Monday, June 19, 2023

The Reeds Of Runnymede A poem by Rudyard Kipling

At Runnymede, At Runnymede,
What say the reeds at Runnymede?
The lissom reeds that give and take,
That bend so far, but never break,
They keep the sleepy Thames awake
With tales of John at Runnymede.

At Runnymede, at Runnymede,
Oh, hear the reeds at Runnymede:
"You mustn't sell, delay, deny,
A freeman's right or liberty.
It makes the stubborn Englishry,
We saw 'em roused at Runnymede!

"When through our ranks the Barons came,
With little thought of praise or blame,
But resolute to pay a game,
They lumbered up to Runnymede;
And there they launched in solid time
The first attack on Right Divine,
The curt, uncompromising 'Sign!'
That settled John at Runnymede.

"At Runnymede, at Runnymede,
Your rights were won at Runnymede!
No freeman shall be fined or bound,
Or dispossessed or freehold ground,
Except by lawful judgment found
And passed upon him by his peers.
Forget not, after all these years,
The Charter Signed at Runnymede."

And still when Mob or Monarch lays
Too rude hand on English ways,
The whisper wakes, the shudder plays,
Across the reeds at Runnymede.
And Tames, that knows the moods of kings,
And crowds and priests and suchlike things,
Rolls deep and dreadful as he brings
Their warning down from Runnymede!

Saturday, June 17, 2023

Apollo Remastered

 https://www.apolloremastered.com/shop

Thursday, June 15, 2023

Tuesday, June 13, 2023

Monday, June 12, 2023

Sunday, June 11, 2023

Saturday, June 10, 2023

Friday, June 9, 2023

TO HOPE! A CELEBRATION (1980)

 https://www.davebrubeck.com/to-hope-a-celebration

Wednesday, June 7, 2023

Hong Kong Lamp Post Location Data (English)

Street, Lat and Long of all 142k lamp posts in Hong Kong


 https://data.gov.hk/en-data/dataset/hk-hyd-plis-lamppostdata/resource/8b2b4d1c-9e1c-4f1d-b795-435c8f15fc54

Monday, June 5, 2023

Sunday, June 4, 2023

Borges: Everness





Everness
By Jorge Luis Borges
Translated by A.Z. Foreman

One thing does not exist: Oblivion.
God saves the metal and the dross, his key
Ciphers in his prophetic memory
The moons to come, and moons of evenings gone.

All there: reflections in the looking-glass
Which, between the huge twilights of the day,
Your face has long been leaving where you pass,
And those it will keep leaving on your way.

And everything is part of that diverse
Crystal of memory, the universe;
Unending are the mazes it engenders

Of doors that shut behind as you walk through;
Only from sunset’s farther side shall you
Behold at last the Archetypes and Splendors.

The Original:

Everness
Jorge Luis Borges

Sólo una cosa no hay. Es el olvido.
Dios, que salva el metal, salva la escoria
Y cifra en Su profética memoria
Las lunas que serán y las que han sido.

Ya todo está. Los miles de reflejos
Que entre los dos crepúsculos del día
Tu rostro fue dejando en los espejos
Y los que irá dejando todavía.

Y todo es una parte del diverso
Cristal de esa memoria, el universo;
No tienen fin sus arduos corredores

Y las puertas se cierran a tu paso;
Sólo del otro lado del ocaso
Verás los Arquetipos y Esplendores.

Saturday, June 3, 2023

THE ADVENTURE OF A PHOTOGRAPHER






A STORY BY ITALO CALVINO TRANSLATED FROM THE ITALIAN BY WILLIAM WEAVERAUGUST 1983 ITALO CALVINO


When spring comes, the city's inhabitants, by the hundreds of thousands, go out on Sundays with a leather case over their shoulder. And they photo graph one another. They come back as happy as hunters with bulging game bags; they spend days waiting, with sweet anxiety, to see the developed pictures (anxiety to which some add the subtle pleasure of alchemistic manipulations in the darkroom, forbidding any intrusion by members of the family, relishing the harsh, acid smell); and it is only when they have the photos before their eyes that they seem to take tangible possession of the day they spent, only then the mountain stream, the movement of the child with his pail, the glint of the sun on the wife's legs take on the irrevocability of what has been and can no longer be doubted. The rest can drown in the unreliable shadow of memory.


Seeing a good deal of his friends and colleagues, Antonino Paraggi, a non-photographer, sensed a growing isolation. Every week he discovered that the conversations of those who praise the sensitivity of a filter or discourse on the number of DINs were swelled by the voice of another to whom he had confided until yesterday, convinced that they were shared, his sarcastic remarks about an activity that to him seemed so unexciting, so lacking in surprises.

Professionally, Antonino Paraggi occupied an executive position in the distribution department of a production firm, but his real passion was commenting to his friends on current events large and small, unraveling the thread of general reasons from the tangle of details; in short, by mental attitude, he was a philosopher, and he devoted all his thoroughness to grasping the significance of even the events most remote from his own experience. Now he felt that something in the essence of photographic man was eluding him: the secret appeal which made new acolytes continue to join the ranks of the amateurs of the lens. He listened as some boasted of the progress of their technical and artistic skill, while others, on the contrary, gave all the credit to the efficiency of the camera they had purchased, capable (according to them) of producing masterpieces even when operated by inept hands (as they declared their own to be, because wherever pride aimed at magnifying the virtues of mechanical devices, subjective talent accepted a proportionate humiliation). Antonino Paraggi understood that neither the one nor the other motive of satisfaction was decisive: the secret lay elsewhere.

