Lend Me Your Geometries

(On Christopher Wren, Restoration London, city planning, fires, Riemann curvatures, the persistence of history, Japanese Metabolist architecture, Agnes Martin, grids, and other things that are or are not a torus)




It felt like everything was fucked. Political systems were in disarray between two bad alternatives. A plague raged amongst the people, tearing through the close quarters of the poor. Then one night a fire ripped through the crowded tenements and slums, destroying huge swaths of the city.  They said the fire might burn out the plague. Others said the world was ending, or at least the world of the city.

The year was 1666 and the city was London. 

It is 2020 and autumn and I live here now.




I am an American in London watching the democracy die at safe remove. I am a coward. I feel like I should be Getting Into Tacitus, Settling Down With Seneca, doing the 17th century thing where you feel belated by way of antiquarianism, where you remind yourself that things were bad then too. Reality television pitch: The Bad Emperors live together in a hype house in LA and make social media videos advertising  their sponcon at an average of 29.5 seconds each. Cut to Nero in the pool on a dolphin floaty. Cut to Elagabulus calling himself Heliogabulus as he eats laundry detergent. 

You don’t have to go back that far though. Right after the Fire, both Christopher Wren and John Evelyn submitted similar masterplans for London for the approval of Charles II. They have elegant piazzas like Venice, and broad Haussmanian boulevards leading to the financial and political centers of the city. Haussmann wasn’t even a twinkle in the imperial French eye yet, but that’s what they feel like, broad enough that they exist for each season in an eventual tableau of 19th century impressionistic paint. Here are the coachmen hurrying to the Royal Exchange in Autumn, past the symmetrical streetlights. Here are the commissioners of luxuries rushing into the Goldsmiths Guild from the winter rain, slick on their large black brollies. Men gather nervously at the Exchequers Office and the Mint, which Wren puts in the same, multi-faceted radial center. Press that fast forward button double and it’s 2009 and spring, and the market crash has the same men in their fine suits, one jumping off the edge at the height of the Bank, itself a facet in the jewel of the avenues. The catkins of London’s plane trees split and dust them with pollen.

People say the pandemic makes time feel flat, like a circle, which comes by way of Nietzsche but rarely in any significant way attached to him. I think this flatness applies to history too, but if it’s slower here for a reason. If you look at the Wren plan, so orderly it is almost sinister, you think he may have done what you do when you’re building a galaxy, which is to say, stick a hyper-massive black hole in the orbital middle. Where the Royal Exchange would be, there’s one there now, and the closer you get to it the more time dilates across the event horizon, stretching into infinity and you are very very flat, like a map on a table at the British Library.

 You get a notification on your phone when it grows, the black hole, it consumes another street or byway. Hammersmith Tube Station is no longer functioning. Canary Wharf was consumed ages ago. Schedules are now irregular, fares are the same. The branches of the Northern Line end in spiral arms and nebulae where stars are born, but the closer you go to where all the avenues meet, the faster you accelerate and the slower time goes.

Nero, Heliogabulus, the dolphin pool floaty, all eaten. It grows along the orderly lines of the Wren plan consuming in a strict ratio. When everything is gone it will explode again into a new London, into another world that is better than this one and all its dead emperors. Big bang. Big crunch. All of Gibbon emerging through a wormhole at the consumed mass of St. Pancras.




Technically the Wren plan is a Riemann geometry, and not the obvious Cartesian one a map implies, because the Earth that those straight-seeming lines are projected onto is a sphere and therefore,  in reality, curved. Let’s talk sectional curvature, manifolds, completeness, topologies and algebras that make sense of things. I am a torus. You are a torus. A donut is a torus. One hole in the middle of the thing. A torus has negative curvature and cylinder, positive. The shortest line between two points on the sphere that is the world, that is also London, is actually a curve. Leadenhall Street, Aldgate, Newgate Holborn—they all warp and curve around the wide earth.

