Let me tell you about a city, an ideal city. It’s not the one you’re imagining, the one from Plato, but another city entirely, the real ideal city. The real ideal city looks like this: imagine a great glass dome, a dome that extends for hundreds of miles, with a ceiling so high that it is indistinguishable from the sky above, and a shining city beneath it. Imagine a golden municipal tower. Imagine fields and green gardens, and four-storied townhouses arranged around squares full of flowers. This is the city I’m talking about. Unfortunately, this ideal city is only as beautiful as it is because everything ugly about it is hidden. The real industry of the real ideal city is buried beneath the ground. Now imagine a city that is in every way the opposite of the city I’ve just described. No flowers, no fields, no plants. No light. The citizens of this city are eyeless monsters that hobble from one task to another; they work all day, every day, because they are afraid of being punished. They don’t even know that they work all day because in this city there is no time. They don’t know that what they do is work because they have never known anything but work. They don’t know that there is another city above them, either, even though everything they produce is sent to it, because they have been taught not to ask questions. You could describe them as maximally alienated from their labor because they have no idea what they make or what these objects are used for. These people will never own the means of production and it’s better that way. They are born in darkness, and they die in darkness. The citizens above do not know about the citizens below, or at least they pretend not to. Some of them are clever enough to deduce the presence of another city beneath them; after all, they wonder, where else can all these things come from? The objects themselves are astonishing: lace, silverware, fluted glasswork, embroidered sashes, vetiver, incense, and all manner of ornamental mirrors. These are created alongside basic products like food and fuel, of course. Every single thing that the citizens of the upper layer might desire appears from below via an extensive series of dumbwaiters. They are so busy enjoying this bounty and this wonderfully intricate world of banquets and drawing rooms and masques and amateur theatrical productions that it never occurs to them to contemplate the mechanisms of their satisfaction. So much the better. Like I said, this is the real ideal city. It’s better than Plato’s ideal city and it’s better than those independent city-states in the Mediterranean that your friends are always dreaming up. It’s better than anything out of Ayn Rand, another writer I know you like. None of these citizens are intellectuals; they’ve never invented a single object or made any money. They simply follow the plans laid out for them millennia ago. They don’t ask questions. And that’s it. That’s the real ideal city. I’ll stop now. You clearly want to say something.

The excluded billionaire was watching me with a confused expression. He told me that he had never liked Ayn Rand, that I was remembering it all wrong. I wasn’t remembering it wrong at all. By this point in time, I had known the excluded billionaire for a good ten years. We had met during my first year at the university when he had lived in the room across from mine, although I had never understood why: he was already so rich that he hadn’t needed to stay on campus. He was so rich that he could have bought his own palace, one of those enormous white compounds on the outskirts of the city. But instead he had chosen to work and sleep in a dark, damp room exactly like mine. I suppose he wanted to be closer to people, or at least to other students. He did his best to be close to me. Every weekend he would jet away to another developing country, but first he would knock on my door and unfold his itinerary while I tried to ignore him and focus on my reading. My indifference to the excluded billionaire’s plans never seemed to bother him. He was fine with talking at me; for the most part, he didn’t need a response, and if he did, he could invent one. I didn’t mind the sentiments he attributed to me. It was easier than responding myself, and in a strange way it was also easier than saying nothing. And although I had only been in his room once or twice, I clearly remembered the poster of Atlas Shrugged that he had tacked onto the wall. It had been the only decoration, the sole splash of color. It was also one of the reasons people hadn’t liked him. It had been much too clear where he got his models.

Even back then the excluded billionaire had liked to lecture me. There were times when I found him very boring. But there were also times when I found him almost intriguing, usually when I caught him unawares in an exercise of power. I liked the excluded billionaire best when he was making threats down the phone or disappearing behind the door of a chauffeured car. Sometimes on those occasions our eyes would meet, but the excluded billionaire was always on the way out: his attention would return to his business, and the momentary flicker I had felt for him would disappear just like that. I would go back to the library and my ordinary life.

You loved Ayn Rand, I said. Don’t ever try to lie to me again.

Your city doesn’t make sense, he said. There are so many problems with it that I don’t even know where to begin.

Then don’t, I said. Just accept the real ideal city for what it is, a perfect vision. Once you start thinking too hard about the mechanics of the ideal city everything goes wrong. It’s supposed to be an ideal, maybe at best a lesson; it isn’t supposed to be realized. It’s impossible for it to be realized. Because of human nature. We’d tear a city like that to pieces.

