
Water Mill (1892) by the Norwegian impressionist Frits Thaulow (1847-1906)
Thaulow painted this almost identical “Bak møllene, Montreuil-sur-Mer” (1892):

Water Mill (1892) by the Norwegian impressionist Frits Thaulow (1847-1906)
Thaulow painted this almost identical “Bak møllene, Montreuil-sur-Mer” (1892):
Abandoned: The Most Beautiful Forgotten Places from Around the World, Mathew Growcoot (Ebury Press 2017)
He isn’t mentioned in this book, but he haunts it like a semiotic spectre at a phantasmic feast. Yes, this is a very Ballardian book and I’m sure J.G. Ballard would have liked it. And perhaps been inspired by it to write one of his haunting stories about abandoned buildings or aircraft, about human artefacts slowly succumbing to nature and the elements and the ineluctable forces of entropy.
But Ballard’s omission isn’t surprising. There’s little room to mention anyone or anything here: apart from a brief foreword by the compiler Mathew (sic) Growcoot, there’s nothing but section headings, photographs and brief captions. I like the absence of words and the abundance of images. Abandoned buildings and artefacts are fertile not only for Ballardianism but also for bullshit. You can imagine what po-mo-ticians would make of the anomic alienation and transliminal alterities on display here.
As it is, the photographs are allowed to speak for themselves: silently, subtly, seductively. There’s everything from fairgrounds and theatres to jails and asylums, from rusting aircraft to sunken ships. The photographs are all variants on the single theme of abandonment, of what happens when bustle and busy-ness turn into quietness and contemplation. And the buildings and other artefacts do seem to be contemplating themselves or their own decay, like a Buddhist monk sinking slowly into deeper and deeper into meditation until he begins to merge into what surrounds him, becoming one with the world. But the power in the photos comes partly from what isn’t there: the human beings who created what nature is now reclaiming. That’s why the graffiti you can see in a few photos spoils the beauty of the abandonment. It’s ugly and intrusive, laying claim to structures that should now belong only to themselves and entropy.
They’re abandoned: human beings should be absent. The ab- of “abandoned” and the ab- of “absence” aren’t actually the same, but it’s appropriate that they seem to be. The ab- of “absence” is from the Latin preposition ab, meaning “from, away”. When a building or machine is abandoned, people have gone away. Something is subtracted and something else takes its place: an eeriness, a melancholy, a murmur of memento mori – “remember that you die”, that all things must pass. That eeriness comes in different flavours with different kinds of abandonment. The section headings run like this: “Abandoned Homes, Abandoned Recreation, Abandoned Rooms, Abandoned Journeys, Abandoned Society, Abandoned Industry”.
The photos of abandoned fairgrounds, theatres and stadiums – “Abandoned Recreation” – are in some ways the most powerful, because the absence is most present there. Crowds of people once filled these places with noise and activity – they laughed, cheered, applauded, had fun. Now paint is peeling off the colourful walls of a “Gym in a derelict school, Arctic circle.” Frost-whitened trees surround a stationary “Ferris Wheel, Chernobyl, Ukraine”. Shadows and slanting sunbeams fill an “Abandoned theatre near Berlin, Germany”.
No-one’s there: the crowds have gone. These places are abandoned to absence. But if the photos in “Abandoned Recreation” are in some ways the most powerful, they’re also in some ways the least powerful. Fairgrounds, gyms and theatres were regularly abandoned even when they were in use: the crowds would come and go, like tides filling a bay. It’s just that one day the crowds went and never came back. The private homes of other sections never had the same noise and activity, but they didn’t fill and empty like fairgrounds and theatres. People were always or almost always there, so their absence now is a stranger and sharper thing. Men, women and children did intimate, ordinary things there, year after year, decade after decade, even century after century. And now the thread is broken: the people are gone. No-one will ever sit in the sagging armchair or play the collapsed piano of a “Living area in industrial site, Austria”. No child will push the wheeled little horse in the “Nursery, Château de Moulbaix, Belgium” or look at the pictures on the walls.
But the sadness isn’t very strong in the nursery, because a nursery isn’t a permanent place. It’s akin to a theatre: abandonment is always natural there, because children grow up and leave. No, the sadness is strongest in places that were built to be in permanent use, like houses. Except that nothing is permanent. A nursery is used for a few years; a house might be used for decades or centuries. But in the end it will pass away, perhaps quickly, if it’s demolished, or slowly, if it’s abandoned. Demolition has its delights too, but abandonment is subtler and slyer. Its power follows a curve, first rising, then falling. The most powerful photos here have the least change in them, because they have been taken when the abandonment is most recent. Dust and shadows have taken over, but everything is still more-or-less intact.
When the abandonment is older and ceilings and floors have collapsed, as in the “Collapsed villa, Italy” and the “Collapsed palace, Italy”, there’s less power in the photographs. Or a different kind of power. Humans have been gone much longer and their absence is less poignant, less powerful. Their ghosts are fainter. And sometimes there are no ghosts, because something else has taken the place of humans. In the “Old overgrown glasshouse, Belgium” and the “Shopping mall, Bangkok, Thailand”, it’s vegetation, green and growing. In the the “House full of sand, Kolmanskop, Namibia”, it’s sand, slanted and scalloped. Or perhaps you could say that here the ghosts themselves have become ghosts.
“Ghostly” is certainly the word for the photographs in this book. The ghostliness comes in different forms and flavours, as the photographs capture both what’s there and what isn’t. Or rather: they capture what’s there and your mind conjures what isn’t. Absence is essence. Abandoned is a Ballardian book of phantasmic photography and I think Ballard would have enjoyed it a lot.
“In terms of those ideas, there’s been specific policies that are intersecting in terms of racist and sexist policies that have targeted and harmed black women. The same thing with black men, in terms of them being a racial group that have been affected by racist ideas and policies. […] So, in terms of assessing other people, we should allow for people to essentially make racist mistakes.” — Ibram X Kendi, The most extreme racists say, ‘I’m the least racist person anywhere in the world’, The Guardian, 30viii2019
Elsewhere other-accessible:
• Ex-term-in-nate! — incendiarily interrogating issues around “in terms of” dot dot dot
• All O.o.t.Ü.-F. posts interrogating issues around “in terms of”…

