We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion ${\bf S4}\oplus {\bf S4}$ . We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers ${\Bbb Q}\times {\Bbb Q}$ (...) with the appropriate topologies. (shrink)

Don't tell terrible stories—everyone here has enough of their own. Everyone here has a whole bloody sack of terrible stories, and at the bottom of the sack is a hammer the narrator uses to pound you on the skull the instant you dare not believe your ears. Or to pound you when you do believe. Not long ago I saw a tomboyish girl on Khreshchatyk Street demand money of an elderly woman, threatening to bite her and infect her with syphilis. (...) Don't stroll through Volodymyr Hill Park, don't stroll around the botanical garden, and especially don't stroll on Kontraktova Square. Don't stroll anywhere. Don't go to the pavilion with the Golgotha panorama near St. Alexander's Church. Not even the twelve-meter-tall crucified Christ will save you. Don't go outside when it's dark and people turn into shadows a shade darker than dark. Also don't go where you can be seen from far away. Not to imply that people used to be like a bunch of lilies, but now they stink like a cellar of cabbage.The city, which earlier might have had some fun, is now going crazy. It's like a fish in warm water: it doesn't react to anything, swims slowly like it doesn't care if it swallows a hook or not. The excitement and exaltation pass into oppression, just as our necks have sunk into our shoulders, our shoulders into our lumbars, our lumbars into our nether regions. The holiday turns into a funeral, the parades into explosions, depression into mania. Winter passes into summer, people turn into beasts, the hours into ages, and the ages into hours. It's worth simply walking around the city to see a soldier from an unknown army taking a piss near the opera. Farther on is a row of identical old widows selling ball gowns and candelabra. Then there are the aristocrats and manufacturers who throw so much at the prostitutes that they'll soon be richer than their wives.I returned late through the Kyryliv Wood, not heeding all the warnings that I myself have given here. It really is dangerous—the place is famous for it. There's a madhouse nearby, caves where criminals and the sick can hide out. Also, once upon a time, as they say in fairy tales, the great dragon Zmei Gorynich lived here beside the Puchai River. The stench in these places drives away the most committed misanthropes and even one type of philanthrope—that is, perverts. It sounds dumb, but the stench is cleansing. I don't know where it comes from. After the operating theaters and the rooms with amputees, the stench no longer repelled or attracted me; it just was. And this was a great place to think. As I walked, I considered an incident with our patient.The patient, a respectable individual whose name carries too much weight for me to state it directly, one day began to assault people. He nearly strangled a merchant who he believed asked too much for a beaver coat. He likewise wanted to kill his business partner when he didn't say hello loudly enough. But the worst was, he lost all shame of his own nakedness. At first it was the police who took care of it. When our future patient slipped off his pants and undergarments, he was taken to Kyrylivska, which has had means for dealing with such cases dating back to the day when unhinged Cossacks and composers from Kyiv Mohyla Academy were taken there.During the examination we determined that the patient was experiencing a severe breakdown. His wife added that lately, more than once, he had allowed himself strong words in front of the children and often suffered from ennui. Furthermore, she said, the patient had been undergoing treatment for “the French disease” for some years—which was, obviously, where we needed to start.“Syphilis!” Skorsky spat out the matchstick he was chewing on. He was a specialist on the psychological aspects of diseases related to the venereal. “Tertiary syphilis! When poorly treated, over time ‘the French disease’ can destroy the central nervous system. Hence the patient's chicanery. Such theater!”Skorsky and I had not spoken since the incident at Bilinsky's. Meanwhile, something significant had happened to him. The most boring person on earth, Skorsky had simply caught fire. He said hello and kibitzed. I even heard the doctor got drunk alone in his office, then wandered through the forest. Could he be using narcotic substances?“Cocaine!” was the doctor's second proclamation. It was his favorite treatment for the psychological complications of syphilis. Skorsky himself never took what he called “the universal drug”—good for alcoholism and toothaches, neuroses and morphine dependency—though he had read in an article by a respectable Viennese physician, who used cocaine as a panacea, that it was not addictive. That doctor subsequently recanted, but Skorsky paid no attention. He believed the retraction was made under pressure from pharmacologists who had no incentive to cease production of the medications that cocaine might supplant. Their representatives either paid or threatened the Viennese to repent.As the patient was escorted to his room, he assaulted the orderly, Alevtyna. They tried pulling him off her, but, though he released his fingers from her neck, he buried his teeth in her leg. The poor orderly, who had not until then been attacked by a psychotic, nearly died of fear. Later, panic set in over Skorsky's diagnosis. He told her about the consequences of syphilis: grotesque patterns on one's face due to infection of the skin, mucous membranes, cartilage, and bones. He went on about the devastation to the central nervous system, which they had just observed in real life: “The face starts to look like lace some mangy dogs fought over before rolling in the mud.”Alevtyna, who had not yet regained her faculty of speech, straightened up. Ignoring the slavering male orderlies, she bared her leg to get a better look at the wound. She then ran down the hall and out into the garden, where she fell on the ground to rip up grass and small bunches of daisies. Alevtyna ate them along with the soil in their roots.“Minor hysteria. She needs fifteen milligrams of cocaine.”Skorsky took a snuff box out of his pocket and scooped up some white powder with a toothpick made from a goose feather. He gave the order to close Alevtyna's mouth and one of her nostrils, forcing her to snort the medication.We fretted over her so long that evening fell. I decided to walk down, along the ravine, behind the church.It was unlikely there were any large beasts there, but something was rustling. The pits and mounds, ravines, paths, graves of witches whose living sisters flew in the treetops from time to time, the whispers of the forest spirits, the spirits of the nutcases who died in the hospital, the spirits of the monks from the St. Cyril Monastery, Zmei Gorynich and the bogatyrs who wanted to defeat him. The city would be calmer without this forest. I saw the gaps between the trees and went off in the direction of the tram tracks.As I was coming out of the forest, there was a patch of Amanita muscaria that had been trampled into porridge. A bit farther on, the body of Professor Bilinsky lay killed in the blackberry bushes. The way he was lying it looked as though he had not struggled before death. I quickly examined his body but saw nothing out of the ordinary. There were no wounds, no dirt under the fingernails. Animals had not yet smelled the carrion, but swarms of various insects covered him. Oh, why did I have to find the putrid body?The best thing would be to take the tram to his house to inform his relatives. The doors closed, and I noticed my own calm. This death had not evoked any emotions in me other than a feeling of responsibility, the need to tell the family. But also—some alarm at the thought of who the murderer could be. I knew that it was murder.