December 2020 – The Inner Frame

Watch Out For – (Wenckheim VIII)

It’s not that I don’t understand why a person has to die, but rather, I don’t understand why a person has to live, Baron Béla Wenckheim pondered,…

So begins this short chapter in Baron Wenckheim’s Homecoming. It is a chapter about disruptions.

First, there is the disruption of space by time:

…where the train station used to be, there still stood a train station; […] — it’s just that these were not the same train stations, main roads, hospitals, castles, or chateaus, they just happened to stand in exactly the same spot where the old ones used to be; they weren’t the old ones, they were new, they were different, they were strange, and they — now that the scales had fallen from his eyes — they left him completely cold,…

How one experiences the return to one’s birth place after years of exile can vary. I have felt Wenckheim’s coldness, but also the opposite, and yet another, rather strange sensation of duplicity in which the exile becomes a second layer over the older home, so that one has the feeling to be at two different places at the same time.

So Wenckheim plots his own death, insists to be taken to the forest, follows the rails to the train station from where he wants to return by train, has carefully memorized the train schedule, and looks for a suitable curve that would make it impossible for the train to stop in time.

While waling between he tracks and waiting and pondering his question from the beginning, Wenckheim is disrupted by a flock of deer – their unquestioned existence proves his own question meaningless. But maybe too late.

Golden blüht der Baum …

Color in winter is a difficult affair. I don’t know how they do it, but the Washington Park Arboretum in Seattle has a special winter section where the trees show off the most wondrous color palettes.

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Above, the leafless small tree with mossy branches seems to partition the colorful background.

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Or here, the delicately branched marvels beam in some shade of green, bushes provide a foreground with contrasting colors, while larger trees stay in the back.

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High point in complexity of the composition was this Japanese inspired garden where two rust colored trees touch upon a pond. The saturation is surprisingly well balanced by the yellow bush.

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What keeps baffling me is the intricate play between structure and color. It feels like the color is the soil in which the abstract shapes can grow.

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Then there are the solo performers, single trees effortlessly covering the ground with leaves while still decently wearing their costume.

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Some leaves just seem to be perpetually falling.

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Infinite Difficulties (Wenckheim VII)

The Professor, international expert on mosses, is back at Thornbush, and busy with thought-immunization exercises.

… not a single moment can be left to the brain to find some pretext in order to escape from the questioning gaze, namely, the brain is looking at itself, and this looking must be comprised of sheer mistrust …

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Facing deathly revenge from the bikers, he acquires an insane amount of gasoline and stages his own death in the flames, re-creating a Burning Thornbush. We are led to expect that he will escape.

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While busy with preparations, the Professor ponders the meaning of life and death in a long monologue (speaking to his dog Little Mutt), beginning with questioning the infinite, and accusing the mathematician Georg Cantor for thinking the infinite is real, which the professor refutes, based on the lack of empirical evidence:

…namely, no one has ever wished genuinely to confront the deeply problematic nature of empirical verification as such, because whoever did this went mad…

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The denial of the infinite leads the Professor further — thinking itself becomes suspect:

…the mere appearance of a thought hauntingly reminds us that the way a person thinks is but one concept of infinity,…

Existence beyond being extant in time and space is questioned:

…there’s only that which takes place…

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The denial of the infinite and with it anything transcendent however causes a problem: our universal fear of being finite, that is, our fear of death:

… what we must deal with here is, namely, Cantor and his god — because if we’re dealing with this, then at least we’re dealing with something, namely we’re dealing with fear, and we have to deal with that if Cantor and his god are interesting — and they are interesting — and that’s why, at this point, we must refocus our attention on this, as fear is what defines human existence, …

The Professor’s monologue culminates in what I would call his theology of fear:

… fear, if we regard it as a creationary force, a general power center, from where the gods evaporate, and finally God emerges, and yes, the God of Cantor too, because the fear of the cessation of existence is a force field which we can’t even measure, …

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Strikingly, the Professor comes to the realization that fearing death and loving to live are identical:

… the fear that is within us and the joy of life that is within us, well, these two things are one and the same, two sides of one fact, because we are a web of events that seeks to sustain one thing and one thing only, namely continuity, …

So he can, simultaneously, affirm life as a process that aims to constitute infinity, and deny the existence of anything infinite, including God.

The simplest infinite set in mathematics, the set of natural numbers, is postulated to have the property that for every number there is a successor. Within mathematics, it is not stated what it means that such a set exists — but most of mathematics is based on the firm belief that there always is a number that’s by one bigger than the previous one, that there always is one more step, just as in life.

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Has the poor Professor not understood yet that if you have lived you don’t fear death?

Thank You, Dear Trail

It’s time to thank my trusted companion, the Pate Hollows Trail, which has kept me mentally and physically healthy this remarkable year.