It must be said that his examination of photography to discover the reasons of a private dissatisfaction— as of someone who feels excluded from something—was to a certain extent a trick Antonino played on himself, to avoid having to consider another, more evident process that was separating him from his friends. What was happening was this: his acquaintances, of his age, were all getting married, one after the other, starting families, while Antonino remained a bachelor. And yet between the two phenomena there was undoubtedly a connection, inasmuch as the passion for the lens often develops in a natural, virtually physiological way as a secondary effect of fatherhood. One of the first instincts of parents, after they have brought a child into the world, is to photograph it; and given the speed of growth, it becomes necessary to photograph the child often, because nothing is more fleeting and unmemorable than a six-month-old infant, soon deleted and replaced by one of eight months, and then one of a year; and all the perfection that, to the eyes of parents, a child of three may have reached cannot prevent its being destroyed by that of the fouryear-old, the photograph album remaining the only place where all these fleeting perfections are saved and juxtaposed, each aspiring to an incomparable absoluteness of its own. In the passion of new parents for framing their offspring in the sights to reduce them to the immobility of black-and-white or a fullcolor slide, the non-photographer and non-procreator Antonino saw chiefly a phase in the race toward madness lurking in that black instrument. But his reflections in the iconography-family-madness nexus were summary and reticent: otherwise he would have realized that actually the person running the greatest risk was himself, the bachelor.

In the circle of Antonino's friends, it was customary to spend the weekend out of town, in a group, following a tradition that for many of them dated back to their student days and that had been extended to include their girlfriends, then their wives and their children, as well as wetnurses and governesses, and in some cases in-laws and new acquaintances of both sexes. But since the continuity of their habits, their getting together, had never lapsed, Antonino could pretend that nothing had changed with the passage of the years and that they were still the band of young men and girls of the old days, rather than a conglomerate of families in which he remained the only surviving bachelor.

More and more often, on those excursions to the sea or the mountains, when it came time for the family group or the multifamily picture, an outsider was asked to lend a hand, a passerby perhaps, willing to press the button of the camera already focused and aimed in the desired direction. In these cases, Antonino couldn't refuse his services: he would take the camera from the hands of a father or a mother, who would then run to assume his or her place in the second row, sticking a head forward between two heads or crouching among the little ones; and Antonino, concentrating all his strength in the finger destined for this use, would press. The first times, an awkward stiffening of his arm would make the lens veer to capture the masts of ships or the spires of steeples, or to decapitate grandparents, uncles and aunts. He was accused of doing this on purpose, reproached for a joke in poor taste. It wasn't true: his intention was to lend the use of his finger as docile instrument of the collective wish, but also to exploit his temporary position of privilege to admonish both photographers and their subjects as to the significance of their actions. As soon as the pad of his finger reached the desired condition of detachment from the rest of his person and personality, he was free to communicate his theories in well-reasoned discourse, framing at the same time well-composed little groups. (A few accidental successes had sufficed to give him nonchalance and assurance with viewfinders and light meters.)

"...Because, once you've begun," he would preach, "there is no reason why you should stop. The line between the reality that is photographed because it seems beautiful to us and the reality that seems beautiful because it has been photographed is very narrow. If you take a picture of Pierluca because he's building a sand castle, there is no reason not to take his picture while he's crying because the castle has collapsed, and then while the nurse consoles him by helping him find a seashell in the sand. You only have to start saying of something 'Ah, how beautiful! We must photograph it!' and you are already close to the view of the person who thinks that everything that is not photographed is lost, as if it had never existed, and that therefore in order really to live you must photograph as much as you can, and to photograph as much as you can you must either live in the most photographable way possible, or else consider photographable every moment of your life. The first course leads to stupidity; the second, to madness."

"You're the one who's mad and stupid," his friends would say, "and a pain in the ass, into the bargain."

"For the person who wants to capture everything that passes before his eyes," Antonino would explain, even if nobody was listening to him anymore, "the only coherent way to act is to snap at least one picture a minute, from the moment he opens his eyes in the morning to when he goes to sleep. This is the only way that the rolls of exposed film will represent a faithful diary of our days, with nothing left out. If I were to start taking pictures, I'd see this thing through, even if it meant losing my mind. The rest of you, on the contrary, still insist on making a choice. What sort of choice? A choice in the idyllic sense, apologetic, consolatory, at peace with nature, the fatherland, the family. Your choice isn't only photographic; it is a choice of life, which leads you to exclude dramatic conflicts, the knots of contradiction, the great tensions of will, passion, aversion. So you think you are saving yourselves from madness, but you are falling into mediocrity, into hebetude."