“Your nose is bleeding.” A woman as round as an onion, carrying two baskets full of strawberries, offered me an ironed and starched handkerchief.“Have I dirtied my shirt?”“No, it's as neat as a pin. It's just your nose that's dirty. Wipe it now before you spray blood on my strawberries.”“No one will see the red on red.”“Ah, but it's salty!”“You know why it's not sweet? We'd drink it like syrup.”“Those with Christ in their heart do not talk that way.”“Are your strawberries expensive?”“Why? What?”“I'm checking to see if you have God in your heart.”“Child, if you knew how I have to work for this berry! I have to weed it a hundred times. In a week, the quitch grass grows as high as a horse. And I water it with water I carry from the stream, it kills my arms... ”“How much are the berries?”“They're not for sale. Anyway, soon money won't mean a thing. Soon all money, all these papers made from the skins of sinners on their satanic presses will be annulled. What matters is how we treat each other.”“So if I try your strawberries for free, my ‘thank you’ will be enough?”“Hands off!” she said and thwacked my fingers.I heard loud laughter behind me—same laughter as from the café near the Continental. There was no one sitting near Alina. (This is what fate looks like, remember.) Without asking, I sat next to her, away from the old lady.“Excuse me, but the night before last didn't you, yes, didn't you intrude on my privacy?” She started right away.“I saw it a little differently. Who was that young man with the mustache who paid me for you?”“Are you checking to see if you can flirt?”The tram stopped. People got on and off.“Are you coming back from the hospital?” she asked. “Don't be shocked. My uncle works there. He's told me all about you.”“An uncle by the name of Skorsky?”(Remember: this is what fate looks like.)“Yes. Skorsky's been strange recently—says things that make me wonder if he hasn't lost his mind. Have you noticed anything?”“I don't know.”“You know perfectly well.”“Where are you going?” I tried to change the subject.“I have to send something to my theater friends in Odesa. By the way, they'll be putting on Oedipus Rex soon in Kyiv—in Ukrainian.”“Greek tragedy in Ukrainian! That's a first.”“Exactly. The troupe is rehearsing now in Odesa. The theater where they will perform this fall is being remodeled.”“Wait. Now I remember where I've seen you before—it was at a performance! Vynnychenko's Black Panther and White Bear, at the Bergonier on Fundukleivska.“The same director is doing the Oedipus. He's my friend.”“He's your friend in what sense?”“Again with that tired subject. By the way, I've been thinking about you.”“And I about you.”“That's good. I was thinking not about you, to be precise, but about that elevator you invited me on.”“Who was that man with you?”“Like a broken record! Even if he had been my fiancé, I'm not bought or inherited. I'm not a brooch or a hundred acres of land, and I'm not a house in Kaniv!... Who was with you when you saw Black Panther?“Ah, so.”“Answer!”“That was my mother. She looks very young. She is coming to Kyiv the day after tomorrow. I can introduce you.”“Oh, this is my stop.”I looked out the window and realized that I had long since passed the stop for Bilinsky's.“Can we see each other again?”“We can. But you have only one chance.”Alina the anarchist wrote something on a scrap of paper and handed it to me.Morning, not morning but a thick porridge (I hate porridge). Dew, thick spit, crushed fruits, urine, all on the sparkling cobblestones. The sun, just barely having made its appearance, is already scorching. The human masses scurry and grumble like poorly digested food inside a stomach.I walked diagonally across St. Sofia's Square, then along the perimeter, then one edge, then again diagonally across. I went underground. The basement café of the Continental Hotel was practically empty. I again asked the server to bring the cloth with the embroidered portrait, but I couldn't remember the musician's last name, only that it ended with -sky. The server said that -sky was currently in the southern cities of Yalta and Odesa. I added that Kurbas, the director, Alina's friend, was also in Odesa, rehearsing Oedipus Rex, and that he'd previously put on Black Panther.I was bored, so I walked along Khreshchatyk and then headed down, calling to mind all the Kyiv churches of Podil: there's Birth of Christ, St. Nicholas on the Shore, Intercession, Pyrohoshcha, Holy Presentation, St. Dymytrii Rostovsky, St. Illia's. And also the Epiphany Brotherhood Monastery, Ascension Convent, and St. Katherine's, all these whipped-cream churches on the waffles of our streets. A few of them reminded me of themselves by appearing suddenly out of nowhere.The smells on Kontraktova Plaza where commerce buzzed were like multicolored light bulbs turning on one after another. Here you could catch the aroma of Balabukha jam, which blended with the next smell, English shoe polish at the Raiskys’ shop. Then the crunchy-smelling cabbage from old women standing in a row like herons and spitting out the shells of sunflower seeds. Farther on, the stench of a good-sized rat that crawled under Mrs. Shevchuk's shop where she sells broadcloth. Oh, she can't scream: no, she'll quietly dig that rat out herself so as to not scare off her clients.I bought a paper and two pairs of underwear. I asked two laughing young chambermaids who were secretly puffing in a grape-filled yard for a smoke. I wandered around Podil until evening when I came across a sawmill near the Dnipro that surprisingly smelled pleasantly of mazut fuel oil. The weather was dry, yet in the middle of the road was an enormous puddle, a deep dark black. A forty-year-old woman in a pale pink dress stood near it. The theatricality of it all provoked me to pose her a question,“Ma'am, what should I do?”But she paid me no attention. I shouted,“What should I do?”“What to do, what to do?” she said in Polish. “Jump in the water and swim so far away that you cannot return.”I quickly crossed a section of the forest. The wind brought a mixture of unpleasant air, like a stinky handkerchief held under one's nose. Passing the trees, I saw light in the spaces between them and exited at the hospital.Outside the windows, two orderlies lay in chairs with their heads thrown back. Two others—fools—ran around the yard in different directions, peering out at... something. The lights on the first floor of the hospital were on, and the staff milled about.“You're just in time!” said Ivan, a tall, young orderly.“For what?”“Your patient ran away! We went into his room and he wasn't there.”