Now it was the excluded billionaire’s turn to roll his eyes at me. But he didn’t have the chance to continue his part of our conversation because the party around us was winding down; people were leaving, and as they did, they came up to us to convey their admiration for the excluded billionaire’s work. None of them bothered to say anything to me. This made sense: I’m not a billionaire. I’m barely even a person. Nobody understood why the excluded billionaire insisted on bringing me to these parties. It’s just that we go back so far, I would tell my other friends when they speculated about our relationship. He’s very needy, I would say. And he doesn’t like new people.

That evening, telling the excluded billionaire about my ideal city, I was sure that nothing would ever change, despite what the excluded billionaire was always telling me about the incredible progress we had made as a species. He was determined to broaden my horizons. My phone rang whenever he had a spare minute, which, when considering how busy he claimed to be, was far too often, and then the excluded billionaire would tell me about the limitless wealth of the world as he saw it, a universe full of wondrous things. The only real crime was wasted potential, the excluded billionaire said. He told me that there were far better utopias in development, cities the like of which I couldn’t begin to imagine, that artificial intelligence would lead us there, all we had to do was let it, which was another way of saying behave nicely. But let me tell you about nature, I would reply, human nature, I would say, and our argument would start up again. It was always the same, until it wasn’t.

I called the excluded billionaire the excluded billionaire because none of the other billionaires liked him. He told me that it was because they only cared about making money while he cared about making the world a better place, but I didn’t believe him. It wasn’t just the other billionaires who avoided the excluded billionaire, but people in general. Even though the excluded billionaire was tall and handsome, people didn’t like him. It didn’t matter how rich he became or how many things he invented. They invited him to their parties, of course, and some of them even dated him. At one point he was engaged to a supermodel; in the end they were together for almost five years. But even with her it had been the same old story, the excluded billionaire told me after the break-up. Even when they had been in bed, even when he had felt himself closer to her than any other living person, there had been a risk that if their eyes were to meet, she wouldn’t be able to hide it—her disgust, her longing to be elsewhere.

It was after the supermodel left him that the excluded billionaire had begun inviting me to accompany him to parties and events instead. Until that point in time he had never shown any desire to bring me into his world, only to relate it from a distance. I took it as a sign not of affection, but of how far he felt his social currency had fallen. It was clear that the excluded billionaire was having a bad year. That summer his fortune was in freefall, and he never stopped comparing himself to the other billionaires. His media empire was much smaller. His electric car was famous for malfunctioning. Shares in his companies were crashing every week. In a year when every single cryptocurrency, even those created as a joke, was taking off, his remained worthless. And worst of all, everything he invented was copied almost immediately, and in his competitors’ hands his inventions would become successful with astonishing speed. Each of the great innovations of our decade was marked with his signature, had originated as the germ of an idea in his awesome brain, but even though everybody knew this, nobody cared. All this, the billionaire told me, was because he had integrity, and the others had none. He was rich, unimaginably wealthy, he said, but now he was also an object of ridicule. At this point they expected him to give up.

He hadn’t given up, the excluded billionaire would tell me, and he wasn’t going to. His empire limped on and the investors continued to straggle in. He experienced success that would be outrageous by any other standard. He was still a billionaire after all. But meanwhile the excluded billionaire grew pale and thoughtful. He led his company, developed his apps, and sold his stocks, only now he did so listlessly. Sometimes, during our calls, he would fall silent, as if he were waiting for me to start talking instead, and sometimes I would humor him. I would tell him about my city until I could see it hanging in the black space of my mind like a massive golden bauble. I would stay on the phone with him for hours, lying on my bed in my tiny room in the dingy midtown apartment that I shared with four other people because it was all that my graduate stipend would cover. As I spoke, the excluded billionaire would ask me questions about my city. He was less scornful, more meditative. Slowly, we began to imagine the city in all its particulars. We started to resolve its difficulties as the excluded billionaire saw them; we organized the division of labor and the various citizens’ roles; together we arranged the pillars of their education. On the weekends when he would fly to see me, we would go on long walks in my university’s botanical gardens and imagine what it would be like to live under scrutiny, the punishment of that perfection, the unbearable brightness of the uppermost level of the dome, the light pouring down through the glass. We imagined the city’s ideal observer, a benevolent yet disinterested deity. If the city had a king, we decided, that king would be silent and unseen: he would direct the fate of the city from a golden tower, and the question of whether he existed at all would be undecidable, the matter of learned debate. Now at those parties the excluded billionaire and I would sit in a corner and argue over the distribution of temples, the lines of certain roads. I would describe the flowers that belonged in every single square, each of which had to have its own unique character, because there could be nothing monotonous about our city, and the excluded billionaire would write my words down in a little black notebook.

