the, say, four-letter sequences in the last line, you might expect that there would be equal numbers of all the 2⁴ = 16 possible sequences:

AAAA
AAAB
AABA
AABB
ABAA
ABAB
ABBA
ABBB
BAAA
BAAB
BABA
BABB
BBAA
BBAB
BBBA
BBBB

However, if you look, you will only find the following 5 sequences

1. ABAA
2. BAAB
3. AABA
4. ABAB
5. BABA

You see this in the following way. For example, there are never more than two As in a row. The reason is that there is no way, from the two rules at the top (A→AB and B→A), to create three As in a row.