Albrecht Dürer, Selbstbildnis (1500)
Post-Performative Post-Scriptum
Christusgleicher Kunstkönig is German for “Christ-like Art-King”, because Dürer represented himself in a way traditionally reserved for images of Christ.
No matter how efficient any physical device is (e.g. a computer or a brain) it can acquire one bit of information only if it expends 0.693kT joules of energy. — Information Theory: A Tutorial Introduction, James V. Stone, Sebtel Press 2015
Mounting n. a backing or setting on which a photograph, work of art, gem, etc. is set for display. — Oxford English Dictionary
Viewer’s advisory: If you are sensitive to flashing or flickering images, you should be careful when you look at the final fourth and fifth of the animated gifs below.
H.P. Lovecraft in some Mountings of Mathness
Two interesting puzzles, one of which looks hard and is in fact easy, while the other looks easy and is in fact hard.
1. Three Cards
The values attached to a deck of bridge cards start with the Two of Clubs as lowest, with Diamonds, Hearts and Ace of Spades as highest.
If you draw three cards at random from the deck, what is the probability that they will be drawn in order of increasing value? (Answer 1)
2. The Hungry Hunter
A hunter, having run out of food, met two shepherds. One of the shepherd had three loaves of bread and the other had five loaves. When the hunter asked for food, the shepherds agreed to divide the eight identical loaves equally between the three of them. The hunter thanked them and gave them $8. How should the shepherds divide the money? (Answer 2)
• Puzzles and answers from Erwin Brecher’s How Do You Survive a Duel? And Other Mathematical Diversions, Puzzles and Brainteasers (Carlton Books 2018)
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Answer #1: The puzzle sounds far more complicated than it is. The deck of cards is a red herring. The question reduces to this: Take three cards, say 2, 3 and 4 of clubs, facedown. What is the probability of turning them over in the order 2, 3, 4? There are six possible ways of arranging three cards. Therefore the probability is one-sixth.
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Answer #2: It would be wrong to split the money into $3 and $5. Each of the three ended up with 2⅔ loaves. In other words, the first shepherd parted with ⅓ of a loaf and the other shepherd with 2⅓ or 7/3 loaves. The first shepherd should therefore get $1 and the second shepherd $7.
In Mandibular Metamorphosis, I looked at two distinct fractals and how you could turn one into the other in one smooth sweep. The Sierpiński triangle was one of the fractals:
Sierpiński triangle
The T-square fractal was the other:
T-square fractal (or part thereof)
And here they are turning into each other:
Sierpiński ↔ T-square (anim)
(Open in new window if distorted)
But what exactly is going on? To answer that, you need to see how the two fractals are created. Here are the stages for one way of constructing the Sierpiński triangle:
Sierpiński triangle #1
Sierpiński triangle #2
Sierpiński triangle #3
Sierpiński triangle #4
Sierpiński triangle #5
Sierpiński triangle #6
Sierpiński triangle #7
Sierpiński triangle #8
Sierpiński triangle #9
When you take away all the construction lines, you’re left with a simple Sierpiński triangle:
Constructing a Sierpiński triangle (anim)
Now here’s the construction of a T-square fractal:
T-square fractal #1
T-square fractal #2
T-square fractal #3
T-square fractal #4
T-square fractal #5
T-square fractal #6
T-square fractal #7
T-square fractal #8
T-square fractal #9
Take away the construction lines and you’re left with a simple T-square fractal:
T-square fractal
Constructing a T-square fractal (anim)
And now it’s easy to see how one turns into the other:
Sierpiński → T-square #1
Sierpiński → T-square #2
Sierpiński → T-square #3
Sierpiński → T-square #4
Sierpiński → T-square #5
Sierpiński → T-square #6
Sierpiński → T-square #7
Sierpiński → T-square #8
Sierpiński → T-square #9
Sierpiński → T-square #10
Sierpiński → T-square #11
Sierpiński → T-square #12
Sierpiński → T-square #13
Sierpiński ↔ T-square (anim)
(Open in new window if distorted)
Post-Performative Post-Scriptum
Mandibular Metamorphosis also looked at a third fractal, the mandibles or jaws fractal. Because I haven’t included the jaws fractal in this analysis, the analysis is therefore agnathous, from Ancient Greek ἀ-, a-, “without”, + γνάθ-, gnath-, “jaw”.
