Old And New (Summer in Berlin III)

There are many good places to contemplate the clashes between old and new in Berlin, and one of them is the area along the Spree near the U-Bahn station Schlesisches Tor. This is where the world ended for people living in West-Berlin while the city was divided. Now one can walk across the bridges and admire the construction circus on both sides.

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Herbert George Wells might have thought that his phantasies have come true. When they are done with all this, will it looks like this?

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And will we get more playful little sculptures like the Molecule Man by Jonathan Borofsky?

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There is some obvious resistance. It feels like the perfection of a finished building is stifling the creativity.
Who wouldn’t want to defend the octagonal brick building below?

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Do we really want to lose all this?

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My taste is more for blending old and new and let them coexist.

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The Door Was Open (Summer in Berlin II)

I like architecture, or, to be precise, certain states of buildings. Ruins are fascinating, but even more so construction sites. Both are usually off limits (as are the corresponding states of human affairs, death and conception, unless you are involved one way or the other). So I am often forced to trespass a little.

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In this case, as you can see, the door was open, and I just couldn’t resist.

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Views like the one above make it instantly clear that we are not on a generic construction site. Somebody with taste has been designing this, and whoever is doing the construction work, is doing an excellent job by creating crystal clear previews of what’s to come.

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Wondrous tools are on display too, just for me. I can only guess their purpose by looking at the ornamented concrete slabs. Everything is purposeful, even the occasional leftover tile.

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What fascinates be most at places like these is the tension between the clarity of the present and the vagueness of an undefined future.

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Bridges, Rivers, and Walls

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Locals rarely go on sightseeing tours for tourists, which contributes to their different perception of things. For instance, living behind a wall is nothing strange when you grow up with it. When I (re)visited Berlin in 2015 for a conference, the conference excursion was a boat trip on the Spree.

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While I knew that Berlin has that river, it had never become part of my perception of Berlin as a city. The Spree does nothing for Berlin like the Seine does for Paris, the Thames for London, or the Danube for Budapest or Vienna, the Rhine for Cologne (to name a few). It is small, largely canalized, and so much covered with bridges that one can easily overlook it.

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These bridges connect the northern with the southern part of the city. Some of them are old, other modern. In contrast, the Spree connects the eastern with the western part, and it did so even when there was a wall. Rivers are hard to stop, like time. Crossing from west to east on this little river was a special moment for me.

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Above is the cathedral, to its left the (re-)construction of the Berlin City Palace, replacing the East German Palast der Republic, that it turn had replaced the original Baroque City Palace in 1950.

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Buildings serve many purposes, but they also mark and preserve time — for a while. The architects should never forget that time will flow on, inevitably.

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When helplessly confronted with historic events, we can be little more than a witness. But we should not underestimate this task: Being a fair witness is both difficult and necessary. This is a skill that should be taught in school.


I have always admired the trees as such witnesses, and maybe the tree can become the name of a pattern that describes the functions of a witness.

The tree images of this are also a personal memory, because they were taken near the event horizon when my own personal history becomes imageless because I don’t have photos from earlier years.


So all these images are from the early 80s, taken near Bonn. I had moved there from (West) Berlin and was beginning to learn that one can spend one’s free time exploring the surroundings.

The shivering tree below is not out of focus. It is a double exposure, with the second image being a long time exposure to motion blur the leaves in the wind.


The Projective Plane

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This image (a variation of which I used for many years as a desktop background) is a close-up of the large sculpture below that can be seen at the Mathematical Research Institute in Oberwolfach.

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It is a model of the projective plane, a construct that simultaneously extends the Euclidean plane and describes the set of lines through a fixed point in space.
The simplest way to make your own model is via the tetrahemihexahedron,


a polyhedron that seems to take every other triangle from the octahedron and twelve right isosceles triangles to close the gaps left by the removed four equilateral triangles. That, however, is not the only way to look at it. These right isosceles triangles fit together to form three squares that intersect at the center of the former octahedron, in what is called a triple point.

So we truly have a polyhedron with four equilateral triangles and three squares as faces which can be unfolded like so


where arrows and equal letters indicate to glue. From this flattened version we recognize a (topological disk) with opposite points identified, which is yet another abstract model of the projective plane. The tetrahemihexahedron suffers not only under the triple point at the center, but also under six pinch point singularities at the vertices. Maybe it was this model that made Hilbert think that an immersion of the projective plane into Euclidean space was impossible, and having his student Werner Boy work on a proof. Instead, Boy came up in 1901 with an ingenious construction of such an immersion, which has an elegant connection to minimal surfaces.


Robert Kusner constructed a minimal immersion of the thrice punctured projective plane into space, with three planar ends, that you can see above. Applying an inversion, as suggested by Robert Bryant, produces images that are very close to what Boy had in mind.

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This explicit parametrization served as the basis for the model in Oberwolfach.

Wesseling at Night

Wesseling is a scenic industrial area about half way between Bonn and Cologne.

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The mostly functional architecture and perpetual construction is rarely as amusing as in the picture above. The time to be there is at night, when the architecture of metal and concrete is replaced by a much more fundamental architecture of light and shadow.

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In the nearby harbor, large cranes appear to be asleep. Are they dreaming of electric sheep, too?

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And then there are the relics from the past, like this barely recognizable wind mill.

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With increasing darkness, the film grain takes over. Is this how Georges Seurat would have painted this? I wish.

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Double Exposures

The Sieg is a tributary of the Rhine northeast of Bonn. The word Sieg means victory in German, but (wikipedia tells me) the name of the stream derives from the celtic word sikkere (fast stream), as does the name of the French Seine via the related Sequana. This must be flattering for the Sieg.

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A slightly elevated dam next to it gives the opportunity to extended bike rides. I have written before about the area here, and I am revisiting the place now, as I revisited it often in the 1990s.

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The dam also provides an excellent perspective on the trees

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or the power line masts.

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The picture above was made using a now obsolete technique, the double exposure. I used to experiment with it quite a bit,
but gave up on it when doing this became more or less trivial in Photoshop. It is disappointing to see how the creative possibilities of multiple exposures have become reduced to automatized photo stacking with the goal to increase the dynamic range or depth of field.

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