The Library of Babel II

Today we are taking the 2-dimensional floor plans of the Library of Babel  to the third dimension. The simplest way is to use a single floor plan and copy it for every level of the library. For instance, last time’s finite hexagon becomes a daunting infinite tower, at least in our imagination.

Babel hex 01

One could also do the same with several separate hexagons, but the resulting library would consist of several buildings, which, while not explicitly prohibited by Borges, seems unacceptable.

Doublyplus 01

But there is another possibility. For instance, using the arrangement of hexagons in horizontal lines, and repeating them vertically (as on the left above), but then, on the second floor, using the same floor plan albeit rotated by 90º (as in the middle), and then repeating this periodically, we arrive at a single building where it is sometimes necessary to climb up, walk across, and then down again to reach a different room on the same floor.

Nearby places can sometimes be terribly far away.

In the double floor plan up above on the right we see that this can be done by aligning the vestibules in a square pattern, leaving star-shaped Voids. Below is a partial view of this magnificent library:

Babel3The condition that the staircases in the vestibules extend infinitely in both directions is quite limiting, even if one doesn’t require that each staircase can be reached at every floor. A good strategy for designing even more complicated libraries is to begin with a floor plan that includes hexagons and squares, and use on each floor a different subset of these squares and hexagons as vestibules and galleries. For instance, we can start with this Archimedean tiling that has large dodecagonal Voids:Archi2 01


One individual floor then could look like this, seemingly giving each gallery three exits to vestibules with staircases, one of which, however, will be blocked off by a bookshelf on two of its sides:

Third 01

This floor plan will be rotated by 120º on each subsequent floor (about the center of one of the dodecagonal Voids), creating a single labyrinthian library.

Here is a deliciously maddening view into the resulting skeleton of this library. I haven’t closed off the inaccessible staircases yet, so please watch your step.


Happy are those of us who can get lost in a single book like in this Borgesian library. 

The Library of Babel I

In the story The Library of Babel, Jorge Luis Borges describes a library whose design follows near axiomatic principles:

It is composed of an indefinite, perhaps infinite number of hexagonal galleries. In the center of each gallery is a ventilation shaft, bounded by a low railing. From any hexagon one can see the floors above and below—one after another, endlessly. The arrangement of the galleries is always the same.Babel2

One of the hexagon’s free sides opens onto a narrow sort of vestibule, which in turn opens onto another gallery, identical to the first—identical in fact to all. […] Through this space, too, there passes a spiral staircase, which winds upward and downward into the remotest distance.

If we remove all the cosmetics, we might end up with a design like the above, clearly unsatisfactory. Nothing is said about the underlying geometry of the library, Euclidean, spherical, hyperbolic, or even more esoteric. We will assume that the universe is Euclidean, for now, because this is still interesting enough. In this first post I will discuss the floor plans of a single floor. The combination of hexagonal galleries and square vestibules suggests that we are looking at floor plans that can be derived from this Archimedean tiling of the plane:

Babel 1

Of course the triangles will be Voids, and we have too many square vestibules. We get one more clue (or axiom) from Borges: Twenty bookshelves, five to each side, line four of the hexagon’s six sides […]

This means that each gallery has just two vestibules where one can enter or exit. As all galleries are identical, this leaves us with three distinct possibilities how a gallery can look like.

Babel straight 01

If we assume that the vestibules are placed at opposite sides of a gallery, our floor plan will necessarily look like the one above (which is used in the top image, too), representing a favorite labyrinth of Borges, the line (!). In the other extreme case, when the vestibules are at adjacent sides of each hexagon, there are two possible floor plans:

Babel 60

As a single floor plan, neither looks exciting, but we’ll see. There is one more option when between the two exits to the vestibules there is just one wall with shelves, like so:

Babel 120a 01

And fascinatingly, this last options allows for much more intricate floor plans, like this infinite double spiral:

Babel spiral 01

Next time we will investigate how the connections between different floors makes the life of the librarians even more exciting.

Palimpsest (Badlands X)

The little dark dots in the middle up above are a small group of bison, a universal presence in this part of the park.

When they noticed me from a distance, they wearily looked at me and moved on, maybe realizing that I was no threat.

During the day, the slowly walk on their tracks alone and in small groups, and pause to graze even more slowly, as if every blade of grass counts.

Their tracks crisscross the landscape like songlines, having a purpose of direction, but also a purpose of protection:

This way, the fragile ground is left unharmed.

Their entire existence seems to be an enormous effort of irrigation, eating only what they need, and fertilizing the arid places on the way.

Indeed, every blade of grass counts, like everywhere else.

At night, they gather as a larger herd, greeting each other, and telling about their dreams in eldritch voices.

I didn’t have a telephoto lens with me, but in the above photo is a small region with maybe a hundred little black bison dots.

So they write on this landscape as if it was an enormous palimpsest, being alive.