A girl named Bice, someone's ex-sister-in-law, and another named Lydia, someone else's ex-secretary, asked him please to take a snapshot of them while they were playing ball among the waves. He consented, but since in the meanwhile he had worked out a theory against snapshots, he dutifully expressed it to the two friends:

"What drives you two girls to cut from the mobile continuum of your day these temporal slices, the thickness of a second? Tossing the ball back and forth, you are living in the present, but the moment the scansion of the frames is insinuated between your acts it is no longer the pleasure of the game that motivates you but rather that of seeing yourselves again in the future, or rediscovering yourselves in twenty years' time, on a piece of yellowed cardboard (yellowed emotionally, even if modern printing procedures will preserve it unchanged). The taste for the spontaneous, natural, lifelike snapshot kills spontaneity, drives away the present. Photographed reality immediately takes on a nostalgic character, of joy fled on the wings of time, a commemorative character, even if the picture was taken day before yesterday. And the life that you live in order to photograph it is already, at the outset, a commemoration of itself. To believe that the snapshot is more true than the posed portrait is a prejudice. . . "

So saying, Antonino darted around the two girls in the water, to focus the movements of their game and cut out of the picture the dazzling glints of the sun on the water. In a scuffle for the ball, Bice, flinging herself on the other girl, already submerged, was snapped with her behind in close-up, flying over the waves. Antonino, so as not to lose this angle, had flung himself back in the water, holding up the camera and nearly drowning.

"They all came out well; and this one's stupendous," they commented a few days later, snatching the proofs from each other. They had arranged to meet at the photographer's shop. "You're good; you must take some more of us."

Antonino had reached the conclusion that it was necessary to return to posed subjects, in attitudes denoting their social position and their character, as in the nineteenth century. His anti-photographic polemic could be fought only from within the black box, setting one kind of photography against another.

"I'd like to have one of those old view cameras," he said to his girlfriends, "the kind you put on a tripod. Do you think one could still be found?"

"Hmm, maybe at some junk shop..."

"Let's go see."

The girls found it amusing to hunt for this curious object; together they ransacked flea markets, interrogated old street photographers, followed them to their lairs. In those cemeteries of objects no longer serviceable lay wooden columns, screens, backdrops with faded landscapes; everything that suggested an old photographer's studio, Antonino bought. In the end he managed to get hold of a box camera, with a bulb to squeeze. It seemed in perfect working order. Antonino also bought an assortment of plates. With the girls helping him, in a room of his apartment he set up the studio, all fitted out with old-fashioned equipment, except for two modern spotlights.
"He too was one of those who pursue life as it flees, a hunter of the unattainable."

Now he was content. "This is where to start," he explained to the girls. "In the way our grandparents assumed a pose, in the convention that decided how groups were to be arranged, there was a social meaning, a custom, a taste, a culture. An official photograph or one of a marriage or a family or a school group conveyed to what extent each role or institution was serious and important but also how far they were false or forced, authoritarian, hierarchical. This is the point: to make explicit the relationship with the world that each of us bears within himself, and which today we tend to hide, to make unconscious, believing that in this way it disappears, whereas. . ."

"Who do you want to have pose for you?" "You two come tomorrow and I'll begin by taking some pictures of you in the way I mean."

"Say, what's in the back of your mind?" Lydia asked, suddenly suspicious. Only now, as the studio was all set up, she saw' that everything about it had a sinister air. "If you think we're going to come and be your models, you're dreaming!"

Bice giggled with her, but the next day she came back to Antonino's apartment, alone.

She was wearing a white linen dress with colored embroidery on the hems of the sleeves and pockets. Her hair was parted and gathered over her temples. She laughed, a bit slyly, bending her head to one side. As he let her in, Antonino studied her ways, a bit coy, a bit ironic, to discover what were the traits that defined her true character.

He made her sit in a big armchair, and stuck his head under the black cloth that complemented his camera. It was one of those boxes whose rear wall was of glass, where the image is projected as if already on the plate, ghostly, a bit milky, deprived of every link with space and time. To Antonino it was as if he had never seen Bice before. She had a docility, in her somewhat heavy way of lowering her eyelids, of stretching her neck forward, that promised something hidden, as her smile seemed to hide behind the very act of smiling.

"There. Like that. No, head a bit further; raise your eyes. No, lower them." Antonino was pursuing, within that box, something of Bice that all at once seemed most precious to him, absolute.

"Now you're casting a shadow, move into the light. No, it was better before."

There were many possible photographs of Bice and many Bices impossible to photograph, but what he was seeking was the unique photograph that would contain the former and the latter.

"I can't get you," his voice emerged, stifled and complaining from beneath the black hood, "I can't get you anymore; I can't manage to get you."

He freed himself from the cloth and straightened up again. He was doing it all wrong, from the beginning. That expression, that accent, that secret he seemed on the very point of capturing in her face was something that drew him into the quicksands of moods, humors, psychology: he too was one of those who pursue life as it flees, a hunter of the unattainable, like the takers of snapshots.

He had to follow the opposite path: aim at a portrait completely on the surface, evident, unequivocal, that did not elude conventional appearance, the stereotype, the mask. The mask, being first of all a social, historical product, contains more truth than any image claiming to be "true"; it bears a quantity of meanings that will gradually be revealed. Wasn't this precisely Antonino's intention in setting up this fair-stall of a studio?

He observed Bice. He should start with the exterior elements of her appearance. In Bice's way of dressing and fixing herself up—he thought— you could recognize the somewhat nostalgic, somewhat ironic intention, widespread in the mode of those years, to hark back to the fashions of thirty years earlier. The photograph should underline this intention: why hadn't he thought of that?