“Let me tell you about a city, an ideal city. It’s not the one you’re imagining, the one from Plato, but another city entirely, the real ideal city. The real ideal city looks like this: imagine a great glass dome, a dome that extends for hundreds of miles, with a ceiling so high that it is indistinguishable from the sky above, and a shining city beneath it. Imagine a golden municipal tower. Imagine fields and green gardens, and four-storied townhouses arranged around squares full of flowers. This is the city I’m talking about.”

Where we differed most was on the question of the suffering of the citizens who lived below. While I believed in an absolute divide between the two halves of the city, a complete lack of sympathy or understanding between the citizens of the upper layer and those beneath them, the excluded billionaire thought that there had to be a way to mitigate that distance; things didn’t need to be so clear-cut. I disagreed. Without that separation, I said, the city would become hopelessly confused. Nobody would know their place.

Sometimes I wondered if I should concentrate on my own work, my own life, but I wasn’t sure what that would look like. I was in graduate school. I studied philosophy. I showed up at the faculty every day and read books full of fantasies. The way I saw it, nothing was real.

One day the excluded billionaire called me and told me breathlessly that he had managed it. I asked what he meant, somewhat confusedly, though I think even then I had an idea. He said that I should come over at once. He promised to show me everything. But we live in different cities! I protested. The excluded billionaire sent over a plane.

During the journey to his city, sitting alone in the excluded billionaire’s private jet, I thought about the time he had taken me to the Caribbean for Christmas in a yacht that his family had chartered. We had both been in our final year at the university. I was surprised he had asked me, and I think he was equally surprised that I had said yes, but it had sounded much better than spending the holidays with my own family, and I was sick of the cold. Together we sloped around dim, humid jungles, climbed up heaps of black volcanic rock, and dived into the crystal blue waters that I had only ever seen in brochures, with the yacht bobbing like a question mark beside us. Neither I nor the excluded billionaire’s family understood why I was there. After all, I could barely swim. One day I almost drowned. I had been swimming, badly, but then I stopped. The excluded billionaire, who had been swimming beside me, had pulled me close and wrapped my arms around his neck. He swam back to the boat with me clinging to his back like a parasite. Another day, his siblings surprised me alone on deck and pushed me into the water. I paddled there grimly until the excluded billionaire came to my rescue again. By then the boat was already some distance away. As we swam in its wake, we shouted as loudly as we could for the boat to slow down and hoped that they would hear us above the crashing of the sails and the plashing of the waves. Afterwards the excluded billionaire had made excuses for his siblings. They were nouveau riche, he had explained to me as we lay on another flawlessly white beach. They had never had to develop any skills or even good manners because by the time they were born his father was already extremely wealthy and universally admired. It had gone to their heads. The excluded billionaire himself had known only a few years of difficulty, and then only in his early life, but he could just about remember it and those years had been crucial. That was the difference between him and them, he said, watching his little sister as she scrolled on her tablet with a glazed expression. His siblings barely knew how to swim either, he said, as if to try and make me feel better. They were too lazy.

On Christmas I saw a ruined city with a dark chasm running through it and a peninsula that had been reshaped by a volcanic eruption. The houses had been buried in ash—only their roofs were still visible. The next day I saw dolphins for the very first time. I had been reading on deck, and then the captain had called out. The excluded billionaire and his family had come rushing from below, and we all crowded to one side. The dolphins were leaping in and out of the water. I watched the dolphins and the others watched me. I suppose they wanted to see what they had spent their money on. The dolphins were fat and grey. I thought that they looked computer-generated. The whole scene felt stagey, fake. I tried to smile, but I wasn’t sure I’d managed it.

Years later the excluded billionaire told me a story about dolphins. He told me that researchers had discovered that every single dolphin had a unique vocalization, a signature whistle. They made this sound as they swam, always the same sound, over and over again. He said there were two theories as to what this meant. The first theory, which was the most likely, was that the dolphins were calling out their own names as they swam through the ocean. They were identifying themselves to others, announcing themselves as they went. According to this theory, these vocalizations had a practical, functional purpose. They enabled communication between pod members. They let each dolphin know who belonged where. The excluded billionaire didn’t like this theory. He was bothered by the idea that the dolphins could only talk about themselves. It was pure narcissism, he said. An endless repeating of selfhood amid the great emptiness.

The excluded billionaire preferred his own theory. He thought that the dolphins were saying the name of their beloved. Although dolphins didn’t mate for life, he explained, the vocalization was not the name of a particular dolphin, but the name of the beloved in general; it was a stand-in for an enormous and inexpressible feeling. However, the first theory was much more likely, the excluded billionaire conceded. For a moment he looked embarrassed.