A la lumière d’hiver

Aide-moi maintenant, air noir et frais, cristal
noir. Les légères feuilles bougent à peine,
comme pensées d'enfants endormis. Je traverse
la distance transparente, et c'est le temps
même qui marche ainsi dans ce jardin,
comme il marche plus haut de toit en toit, d'étoile
en étoile, c'est la nuit même qui passe.
Je fais ces quelques pas avant de remonter
là où je ne sais plus ce qui m'attend, compagne
tendre ou détournée, servantes si dociles
de nos rêves ou vieux visage suppliant...
la lumière du jour, en se retirant
                                                                      – comme un voile
tombe et reste un instant visible autour
des beaux pieds nus –
                                                   découvre la femme d'ébène
et de cristal, la grande femme de soie noire
dont les regards brillent encore pour moi
de tous ses yeux peut-être éteints depuis longtemps.
La lumière du jour s'est retirée, elle révéle,
à mesure que le temps passe et que j'avance
en ce jardin, conduit par le temps,
                                                                     autre chose
– au-delà de la belle sans relâche poursuivie,
de la reine du bal où nul ne fut jamais convié,
avec ses fermoirs d'or qui n'agrafent plus nulle robe –
autre chose de plus caché, mais de plus proche...
Ombres calmes, buissons tremblant à peine, et les couleurs,
elles aussi, ferment les yeux. L'obscurité
lave la terre.
                      C'est comme si l'immense
porte peinte du jour avait tourné
sur ses gonds invisibles, et je sors dans la nuit,
je sors enfin, je passe, et le temps passe
aussi la porte sur mes pas.
                                                               Le noir n'est plus ce mur
encrassé par la suie du jour éteint,
je le franchis, c'est l'air limpide, taciturne,
j'avance enfin parmi les feuilles apaisées,
je puis enfin faire ces quelques pas, léger
comme l'ombre de l'air,
l'aiguille du temps brille et court dans la soie noire,
mais je n'ai plus de mètre dans les mains,
rien que de la fraîcheur, une fraîcheur obscure
dont on recueille le parfum rapide avant le jour.

(Chose brève, le temps de quelques pas dehors,
mais plus étrange encore que les mages et les dieux.)

Philippe Jaccottet
June 30, 1925 – February 24, 2021

And Every Poem and Every Picture

And every poem and every picture
        a sensation in the eye and heart
Something that jolts you awake
            from the rapt sleep of living
    in a flash of pure epiphany 
          where all stands still
            in a diamond light
                for what it truly is
                         in all its mystery
So a bird is an animal
                    flown into a tree
        singing inscrutable melodies 
As a lover stands transparent
        screened against the sun 
    smiling darkly in the blinding light

Poem #46 from A Far Rockaway Of the Heart, 1997.

Lawrence Ferlinghetti 
March 24, 1919 – February 22, 2021

The Ice Palace (Frost VI)

The ice on the lake shone so brightly that it did not look like ice at all.

Frozen into this block of ice were broad, sword-shaped leaves, thin straws, seeds and detritus from the woods, a brown, straddling ant – all mingled with bubbles that had formed and which appeared clearly as beads when the sun’s rays reached them.

And what was this?
It must be the ice palace.

But this was unexpected, too: she was standing in what looked like a room of tears.

No one is involved deeply enough to be present. A blast of noiseless chaos may cause the air to vibrate in distant bedrooms, but no one wakes up to ask: What is it?
No one knows.
Now the palace, with all its secrets, goes into the water-fall. There is a violent struggle, and then it has gone.

Quotes from The Ice Palace by Tarjej Vesaas, translated by Elizabeth Rokkan.

Whoever Hid Away (Wenckheim XI)

The last chapter of László Krasznahorkai’s last (?—?) novel Baron Wenckheim’s Homecoming provides the musically inclined reader with a very loud finale. 

DSC 5628

The entire town is paralyzed in fear:

… what had been happening these past days, all of them were already living deep inside the fear that if they went outside they’d be the next to be murdered, raped, harassed, and disappeared without a single trace,…

DSC 5608

And they are wondering about the gasoline tanks and their drivers:

… but unanimously, they agreed that these drivers were waiting for something, and that’s why they didn’t get out of their trucks, they just sat behind the steering wheel, not even eating anything, they just all kept their hands on the steering wheel, as if waiting for some sign that could arrive at any moment,…

DSC 5634

As the reader expects, things get more ominous: The trucks disappear again, all animals leave the city, and knots of toads arrive from nowhere, signaling the imminent apocalypse.

… these lunatic toads had come forth from beneath the earth, as there below, in the bountiful darkness, they had all gone mad, and they had wrenched themselves out of the earth and emerged, at first they began to jump back and forth, who the hell would have thought that so many hideous toads existed beneath the earth ,…

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…then he took out a cigarette from the Egyptian pack, and he lit up, and in that moment, as he clicked the flame of the lighter, and he was already about to take a drag on his cigarette,… … … 

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A town has come to its end, a book has come to its end, and, simultaneously with me finishing reading it, here an era of an eerily similar nature has come to its end, too. 