Antonino went to find a tennis racket; Bice should stand up, in a three-quarter turn, the racket under her arm, her face in the pose of a sentimental postcard. To Antonino, from under the black drape, Bice's image—in the slimness and suitability to the pose and in the unsuitable and almost incongruous aspects that the pose accentuated—seemed very interesting. He made her change position several times, studying the geometry of legs and arms in relation to the racket and to an element in the background. (In the ideal postcard in his mind there should have been the net of the tennis court, but you couldn't demand too much and Antonino made do with a Ping-Pong table.)

But he still didn't feel on safe ground: wasn't he perhaps trying to photograph memories, or rather, vague echoes of recollection surfacing in the memory? Wasn't his refusal to live the present as a future memory, as the Sunday photographers did, leading him to attempt an equally unreal operation, namely to give a body to recollection, to substitute it for the present before his very eyes?

"Move! Don't stand there like a stick! Raise the racket, damn it! Pretend you're playing tennis!" All of a sudden he was furious. He had realized that it was only by exaggerating the poses that he could achieve an objective alienness; only by feigning a movement arrested halfway could he give the impression of the unmoving, the non-living.

Bice obediently followed his orders even when they became vague and contradictory, with a passivity that was also a way of declaring herself out of the game, and yet somehow insinuating, in this game that was not hers, the unpredictable moves of a mysterious match of her own. What Antonino now was expecting of Bice, telling her to put her legs and arms this way and that way, was not so much the simple performance of a plan, as her response to the violence he was doing her with his demands, an unforeseeable aggressive reply to this violence that he was being driven more and more to wreak on her.

It was like a dream, Antonino thought, contemplating, buried in the darkness, that improbable tennis player filtered in the glass rectangle: like a dream, when a presence coming from the depth of memory advances, is recognized, and then suddenly is transformed into something unexpected, something that even before the transformation is frightening because there's no telling what it might be transformed into.

Did he want to photograph dreams? This suspicion struck him dumb, hidden in that ostrich refuge of his, the bulb in his hand, like an idiot; and meanwhile Bice, left to herself, continued a kind of grotesque dance, freezing in exaggerated tennis poses, backhand, drive, raising the racket high or lowering it to the ground as if the gaze coming from that glass eye were the ball she continued to slam back.

"Stop, what's this nonsense? This isn't what I had in mind," and Antonino covered the camera with the cloth and began pacing up and down the room.

It was all the fault of that dress, with its tennis, '20s connotations... It had to be admitted that in a street dress the kind of photograph he described couldn't be taken. A certain solemnity was needed, a certain pomp, like the official photos of queens. Only in evening dress would Bice become a photographic subject, with the décolletage that marks a distinct line between the white of the skin and the darkness of the fabric underlined by the glitter of jewels, a boundary between an essence of woman, almost atemporal and almost impersonal in her nakedness, and the other abstraction, social this time, the dress, symbol of an equally impersonal role, like the drapery of an allegorical statue.

He approached Bice, began to unbutton the dress at the neck, over the bosom, and slip it down on her shoulders. He had thought of certain nineteenth-century photographs of women in which from the white of the cardboard the face emerges, the neck, the line of the bared shoulders, and all the rest disappears into the whiteness.

This was the portrait outside of time and space that he now wanted: he wasn't quite sure how it was achieved, but he was determined to succeed. He had the spotlight on Bice, moved the camera closer, fiddled around under the cloth adjusting the aperture of the lens. He looked into it. Bice was naked.

She had made the dress slip down to her feet; she wasn't wearing anything underneath it; she had taken a step forward; no, a step backward, which was like her whole body's advancing in the picture; she stood erect, tall, before the camera, calm, looking straight ahead, as if she were alone.

Antonino felt the sight of her enter his eyes and occupy the whole visual field, removing it from the flux of casual and fragmentary images, concentrating time and space in a finite form. And as if this visual surprise and the impression of the plate were two reflexes, connected, he immediately took the picture, loaded the camera again, snapped, put in another plate, snapped, and went on changing plates and snapping, mumbling, stifled by the cloth: "That's right now, yes, again, I'm getting you fine now, another."

He had run out of plates. He emerged from the cloth. He was pleased. Bice was before him, naked, as if waiting.

"Now you can dress," he said, euphoric, but already in a hurry. "Let's go out."

She looked at him, bewildered.

"I've got you now," he said.

Bice burst into tears.

Antonino realized that he had fallen in love with her that same day. They started living together, and he bought the most modern cameras, telescopic lenses, the most advanced equipment; he installed a darkroom. He even had a setup for photographing her at night when she was asleep. Bice would wake at the flash, annoyed; Antonino went on taking snapshots of her as she disentangled herself from sleep, of her becoming furious with him, of her trying in vain to find sleep again plunging her face into the pillow, of her making up with him, of her recognizing as acts of love these photographic rapes.

In Antonino's darkroom, strung with films and proofs, Bice peered from every frame, as thousands of bees peer out in the honeycomb of a hive, always the same bee: Bice in every attitude, at every angle, in every guise, Bice posed or caught unaware, an identity fragmented into a power of images.

"But what's this obsession with Bice? Can't you photograph anything else?" was the question he heard constantly from his friends, and also from her.