“What patient?”“The one who bit Alevtyna,” said Danylo, the other orderly, short and middle-aged.“That's Skorsky's patient, not mine.”I had no intention of helping them. This was all history—like my family, Kyiv, and my previous life. I had no intention of thinking about it. I wanted to go to my office, pack up my field surgery kit, and get out. So what? Their psychotic syphilitic ran away—it happened.Of course, that patient could have something to do with Bilinsky's murder. But that was no longer my problem.“What a strange coincidence!” the doctor on duty said. “Comrade doctor, the other one responsible for this patient was just here.”“And where is he now?”“He took off toward the church to look for the patient.”“Didn't the patient escape earlier?”“Don't know.”“How do you not know? You had better call the police, moron, before he kills someone. And get those sleeping orderlies to look for him.”“They can't... ”“Why not? Should I go wake them?”“They're on morphine.”“And you, I can see, have lost your mind. Go, catch your psycho! If it turns out that he killed Bilinsky—and on your watch—you can't imagine what's in store for you.”I adjusted my homburg and set off in the direction of St. Cyril's, that unwelcoming monolithic cube. I glanced around—what if our escaped syphilitic were to jump out of the bushes and bite or strangle me. I looked around because I wasn't sure of my actions, wasn't sure of my choices. Tripping over a clump of clover, I reached the open doors of the church. I couldn't stop myself from going in.The walls and ceiling were covered with frescoes. There was what used to be an angel rolling up the sky on the southern column of the narthex. But also graffiti: people scratched their names on it so as not to be forgotten—their idea of eternity. Prince Volodymyr the Great compared this activity to the desecration of graves. The vandals paid a fine and were beaten with canes. During the raids of Batu Khan, the church was deserted and cracks appeared all over it. Wild martens and feral dogs sought shelter here; insects swarmed under the ceiling with its red mosaics. Birches grew in its midst. Water seeped in the cracks, the water became ice, the ice widened the cracks, more water seeped in the cracks, becoming more ice that further widened the cracks, the wall split and nearly fell over, and then the wall fell over. Yet the angel is still rolling up the sky... When I reached the exit, I heard a rustling behind me. I turned after I stepped outside: in the depths of the church, like a stick in a pot of tar, stood a man with a large bag thrown over his shoulder and a revolver pointed right at me.“Is that you, Doctor?“Don't move!”“What's... Skorsky, what's with you?”“Don't move, I say!”“What are you doing here?”And finally I understood... Skorsky was himself the psycho! (Really, I had known for a while.)“You are the murderer! I knew it! But—why?”“Shut up.”“It was you. You! The stolen cigarettes, the strange behavior, Bilinsky. If I shout, everybody will come running. They've already called the police!”There was heavy breathing behind me. And then a gun rang out.The city is overgrown with new buildings. They encircle everything that was once on the periphery. Kyiv has become an old lady that can no longer restrain herself in the face of pastries. The city climbs farther. It steps over the swamps, turns the old rivers into a series of lakes; the other bodies of water it drives into canals. The grain that falls from the wild wheat is black. When the sun heats it, the grain melts and trickles into the earth. St. Cyril's stands indestructible. No one spackles the small cracks in its walls with either expensive putty or glues, nor with cheap cement and whitewash. One day a small fox appears in the doorway. It runs inside and along the floor of simple gray tiles. The gods watch from the walls, watch and fall into ruin. The fox runs to the iconostasis. Before it is a time-darkened Virgin Mother and Child in oil on sheets of zinc. The fox runs the metal steps that wind up to the second floor. The fox runs past all the vaults, naves, all the frescoes. A buckthorn seed flies in through a broken window. It will be the first. Soon the buckthorn will grow everywhere. A dumb hare will make its nest in the buckthorn bushes and nightingales will settle in the upper branches to sing until the end of the world. The fox runs between the thick rays that penetrate the windows. It catches one of the rays, squints its eyes, and warms itself in the sun.The shot rang out, but I did not fall. I looked around—and on the church threshold was our syphilis patient bearing a rod. His head lay on the rocks by the doorway.“If only he'd been at the stage of nose deformity! Just imagine: a hole instead of a nose plus a hole from the bullet—like an extra pair of eyes!” Skorsky laughed at the corpse.“We need to call the orderlies.”“They heard the shot. They'll run here on their own. You see, Professor Bilinsky believed it would take two or three years to wrap up this patient's case,” Skorsky told me. “But I took care of it much faster!”“Excuse me, but I'm going crazy in this city. I thought that you were Bilinsky's murderer.”“Just so. Why not? I am Bilinsky's murderer.”“Don't tease. You've changed a lot recently, so... ”“Yes, I've started killing people. You might term such a change significant.”“You have the right to irony.”“I am not being ironic.”“Let's call it sarcasm.”“It's the honest-to-God truth.”“And yes, you have the right to mock me.”“Well then, let's be done. To the horses!”“What horses?”“Alina's waiting!”Alina, her uncle Skorsky, a few others I didn't know, and I rode like the wind that ripped off my homburg and carried it back to Kyiv.“There's a fresco in the choir loft at St. Cyril's where Vrubel painted himself and patients from the hospital as the apostles. When I came across it by accident, I really believed they were saints,” Alina said.“I've never been up there. I've only seen the church from below.”“Remember the way back so you can see it sometime.”“The Puchai River used to flow here. You shouldn't trust the landscape,” Skorsky said, reaching for something, perhaps his bag, just when we left the darkness of the trees and saw the endless steppe ahead of us.We rode all night without stopping. Though no one was chasing us. Though we had nowhere to be. We rode like beasts released from a cage. The promises of the horizon turned what we'd left behind into a cage fit for those from whom freedom had been severed, like an anomaly, at birth.The pre-morning sky looked at first like a sack of turnips—filled with something heavy. But with each verst, the sky became lighter. When it was finally light enough to see clearly, we arrived at a knoll at the foot of a stone wall that from a distance had appeared to be a gigantic piece of halva. The exterior ruins of the castle gave no hint of how it was when all was fine here, when people defended themselves successfully from the nomads’ raids. From far off, the wreckage looked like a natural agglomeration of stones—a rocky elevation, no more: a cluster of cliffs. It would rain a few hundred more times, a few hundred more winds from a few hundred directions would blow on this heap, and it would collapse as though nothing had ever been here.A few stalks of wheat grew from one of the rocks. Someone had probably cast a handful of grain here for some birds that forgot to eat it.