The summer and fall 1992 I spent my free time reading Marcel Proust’s À la recherche du temps perdu. That winter, I took the photos from this page, and revisiting them now is just one of several connections to Proust’s recherche.
Of course these were shot with film, and in black and white, appropriate for season and theme. The location is the Sieg valley near Bonn in Germany, where I happened to come across a temporarily abandoned construction site.
The time was literally frozen. Everything had been more or less orderly put ready to use.
This was a curious sight. Unless our daily business is construction, we usually do not see these things, because they are buried or covered up, in the hope that they will function even in hiding.
Not esthetics, but pure purpose is the reason for these designs. And because I did and do not know the actual purpose of them, they became for me the abstraction, the idea of purpose itself.
This tilting away from reality towards abstraction has always fascinated me, already (at least) 23 years ago.
Of course this landscape has a sky. But everything in Zion National Park is so big that our human field of vision is somehow inappropriate.
It’s like the romantic landscapes of Caspar David Friedrich about which Heinrich von Kleist wrote that when looking at them, he felt like his eyelids had been cut away.
After a while, the desire to grab the widest lens in the bag and to take it all in fades. We become aware of a landscapes full of still lives.
This is in particular true for the eastern part of the park, where most hikes are off trail (and which is much less overcrowded).
Navigating this terrain is fun, but one needs to be careful. What appears easily accessible can well end in sheer cliffs.
Also, be sure to pack plenty of water. The trees will thank you for it.
This, like most of my images from the Sphere series, has its origin in a 2-dimensional picture. Below you see (parts of) the Apollonian Gasket. Descartes and Princess Elisabeth of the Palatinate discussed formulas for a fourth circle tangent to four other circles, more than 300 years circle packings became fashionable.
Now, in three dimensions, begin by placing four equally sized spheres into a larger sphere, like so:
Start filling the empty space with more spheres, each as large as possible to touch four other spheres.
and going, and going.
Finally, when you are tired and done, remove the first four largest spheres to create an empty space, and have a peek inside. What you see might look like the image at the top.
This continues the series of revisits of my year 1993/94 in California. Very rarely a landscape hits you with such a force that you are left with a lifelong desire to return.
The climb from Lake Tahoe to Mount Tamrac is through lush forests, and nothing but the weathered trees prepares you for the view from the top.
In the front is Gilmore lake where we had memorable swim, and further behind follow Susie Lake, and, already in the granite, almost invisibly, Lake Aloha.
The landscape gradually transitions from impossibly green vegetation to gray and white granite rocks. The latter
are, however, not steep and ragged but smooth and almost plane. No invitation to hell could be sweeter.
The heroes of this place are the trees. They struggle on without almost no soil, withstand harsh weather, and even when long dead, remain.
On the other hand, there are some really spooky places in Spring Mills State Park, provided you come at the right time.
Next to Bronson cave, some fallen trees have assembled themselves in something that looks at an ancient rune.
In the fall and just before sun rise, the Spring Mills lake offers the best lake shore views in Indiana.
For whatever reason, there is always a healthy tree among the many dead.
Even without the fog, the scenery is awe inspiring.
For whatever reason, there is always a photogenic dead tree among the healthy. I wonder what ghost stories the settlers told here.
Every culture seems to have their own metaphorical approach to the mill.
I grew up in Germany. My early childhood was infused with fairy tails featuring increasingly spooky millers,
and of course with Wilhem Busch’s famous Max and Moritz, where the two brothers, after plenty of enjoyable mischief, end up ⎯ no, I won’t tell.
One of my favorite childhood books is Ottfried Preußler’s Krabat (translated as The Satanic Mill), that tells the story of a young boy becoming the apprentice of a miller, who, incidentally, also teaches sorcery. For a price. Check also out Karel Zeman’s animated movie with the same title.
And of course there is Schubert’s some cycle Die schöne Müllerin.
Other cultures have a very different take on mills, like the Spanish with Don Quixote by Cervantes.
Seeing a truly impressive historic water mill (from 1817) in Spring Mills State Park made me feel quite at home.
It is still in use and produces cornmeal.
There are essentially two very symmetric ways to tile the plane with circles. One can use the square tiling, of the more efficient hexagonal tiling.
In space, we can use the cubical tiling to generalize the square tiling, as I did in Spheres V. But one can do better. On one hand, one can put down one layer of spheres in the square tiling pattern, but shift the next layer diagonally to save space:
Or, one can put down one layer of spheres using the hexagonal pattern, and again shift the next layer so that its spheres fit snugly into the gaps left by the spheres of the first layer, like so:
I hope it surprises you like it did surprise me that these two approaches lead, in fact, to the same packing of spheres:
The mystery behind this is the geometry of the cuboctahedron, an Archimedean solid with both triangular and square faces:
Putting highly reflective dark blue spheres in such an arrangement within an off white cage cuboctahedral shell results in today’s sphere theme image: