The End of Spring

With the end of spring, the Brood X cicadas are finally gone, together with their song.

After 17 years under ground (17 years — a measure of life?) they have emerged for a final dance.

It’s precisely choreographed, and slow.

Who taught them all this?

Then, after a very long embrace, they rest. They now have all the time in the world.

Here are 30 minutes of cicada song, fading into rain at the end.

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.

Correspondences (Badlands XI)

In the Badlands a natural focus is the horizon, a verbose border between sky and ground, between dream and reality.

But if we look carefully, there are more forms of dialogue everywhere.

The horizon seems to show the solitary visitor the limit of the inhabitable space, itself unreachable.

And these other dialogues seem so small and irrelevant, being mere events, they only constitute time.

But I think this is all misconception. Every dialogue takes place at a horizon.

Prairie milkvetch (Astragalus laxmannii )

And only this: inhabiting the horizon: allows to define each other’s position.

Northern Cryptantha (Cryptantha celosioides)

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.

Border Districts (Badlands IX)

The mind is a place best viewed from borderlands

Gerald Murnane, Border Districts

After yesterday’s more technical description of my Sage Creek Valley flight, today an attempt of a second layer.

I think about photography as a dialogue — between the features of the subject and my abilities to perceive them.

The sparsity of the landscape and its contrasts call for black and white, and this is a good choice, because it also helps emphasizing the occurrences of natural borders.

Here the borders occur at different scales and in different contexts, in the texture of the ground, the vast horizons,

and in the transition between grassland and desert.

Sage Creek Valley (Badlands VIII)

So off I went for an overnighter in the backcountry. My route is above, clockwise, about 12 miles, which one could do in a day, but maybe not with taking as many photos as I did … Here is a first layer.

While there are stream crossings, there is no pumpable water, neither at the campground, nor in the wilderness. For me, that meant carrying 4 liters of water, barely enough for two days.

What struck me first was the lush greenness of this region. Where did all the arid rock formations go?

Then there are no trails. What sometimes looks like trails are bison tracks. More about them in a later post.

Now I have reached the north fork of Sage Creek, which I didn’t dare to cross. Sinking in ankle deep is ok, but not knee deep without guarantee that it ends there.

So instead I followed the middle fork for a while, crossed when it looked reasonable, and continued east. The landscape underwent some changes soon.

It’s is very tempting to keep going beyond exhaustion. Don’t. Use map, compass, GPS, and set goals. Easy to say.

Pitching a tent early gives shelter in the scorching sun and allows to enjoy the sunset. Finding a good spot for a tent in this vast emptiness was surprisingly difficult. I wanted to avoid wind, bison tracks, mud, and tall grass.

The next morning looked a bit gloomy, but I didn’t get any rain.

Time to return. Isolated trees are ideal landmarks, as the bisons obviously know, too. Tomorrow we’ll get the second layer.

Sage Creek Road (Badlands VII)

Today the journey takes you from the town Interior (what a fitting name) to Sage Creek Campground, a convenient door to the Badlands backcountry.

For most visitors, this is a drive-through road, offering stops for spectacular views.

Short hikes are possible here, but the terrain is steep and endless.

The Bighorn Sheep are going on family trips, too.

Then, slowly, the landscape begins to change. You first encounter patches of green,

and then colorful hills

with nuances of yellow.

Then you arrive, grab the backpack, and look back for a moment.

Window and Door (Badlands VI)

Rooms without a view are prisons for the people who have to stay in them.

From Windows Overlooking Life in A Pattern Language by Christoper Alexander et al.

At the Notch trailhead and the Castle Trail trailhead there are two more short trails, the Window and the Door.

These are also obvious architectural design patterns whose lack or presence in a building we much more easily perceive than their lack or presence in ourselves.

Windows offer a protected view, the exchange between inside and outside is virtual, and, like at the Window Trail, there is no safe way to step outside.

The Door is an entirely different story. And what Alexander writes about doors is valid also for our personal doors: Placing the main entrance is perhaps the single most important step you take during the evolution of a building plan.

On the map, the Door trail looks even shorter than the really very short Window trail, but the former does allow us to step outside into a vast landscape.

We instantly encounter unfamiliar heights, dangers, and the fear of getting lost.

So why should we step vvvvv

So why should we step outside? What are the benefits of an encounter with the undesigned?

In essence, I think, this is a form of survival instinct. Life needs protection but doesn’t like confinement.

Tomorrow, we will begin to step outside — — —