Today, on Christmas day, we had a bit of powdery snow, providing just the right amount of contrast to what makes the trail, the ground.

Thanks for the leaves, the ferns, the moss and the mushrooms.

Thanks also for the water and the roots.

A loop trail like this has no other purpose than to be walked.

Which teaches us an important lesson, maybe the only one: There always is one more step to take.

Light

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Darkness is for us humans not just the lack of light. We fear it as an abstraction, as a general absence, as death.

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And so we have to come to adore light as that what eradicates darkness, that makes us see, and allows us to live.

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Nothing more seems to celebrate light better than illuminated glass sculptures like the ones here, by Dale Chihuly.

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Having lost its purpose to illuminate something else, light has become the object, an abstraction of its purpose.

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Objects like these don’t exist in nature. It is, as if we have finally left reality behind and can experience light as pure form.

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It is hard to return.

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Consistency

Two Lakes Trail is a 13 mile loop in Southern Indiana that took me 6 hours to hike today.

I met not a single soul on the entire trail, leaving plenty of time to think about place, time, and consistency. Now that winter is almost here, colors are not as vibrant anymore, and I like the distance this creates. It allows a strong focus.

I also like the concept of a loop, as a design pattern, a way to return to oneself, remaining consistent, but still transformed.

We are familiar with transformation through time (I can still feel my sore muscles). The transformation through space is more subtle, it requires to inhabit a place, and the only way to do this is through consistency.

Grow, Contact, and Trinity (Cooperation Games VII)

Let’s bring back a bit of color. Today we get a trio of games, played with similar cards and similar mechanics. The simplest version I call Grow, and it’s a game for two players One and Two, to be played with triangular cards on a triangular board. The pieces are called (top to bottom) root, branch, and twig.

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We will need a single root-piece, 12 twigs for player One, and 12 branches for player Two. We begin by placing the root somewhere on the triangular board. Then we take turns by adding twigs and branches so that adjacent edges match and we have a connected growing tree.

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There are two more rules: We don’t allow loops, and the branches must branch away from the root. The layout above on the left is still correct, but in the middle we illegally have closed a loop, and on the right we closed a loop and are also branching in the wrong direction. Triangle game 01

Above are two solutions. The players need to collaborate in order to fill the entire board. Can we find a solution for every position of the root-tile? Can we solve this on a triangle with edge length 7 instead of 5?

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Contact uses tiles with two colors, and adds leaf tiles. We begin by placing two socially distanced roots, one of each color, inside a regular hexagon of edge length 6, like so, for instance.

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Again this game is played with two players, Orange and Green, but this time a player controls all pieces of the same color. There is only one root tile of each color, and sufficiently many leaves, twigs, and branches. The goal is to tile the entire hexagon by taking turns, so that all twigs and branches end in leaves, as shown below. Note in particular that no loose ends of twigs or branches are allowed on the boundary of the hexagon.

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However, this solution has a flaw: We have used 27 orange and only 20 green tiles. Can we do it with the same number of tiles for Orange and Green?

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Finally, Trinity is played with pieces in three colors, and two chiral leaf tiles. Again, each of the three players controls one color. This time, multiple roots are allowed, but watch out that different trees of the same color don’t grow together.

At the beginning, each player places one root tile on the board, again socially distanced. Then we take turns either growing our own tree, placing a leaf tile that fits at least our own tree, or placing a root for a new tree. Below are two solutions on a hexagon of edge length 6. Enjoy.

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He Will Arrive, Because He Said So (Wenckheim VI)

What could possibly go wrong? Baron Wenckheim has returned, and his main desire is to meet the love of his youth, who is eagerly expecting him.

In Photography, we typically expect what’s important to be in focus.

Krasznahorkai’s prose, however, has a shallow depth of field, and often the blurry part is where we should look.

Right at his arrival at the train station, Baron Wenckheim walks right beside her, himself a victim of this looking elsewhere: … he just went beside her like a sleepwalker,…

When Wenckheim finally meets Marika (or Marietta, as he remembers her name), the misfocus becomes extreme: He doesn’t grasp that she has aged, too, and takes her for her mother or aunt: …yes, he thought there is a resemblance there, he wouldn’t say that Marietta had completely inherited the traits of this lady, still, though, there were in her face and in her bearing a few minor characteristics that connected them,…

Dialogue between the two becomes impossible, but Wenckheim’s more and more devastating monologue is not without effect: …and she wasn’t trembling, although she knew that soon she would be, but for the time being she was still in that state in which a person simultaneously grasps and refutes what has just happened,…

In photography, the object in front of the lens can be so much out of focus that it becomes part of the optical system through which everything else is perceived. Focus becomes secondary.

