The Kingdom of Saudi Arabia wants me to know that it is building a new city. Its adverts follow me around the internet. ‘Imagine a traditional city and consolidating its footprint, designing to protect and enhance nature.’ I’m imagining. Their city ‘will be home to nine million residents, and will be built with a footprint of just 34 square kilometres. And we are designing it to provide a healthier, more sustainable quality of life’. According to its website, this new town ‘is a civilisational resource that puts humans first’. Which all sounds vaguely nice, if also nicely vague (although as I happen to be a human myself, I do appreciate the gesture). That is, until you see what they actually mean by this. The Line is not so much a city as a single cuboid structure, covered in blank glass walls. If it’s built according to plan, it will be taller than the Empire State Building, about as wide as Euston station, and roughly as long, east to west, as Portugal. It’s called the Line.

In their promotional videos, the Saudis show an immense mirrored scar cutting 170 km across the desert. There will be high-speed trains that allow you to travel from one end of the Line to the other in 20 minutes, which means no need for roads or cars. In the middle of one of the world’s hottest deserts, it will use ventilation and passive cooling to maintain a year-round temperate climate. The city will get all its water from desalination, all its energy from renewable sources, and all its governance from a terrifying omniscient artificial intelligence. In the space between its two perfectly smooth outer faces, there will be a hollow crisscrossed by walkways and what look to be flying cars, along with trees bobbing about in levitating pots of earth. (Some of the visuals were designed by Olivier Pron, who is not an architect, but a concept artist best known for his work on Marvel’s Guardians of the Galaxy franchise.) You, the resident of the Line, will apparently live in a glowing orange cube stuck, limpet-like, to the inside wall of the structure. This does not seem ideal.

The Line, Saudi Arabia’s $1 trillion eco-city, will be criss-crossed by walkways with trees bobbing about in levitating pots of earth. Credit: Neom

I’m not sure exactly what I’m supposed to do with this information. I am, for various theological and geopolitical reasons, explicitly banned from ever setting foot on Saudi soil, so the chances of my upping sticks and moving to the Line are roughly nil. I also doubt they’re looking for me to invest in the project, since they seem to have that end covered: the Saudi state has put aside $1 trillion. Earthworks have already begun; in satellite images you can already see the faint trace of a single ungodly line inching through the desert. The Howeitat tribe, who have inhabited the area for hundreds of years, are being cleared off their land. In April, Abdul-Rahim al-Howeiti, a tribal activist who refused to leave his home, was shot dead on the street by Saudi security forces. ‘I don’t want compensation,’ he’d said. ‘I don’t want anything. I only want my home.’ The Saudis appear to be genuinely serious about this, serious enough to kill.

This does not mean that the project is going to succeed. There’s a reason most cities tend to be vague, splotchy circles, rather than perfectly straight lines, and most of it has to do with some quite basic geometry. In a circle, the potential distance between any two points is minimised. In a line, it is maximised. In a circle, you can have a central services hub that’s equally accessible to everyone, with smaller local centres built around it in a way that efficiently uses all the available space. In a line, you live in a baffling and pointless plank. In a city that is not just a single straight line, there’s usually a good amount of redundancy built into the transport system: if one road is blocked off, you can always take another. In a city that is just a single straight line, if absolutely anything goes wrong – say, a brief signal failure somewhere in the middle of the line – the two halves of the city are cut off from each other.

That’s not even considering the more practical questions. Say you do decide to move to this city without cars or roads: how, exactly, are you going to bring your furniture? Who is going to clean the dust and sand off its Empire-State-Building-by-Portugal-sized windscreen, and how? It’s very easy to imagine how this thing would ultimately turn out. The Line would be a dark, gloomy, moist, fetid place. The desert winds would heap an enormous bank of sand against its mirrored façades: the place would feel subterranean, walls closing in, a bunker in the wilderness. If your windows look out on to the central atrium, you’d get maybe a few minutes of sunlight every day: enough to see the piles of rubbish filling up its voids, the wreckage of autonomous drones, the bullet holes and body parts in the windows on the other side. They say that there are parts of this city, miles from anywhere in the middle of the desert, where the water still runs and the authorities are still in charge, but you can’t get there. Mobs of former graphic designers and biotech consultants pile wreckage in the mass-transit tunnels to seal off their fiefdoms. At night, the jackals scream. Once all its residents have eaten each other, the creatures of the desert will reclaim this place. Snakes will make their burrows in its exciting vertically stacked neighbourhoods, and lick the moist air, unblinking.