A cow is a torus. A snake is a torus. An angel is a torus only if angels urinate but insofar as some theosophy posits they don’t have genitals, so maybe an angel isn’t one. Maybe an angel is what geometers call a cissoid of Diocles; κισσοειδής, like the shape of ivy. This idea in geometry comes from the 2nd century BCE. Newton comes back to it around the time of the Fire, as a way to project curves as rotations. Like Newton, Christopher Wren was trained as a geometer. He was a professor of geometry at Oxford until he took up the architectural commission to rebuild the whole city. The trope of painting angels with eyes on their wings had become uncommon by Wren’s time. They were mostly underthreatening putti, when they were represented at all. After the Reformation, there was lots of anxiety about representing things, especially in Churches. The altarpieces for Wren’s churches, sometimes carved by the master Grinling Gibbons, had limewood carved so delicately that the leaves seem like real ivy, like you could pluck an overripe peach from the plethora hanging off his paired garlands. 

Wrens’ geometries of the city were anchored by churches, each formed to its parish specificites, dotting the skylines with gold along the river from his new St. Pauls. Wren likes domes, which are almost halves of spheres, except his are often elongated. In tight quarters, the city churches often have just one entry and egress, sometimes fronted out on a grand porch with white colonnades. Topologically speaking, these would be the same as the angels, the mouths-only version.

Utopias, or cities that try to be, are implicitly also biological to me, unable to form between neatly compassed lines as mere theoretical topologies alone. The angels; the buildings they are both in a sense fleshly, both in another sense, unnatural, plunked down on the sphere of the world to do some duty from on high. One hand is God’s. The other, the architect’s. This is an not infrequent analogy in the theology of the 17th century. Angels and buildings meet in the category of this oddly formed body, set down on earth to negotiate with the heavens.




The plane trees in London are special. You don’t sit under them debating the nature of the soul often because it rains a lot, but they look good in the rain. They date to near Wren’s time too, to gardener to the King, collector, and cultivar of that first all-important British-grown pineapple;  John Tradescant. It is supposedly a hybrid he made with American sycamore, hence the species name Platanus × hispanica which is weird as hell as species names go, very not Linnean proper that x, that unknown variable. Anyway the plane trees are called London’s lungs, and the Victorians loved them and planted the ones in Russell Square and I think Primrose Hill too, the ones that are my planes with my catkins. Their strange quotidian hybridity comforts me.

There is very little green space explicitly denoted in Wren’s plan. Evelyn has a bit more, south of the river. This is funny because London is generally considered very green. Then again, we didn’t accept the plan. Somewhere between King and Parliament, Wren’s son writes adoringly, some foe conspired against his father’s perfect scheme for the city. So lots of avenues stayed narrow and when the railway moved away from the Hill and the war bombed out a bunch of city churches, the planes came and grew where I live, in the North, instead of piazzas.  Notwithstanding this benefit, I’d like to think, that if Wren had succeeded, we would have better coffee. The espresso machine would have been suited to a piazza-fied London, where we would have gathered in outside droves despite the weather instead of in the narrow Penny Universities of the coffeehouses. 

The plane trees I see are not old enough to have seen two plagues themselves but I think some of them just about are. Some of them are old enough to have snuffled politely at the plans for London then. But they don’t see it from street level, they shoot up, like the spires of Wren’s churches; they too are dappled with gold. 




One of the post-1666 plans for London that does show quite a few green spaces is Robert Hooke’s. A fact I cannot forget about Hooke is that he took his own niece as a lover at sixteen. The seventeenth century ruins itself for you in that way.  Who has not wanted to remark, “O My America, my newfound land!” upon seeing a lover’s body naked for the first time. But Donne’s America was the colony America was Virginia after 1619, was genocide and slavery and rape. Hooke’s microscopy too, his words for the flea, for the beauty of the onion cells. They are love letters too. His niece was named Grace. She is the beautiful woman he mentions in the Microscopy. History is one long devastating poem sometimes, like being shivved in the side by Philip Larkin continually.

