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gravity well

'They are for having maps, not pictures of the world we live in.'
Hazlitt, on Reason and Imagination

'Why do we take pleasure in lingering over maps of places we already know, if a map is not an instrument of understanding, a poetics of space?'
Hunter Sidney

'Anatomise the city? May as well try to classify the spirits of the air.'
Alfred Cannoner























































































































Le citta invisibili, 1993








Like Gulliver in Laputa:
'Nuovo arrivato e affatto ignaro delle lingue del Levante, Marco Polo non poteva esprimersi altrimenti che con gesti, salti, grida di meraviglia e d'orrore, latrati [barks] o chiurli [hoots?; un chiurlo is a curlew] d'animali, o con oggetti che andava estraendo dalle sue bisacce: piume di struzzo, cerbottane [blowpipes], quarzi, e disponendo davanti a sé come pezzi degli scacchi. Di ritorno dalle missioni cui Kublai lo destinava, l'ingegnoso straniero improvvisava pantomime che il sovrano doveva interpretare...'
p.21


kublai khan...troubling plenitude...








...although in fairness, as the etymology suggests, the surviving examples are Roman; I use Phoenician and Roman here as Ruskin might, for their poetic value, their rhetorical force, or if you prefer, their duplicitous vagueness.


































































































Although, as J.V. Field's remarks, 'In Piero della Francesca's time, space did not exist... One significant element in this [Aristotelean] natural philosophy was its avoidance of the notion of infinity.' J.V. Field, Piero della Francesca: A Mathematician's Art, p. 95
However, Field also wrote a book called The Invention of Infinity: Mathematics and Art in the Renaissance which might, if I read it (and understood it) get me off the hook in a variety of ways.
































lorenzetti entry to jerusalem
Lorenzetti - medieval cluster


























In Piero della Francesca: A Mathematician's Art, p. 174. Field says of Piero della Francesca's Flagellation that 'the evidence is not only that the perspective is indeed correct, but also that the picture is, in this respect, extremely exceptional, at least among works painted in the fifteenth century.'










































































































































































































































 

 


 

cartographical

What would a map of Norbiton: Ideal City look like? And what would you use it for?

Alfred Cannoner, when I visited him in his bluebeard’s lock upbluebeard to ask his advice, suggested the following:

It would be a map of what we think we know overlaying a map of what we thought we once knew. And, ample though that brief is, it would as likely as not be inaccurate. It would need to be updated on an almost hourly basis and perhaps animated, like a weather map. It would need to store anecdotal information, supposition, wrong guesses; it would have to encode spatio-temporal information across a variety of scales simultaneously. It would (not?) tell you how to get there, and (nor?) how to recognize it once you were there; it would show you not so much what was under your nose as what you could expect to see out of the corner of your eye; you would be able to carry it not in your head, but in your pocket.

It would be, in short, a complex object.

hyperbolic orthogonal dodecahedral map of the city

As I was walking away, however, with this head full of a drunk artist’s defiantly useless advice, I resolved that, no matter how fluid and eccentric it need be, and no matter what fudges its construction might entail, I would start, if I started at all, by drawing a grid, and labelling its axes.

 

 

I have a paradigm of cartographical endeavour which I derive from experience, as follows:

When I was about 16 I spent more or less the whole of one summer making a genealogical tree of all of the gods and heroes in Greek myth – basing my work entirely (I think) on Robert Graves’s The Greek Myths.

It was a project that grew from modest ambitions. I started by making a small family tree of the house of Atreus, or some other house, in order to get them straight in my head. But the nature of family relations being what it is (i.e. tending to infinity), bit by bit my map grew.

Before long it was drawn on a rolls of yellowish ammonia paper purloined from my father's office and was at least as wide as the table I worked at was long: two metres. I used my father’s old drawing tools, dating probably from his days of study in the late 1940s: hefty wooden rulers, opaque yellowish set squares with a two-foot hypotenuse, a tool for drawing parallel lines hinged with tarnished brass. The sort of drawing instruments Brunel probably used to design bridges or ironclads.