“Who could this castle belong to?” I asked Skorsky.“I reckon the Swan Princess,” the doctor rejoined, hoping to sound knowledgeable.From behind one of the piles of gray sandstone emerged a young man in a black reptilian coat and a white papakha as lush, bright, and out of place as a dahlia. His name was Artem. The heat was melting our brains, but he was dressed like that, in rooster fashion, which was popular among the otamans. Artem helped Alina dismount her horse and tried to kiss her on the lips, but she offered him a cheek instead.Had she been racing to see this clown?We entered the yard—the ruins had fashioned an internal space that was more or less protected, at least from strangers’ eyes. It turned out that there were even places where it was possible to hide from the rain, and from there the ruins didn't look half bad.In the center of the court was a table, and on it a wooden bucket with pink gladiolas. How romantic! It all looked like it came from outer space. Where on earth, in the middle of the steppe, far from any village or town, did this table, this simple table, come from? And the gladiolas? The steppe hadn't been plowed in so long that any cultivars would have gone wild, degenerated, dried up completely.A campfire crackled nearby—a little preview of what we would soon do to the houses, villages, and cities. Artem the otaman brought over a cezve from the fire and poured the first portion into a small, copper cup for Alina. He also got out a porcelain cup with images of rosy cherubim—but how...?“Who else would like coffee?”Only Skorsky and I responded. The question excited me, even distracted me from the thought of the kiss I had recently witnessed and the Kyiv I had recently left.“It's obvious who the professors here are; cultured people drink coffee. Are you both doctors?”“Uh-huh.”“For wolves of the steppe, like us, doctors are gold, even more precious than gold. Actually, a Hippocrates like you should eat more, because those in your profession will soon be worth your weight in gold. Work on your figures, both of you.”“Who will take pity on the horses that have to carry us?”“We'll find the horses. And very large doctors can be transported on machine-gun carts. We'll need to seat the otamans near you. Only a fool would shoot at a doctor.”“I think we'll find quite enough fools here.”“With your beard, Doctor, you look like Tsar Nicholas II. But even so you won't be shot. You might even be canonized!”“We've only just arrived and you're going on about executions,” Skorsky grumbled and checked to make sure that he still had his bag.“Apologies, apologies, pardonnez-moi. But you are not merely a doctor. A venereologist! Skorsky, you're a specialist! A venereologist is the most important person in wartime. The most valuable! You are the botanists of war. You can't imagine what varieties of flowers grow here, and these beds have long awaited a proper gardener. Or even just a man with a scythe!”“Bite your tongue,” Alina said. “I don't need to listen to this.”“Yes, yes, of course. Excuse me, my r—. ” He almost said “rose.”We rested all day. We went down to a surprisingly close river overgrown with lilies. We rowed the boats left by fishermen. I talked to Skorsky. He took his bag everywhere, refusing even to swim so he wouldn't have to part with it. I asked him what he had in it, but he said it wasn't my damned business.Alina rowed with the otaman to the middle of the river. They were having a loud discussion. She was waving her hands. The current carried their boat downstream slowly and smoothly. What a nuisance, that current!I tried to meet with Alina one-on-one, but she was avoiding me. In the morning I was confused, by lunch I was sad, and after lunch I got angry.In the evening, I lay on the hot grass and drank another cup (I have no idea where they got such good coffee), which had no effect at all on my sleep. I watched the Perseids. Every year, the Earth passes through the tail of Comet Swift-Tuttle. People can see the meteor shower and make a wish. I wished. I counted forty-seven falling stars. All forty-seven of my wishes were for the same thing.Around the campfire, they were sitting, talking. I saw how he tickled her face with a piece of grass and she brushed him off in annoyance. Then they were screaming at each other. Later they again spoke kindly, after which they again quarreled. My joy grew after each tiny mistake that Artem made. I wanted him to show the worst he was capable of.They were screaming at each other, but all I could hear was beautiful opera singing. The stars fell to the sound of their screaming. The stars blessed my joy.Then this happened: Alina kicked the fire, scattered burnt kindling, and burned some of the grass. Artem grabbed her by the arm, but she broke away from him and ran off to the horses.“Go then! I guarantee you'll get to Katerynoslav and return with your tail between your legs.”“I'm going to Huliai-Pole! To Father Makhno!”I jumped up and ran after her.“Where do you think you're going?” Artem shouted.Really—where was I going? I was going after her: to Huliai-Pole, to Katerynoslav, to Rome, to Washington, to Istanbul, to Montevideo... “Go to sleep,” he said. “Come morning, this coquette will be here, right as rain. We've already been through this show. Tomorrow she'll be right here next to my boot!”... No, she won't.In some sort of shape we entered some town. There were some buildings that were some colors, some trees, some streets, some roads, and some signs. Posts, flustered birds’ nests, echoes, colors, shapes—each of some kind. A wedding procession was coming toward us. If you want to make orange, you need to add yellow to red, and then bam—it's black. If you want to salt the soup, shake in a little, and then bam—two handfuls. You want to say a kind word, and then bam—a punch in the face. I was rocked around like a watermelon on a boat and threw up my breakfast straight into the horse's fluffy mane. Sanko found this hilarious, but I said I'd pulverize him. So Sanko sped ahead.No one knew anything about Alina. The daytime sky was like a poorly washed bowl. The sun was a squashed, rotten apricot. The night sky looked like the sole of a boot to me. The moon was a dirty cheap copper coin that had gotten stuck to the sole. Everything seemed spoiled to me, irrelevant, unnecessary. Without her, this journey was a waste of time.“You'd better stay away from everyone,” Artem said. “You'll infect us with your pining, and pining is worse than the clap.”The wedding procession was before us. The young couple, still utter children, walked so calmly it was as if they didn't see us. As if we were made of a light breeze—our bodies, clothes, our horses and their iron shoes—of the lightest gasses. As if we were visible only to ourselves and the coal-black dog that barked, panting and gasping.The wedding was headed straight for us. We were in the middle of the road, and so were they. We approached each other slowly, a wave going toward a wave. Some ten meters before their indifferent faces, I noticed the color of the bride's eyes. And the coral-colored tulips that fell on the road before her. Round goose eggs on meaty stems, the flowers were falling and falling before her. The bride's eyes were almond shaped.