## Friday, September 29, 2006

### Øieblikket part 4

I finally made it to Copenhagen, and I didn’t see a single Kierkegaard-related building, statue, historical marker, or souvenir. I simply wasn’t ready for this trip.

Of course, that begs the question of why I’m in Denmark at all. There’s a dynamics conference going on at an out-of-the-way guest house belonging to one of the universities here. The topics are currents and bifurcation loci—respectively, those terms refer to very nice, but very general topological/geometric objects and to sets that describe how systems with parameters change as the parameters change. I can’t possibly convey the notion of currents in this medium, but I can at least give an example of bifurcation: say you have a system of one-way paths in the plane, with two distinguished points, one of which absorbs paths (called a sink), and one of which emits paths (called a source), and somehow you’re varying the distance between these two points. One can imagine reducing the distance to zero, so that the points coalesce—maybe then all the paths just flow straight through (the source and sink annihilate each other), or maybe they start orbiting a single point (the source and sink together form a center). The change in the number and kinds of distinguished points is called a bifurcation.

This isn’t really my area of mathematics, at all. I know a bit about currents, from geometric studies, but I’ve never put in time studying bifurcation of dynamical systems. Yet I’m actually excited to be here. I’m looking forward to learning a lot. It’s not a large or a long conference; it just runs two and a half days, and there are perhaps thirty participants. There are dynamical aspects of the areas I do usually study, but I’ve always considered myself a geometer rather than a dynamicist. This is a good chance to learn about other interesting fields—areas in which Dr. Hubbard is very active.

We’ve gotten through the first day of the conference, but I’ve said about all I’m going to for now on that topic. Yesterday Sarah and I had the day to spend wandering about Copenhagen. Mostly we split up and indulged our respective interests. I quickly ended up at the Christiansborg Palace, home of the royal, legislative, and judicial branches of government (the foundation stone reads “Rex, Lex, Jus”—I may get a picture of it posted in the next few days). It is the fifth castle or palace to stand on that site. The first was built in 1167 by Bishop Absalon, and you can go underneath to see ruins from the walls of Bishop Absalon’s castle and the second castle. I like ruins; it’s amazing to see the way buildings were laid out, how homes were shaped, how wells and drainage systems were placed in the community, and all that. I once saw in Geneva a baptismal font that had been used since the 8th century or so; you could see how its size had decreased as practice moved from adult baptism to infant baptism. At the Christiansborg Palace, you could see where walls from the first castle had fallen and been used as foundations for later generations of buildings.

After the palace, I wandered down to the waterfront. I ended up in the Royal Library, rather unintentially. On the ground floor is a café called Øieblikket. I was seriously tempted to buy some coffee there, just because it was the only thing remotely resembling a Kierkegaard connection that I found, but it was very expensive. Instead I wandered the stacks (as much as I could; they were mostly closed except to folk with research purposes). At 1 pm, music began playing throughout the main hall: it was a mixture of massive chords, tinkling bells, and light drumming (I think it was supposed to be a drum; it sounded like claves at first). It lasted three or four minutes and was marvelously relaxing.

Next I starting walking back to the train station, thinking I’d find a cheap cup of coffee and an internet connection there. Instead I was sidetracked by a sign indicating the National Museum was having a special exhibit on the life and times of Tycho Brahe. There were period furniture and costumes, including a full suit of armor. They also had reproductions of some beautiful plates from a 1603 book on astronomy, and instruments like those Brahe used (his tools have apparently been lost). I just browsed for a bit and moved on.

Copenhagen is a neat city. It seems like the bicycles almost match the cars in number. The buildings are a mixture of grand old architecture and chic modern flair. Next time I go, however, I’ll be ready for my Kierkegaard pilgrimage.