As I moved from version to version it never occurred to me to draft the next: the next was always definitive, and I would ink in my lines confidently, then less confidently; before long I would be annotating, sketching corrections over the top, making notes for the upcoming finished work.

My summer holidays were three months long.

I had no experience or knowledge of genealogical trees, so it wasn’t until some way along that I realised the same generations should fall on the same transversals.

This apparent rationalisation rapidly exposed the insanity of familial relations in (Graves's) Greek mythology: there were duplicate names, conflated retellings, dubious connections, compressed chronologies. I persevered, however, and before long my map looked like a plumbing diagram.

I can remember certain zones of it very clearly, like some retinal after-blur or damage. Some of the transversals were as close to one another as they could possibly be within the tolerances of the pen I was using (0.5 mm). I would project long structural lines out to blank areas of paper which would provide Lebensraum for my swelling population.

The root of my difficulty, had I known, was not my technique but my source, although also this might in turn be classified as a technical deficiency: I did not have the philological experience to question the reliability of Robert Graves. I puzzled over the text and the index for hours together, as though an accumulated charge of brain power (think more!) might spark off a gloomy watt of insight.

What are the generalisable features of this experience, twenty-five years on?

I recall that my father, glancing fondly at my shoddy work, commented that I should indicate which line crossed which by drawing a little hump-backed bridge at their intersection – positing a sliver of a third dimension which, had I been more alert, might have served to unperplex my project. I should have realised that the heaped proliferation was traceable to a few sources: Homer, Hesiod, Aeschylus, Ovid, and so on. I could have nested my stories, overlaid the suffering of one family with that of another, integrating the nodes common to different branches or different histories, separating out those on independent orbits.

It would have been hard to read but more coherent, more accurate than my flayed two-dimensional version. A better projection, so to speak.

The map, in the end, became an object in its own right that, like a cuckoo in my sparrow-brained intellectual nest, began to jostle its referent – Graves’s book – towards the margins, and demand its own thinghood. And that new object, long since discarded, forgotten, destroyed, nevertheless enjoys the ghostly persistence accorded to wrong turns, feckless wanderings, pointless endeavour.

 

 

Calvino’s invisible cities inhabit undifferentiated space. The only thing in the landscape is the city, and the camel trains or solitary ships which do not so much connect them as oscillate imperceptibly, if doggedly, between them. The cities stand in no particular relation to one another. They are discrete psychic objects, loosely corralled (by Calvino) into abstract sets.

Each of the cities has the name of a woman. Olinda, Raissa, Marozia, Teodora, Berenice, Melania, Adelma, Eusapia, Argia, Laudomia...

Kublai Khan, sitting listening to Marco Polo (or watching him), forced to consider the troubling plenitude and multiplicity of his domain, does not really need to know where each city actually is, only the nature of its quiddity. We understand that Marco Polo himself is an adept of this land’s geography (he is employed in the Khan’s administration of his empire), but does not need to supply it in any formal way to Kublai Khan. Or rather, the formal lineaments of the geography of the Empire – provinces, rivers, mountains – are irrelevant to the relational nature of Marco’s own geographical shorthand (three days journey beyond x you arrive at y).

The Khan might also have his maps, his cartographers. Perhaps, like the College of Cartographers in Borges’s story Of Exactitude in Science, whose map of the Empire grows so large that to unfold it requires first a whole province, then the Empire itself, their ambitions are suitably aggrandizing: their form of enquiry will dissolve, in time, into the object of knowledge.

Perhaps the Khan knows this – he is an Emperor, after all – but knows also that the maps his cartographers produce are political objects, expressions of power, a form of spatial census.

Marco provides a different class of data. Empires change, after all, necessarily faster than the maps of them.

Marco relates phenomena – ghostly tales of places shimmering out on the far margins; places emerging from the desert and subsiding into the sea; a spectral landscape that comes into being as he passes through it and disappears as he moves on. If he has a map of any of this it is carried in his head, or perhaps his saddlebag, in the form of a traveller’s tale. It is a periplus, or an isolarion.

 

 

The attentive citizen will already know what a periplus (see glossary) is. It is a mariner’s-eye view of the world, a map made by Phoenician sailors, not by Roman engineers; it is a rough guide fined down by the annotation and emendation and amplification of generations.