THE SESSION OF THE POETS.—August, 1866.
Dî magni, salaputium disertum* — CAT[ullus]. Lib. LIII.
AT the Session of Poets held lately in London,
The Bard of Freshwater† was voted the chair:
With his tresses unbrush’d, and his shirt-collar undone,
He loll’d at his ease like a good-humour’d Bear;
“Come, boys,” he exclaimed, “we’ll be merry together!”
And lit up his pipe with a smile on his cheek;
While with eye like a skipper’s cock’d up at the weather,
Sat the Vice-Chairman Browning, thinking in Greek.
The company gather’d embraced great and small bards,
Both strong bards and weak bards, funny and grave,
Fat bards and lean bards, little and tall bards,
Bards who wear whiskers, and others who shave.
Of books, men, and things, was the bards’ conversation
Some praised Ecce Homo, some deemed it so-so —
And then there was talk of the state of the nation,
And when the unwash’d would devour Mr. Lowe.
Right stately sat Arnold — his black gown adjusted
Genteelly, his Rhine wine deliciously iced, —
With puddingish England serenely disgusted,
And looking in vain (in the mirror) for “Geist.”
He heark’d to the Chairman, with “Surely!” and “Really?”
Aghast at both collar and cutty of clay, —
Then felt in his pocket, and breath’d again freely,
On touching the leaves of his own classic play.
Close at hand lingered Lytton, whose Icarus-winglets
Had often betrayed him in regions of rhyme —
How glitter’d the eye underneath his grey ringlets,
A hunger within it unlessened by time!
Remoter sat Bailey — satirical, surly —
Who studied the language of Goethe too soon,
Who sang himself hoarse to the stars very early,
And crack’d a weak voice with too lofty a tune.
How name all that wonderful company over —
Prim Patmore, mild Alford — and Kingsley also?
Among the small sparks who was realler than Lover?
Among misses, who sweeter than Miss Ingelow?
There sat, looking moony, conceited, and narrow,
Buchanan, — who, finding when foolish and young,
Apollo asleep on a coster-girl’s barrow,
Straight dragged him away to see somebody hung.
What was said? what was done? was there prosing or rhyming?
Was nothing noteworthy in deed or in word?
Why, just as the hour for the supper was chiming,
The only event of the evening occurred.
Up jumped, with his neck stretching out like a gander,
Master Swinburne, and squeal’d, glaring out through his hair,
“All Virtue is bosh! Hallelujah for Landor!
I disbelieve wholly in everything! — there!”
With language so awful he dared then to treat ’em, —
Miss Ingelow fainted in Tennyson’s arms,
Poor Arnold rush’d out, crying “Sæcl’ inficetum!”‡
And great bards and small bards were full of alarms;
Till Tennyson, flaming and red as a gipsy,
Struck his fist on the table and uttered a shout:
“To the door with the boy! Call a cab! He is tipsy!”
And they carried the naughty young gentleman out.
After that, all the pleasanter talking was done there
Whoever had known such an insult before?
The Chairman tried hard to re-kindle the fun there,
But the Muses were shocked, and the pleasure was o’er.
Then “Ah!” cried the Chairman, “this teaches me knowledge,
The future shall find me more wise, by the powers!
This comes of assigning to younkers from college
Too early a place in such meetings as ours!”
CALIBAN, The Spectator, September 15, 1866
*Dî magni, salaputium disertum = “Great gods, an eloquent mannikin!”
†”The Bard of Freshwater” is Tennyson, who lived at Freshwater on the Isle of Wight
‡”Sæcl’ inficetum!” = “Uncouth age!”
Caliban was Robert Buchanan (1841-1901), later the author of “The Fleshly School of Poetry”, an attack on immorality and sensuality in the poetry of Swinburne and Rossetti.
Here’s the famous Sierpiński triangle:
Sierpiński triangle
And here’s the less famous T-square fractal:

T-square fractal (or part of it, at least)
How do you get from one to the other? Very easily, as it happens:

From Sierpiński triangle to T-square (and back again) (animated)
(Open in new window if distorted)
Now, here are the Sierpiński triangle, the T-square fractal and what I call the mandibles or jaws fractal:
Sierpiński triangle
T-square fractal
Mandibles / Jaws fractal
How do you cycle between them? Again, very easily:

From Sierpiński triangle to T-square to Mandibles (and back again) (animated)
(Open in new window if distorted)
Elsewhere other-accessible…
• Agnathous Analysis — a closer look at these shapes