“Hey there,” Artem shouted at me. “Wake up!”I came to and saw the whole village, everyone there, not realizing my group had turned left onto a side street away from the procession. The tulips disappeared—where'd they get tulips in the fall? I was sitting alone on my horse in the middle of the road, and the entire wedding procession came to a stop. I moved to the side, and the throng marched on, cutting off our escape route. We rode a few more meters and came across the synagogue.“You know what, you're right,” said the otaman.“Who is?”“Oleksii is the only one here who's right.”“About what?”Artem turned his horse and raced back. Everyone stood still while he ran his horse into the crowd and began firing his revolver. People scattered in all directions. Artem trotted, cackling like an imbecile. The horse kicked an old guy in the mouth. The man fell, spitting out his gold teeth. We rode up to the commotion and formed ranks, but none of us wanted to join the otaman.The bride stopped in the middle of the street. On both sides were buildings and trees, as well as dust, sky, and sun. She stood still, beautiful, as if nothing had happened. Then she adjusted her garland and walked calmly on.“Well, should we get some sugar now?” Artem laughed, looking at the bride, and off he went toward the sugar factory.It was then I noticed that all of the houses had shutters—fuchsia, blue, ocher—and that all the shutters were closed.We flew toward the dirty building, whistling and shouting. If there had been aesthetes among the otamans, they would certainly have razed the abomination in this field after seizing it. They would have spread soil on top and sown buckwheat. Long live buckwheat!, that wonderful crop. Like hunting dogs hot on the trail, we raced to our defenseless victim, with the baying of hundreds of hounds behind us. The field shook beneath us. We became an artist's canvas, evolving from Realism to Romanticism, Romanticism to Expressionism, Expressionism to Suprematism. If we had been painted in black and white, we would have been splotches (until the ink ran, annihilating all remaining patches of white).Two men stood near the gate—unarmed and undressed, in nothing but their undershirts and boots. Our fervor, our kinship with the elements, our entirety, were all for naught.“Jesus Christ! What bores!” Artem exclaimed. “How boring you are!”“Maybe boring for us, but fireworks for them,” Sanko said, dismounting his horse.“The fear of death engenders creativity,” our otaman—a distinguished philosopher of the early twentieth century, that demonic breed—prophesied.He went on, “Excuse me, but with all due respect, we are not going to search you. Just show us right away where the money is. Why are there so few of you? Don't say there's not much money. I want piles and piles of money! If you don't show it to us, we'll print our own on your skin. Believe me, we will.”We entered the factory grounds. There were no workers, only an enormous mountain of sugar beets that looked like a pile of coal from a distance and a pile of dead rats from up close.“So, did you have a good year?” Artem asked a man in an undershirt.“Not really—too dry.”“Nah, that's fine. You wouldn't have been able to gather most of the harvest this year anyway. There's a fire burning across all of Ukraine, all of Russia. The whole world!”While Artem tossed thoughts like well-chewed sunflower seeds into the crowd, the two men quietly stepped aside and then ran fast ahead to the factory's main hall. The gigantic door slammed shut. The gate was locked behind us! The windows were smashed! The factory roared from inside like a cumbersome machine starting up. Bullets whirred through every window.“Bastards! It's a trap! Quick, after me!”Still on horseback, Artem bounded over to a vast window, low to the ground, and smashed it mercilessly. He broke the frame and jumped inside on his horse. I and a few others followed. We broke into their lair, threw open the doors, and let the other warriors inside.Iron vats of hot sugar were steaming, pipes were clattering; machinery groaned.“Parasites!” Artem gritted his teeth. “I'll get you. I'll get you red sons of bitches. Painted whores!”At the word “painted,” his horse fell to the ground. Lying prone, Artem continued fighting, but the red soldiers wouldn't let him stand. Fighting nearby, I rode over to assist but did not know where to aim. Artem got up, ran forward, and brought his sword down on the head of the closest soldier, all the way to the middle of his skull, to the bridge of his nose. It was like butchering a pig. Artem thrust the sword into the buttock of another who was fleeing and cut off his leg at the bend in the knee.“I'll cut off every last one of your asses! Cut off your asses!” Artem bellowed.A half hour later, the dead were lying, the captured sitting, and the victors doing anything they pleased.“Skorsky, are there a lot of casualties?” I asked the doctor, whose hour it was. I hoped not, because I was too tired to help him.“Just a few. The dead are already dead, and the wounded are not ours.”Though Skorsky rarely asked my help, and though I'd become an ordinary soldier, the doctor in me was still present in the most unpleasant attribute—knowledge. Others saw an eviscerated man, pieces of dusty flesh smeared with clay, soil, sand, and straw. I saw a perfectly formed kidney hanging perfectly from the rest of its body like a child's mitten from its coat. You could try this death on for size. Wear it like a sanbenito of the Inquisition.Artem counted the money and then lay on the floor alongside the gigantic sugar mountain in the middle of the room. From time to time, the crystals rustled as they fell.“I didn't think you'd be such a fighter!” the otaman said without turning toward me. “I thought you'd be healing us. You'd keep to the rear and we'd hide you like a girl. But here you are, in the vanguard, like a lion!”“I got excited,” I told him, choosing not to react to the “girl” part.“’Cause Alina said there was no sense counting on you to fight.”“Really?”“Does that sting?”“Why would it? I'm a doctor—not everyone is. It requires a brain. Unlike waving a sword.”“Yeah, yeah. I gave her gladiolas. We were lying in the boat near that castle, doing all manner of things, and she told me all about you. How you met.”“You were lying in that boat talking about me?”“It was the day before you left Kyiv. You agreed to go with the anarchists so quickly!”“Were you surprised? Doctors make fast decisions.”“But you probably had great prospects. Your parents are rich, right?”“And who are your parents?”“Probably all your relatives fled abroad—bourgeois. Why did you stay?”“What the hell's your point?”“Alina, by the way, died a while ago. Probably.”“Don't jinx her.”“Listen here,” he said, staring at the ceiling. “And listen good. If you have designs on her—dead or alive—it's best you castrate yourself now.”“After you.”