So I know that the Line is a deeply stupid idea. I know it’s ugly and doomed, the vanity project of a nightmarish, head-chopping theocracy. I know that Saudi Arabia is one of the most obese countries on the planet, with an economy built on vast pools of oil, and this fictive walkable eco-city will change nothing. I know how absurd it is to tout the Line’s compact footprint when it’s unspooled over the width of an entire European country in a place that lacks almost everything except empty land. I know it will consume the lives of thousands of migrant labourers, that it’s killed before and will kill again. But despite it all, there’s something in me that admires this monstrosity, and not just because it’s big and audacious and absurd. It’s because this is, at long last, a city with a shape.

A century ago, anthropologists started noticing that the villages built by small tribes in their jungle clearings were not just circles of huts; they had a very precise meaning, in the same way that the layout of a European cathedral has a meaning. Claude Lévi-Strauss, visiting the Bororo, noticed that ‘their wise men have worked out an impressive cosmology and embodied it in the plan of the villages and the layout of the dwellings’. Each settlement is split in half, to represent the two social moieties; houses for the different clans are arranged radially, like the hours of a clock, with clusters for subclans, social classes, minute social grades. Because every group within the society has its own totems, colours and stars in the sky, the layout of the village becomes a map of the entire universe and everything in it.

Every Roman city was built on an identical plan. They were square, with two major streets: the cardo, running from north to south, and the decumanus, running from east to west. The forum would be placed at their crossroads. Anyone from anywhere in the empire would be able to find their way around any unfamiliar city. Cardo means heart: this is a city on the plan of the human body. Decumanus refers to the organisation of a Roman military camp: this is a city that models its highly organised and militarised state. In the Roman city, biological and political life are forced together. But the very earliest Latins, like the Etruscans, built their cities in circles, arranged around the mystic number three: there would be three major streets, three gates, three temples. ‘The magic circle,’ Henri Lefevbre comments in his Metaphilosophy, ‘is above all the object of prohibitions.’ The circular city weaves a protective spell. The square city enforces order. This is how we find ourselves in a meaningful world.

When the Abbasid caliphs founded Baghdad in the 8th century, it was as a series of concentric circles, a mirror for the rational movements of the cosmos, with a mosque at its centre. In Europe, medieval cities were split into their quarters: the people and the work they did would change, depending on where you went.

Near the end of Italo Calvino’s Invisible Cities, there’s a nightmare. Marco Polo and Kublai Khan pore over an atlas that contains the plans of every city that could ever exist. But ‘when the forms exhaust their variety and come apart, the end of cities begins. In the last pages of the atlas there is an outpouring of networks without beginning or end, cities in the shape of Los Angeles, in the shape of Kyoto-Osaka, without shape’.

We’re not quite there yet. Modern cities still have their wealthy, sterile cores, walled in by slums, then the prosperous suburbs radiating outwards. There are still ethnic enclaves. The names west London and east London still conjure a different kind of life. But we’re getting there: this doesn’t express anything profound about the cosmos, just the awkward legacy of race and class. (In Gravity’s Rainbow, Thomas Pynchon suggests that London was arranged facing east so the poor would have to take the brunt of whatever headed up the Thames: Viking raiders, rocket bombs.) New developments, meanwhile, are all amoebalike, formless blocks, retail zones, shopping centres like sadistic mazes fringed with vague tufts of green. Human life reduced to a homogenous mixed-use blob.

Not far from the Line, Egypt is also building a city in the desert: a new capital that’s secured $45 billion in funding but still doesn’t have a name. Some of the city is already complete. A central park, neurotically overlandscaped, that could have been pulled off the same shelf as the Olympic Park in London. Then skyscrapers and freeways, then miles of featureless American-style suburbs, which are – of course – described as ‘villages’. Not a city, just a vomit-splatter of mulched-up space. I can’t say exactly what a big stupid line in the sand might mean, and it’s probably not anything nice. Maybe a headless body, slumped. But at least it suggests that something might, some day, be meant.