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Our imposed order of things gives time a direction, and all else seems to follow. But sometimes, this direction is lost, and certainty fails.

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Uncertainty means chance. Do we belong here?

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 It seems there is another inward structure, more punctual, more concentrated, like a poem, that manifests itself when the flow of time is obstructed.

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What Paul Celan wrote in his Meridian Speech  — the poem claims itself at its own limits, it calls and retrieves itself from Not-anymore to Still-there to persist without pause — becomes visible in extreme natural environments. In both there is seeking beyond these limits, words there, branches here.

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Is it possible to teach time to walk, to slide sideways?

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Poems, like dreams, are landmarks that help us to cross what we perceive as darkness of the mind. What seems wild and empty becomes possibility.

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Or do we prefer to sleep in our dreams?

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Memory and Imagination

Lick Creek Trail near Paoli is an 8 mile loop for hikers, mountain bikes, and horses. The southern branch is more scenic (and more muddy). Trail markers help to find the way…


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On a late fall day, much of it looks like everything else in Southern Indiana.

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Some trees offer perspective.

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But there is a highlight. Half way, there is a cemetery, which is all that’s left from a 19th century African-American settlement.

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There are just a few tombstones and wooden crosses, and it is hard to imagine what life was like for them.

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It’s a solemn place, reminding us that what others want to remember of us is more important than what we want to be remembered for.

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Praise of the Shadow

… and in the pale light of the shadow we put together a house.

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I usually prefer the early hours for taking pictures, and avoid the harsh daylight.

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But light allows to objectify darkness, in form of a shadow.

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Sometimes it’s not so much the question what creates the shadow on the wall, but what lies behind the wall.

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The interior (if there is one) should allow cause and effect to coexist.

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Light and shadow are folded together.

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But the gate is always open, which means that ultimately we have to leave again.

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In Chains (Cooperation Games IV)

We continue with translucent trominoes, add an I-tromino, and select those that have two translucent squares (gray with red border). There are just three of them, shown below to the left. To the right are how they can be attached to each other, overlapping in exactly one translucent square:

Linkages 01

What we don’t allow today is that two trominoes overlap in both of their translucent squares, as below.

Nono 01

This has the interesting consequence that the gray squares will necessarily form chains or loops, which adds useful structure. A tiling is complete if all translucent squares are covered twice. We will then have twice as many translucent squares visible than colored squared.

Chains 01

Below is an example of a complete tiling of a 6×6 board.

6x6 01

And here is our game: Each player gets the same number of tiles. For two players, is a good choice, say three of each kind. The players take turns placing one tile on the table so that 

  1. each new tile links with a previous tile
  2. two linked tiles are of different color

Alternatively, a player can also remove the last played tile and replace it by another one.

The goal is to create a complete closed chain when all tiles are used up. 

Below is an example of a successfully closed loop of length 8.

Loop 01

Lugentes Campi (Twin Swamps III)

I promised to return, and this time I came early enough, before sunrise, when the colors are still carried by darkness.

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The cypress trees with their robe like stems seem to have been waiting like limp angels.

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The boardwalk had suffered damage, and the railing had been removed for repair, providing unobstructed views for the adventurous.

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Are there swamp-green and cypress-red? 

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With colors like these, this place belongs elsewhere. 

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Thorn Bush (Wenckheim II)

… and then the thorn and the acacia bushes and a thousand kinds of weeds grew over them, and the Thorn Bush came into being — that’s what the residents of the city called it — as if it were some kind of proper neighborhood or something, …


The first chapter of László Krasznahorkai’s novel Wenckheim takes place in Thorn Bush, a derelict district, where the Professor has taken residence, amidst huge piles of styrofoam panels, … that if anyone should come along and pester him, let all and sundry be warned that whomever dared to approach his hut in the Thorn Bush would be shot immediately and without warning.


This chapter is about rejection — the city rejects one of its districts, the Professor reality, his daughter him as her father.


… but even then its reputation was enhanced not by the spice of juicy murders or sexual violence, but rather by being a no-man’s-land in the city, completely left to its own fate, an ownerless piece of land, needed by no one, and about which no one even debated who might need it and how it might be used; it was, accordingly, completely left to itself, …



Places like this give an opportunity for isolation, but the Professors needs go further:

…the basic problem with a window wasn’t a question of this or that practical advantage or disadvantage, but it was the principle of the window that troubled him greatly, and namely not because a window could be gazed into, but because that window could always be gazed out of — …


In the book, this leads to violent escalation, maybe because nobody truly can lock oneself in.


Has every city its own Thorn Bush, has everybody a place of self-abandonment?


The pictures here are from my city, taken 10 years ago, near a defunct railroad line that had been converted into a trail. Since then this area has changed, but this is another story.



Different Trails (North VII)

My fourth stop on the excursion north was not planned, I just happened to pass by Cicott Park, named in honor of the owner of a trading post at this place, and decided to have a look.

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According to the small brochure, the area has never been plowed, and is therefore relatively intact. The two trails lead through a lush forest and give access to the Wabash.