"It isn't just a matter of Bice," he answered. "It's a question of method. Whatever person you decide to photograph, or whatever thing, you must go on photographing it always, exclusively, at every hour of the day and night. Photography has a meaning only if it exhausts all possible images."

But he didn't say what meant most to him: to catch Bice in the street when she didn't know he was seeing her, to keep her within the range of hidden lenses, to photograph her not only without letting himself be seen but without seeing her, to surprise her as she was in the absence of his gaze, of any gaze. Not that he wanted to discover any particular thing; he wasn't a jealous man in the usual sense of the word. It was an invisible Bice that he wanted to possess, a Bice absolutely alone, a Bice whose presence presupposed the absence of him and everyone else.

Whether or not it could be defined as jealousy, it was, in any case, a passion difficult to put up with. And soon Bice left him.

Antonino sank into deep depression. He began to keep a diary: a photographic diary, of course. With the camera slung around his neck, shut up in the house, slumped in an armchair, he compulsively snapped pictures as he stared into the void. He was photographing the absence of Bice.

He collected the photographs in an album: you could see ashtrays brimming with cigarette butts, an unmade bed, a damp stain on the wall. He got the idea of composing a catalogue of everything in the world that resists photography, what is systematically omitted from the visual field not only by cameras but also by human beings. On every subject he spent days, using up whole rolls, at intervals of hours, so as to follow the changes of lights and shadows. One day he became obsessed with a completely empty corner of the room, containing a radiator pipe and nothing else: he was tempted to go on photographing that spot and only that till the end of his days.
"Snapshots of her making up with him, of her recognizing as acts of love these photographic rapes."

The apartment was completely neglected; old newspapers, letters lay crumpled on the floor, and he photographed them. The photographs in the papers were photographed as well, and an indirect bond was established between his lens and those of distant news photographers. To produce those black spots the lenses of other cameras had been aimed on police assaults, charred automobiles, running athletes, ministers, defendants.

Antonino now felt a special pleasure in portraying domestic objects framed by a mosaic of telephotos, violent patches of ink on white sheets. From his immobility he was surprised to find he envied the life of the news photographer, who moves following the movements of crowds, bloodshed, tears, feasts, crime, the conventions of fashion, the falsity of official ceremonies; the news photographer, who documents the extremes of society, the richest

and poorest, the exceptional moments that are yet produced at every moment and in every place.

Does this mean that only the exceptional condition has a meaning? Antonino asked himself. Is the news photographer the true antagonist of the Sunday photographer? Are their worlds mutually exclusive? Or does one give a meaning to the other?

And reflecting like this, he began to tear up the photographs with Bice or without Bice that had accumulated during the months of his passion, ripping to pieces the strips of proofs hung on the walls, snipping up the celluloid of the negatives, jabbing the slides, and piling the remains of this methodical destruction on newspapers spread out on the floor.

Perhaps true, total photography, he thought, is a pile of fragments of private images, against the creased ground of massacres and coronations.

He folded the corners of the newspapers into a huge bundle to be thrown into the trash, but first he wanted to photograph it. He arranged the edges so that you could clearly see two halves of photographs in different newspapers that in the bundle happened, by chance, to fit together. In fact he reopened the package a little so that a bit of shiny pasteboard would stick out, the fragment of a torn enlargement. He turned on a spotlight; he wanted it to be possible to recognize in his photograph the half-crumpled and torn images and at the same time to feel their unreality as casual inky shadows, and also at the same time their concreteness as objects charged with meaning, the strength with which they clung to the attention that tried to drive them away.

To get all this into one photograph he had to acquire an extraordinary technical skill, but only then would Antonino quit taking pictures. Having exhausted every possibility, at the moment when he was coming full circle, Antonino realized that photographing photographs was the only course that he had left, or rather, the true course he had obscurely sought all this time.

Italo Calvino's collection of stories Marcovaldo, or The Seasons in the City will be published by Harcourt Brace Jovanovich, Inc. in November. "The Adventure of a Photographer" is from Difficult Loves, a collection of stories to be published by Harcourt Brace Jovanovich, Inc. in the spring of 1984.

Friday, June 2, 2023

Kipling Society

https://www.kiplingsociety.co.uk/ 

Monday, May 29, 2023

Saturday, May 27, 2023

The Lay of Love and Death of Christoph Cornet Rilke von Langenau.




The Lay of Love and Death of Christoph Cornet Rilke von Langenau.


By RANIER MARIA RILKE.



Die Weise von Liebe und Tod des Cornets Christoph Rilke von Langenau1

Translated by Harry Guest.



“…den 24. November 1663 wurde Otto von Rilke / auf Langenau / Gränitz und Ziegra / zu Linda mit seines in Ungarn gefallenen Bruders Christoph hinterlassenem Anteile am Gute Linda beliehen; doch mußte er einen Revers ausstellen / nach welchem die Lehensreichung null und nichtig sein sollte / im Falle sein Bruder Christoph (der nach beigebrachtem Totenschein als Cornet in der Kompagnie des Freiherrn von Pirovano des kaiserl. österr. Heysterschen Regiments zu Roß. . . . verstorben war) zurückkehrt…”

“…on the 24th of November 1663 Otto von Rilke auf Langenau came into an inheritance left by his brother Christoph who had been killed in Hungary. However, there is a counter-bill according to which the inheritance is null and void since, according to the death-certificate, his brother Christoph was killed when he was a Cornet (the soldier who bears the regimental flag) in the Company of Baron von Pirovano in the Imperial Austrian cavalry Regiment. ..”