Anyways, for London, Hooke had another kind of love, or probably it was Hooke, we cannot be sure. It is a city on a grid system, a unique innovation that later came to the attention of those wanting to promote an equitable idea Philadelphia. This plan is strangely probably the reason I grew up in a city that was a grid in Florida, that on one of my early trips to London, a kind clerk at a hotel was confused that my family could live in the 12,000th or so house on a street. The benefits of a grid include actually knowing where you’re going with a Cartesian definiteness that London decidedly did not hew to. Until recently, most kept a small book, called the A-to-Zed, in there houses, a cross referenced list and map of all London’s streets for when you invariably got lost or needed to get somewhere unfamiliar. London required a guidebook even for natives.

The little even squares of the proposed grid map do look like cells though. They look forward to the idea of the city as a living thing, an idea that became Archigram in England and Metabolism in postwar Japan. A city plan could be a megastructure too, in the right hands. To make an order is a powerful thing. In my head I link the post-Fire building spree with the midcentury post-war both because they cleave to each other formally, but also in terms of sheer historical coincidence, share much. The Rebuilding Act of 1670 resulted in at least 51 new churches. In postwar Tokyo, meanwhile and slantwise, what the architectures called the Construction State was taking parallel root. You could use Kiyonori Kikutake or Kenzo Tange’s name like you use Wren’s or Hawksmoor’s. Architects use measures of scale to show you what ratio a sketch or plan has to the real world. Grids are a system that lends itself to this. When you look at the 17th century grid plan for London it looks eerily doable, modern. 

Rome burned while Nero fiddled, but actually fiddles didn’t properly exist, and Rome you know, wasn’t built on a grid, though a Roman army camp was—to wit, Polybius. So we who lived in gridded cities all lived in army camps, or Hellenistic settler towns plopped down on foreign plains. Elagabulus who was Heliogabulus is portrayed in one famous iteration to have drowned in flowers.I think of Agnes Martin’s Flower In The Wind, this too a grid. But Martin’s grid, from 1963, is unruly, almost wild within its constraint. On background of soft, deceptive pink the vertical lines in each row differ in width, almost rhythmically but just chaotically enough to feel like billowing petals, caught up in a draft. The facility of the suprising pastel pink against the grid makes it unsterile, alive in the way cities can be between the lines. Agnes Martin makes these kinds of pastels feel dangerous, makes steady grids feel dizzy again, drunk on their own dancefloor. The biological and topographical slide into each other, over the girders of the geometric form, the underpinnings as squeaky clean as its components are visceral, but each cannot be itself without the other. To wit; organs against their cages of bone. Gross anatomy is not named as such because of disgust but because it is visible without Hooke; that is, without the microscope.

The planned megastructures that were actually built, some to grids and others to the concept of cells, didn’t quite work as expected. The famous Metabolist Nagakin Capsule Tower is one of these. The concrete has structural and leaking issues. The temperature gets to unlivable extremes. The machine for making new capsules as the building needed them was never built, so it couldn’t grow like the cells of an algae or the connected city of coral polyps. It was a skeleton when it was finished. Even if London had been a grid, it wouldn’t be one now anyway. It would have slipped out of its lines, snuck back to Pudding Lane where the fire started and wept. An Agnes Martin that is a golden grid was exhibited at the Tate Modern at a retrospective in 2015. You can get there by crossing the newish Millennium Bridge on the River Thames, which is of course in none of the 1666 city plans. It is made with gold leaf and gesso. It is one of three such panels. It is called simply ‘Friendship’.




Cities and buildings conjure strange bodies. Wren’s post-Fire city churches almost never have protruding apses. A church without an apse can feel like a body without a head; consider the ribcage to be the long nave of a medieval cathedral, rich with webbed vaulting. Wren cuts off the head at the neck, though Charles II, his royal patron, would have blanched at such a comparison. Charles I’s neck and head infamously came off at the Banqueting Hall, which like Agnes Martin has lots of pastels in the ceiling like Rubens, and never fails to be electrifying, even when you’re not beheading the Divine Right of Kings in person. 