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It was here that I met the first other hiker that day, a local. Despite there being absolutely nobody around, he was wearing a mask, and excused himself right away: He was recovering from chemotherapy and needed to protect his immune system. 

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He also said he was essentially the only person using these trails, and that the town was considering to abandon the place.

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For him, walking here almost daily had acquired a special meaning.

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The park also has a Potawatomi Trail of Death historical marker, in memory of the forced removal of over 800 members of the Potawatomi Nation.

Some trails you can only walk once.

Translucent Trominoes (Cooperation Games III)

After the translucent dominoes let’s continue with translucent L-trominoes. There are eight of them:



Trominoes 01

The dark-gray one is a solid tromino, which will be a bit lonely, as it can’t connect to the others.

As before, a region is tiled if either any square is covered by a solid color or by two translucent (gray) squares.

Tromino mono

Let’s begin with a simple puzzle. Above you see an attempt to tile the 5×5 square just with copies of the purple tromino. This is of course impossible, because each purple tromino tiles 1+1/2+1/2 = 2 squares, so it can only tile regions with an even number of squares. Clearly one can tile a 2×2 square, and thus every 2n x 2n square. But can you also tile a say 6×6 square so that the tiles are all connected?


Above is an example how you can tile a 5×5 square with two copies of each tromino except the orange and the dark gray one. There is an abundance of tiling problems like this. You usually begin by determining for a set of tiles the total number of squares they will cover, counting each gray piece as 1/2. As all eight trominoes cover 18 full squares, two sets of them should be enough to cover a 6×6 square. One solution is shown below.

6x6 01

This suggests the following cooperative game for two players: Each gets a set of the seven trominoes without the dark gray one, shuffled, and stacked face up. They take turns by either

— placing the top tromino from their stack on a 6×6 board so that the newly placed tromino connects to the network of previously placed trominoes; or
— removing a previously placed tromino from the board so that the network remains connected, and placing it under their pile.

The goal is to leave at the end just room for the two dark gray trominoes. The example above is therefore no solution, because the network has too many components.


Warning (Wenckheim I)

because there could be no mistakes…


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When almost four years ago I congratulated You-Know-Who to his inauguration, I used pictures from the spectacular Tulip Trestle near Solesbury as an illustration. These days I have revisited this place, and it is as imposing as four years ago.

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In the last two years, I have found in László Krasznahorkai’s books consolation for the state of the world and the human soul, and with the imminent beginning of winter, I decided to read his latest (and maybe last) novel Baron Wenckheim’s Homecoming.

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I also decided to do this as an excruciatingly slow read, and I will occasionally accompany my postings here with quotes from this book.

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It begins with a brief chapter titled Warning, where an orchestra conductor imposes himself on his orchestra:

… because there’s only one method of performance here which can be executed in only one way, and the harmonization of those two elements will be decided by me …

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But there is not just pure control, there also is purpose…

… because in reality what awaited them now was suffering, bitter, exhausting, and torturous work, when shortly (as the one single accomplishment of their cooperation, albeit an involuntary one), they would insert into Creation that for which they had been summoned; …

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This brief chapter sums up  how a human being usurps what is not his to claim.

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… because I am the one who, by the truth of God, is simply waiting for all of this to be over.

Translucent Dominoes (Cooperation Games II)

Most tiling problems are strictly segregational, i.e. the tiles are not allowed to overlap. To change this, let’s consider tiles that are partially translucent, so that in order to really tile a part of the plane, one needs to cover it multiple times.

This is the first in a series of posts about partially translucent polyominoes, and we begin with translucent dominoes, of which there are three:

Dominoes 01

The purple one is a regular (non-translucent) domino, and to the right you can see my feeble attempt to tile a 4×4 square of which two opposite squares have been removed (This is of course a very classical puzzle). The other two dominoes have one or two translucent squares, which are shown as gray. This translucency means that in order to properly tile a square with dominoes, we need to cover it either with a single solid color square, or with two translucent (gray) squares, i.e. the gray portions of two dominoes must overlap, like so: Connect 01

The left image shows two fully translucent dominoes that overlap in the middle square, while the left and right squares are still only covered once. By counting the small connector squares you can see how many gray squares sit on top of each other. In the middle is a chain of four dominoes, all gray tiles are doubled. And to the right we have covered the middle gray square three times, which is illegal for now. 

If we use only the blue singly translucent domino to tile, two of them need to overlap to form a single classical (segregational) tromino, so tiling with these dominoes alone is equivalent to tiling with trominoes.

Domino tromino 01

You should try to tile the 4×4 square (with two opposite corners removed as above) with copies of either the singly or the doubly  translucent domino. In both cases, this is impossible (and impossible for larger squares as well, again with opposite corners removed. You will enjoy finding the arguments). Tiling becomes easier when you allow both types of translucent tiles, a simple solution to the 4×4 puzzle is shown below to the right. The left figure gives a hint what limitations you face when you try to tile with the doubly translucent domino alone.

Domino4x4 01

As a cooperative game, start with a 6×6 square, mark a few tiles as forbidden, and then take turns to place translucent dominoes on the board with the goal to tile the board completely, following the translucency rule.