THE LAY OF LOVE AND DEATH OF CORNET CHRISTOPH RILKE VON LANGENAU

I

Riding, riding, riding, through the day, through the night, through the day.

Riding, riding, riding.

And courage is so exhausted while longing remains so strong. There are no hills now, hardly even a tree. Nothing risks standing up. Strange huts squat thirstily near a marsh for water. There’s not a tower to be seen anywhere. Always the view’s the same. We have two eyes, too many. Only at night sometimes can anyone know where we’re going. Do we perhaps ride back in the dark to the same bit of land we fought so hard to win under a strange sun? That could be true. The sun’s strong here, the way it is at home in the depth of summer. It was summertime when we left. The clothes women wore shone in green fields. We’ve been riding for so long. It must be autumn. At least there the women know about us and are sad.

II

Von Langenau turned in his saddle and said “Herr Marquis. . .”

For three days now the slim little Frenchman beside him has never stopped chattering and laughing. Now he doesn’t know what to say. He’s like a child who’d like to sleep. There’s dust on his white lace collar. He doesn’t notice it. He’d only like to sink down slowly in his velvet saddle.

But Von Langenau smiles and says “You don’t seem to see very well, Herr Marquis. Surely for your mother you’d be looking more like ̶ “

That makes the little Frenchman bloom once more. He shakes the dust from his lace collar and looks like new and ready for anything.

III

Each soldier talks about his mother. One of the Germans isn’t at all shy about it. He brings his words out slowly, clearly. Like a girl arranging a bouquet, testing flower by flower so thoughtfully, not really knowing what they’ll look like as a whole. He’s fitting his words together like that. In pleasure? In sorrow? They all keep listening. Even the spitting stops. Because, like him, they enjoy hearing themselves talk. And anyone in the crowd who can’t speak German still can still catch the odd phrase: “One evening . . .” “When I was little . . .”

IV

They’re all near each other now, soldiers coming from France and Burgundy, from the Netherlands, from out of the valleys of Carinthia, from Bohemian castles, from the Emperor Leopold himself. They all know what he’s talking about. It’s almost as though there’s only one mother. . .

V

So they ride away into the evening, into any evening. They say nothing but then they’ve brought lucid words with them. Then the Marquis takes off his helmet. His dark hair is soft and, as he lowers his head, it falls on to his neck the way a girl’s would. Now Von Langenau understands something: a long way away, standing out, a radiance, something slender, something shadowy. A lonely statue, half decayed. And long after, much later, it occurs to him that it was a Madonna.

VI

Watchfire. They all sit around and wait. Wait, hoping someone will sing. But they’re all so tired. The reddish light is harsh. It reaches the dusty shoes. Creeps to the knees, peers into folded hands. However it doesn’t have wings. Faces stay dark. Even so, the eyes of the little Frenchman light up for a moment with a same kind of glow. He’s kissed a small rose then put it back to wither against his chest. Von Langenau saw him do that because he can’t seem to fall asleep. He thinks: I don’t have a rose, not one.

Then he begins to sing. And it’s an old sad song that girls back at home sing in the fields, in autumn, when the harvest is almost over.

VII

The little Marquis says “You are very young aren’t you, sir?”

And Von Langenau, half sorrowful half defiant, answers. “Eighteen.” Then they fall silent.

Later on the Frenchman asks “Have you got a fiancée?”

“How about yourself?” Von Langenau throws back at him.

“She’s blonde. Like you, Herr Junker.”

And they are silent once again until the German cries out “But then why the devil d’you just sit in a saddle, ride at the Turkish dogs, gallop all over this land of poison?”

The Marquis smiles. “To go back home again.”

And Van Langenau’s face goes sad. He thinks about the blonde girl he used to play with. Wild games. And he’d like to go home, just for a moment, only long enough to say “Magdalena — I know I was always like that. Forgive me.”

Like — was? thinks the young Junker. — They’re far away from each other now.

VIII

One day, during the morning, a man on horseback turned up, then another, then four more, ten. All of them big and tall. In armour. And then a thousand coming up behind: the army.

They’ll have to part.

“Go home safely, Herr Marquis —”

“May Our Lady protect you, Herr Junker.”

And they can’t leave each other. They’re friends for life, brothers. They’ve trusted one another, learnt so much about each other. Hesitate. All around about them there’s hurrying and the clatter of hooves. The Marquis slips his right glove off. Brings the tiny rose out, chooses a petal for him. The way a priest would place a wafer on the palm.

“It’ll look after you. Farewell. For now.” Von Langenau doesn’t know what to do. He looks longingly at the Frenchman, then puts this foreign petal inside his greatcoat where it will drift up and down on the tides of his heart. A horn’s blown. The Junker rides up to his regiment and smiles sadly. He’s protected by a woman he’s never met.

IX

One day all the camp-followers turn up. Cursing, colours, laughter. They dazzle the countryside. Lively boys running around. Scuffling. Yelling. Harlots arrive with purple hats on their floating hair. Becks and calls. Mercenaries come wearing iron, black like wandering nightfall. They grab the whores violently, tear their clothes, push them where the drums are kept. And from the eager hands of soldiers the drums awake, rumble as if inside a dream, go on rumbling. ̶ And in the twilight lanterns are held out. Makeshift ones, strange-looking. And wine, glinting on the helmets.