The Wren City Church is thus acephalgic  like Acéphale, like Bataille’s Acéphalistes in a secret cult of Surrealist death ecstasy. Sir Ernst Gombrich once called Wren churches “sober” and a space for contemplation, but I think the latter renders the former moot for me. Contemplation under plane trees or at dinnertime symposia is never strictly sober, even in the absence of literal wine. Tallis isn’t sober, a soaring choir of boy voices singing miracles into being. It’s ecstatic too, like the coffers on Wren’s ceilings, white on gold on white, an infinite regress of plasterwork and perspectival glee.

In 1958 Kiyonori Kikutake built a house for himself in the proto-Metabolist style called The Sky House. The bottom of the house is raised above the ground. It’s gridded but its like a coffered ceiling in the place of a floor. It is a concrete slab with an open floor plan on top, because Kikutake believed that individual structures, like whole cities, had to be able to change with its people. The Sky House doesn’t have a head either, it’s just a whole body of cells on concrete-pillar legs, moving and moving, and might just walk off one day.

 After the Blitz, when many of the Wren churches had to be wholly or partially rebuilt, some added stained glass where the clear Restoration windows had been. A special round altar by sculpture Henry Moore was placed in St. Stephen Walbrook, changing the configuration of worship at the square church to an egalitarian middle. In 2014, in the art magazine Apollo, a critic with the Pynchonian name of Gavin Stamp writes that the new altar looks like a wheel of cheese and decries it as  something “… that wrecks the subtle tensions and ambiguities of the interior space”. For the traditionalists it seems, Wren churches were never meant to live at all, but rather ossify. They claim them as High Britishness and they turn them all to ash in their mouths instantly. Plot that on a grid, a straight line, d/dx of a boring fixed integer. No curves for Newton there, nor manifolds for Riemann. Flower without a wind.




The Acéphalistes thought they were preparing themselves for the brutalities of wartime resistance by first brutalising themselves. Chop off the brain, leave the stem in the stump and feel. I don’t know if it worked. But if we start to feel that everything is Vichy-France-level fucked, it might just be a proposal. The Fire may have truly burnt out the plague in that it tore through old Tudor and Medieval slum streets, narrow and packed, to gain momentum, and that was where the disease most easily spread. Today in Britain, the Tories propose a new housing plan: change all the closed High Street shops into flats. They aren’t even the size of some graves. Some have no egress to the street, others no windows. It invites a spark. These will not be buildings that shape themselves to people, but extant structures that try to shape people themselves into their geometry. Work, sleep, rest, repeat. The grid stays regular. There is no piazza, it has been converted to a car park, in which we someday might find another buried king.

It is possible the world is ending. After the world ends though, you have to plan a new one, and that’s harder. You have to tug and tug at the gravity of the old world until you achieve escape velocity, but the ruins are hyperdense and pull you back in treacherously. Scylla and Charybdis. I will hide in the plane trees and talk to the angels with eyes on their wings and ask if they are torii, which is the plural of torus but also the phonetic romanji of the Japanese word for bird, 鳥.

Maybe time is flat, or runs flat in parallel to the six other dimensions of Calabi–Yau space, where string theory is true. Maybe this is just the B-variant universe and in the others, the Fire didn’t burn or they built the radiant avenues or there is a true democracy or hope is still hiding. Some astrophysicists speculate that black holes are actually wormholes that may open up to alternate universes, or just to somehow else in space entirely. They’re called black holes because not even a photon can escape them, neither the particle nor the wave, bouncing off the gessoed gold or the bricked pilasters the bear the weight of the nave of St. James Piccadilly. But you’re reading this, a fact that is. I’m slowly catapulting to the Event Horizon– if you’re reading this, it’s proof that I haven’t ended up inside just yet; a phone signal disappearing as I step for the first time in half a year into the Tube. 

It is the autumn of 2020; I live in London. I ask of you for your other self, the one that will be: lend me your geometries.