An isolarion is a map that prioritises local detail over accurate relational information. It has been described as a form of topological myopia – not a map at all but an unhealthy dilation of focus.

It is a tool of, or rather an adjunct to, the (cinquecento) Renaissance version of geography called chorography, which is really a catch all for the local, anecdotal, aetiological. A chorography of a place would include tales of its origins, both mythical and suppositional, stories of titular or patron saints and heroes, tales of the ancestors; it would tell you on which street the dyers worked, on which the cobblers, and the goldsmiths, and why. It would tell you the feast days of the city, and the order and dignity of the guilds in the various civic and religious processions; and so on.

And, if it included a map at all (it is, by the late cinquecento, a  predominantly literary form) it would be an Isolarion. Ptolemy, who invented the genre with a throwaway remark, noted that while a map required scientific know-how, an Isolarion, or more precisely a chorographical map, required pictorial or artistic skill.

A grid requires no pictorial or artistic skill. It imposes a relational structure on its constituent parts. It holds them at a known distance, one from the other, and regardless of your own experience of them. It allows them to breathe.

 

In Star Trek: Voyager, the character known as Seven of Nine is released from the Borg collective, the hive mind, and is forced to seek ‘perfection’ by other means.

astrometricsShe spends most of her time in the Astrometrics Laboratory, the seat of Stellar Cartography, where she combines various Borg technologies with Starfleet Yankee know-how in the pursuit of improved navigational charts. The Borg, it transpires, impose a series of matrices on space through which they then enumerate spatial grids, on which grids they can map any object you care to mention: galactic clusters, nebulae, star systems, planets, species, rocks.

A navigational chart presumes no route. All eventualities are covered with equal attention. Voyager is torn between one route of paramount interest – the route home – and the infinity of alternative routes encapsulated in the drive to explore. Exploration is one way of making maps – you jot down what you see as you go, like leaving breadcrumbs. But having the grid prepared so that you can pin  down the clustered objects as you encounter them is a form of ersatz sanity. No object that comes into sensor range as you bolt around space cannot be pinned in relation to every other known object, even if you know that some of those objects have orbits, are wormholes, singularities, inexplicable entities.

Did I say ersatz sanity? No, this is a model of the real thing.

 

 

If the Borg did annunciations, they would be done in linear perspective.

veneziano annunciation

Linear Perspective, properly understood, is a fully-worked out and mathematically coherent (if necessarily incomplete) description of space, not a mere accumulation of foreshortened objects.

A discovery of the quattrocento, its single great innovation was a series of techniques for calculating the ordered recession of transversals into the picture plane – so a tiled floor, for example, or a coffered ceiling looked right because it was right. In this way the recession of the transversals corresponded to the convergence of the orthogonals, and the box, so to speak, was closed.

Objects could now be located in (imagined) space rather than daubed over the front of a bit of wood or the wall of a chapel. The picture plane erases itself, becomes a window on another world, a world which in turn becomes mappable.

In Erwin Panofsky’s view, we are now looking, for the first time in the history of art, at a space that is homogenous, isotropic, infinite. Some would go further. Infinity itself, such a horror even to Kepler, to Pascal, was born, it has been argued, of this (fundamentally technical) leap of understanding.

 

 

Clarke is intent on mapping Norbiton: Ideal City.

Clarke mapping NorbitonHe is not very clear or articulate about what exactly he intends, but broadly it involves creating a chorographical map from the top of Madingley Tower (where he lives) – a spot which he now calls the Isolarium.

The map will be made of photographs, from what I can gather, taken with frog-eyed wide-angle lens and telephoto lenses, superimposed and stitched together.

He has ambitions, he intimates, to create a clickable, navigable map of Early Modern Norbiton, as he chooses to call the Ideal City. This bulbous and distorted panorama will be hyperlinked to, I don’t know what, slurries of anecdote, aetiologies. He will achieve all this with the help of Emmet Lloyd, who has access to programming resources.

Clarke intends to call it, The Atlas of Norbiton.

Interesting though the idea doubtless is, I cannot help but wonder if it is not set up in rivalry to the Anatomy of Norbiton which, I now realise with no little smugness, is swelling to Borgesian dimensions of completeness.