Wine? Or blood? — Who can tell the difference?

X

Before Count Spork at last. He’s standing by his white horse, towering. His long hair’s the colour of iron.

Von Langenau hasn’t had to ask. He knows the General and leaps from his steed to give a salute out of a cloud of dust. He’s brought a message commending himself but the Count simply gives an order “Read me what’s on that scrap of paper.” His lips didn’t move. They don’t need to. They’re good enough to curse with. For anything further he just gestures with his right hand. That’s it. And anybody’ll see what he means. The young man is not quite there. He’s unsure where he stands. The General’s in front of them all. Even the sky is. And then the great general speaks:

“You’ll carry the flag, Cornet.”

That’s all. But a lot.



XI

The Company lies beyond the River Raab. Von Langenau rides away, alone. Over a flat piece of land. In twilight. Metalwork on the saddle glints through the dust. And then the moon rises. He sees the shine on his hands.

He has a dream.

Someone yells out to him.
Screams, screams, rips his dream apart.
That’s not an owl. It’s a yell for help:
the only tree there is calls out: “You there!”
And he can see a shape leaning against it,
a woman, bloody, naked. He hears what she’s saying: “Get me free!”
And he springs into the green darkness,
cuts through the cords
sees her eyes glowing
her teeth grinding.

Is she laughing?
He’s afraid,
gets on his horse
and gallops into night. The cords gripped in his fist are wet with blood.

XII

Von Langenau’s writing a letter, in gratitude. He makes the letters large, upright, serious:


My dear Mother,

“Be proud: I carry the flag,
“Don’t worry: I carry the flag,
“Love me: I carry the flag ̶ “

Then he sticks the letter inside his greatcoat, on a secret place. Near the rose-petal. And he thinks: it’ll soon smell sweet. And he thinks: maybe someone else will find it . . .

And he thinks again . . . For the enemy is close.

XIII

They are riding over a slain farmer. His eyes stay wide open and something is mirrored in them, but not the sky. Later they hear dogs howling. There’s a village. At last. And above the huts a castle like a rocky hill. They come up to the drawbridge. There’s a huge gate. A welcome blow on a horn. Listen: rumbling, rattling, hounds barking. Neighing in the courtyard, horses kicking, summons.

XIV

Repose! To be a guest for once. Not just to get for yourself what you can afford. Not always having to grab things frenziedly. Just for once letting it all come and know that what you’re getting is bound to be good. Forget about bravery for a while and tumble between silk sheets. Not always just being a soldier. Letting your hair go loose for once, sprawling on an easy chair with a white collar on, feeling all’s well all over, right to the fingertips. After a bath. To learn again what women look like. How they cope with colour like whites and blues; what hands they have and how they sing and laugh when blond boys bring beautiful dishes in, laden with juicy fruits.

XV

It all started over dinner. Turned into a festival, no-one really understanding why. Torches flaring, voices bawling, weird songs clinking from glass and glitter and then, as soon as all’s fallen in rhythm: dance. Everyone swept away like waves breaking in the solar ̶ losing each other and finding each other ̶ glare of enjoyment and light that’s blinding ̶ swaying of summer winds into the clothes of women so warm.

From the darkness of wine and a thousand roses the hour runs rustling into the dream of nightfall.

XVI

There’s one who stands and stares into this splendour. And he’s so well-disposed that he waits to make sure he’s awake. Because only in sleep can anyone observe such finery, such a celebration with women like that: their slightest gesture makes a pleat recurring in brocade. They create hours from silver conversations and often lift their hands somehow ̶ and you have to fancy they go somewhere you don’t know to fold soft roses you’ll never see. And then you dream ̶ to be decked out like them, pleased in a different way and to deserve a crown for your vacant forehead.

XVII

One who is wearing white silk knows he can’t wake up because he is awake and bewildered far from reality. So he flees scared into the dream to stand unmoving in the park, alone in the black park. And the festivities are a long way away. And the light tells lies. And the night is all around him and so cool. And he asks a woman who’s nodding her head at him:

“Are you the night?”

She smiles.

And he feels ashamed about his white clothes.

And wants to be far off and alone and armed.

Well-armed.

XVIII

“Have you forgotten you are my page for to-day? Why have you abandoned me? Where are you off to? Your clothes tell me you’re —”



“Do you wish you were wearing your ordinary coat?”



“Are you cold? ̶ Are you perhaps homesick?”

The Countess smiles.

No. That’s only because childhood, that soft dark cloak, has fallen from his shoulders. Who has taken it off? “You?” he asks in a voice he’s never heard before.” You!” And now there’s nothing on him. He’s naked like a penitent. Luminous and slender.

XIX

The castle loses its light slowly. A heaviness now: being weary or in love or drunk. After so many long empty nights in the open: beds. Wide, oak beds. Where you don’t say your prayers as you did on your way here, lying in a damp furrow like a grave, trying to fall asleep.

“Lord God. As Thou wilt.”

Prayers are shorter in bed.

More heartfelt though.

XX

The tower chamber is dark.