Upset about Marika’s absence, Wenckheim talks to her about his deep love to her, and she listens with growing desperation. — he saw no other way than to speak to her, in the most sincere way possible, of his most sacred feelings;…

… and he reached into the inner pocket of his jacket and pulled out the photograph from an envelope, he handed it to her saying, please have a look, Madame, and see how beautiful she is, and Marika bowed her head and she looked at the photograph, she looked and she looked, then she couldn’t bear to look anymore, …

Rácsos Linzer (Wenckheim V)

…because this Linzer torte was always his favorite,
and that’s why she was taking it to him,
three baking pans’ worth…

Rácsos Linzer is Hungarian for Linzer Tart, which used to be my least favorite cake. I remember it came with a chewy jam underneath a deliberate looking crisscross pattern of dough.

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My sequential reading diary of László Krasznahorkai’s novel Baron Wenckheim’s Homecoming requires an intercession to discuss the significance of this tart in the book. It is all over.

…she could make such a Linzer torte that no one else ever could, certainly not me, to be sure, but it was grand, they ate it up, …

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Of course I had to make my own.The recipes ask for hazelnuts or almonds. I am a subversive person. So I went for black walnuts. Most highly recommended. In the meantime, Krasznahorkai uses that little tart for metaphysical speculations:

— it all depends on whose intuition we’re talking about, are we talking about the intuition of Auntie Ibolyka or the intuition of the Buddha, because it’s not the same, not at all — if, on the one hand we feel like having a piece of Linzer torte, or, on the other, we want to step off the edge of the precipice straight into a freefall —

The recipes suggest red currant or raspberry jam. I didn’t have access to the former, but spiced up the latter with a few jalapeño peppers. Don’t the Hungarians like it spicy? I also quarantined a quarter and spread plum mus on it instead (spiced up with cardamom, in addition to cloves and cinnamon).

…the big problem is with this attack, presumably with this attack there’s the possibility, namely the high probability that in our great hurry we’ll end up burning that Linzer torte, …

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No, I set a timer. Thank you very much.

As you can see, I replaced the crisscross pattern by something else which was meant to look like a tessellation of the hyperbolic plane. János Bolyai would have been confused. Computer graphics is easier.

In the appendix, Krasznahorkai lists under UTILIZED MATERIALS — DESTROYED: Auntie Ibolyka’s Linzer torte with two baking dishes …

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So be it.

Ninety-Six (Collaboration Games VI)

Today Alan Schoen is celebrating his 96th birthday (below you can see him at the youthful age of 93),

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and this gives me the opportunity to congratulate him with a puzzle. Its mechanics is motivated by the genus 3 Riemann surface which is the double cover branched over the vertices of a cube, the Riemann surface that underlies the Schwarz P surface, the Diamond surface, and Alan’s Gyroid, his best known discovery. Not quite incidentally, this surface has 96 symmetries. Today’s puzzle is also motivated by Alan’s puzzle RotoTiler.

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Above is the first version of the puzzle, consisting of 12 squares. You are allowed to put two of them next to each other if the adjacent edges have the same color and the same orientation of arrows, but opposite shading. It is also prohibited to place two tiles next to each other that use the same pair of edge colors. All that is forbidden is shown below (wrong edge colors, wrong edge direction, wrong shading, same edge pairs).

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It’s not that hard to lay out all 12 squares in a single connected way. You will notice that it is impossible to place four squares around a single vertex.

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As a simple puzzle: The above layout fits in a 4×7 rectangle. Can you find a solution that fits into a smaller rectangle?

And, if you have a partner to play: print say 8 sets of the tiles so that you have 96. One player gets all the dark squares, the other the light squares, and you take turns creating a connected layout of all tiles. It is quite easy to get stuck, so the players have to collaborate.

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The two crosses above give a hint how this is related to cubes. They can each be wrapped around a cube, one from the inside, the other from the outside, so that the two tiles on each face differ only in shading.

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Next we have a rhombic version of the same puzzle, now with 24 different tiles. This more truthfully can be used to represent a walk on the Schwarz P-surface. We have one additional rule: 60º vertices are not allowed to meet with 120º vertices. All that’s forbidden is listed below:

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Below are a few partial layouts. None of them can be extended.

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Can you lay out all 24 tiles in a single, connected figure? That you can’t has to do with the Schwarz P surface having congruent insides and outsides, and it being impossible to reach the inside from the outside.

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More down to earth is the following explanation: You can lay out all 24 tiles in the two rings above, but no tile from the left ring can be legally placed next to a tile from the right ring. To remedy this, we can relax the rules a bit. If we allow that two tiles that use the same pair of colored edges can be placed next to each other, a single chain can be found:

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This was not so easy. Can you find smaller displays? And again, you can play with two player, using four sets of tiles, and take turns trying to complete a single layout.

Happy Birthday, Alan!