Then the excluded billionaire told me that he had remembered this story on the day we saw the dolphins leaping across the blue water. It was strange, he said. He had seen dolphins many times, but it hadn’t been until that day, watching me watch the dolphins with an expression he couldn’t decipher, that the two theories had come alive for him. He supposed we would never know the answer. I said nothing. It was obvious that he wasn’t expecting a reply.

At that moment, the flight attendant came by and instructed me to fasten my seatbelt. The plane was about to begin its descent, she said, and we would be landing in twenty minutes. As we dove through the night sky, and the lights of the city below swung into view, I thought about the excluded billionaire’s two theories, and then I came up with my own. I decided that they were calling out their names in the hopes of having them repeated by another dolphin. I thought the real question was whether or not the dolphins could name each other.

The excluded billionaire was waiting for me on the runway. He ushered me into his car and we sped off into the night. He was taking me to his house, he told me, which I’d never visited before. When the excluded billionaire realized this, as if for the first time, it had surprised him because we had been friends for over a decade, and I had been his only friend. It was astonishing, how we lived, he said. Each so distinctly. We had shared everything and nothing at once. There was an edge in his voice that was unfamiliar, and as he spoke the excluded billionaire kept his gaze straight ahead of him and his shoulders facing forward. The driver was hidden behind a black pane of glass.

The excluded billionaire finally turned to look at me and I noticed at last that he was wearing sunglasses. I wouldn’t have been able to see his eyes anyway: it was too dark in the back of the car. He repeated that he had something to show me. As we climbed the sweeping marble steps to his gigantic front door, the excluded billionaire took my hand. I didn’t stop him. Instead, I glanced at the stars above our heads. I had never seen such a black sky. In the mountains where the excluded billionaire had built his palace there was no extraneous light, no trace of another person. He had never told me about the sky out here either, how it fell over you like an enormous velvet quilt. After all these years, it surprised me that there were things the excluded billionaire had kept to himself.

I followed him down a long corridor. We travelled through his mansion for what felt like hours, through lonely, rectangular rooms, all equally empty and coldly lit, because the excluded billionaire said that his secret was hidden in the heart of his house—he hadn’t wanted any of his competitors to discover it, and he was sure he was being watched. No doubt they were desperate to learn what it was that he had being doing during all those solitary months that he had spent talking to me. As we walked the light seemed to grow dimmer; it was no longer clear where it was coming from. Eventually we began to descend a dark spiral of stairs. The excluded billionaire pulled out a torch and I concentrated on that small circle of orange light. By the time we reached a room that was different from the others, my legs were aching.

In this room a circular skylight had been set into the ceiling. There was a pool of light beneath it. But I couldn’t believe my eyes—despite the hour and despite the depth, it was sunlight, the purest sunlight I had ever seen, and it lit up the dust floating beneath into slow, meditative columns. There was something ancient about that light: it had a quality that terrified me. Beyond the circle everything was as black as the night sky draped over the excluded billionaire’s mountains. I realized that he had switched off his torch. When I held out my hand in front of me, I saw nothing: it was as if I had been disembodied. Ahead of us, though—that pool of light.

I heard the excluded billionaire take off his sunglasses somewhere behind me. He said that late one night he had happened on the idea of mirrors. He had been thinking of Plato, of all the things that I had told him. He had remembered how Socrates describes the trick of the man with the mirror, the fake artisan who duplicates the world with ease, and all of a sudden he had seen the ideal city, my city, differently. Now the vision had had a clarity that astonished him. He had imagined enormous conduits of mirrors tunnelling from one level of the city to the next, directing light below. He told me that usually every reflection would involve a degree of loss, a degree of diminishment. What arrived below would be weakened significantly, and the excluded billionaire hadn’t wanted that. So he had invented a new kind of mirror, he said, one that lost nothing, a perfect mirror. The two halves of the city could be connected at last. The citizens below could experience exactly the same radiance as those above. There would be a total equality. The excluded billionaire wasn’t sure what this would mean for the city.

I stared into the circle of light. I knew that he was remembering the dolphins, his theories, the names, all of it. But we had looked at them and seen two different things. The excluded billionaire had gotten it wrong again, but it didn’t matter, because the fact that we couldn’t share everything didn’t mean we couldn’t share this, and so I took his hand and pulled him with me into the light, and then I turned around and saw myself reflected in the excluded billionaire’s dark eyes, and he was smiling, although not without a kind of sadness, and so I smiled too.