Multiple Exposure (Wenckheim X)

The chapter To the Hungarians begins with newspaper editors discussing whether a certain tract they have received should be published. This tract is a hate sermon against the Hungarians, and some excerpts are read to us:

… and you’re spineless and two-faced, perfidious and contemptible, lying and rootless, because after you’ve exploited somebody, you do the same thing, namely you throw them away, you spit into their eyes, if they’re not good for anything else, because you’re primitive,…

DSC 5556

The text culminates in a generalizing damnation of all of humanity.

… moreover this true monstrosity, while he has his bad moments, at times stumbles across a good intention within himself, but he quickly forgets about that, and it remains a mere memory, but he builds upon it later, as this sort of monstrosity is convinced that fate has selected him for good, or at the very least as the representative of truth, his own truth, …

DSC 5538

In the meantime, violence is erupting in the city, a first to statues,

unknown assailants knocked over the bust of Countess Krisztina Wenckheim, but not only that, they completely smashed apart her face with a hatchet,

then to animals,

…on Wednesday at midnight he found two cattle frozen in their own blood, their heads were also smashed apart,…

and finally to humans

…Irén’s horrific death — as they found her on the sidewalk, having to see that beloved human face now smashed into fragments…

DSC 5516

This is a chapter about fear, incited by propaganda, and backed by the actions of a nameless mob.

… she had a bad premonition about things, but what was so bad wasn’t even that people had forgotten the events of the past few days, but that the speed of all these events was like that of some kind of flood when it breaks across a dam, the events occurring and occurring one after the other,…

DSC 5464

What we fear is not the singular incident but it becoming the daily routine. Krasznahorkai invokes this mechanism by using repeating patterns at the level of the narrative as well as that of language itself:

… because they came down Csabai Road, and they came down Dobozi Road, and they came from the Romanian border, they came from the direction of Eleki Road, from every single direction they came, rumbling, the pneumatic brakes screeching, then the engines revved, then the pneumatic brakes again, they came in a line, one after the other, and within the space of barely an hour the entire city was full of these gigantically enormous fuel carriers, and the whole thing was as if they’d ended up here by mistake, as if they wanted to go someplace completely different,…

DSC 5571

All this, the threats, the violence, the feeling of foreboding, the arrival of an enormous number of gasoline tanks, is only preparation:

… and then suddenly — as if the entire thing were dependent on a single switch — the entire city was plunged into total darkness,…

Memory Eternal (Wenckheim IX)

…they didn’t need any prayers, because they had their own…

Neg 2

The two images I am using today were taken in 1992 in Budapest with 35mm film, scanned at 9600 dpi (which is a silly thing), and cut apart.

Gen neg 3 95

In László Krasznahorkai’s Baron Wenckheim’s Homecoming, the chapter Losers carries out a similar dissection. We revisit most of the previous characters in separate paragraphs (in fact, sentences), which are dedicated to memory in one way or another.

Gen neg 4 90

In the time of film, the detail of a printed image was determined by many physical factors — the format of the film, its quality, its grain, the quality of the equipment, lighting conditions, magnification, and the skill of the photographer. Today, grain has been replaced by noise, which has a different character, but the problem remains the same: outrageous enlargement will result in artifacts.

Gen neg 5 80

He was out by the train stop at Bicere and trying to dissect what he was seeing down to the minutest elements,
because while he thought the bikers’ suspicions were exaggerated, he still couldn’t completely let the matter rest, because that’s how he was — …

Gen neg 6 70

Does this frighten us? I think so, as the megapixel wars between smartphone makers indicate. We believe to be safer with more megapixels.

Gen neg 7 60

… this matter, then, had no meaning, cause, or goal, and this in fact might have been the essence of that matter, if words themselves hadn’t given up the ghost in the mind of an eyewitness (one, moreover, not even present at the scene), because words would have come to a dead halt in this brain, …

Gen neg 8

Is it the fear that our reality itself is like this, too, that if we look too closely, it will dissolve?

Gen neg 7 40

The people who met the Baron now want to forget him. The city photographer gets busy in an unusual way:

… for the naive ones, I just delete the pictures they want me to, the pics from the train station or the entertainment events, I do it in front of them, I look for the memory card, put in the camera, and together we look for the pictures they want me to erase, and I delete the pictures in front of them; then they ask me, and I tell them that no one will ever see these pictures again, well of course, no one ever will see them, never again, rest assured, and this is all so much work that I can’t keep up with it …

Gen neg 6 30

I think this is what Krasznahorkai tries to accomplish in his books: slowing down time and thus expanding the monologues of his protagonists, while they are desperately trying to remain themselves.

Gen neg 5 20

Reporters and politicians deny that certain events have happened:

…and now he was volunteering to completely erase the speeches in question from the offices’ computers and destroy every such trace of any one of these speeches…

Gen neg 4 10

We insist that reality is more than that, but in trying to prove it, we follow always the same process of dissolution. Can we find an answer if we just zoom in a bit further?

Gen neg 3 05

Finally, there is the Baron’s funeral, the cheapest available.

…but still, as he stood behind the coffin, about to commence the service, he felt the cold sinking into him, what should he do now, he reflected, while — his head lowered — he recited Psalm 119 to himself, should he go back for another layer,…

Gen 2

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.