“If I want to kill somebody, you know, I just do it.”At last he looked at me. I was lying on the floor nearby and looking in his direction, sweaty and relaxed, my appearance complemented by my disdain for his opinion, his authority, his stupid hat. His everything.Artem raised his arm above his head, stuck a finger in the sugar mountain, and licked it. We both got up. Had I anticipated this turn of events, I would have readied a gift for him. Artem held his revolver. Under my hand I found a knife the workers used for gathering beets: it was a deliberately sharpened arc they sank into the swollen brassicas. I jumped up and quickly stepped around the sugar mountain.Artem's bullet hit a pane and broke the glass.“Not man enough for hand-to-hand?”The otaman shot again.“You should've challenged me to a duel, you romantic!”Encrusted with white crystals, I charged Artem from the sugar mountain. We fell in, and the sugar stuck in our hair, mustaches, nostrils, armpits.The gang ran in to get us apart, then backed off because it had nothing to do with them. By now the sugar mountain had burst its banks. Of the once perfect pyramid, a deformed mound remained.Wounded, Artem fell on the sugar mound, turning the white red.I stood before the gang sugar-coated and holding a bloody hook. The old otaman was drawing his last breath. Blood trickled from the corner of Artem's mouth and streamed from the left side of his breast.“What's the commotion?” Old Roman had just come in.“Be quiet,” the boys told him. And a good thing they did.“You killed him? You killed the otaman!”“Shut your mouth,” the boys told him.“You... ”I slugged Roman's stinky herring mouth. How did that son of a bitch find pickled herring in a sugar factory? My fist was now bigger and stronger than ever before, a steel anvil that could split nails and shatter memorial plaques. The unfortunate man's jaw twisted like an upper millstone that had gone off track from the lower.“Let's get out of here and go to Makhno's camp,” I gave my first order.We galloped so fast the grass burned beneath us. The birds and bugs had no time to fly out of the way; hooves trampled the burrows of rodents who didn't dare crawl out of their holes for a long time after. We raced like no one had ever raced before.The steppe, that sly fox, pretended to be an innocent fool. The steppe said, “I'm like Adam: I don't even know my own name.” But its grass harbored the tracks of thousands of armies and the heels of Herodotus, the crunch of Trypillia vessels, and the smell of Scythian hemp, Roman coins, clay figures of wolf people, the chevrons of Denikin's army, glass from the Chekists’ ruby stars, traces of uranium from flying saucers. I threatened it: “Steppe, show me your layers, or I will burn you, plow you under, flood you.” But it just replied: “I'm like Adam: I don't yet know my name.”I lost geography as if it were a silver coin. It fell out of my pocket and rolled through the feather grass that blanketed the steppe in white foam. The open space ahead was so endless that the whole world might as well have been steppe. If people ended up here from somewhere else, they would conclude they were on another planet. The coin fell and became an argentum, became one with the ring on the hand of the princess who had one green eye and one blue, with the twisted candlestick at the monastery on the other side of the steppe, with melted ingots. It broke down into simpler elements, simpler and simpler yet. The horse carried me spreading the seeds of northern plants to the south, just as southern riders had once brought flowers and weeds to the north. And then I turned back. Just as I had no geography, I had no time. Every night I fell asleep with the thought that the next day I would again race. Through all spacelessness, all timelessness. I exchanged one horse for another, got on a train, on a boat, traversed forty versts on foot—in rain that brought the river up to the road, in heat that overturned cattle. The earth I walked on became mine. Mine was the water in the lakes and springs, clean water, dirty water, enlightened water, contaminated with oil, stinking of algae, of fish that died in wells, stinking of the memory of atrocities, water as clean as broken bread. The water did not become Alina.I was doing this for her: I got the basturma out from under my saddle, sodden with the horse's sweat, sliced the throat of a rich man whose daughter I had danced with at a ball, climbed into a vat of beet juice and took a sugar bath, carried out the expropriation of the savings banks, wiped the sweat from my face with my shirt—and the cloth turned red; I didn't know from what. If it was someone else's blood, I didn't care; if it was my own, even less.We mostly came across Reds. We scraped them up like old red paint on a door in order to repaint the boards black. Black looked better. Red is tasteless, but black has style. Healthy men died before us of myocardial rupture like bunnies found in the nest. The ones whose hearts were sewn of steel wire envied the deceased. Seizing estates, banks, distilleries, and prisons reminded us of gathering in the harvest. If you're too lazy to pick an apple, you can shake the tree; some of the fruit gets bruised when it falls. We seized buildings like we were shaking apple trees. No one picked the fruits, we just shook: shook under the beds, under the tables, behind the curtains. No, there was no picking. We just shook until the red juice spurted from the apples.Near the Khorol River with Father Makhno and me in charge, we captured sixteen machine guns and four cannons, as well as five hundred prisoners who immediately came over to our side. The villagers voluntarily gave us bread and cheese, chickens and kvas. People joined us. The front of the machine-gun cart said “You can't run,” and “You won't catch us” at the back. We took factory after factory. Millions of karbovantsi, thousands of poods of sugar, weapons. We smashed the telephone exchanges and captured the telegraphs. We made alliances with some and then with others. Lenin, Wrangel, Frunze, the Germans, Chinese, Australians, Kaiser Wilhelm II, Cleopatra, Maria Theresa Walburga Amalia Christina. We ran the steppe. There were a hundred thousand of us. There were three hundred thousand of them. There were three hundred thousand of us. There were a million of them. There were two million of them. We were all of humanity. We were so many that we were none.The nobles’ estates were long ago forsaken. In the people's deepest trunks lay silks and guipure laces that were once perhaps used only to cover a table. Five steps from the barn in the direction of the pear tree, some silver candlesticks are buried; there's a plaster figure of an angel in the chicken coop, covered with shit and feathers.I was reluctant to be going to my home, but I didn't see any way out. Fate intended me to be a different being from the one I was before.Here my grandfathers and great-grandfathers were born. Here the ones who caused my grandfathers and great-grandfathers to flee had stopped. When we were still far off I noticed that someone was in the house. It was our men—Skorsky had brought them here, about twenty in all. I asked Sanko, whom I had walked with side by side more than once, where the doctor was now. All the men answered that he was around somewhere, but I didn't see him that evening.In 1918, the spirit of my great-grandfather Stepan, along with my mother and uncle, had gotten into a britzka and scrambled off to Paris, to