But they lighten faces by smiling. They fumble on their way as if they are blind and find each other like a doorway. Almost like children who, frightened by the night, keep close to each other. And yet they aren’t afraid. Nothing is against them ̶ neither yesterday, nor to-morrow; because time has collapsed. And they are coming out like blossom from the rubble.

He does not ask “Your husband?”

She does not ask “Your name?”

They’ve discovered each other so they can take a new identity.

They will give each other a hundred new names and then take them away again, lightly, as someone would lift off an ear-ring.

XXI

In the entrance-hall the armour, a shoulder-belt and the greatcoat belonging to Von Langenau hang over a chair. His gloves are lying on the floor. His flag, dark and long, droops on its staff leaning against the crossbars of a window. Outside, a storm is racing across the sky, breaking the night into pieces, white pieces, black ones. The moonlight goes past like a drawn-out lightning flash and the flag which doesn’t move has restless shadows. It is dreaming.

XXII

Was a window open? Has the storm got inside the castle? Who’s slamming the doors? Who’s just passing through the room? ̶ Leave it alone. Doesn’t matter who it is. He won’t find anything in the tower chamber. Behind a hundred doors lies an ample sleep that two have in common ̶ like one mother or one death.

XXIII

Can it be morning? What’s that sun rising? How big it is. Are those birds? You can hear them all over the place.

Everything’s bright but it’s not daybreak.

Everything’s loud but it’s not birds we’re hearing.

It’s the rafters that are lit. It’s the windows that scream. And everyone’s screaming, scarlet in the face, screaming to the enemy standing outside in the flickering landscape, screaming: Fire.

And with sleep torn from them they all force their way, half of them in iron, half of them in nothing, rushing from room to room, all over the place, trying to find the staircase.

And with forced breath horns stammer in the courtyard:

Gather round! Gather round!

Quivering drums.

XXIV

But the flag is not there.

Shouts: Cornet!

Maddened horses, prayers, screams,

Curses: Cornet!

Iron on iron, commands, signals.

Silence. Then: Cornet!

And again: Cornet!

And away with the thundering cavalry.



But the flag is not with them.

XXV

Running as fast possible he pushes through doors that are on fire, gets scorched descending the stairs, breaks out of the raging building, carrying the flag on his arms as though he was holding a pale unconscious woman. He finds a horse like a hoofed scream and gallops ahead, past all once gone by, to be again with his own. The flag is coming where it belongs, never looking so regal and now they all recognise far in the distance the shining man with no helmet who’s bearing the flag . . .

But it starts to gleam, twists about, turns larger, goes red.



Then their flag is burning in the midst of the enemy and they’re rushing towards it.

XXVI

Von Langenau is in the thick of the enemy but not alone. Terror has made a circle around him and he checks his steed in the centre under his slowly blazing flag.

He looks around slowly, almost wistfully. So much that is strange, so many bright colours in front of him. Gardens ̶ he thinks for a moment then smiles. But he can feel that eyes are holding him, recognises them and knows who they are, heathen dogs ̶ and he urges his horse among them.

But when it got knocked down under him he found gardens again, also the sixteen curved sabres springing at him, catching the light, ray by ray, like a fête.

A laughing fountain.

XXVII

The greatcoat got burnt in the castle, along with the letter and the rose-petal that once belonged to a woman from a foreign land.

Next spring (it came sadly and cold) a messenger from the Baron of Pirovano rode slowly into Langenau. He has seen an old woman weeping there.

Friday, May 26, 2023

Difference Dynamics







Choose any three numbers. The differences between your numbers give you three new numbers. Repeat this operation to give a sequence.

In this example the sequence starts: 15,39,8→24,31,7 → 7,24,17 →17,7,10 ....

What happens to this sequence. Investigate for different starting points.


Start with a finite sequence, for example (25, 42, 6). The differences between your numbers give you three new numbers (17, 36, 19). Repeat this operation to give a sequence of sequences. In this example the sequence of sequences continues: (19, 17, 2), (2, 15, 17), (13, 2, 15), (11, 13, 2), (2, 11, 9) , (9, 2, 7), (7, 5, 2), (2, 3, 5), (1, 2, 3), (1, 1, 2), (0,1,1) etc. You can produce chains of sequences like this for sequences of any length. The rule for generating these sequences is that you take the moduli of the differences between adjacent terms, taking the difference between the last term and the first term, to get the next sequence in the chain and repeat this process to get a sequence of sequences.

Read no further. You can try this for yourself, starting with a sequence of any length. Carry out your own investigation, make some conjectures about the behaviour of the sequences that you observe, at least for sequences of two, three and four terms, and try to prove your conjectures. When you tire of your own thoughts and you want to know what others have done with these ideas then read on.

This investigation is well known and has a long history. The problem is attributed to the Italian Enrico Ducci in the late 1800's, and the first proof of the theorem that is proved in this article seems to have appeared in 1937. The usual proof involves, among other things, expanding a sum of matrices by the binomial theorem over the field Z2. However, as the problem can be tackled by school students, it seems desirable to have elementary proofs of the conjectures they might make. The purpose of this article is to provide such proofs.

A little experimentation leads to sequences that repeat in a cyclic pattern or to the sequence of sequences stopping with the zero sequence (0,0,...0) which we call a fixed point of this iteration. This behaviour is typical of dynamical systems which are very important in mathematics.