Napoleon, against whom my great-grandfather had fought with the Cossacks, to whom the Russians promised to return self-rule. Following him in the cart went the soul of Grandpa Oleh, who lost a finger when he cut down the old linden near the house; his second finger was blown off by a cannonball near Balaklava, and later his entire hand was cut off by some Turk. Next went the spirit of my father, also Stepan, who did not take part in any war but died of measles at the age of forty. They all got the hell out of here. First, they went to Kyiv, led by my mother, Tamara Makarivna, in order to collect Uncle's family and me, their son. And their son, it turns out, has now come back to rob his own home (I didn't drive my war buddies away, did I?). It's a shame that I didn't know where the bathtub was, or whatever they bathed me in when I was small. It would have been good to walk through the ranks of anarchists with that basin and tell them all to spit into it.Remembering every room, I carried Alina upstairs to my mother's bedchamber. There was no longer furniture or pictures, only bare walls. The bed and mattress remained, but that was enough. Mother hated noise, so she set up her room far away from the running in the halls and the creaks on the stairs. I adjusted the mattress; in a gap, looking like a stalk of wheat, there lay a gold bracelet that she lost in the haste and that the thieves could not find in the mayhem. I tucked it into my pocket.The place could still be saved. It was strong, built under the leadership of my grandfather, who knew how to do it right. He built a sawmill, a gristmill, a dress factory (today it's probably been ransacked, maybe even by our own men).Alina had a complete, displaced break in her right fibula. We needed water first. I went downstairs—the guys were dragging out the piano like an old cow to the slaughter.“What are you doing with that?”“Taking it out.”“Why?”“What's it to you? We want to have fun.”“Can you play?”“We're not your bourgeois lily-handed bitches.”They couldn't play, but they were famous at destruction. “Noise is the music of the new time,” one of the smarter among them might have said. “But noise is the opposite of music. Just as a rose is the opposite of your ugly mugs,” I'd have responded if there was anyone to say it to. I could also have said that this was a Bosendorfer grand piano, that it was very valuable—but do the guys not deserve such a luxury?“Why are you so boring? We're relaxing.”“Then let me play a little first.”“Go ahead, but fast. One-two.”So I played. As before. My fingers ran up and down the black and white keys, which weren't simply keys of these, the simplest, colors. These were the keys that remembered my fingers specifically—achieved by that slovenly German Katerina, our governess. She knew a bundle of languages, could play the piano, and was interested in the latest scientific discoveries. But she had not an ounce of sympathy for anyone who couldn't master anything on the first try. More than once she hit my pinkie against the black key that remembered every one of its four thousand touches. She would pound it on the key and shout, “Si bémol! Si bémol,” and later bang my fingers and translate, “B flach! B flach!”I played. I could not expose myself, so the only thing I could do was believe in miracles. What if these coarse men saw value in this bit of furniture so unintelligible to them? And what if they didn't destroy it, this emblem of my childhood, my land, my air, which I could protect in no other way? My air. My water.“Shchedryk, shchedryk, shchedrivochka,” one of them who recognized the tune began to sing along.“Look at you.” They did not expect music from me, who had until recently been drinking blood like water.They said, “Again, again!”A group of curious men gathered around me. They were ordinary farmers, thieves, and recidivists, peasants and workers, everyone except for Skorsky. They needed this music as they needed baths. The music cleansed them from the inside, perhaps. They had not heard anything besides the whistle of a bullet, the neighing of a horse, or the knocking of a chisel and the whirring of a saw, amputating limbs, for a long time.But it could not go on long. I did not close the piano lid, just stood and went to fetch water for Alina, leaving the unfinished song for later. The well was to the north—that is, at the “Head.” My father once promised to give me a compass if I could learn to identify the ends of the earth by means of the sun. And to make it easier to remember, I gave each one of them a name: the east where the day begins was “Right” (my right hand), the west “Left,” the north “Head,” and the south “Feet.” Back when I could still do whatever I wanted all day long, I would wake in the morning and say: I'm going to the Feet. The mound was at the Feet, Left had the river, Right had the forest. It was only to the Head that I rarely went, because a village was located there. When the villagers saw me, they would speak in whispers and avoid the master's son.... I wiped her brow and her burning, sunken cheeks. I lay down next to her to feel the heat of her skin.When the fire in Alina calmed slightly, I went out into our orchard. My father had once been given a gift from Japan—a tulip tree that blossomed with yellow-green flowers. It had to have grown in the time that I was away. It would have been fatal had it been cut down. I again took the stairs down into the drawing room and came across nobody—they had all disappeared in search of food or were hidden away in their burrows. In the middle of the hall, like an opened rib cage, was the piano, irreparably shattered.B Flach! B Flach!Translation © Ali Kinsella 2022. (shrink)

Interactive technology assessment (iTA) provides an answer to the ethical problem of normative bias in evaluation research. This normative bias develops when relevant perspectives on the evaluand (the thing being evaluated) are neglected. In iTA this bias is overcome by incorporating different perspectives into the assessment. As a consequence, justification of decisions based on the assessment is provided by stakeholders having achieved agreement. In this article, agreement is identified with wide reflective equilibrium to show that it indeed has the potential (...) of justifying decisions. We work out several conditions for this agreement to be achievable and just. (shrink)

Health technology assessment (HTA) is often biased in the sense that it neglects relevant perspectives on the technology in question. To incorporate different perspectives in HTA, we should pursue agreement about what are relevant, plausible, and feasible research questions; interactive technology assessment (iTA) might be suitable for this goal. In this way a kind of procedural ethics is established. Currently, ethics too often is focussed on the application of general principles, which leaves a lot of confusion as to what really (...) is the matter in specific cases; in an iTA clashes of values should not be approached by use of such ethics. Instead, casuistry, as a tool used within the framework of iTA, should help to articulate and clarify what is the matter, as to make room for explication and consensus building. (shrink)

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.

A prominent way of justifying civil disobedience is to postulate a pro tanto duty to obey the law and to argue that the considerations that ground this duty sometimes justify forms of civil disobedience. However, this view entails that certain kinds of uncivil disobedience are also justified. Thus, either a) civil disobedience is never justified or b) uncivil disobedience is sometimes justified. Since a) is implausible, we should accept b). I respond to the objection that this ignores the fact that (...) civil disobedience enjoys a special normative status on account of instantiating certain special features: nonviolence, publicity, the acceptance of legal consequences, and conscientiousness. I then show that my view is superior to two rivals: the view that we should expand the notion of civility and that civil disobedience, expansively construed, is uniquely appropriate; and the view that uncivil disobedience is justifiable in but only in unfavorable conditions. (shrink)

Frank Wilderson: I introduce a semiotic configuration. The point is, at important levels of abstraction, people who are positioned as Black—which is very different from saying people who think of themselves as Black. One of the basic premises of Afropessimism, which makes it resonate with psychoanalysis or Marxism, is that where one is positioned in a paradigm might not be where one thinks one is or where one desires to be. When I teach undergraduates, I say: “Look, I used to (...) study neorealism. In these neorealist films, we have these people who are bona fide fascists, and then you have those people in the Communist Party, so they could not agree on much. They don’t see themselves as having much of a connection. But in a Gramscian sense, they are both positioned as the host of capitalist parasites. Both groups rely on the wage. So, they are both workers.” One of the big points with respect to the narratological question is that I, as a Black person, trained at Columbia University in creative writing, trained at UC Berkeley in critical theory, love narrative, but narrative does not love me. In other words, it is impossible for me to be “emplotted” as a speaking subject. I can only be “emplotted” as an object of narrative. But I am always struggling to attain that love of humanity; and if I were to attain it, the Human would not have a foil against which to know itself. So, what I am saying is that in a book like Red, White & Black, I am just being very categorically clear about the divisions. In Afropessimism, I am actually talking about the desire of a sentient being who cannot be allowed into an arena where people are recognized and incorporated, in Lacanian terms, as “contemporaries” of human beings. So, there is all this back and forth. I don’t think this speaking subject in Afropessimism ever achieves anything in particular. It is always struggling toward being a subject that can actually travel on a narrative arc and yet ultimately is an object that can never travel from dispossession to redemptive recovery. (shrink)

Addictive behaviour has qualities that make it ideal for study using implicit techniques. Addictive behaviours are mediated in part by automatic responses to drug cues, and there is sometimes social pressure to distort self-reports. However, relationships between implicit attitudes and addictive behaviours have been inconsistent. Using a new implicit measure, the affect misattribution procedure (AMP), we found consistent evidence that drinking-related behaviours are systematically related to implicit attitudes. The procedure predicted a behavioural choice to drink beer and self-reported typical (...) drinking tendencies, including hazardous drinking and alcohol-related problems. The AMP showed larger relationships with drinking behaviour than other implicit measures, and explained unique variance in drinking beyond those measures and beyond explicit measures. Though self-presentation distorted self-reports, it did not affect AMP scores. These studies highlight the importance of automatic affective responses in addictive behaviour and suggest a useful means for measuring those responses. (shrink)

In the face of environmental crises such as climate change, pollution and biodiversity loss—which all adversely impact on health—Gils-Schmidt and Salloch explore whether physicians can be justified in taking climate issues into account in clinical care.1 While their approach centres on the ‘climate-sensitive’ decisions, physicians can carry out on the micro-level of clinical decision-making, they encourage further discussions on how climate-related issues can be included across different levels of decision-making in healthcare. We propose a list of tasks and a model (...) to assist with navigating the range of factors and structural elements an environmentally sensitive ethics must address. Stephen Gardiner’s notion of a perfect moral storm is central to understanding these issues.2 Gardiner describes how a perfect moral storm occurs in the centre of three overlapping conditions for human action and policymaking in the face of climate change. This storm is driven by: (1) a lack of interest among current generations to meet global needs and accommodate the well-being of future generations, (2) a lack of ecological concerns for other parts of nature than humans and (3) weak ethical and political theories and institutions shaping policy decisions on issues with severe implications across borders and generations. Moreover, these conditions are embedded in the existing, complex world of ethically unjustified power imbalances and social injustice. The growing awareness of healthcare’s climate footprint has amplified and accelerated global, grassroots action to make healthcare more environmentally friendly. This includes incorporating environmental impacts into quality improvement methodologies, building communities of practice to explore how to make …. (shrink)

This book is not a study of Plato's philosophy, but a contribution to the literary interpretation of the dialogues, through analysis of their formal structure, ...

As Rutherford acknowledges, there remains much disagreement on basic methodologies for the study of Plato. Briefly put, the dominant view has been that the dialogues present and argue for a range of doctrines, that is, offer us extensive and reliable evidence regarding theories espoused by Plato. Although there are numerous versions of what commentators have labeled the "doctrinal" approach, most generally put they emphasize either development or overall unity. While a second group of interpreters grants that Plato embraced theories, it (...) contends that his views were not promulgated in writing but instead transmitted orally. A third methodology, deeply opposed to the doctrinal stance, emphasizes that the dialogues pose a host of questions. On this view, the primary value of Plato's writings lies here, and in their prompting us to search for answers, rather than in any answers that they themselves allegedly provide. In the process of raising issues Plato may evince some general philosophical commitments, but this is to be distinguished sharply from the presentation of arguments, often interrelated, for philosophical views about the nature of reality, knowledge, and so on. (shrink)

In Overdoing Democracy, Robert B. Talisse turns the popular adage "the cure for democracy's ills is more democracy" on its head. Indeed, he argues, the widely recognized, crisis-level polarization within contemporary democracy stems from the tendency among citizens to overdo democracy. When we make everything--even where we shop, the teams we cheer for, and the coffee we drink--about our politics, we weaken our bonds to one another, and work against the fundamental goals of democracy. Talisse advocates civic friendship built (...) around shared endeavors that we must undertake with fellow citizens who do not necessarily share our political affinities as the best way we can obtain a healthier, more sustainable democracy. (shrink)