My smugness is alloyed, however, with the knowledge that I will perhaps at that point need to provide a map of the Anatomy itself.

And I have no idea how to do that.

 

 

The city, from the quattrocento, is a unified space; a perspectival space. It is no longer represented or experienced as a medieval cluster of objects – castle, cathedral, tower jumbled within the walls – but as a homogenous, infinite, isotropic space in which, Panofsky avers, the bodies inhabiting that space do not have any greater weight or so to speak density than the space between them. The city is not, as in Calvino, something squatting in the desert, something you arrive at; it is an intelligible and relational, open and geometric sanity, through which you can move.

In quattrocento art the miraculous events of biblical and classical history take place, for the most part, in cities, have a civic backdrop. Linear perspective craves straight lines and the new architecture provides them: colonnades, entablatures, tiled and paved floors, coffered ceilings.

Unlike the wilderness, the city is a space that can be managed. Handled. Done in perspective. It is separated into distinct blocks and squares, named, numbered perhaps. A mappable space.

And as with the city, so to with domestic space. Rooms, staircases, bed chambers can be mapped on a grid: are a grid, in a manner of speaking.

What this should mean to my own experience of space, as I leave my room and walk the placid streets of Norbiton, is something I puzzle over.

 

 

J.V. Field notes that virtually no pictures in the quattrocento were in fact done fully, which is to say remorselessly, in linear perspective. What he means is that, in the first place its take up was sporadic, even if it appealed to the most modern tastes; and then even when a coherent spatial scheme is attempted, and carried off, there will be accommodations to pictorial taste, perhaps to iconographic convention: a good painter will not simply do the math.

Linear perspective does not solve problems. It creates them. And the problems that it creates – like the technical, aesthetic and conceptual problems of providing a projection of the globe in two dimensions - are insoluble. If you designate a position from which a painting should be (ideally) viewed, you have to rethink everything. If a painting is going to be viewed from below, how do you paint a crowd such that the rear ranks are not obliterated by the front? The serried ranks of the duecento, trecento, are now a jostling melee; heads crane, peer, catch a glimpse. This is not how heaven was supposed to be. It is not a procession, it is a scrum.

And what about narrative? If the pictorial space is coherent, designed to provide a metonym of the space we are accustomed to associate with our subjective experience of 'reality', then how do you tell the whole story of, say, the Tribute Money without showing Peter three times in the same space?

The great paintings of the quattrocento did not ‘do’ Linear perspective, so much as wrestle with its implications.

 

 

Witness, for example, the following:

bartolini tondo

This, the Bartolini tondo, was painted by Filippo Lippi in about 1452. The tondo was typically a decorative domestic item, and like the cassone or marriage chest it was associated with a specific domestic ritual –in this case the birth of a child. They are known, in fact, as deschi da parto, or birth trays.

The Bartolini tondo depicts the Madonna and Child against a bi-partite narrative scheme illustrating moments of the Virgin's pre-history, so to speak: on the left is her birth and on the right the meeting of Anne and Joachim in which moment she was, according to legend, immaculately conceived.

This collapsing of iconic and narrative pictorial conventions is catastrophically odd. What exactly is being mapped back there? The spaces are coherently handled, but precarious. The little boy seems to be sliding off the floor: he is clinging on to the skirts of his mother not for comfort but for dear life; the serving woman in the centre-right is pinned and observed (from behind?) like a butterfly; Anne is hoiking Joachim up the steps at the back as though the pair are roped together on the Eiger.

mind how you go

The windows and doors interpenetrate the space, seem to be constructed in divergent planes. Do all those floor planes really converge? It's possible (although just why the floor of the bedroom and the pavement of the city should converge is anyone's guess) but the foot of the bed (near the critical centre of the composition), isn’t that just wrong? The honeycomb ceiling certainly vanishes, into some pitchblack wormhole of memory; the bedroom might be on the extreme outer edge of a vast wheel of an Ideal Fortress-Palace.

Understood as a map of space, there is nothing sane, rational, coherent about this. But sitting at the front, quite comfortable, is the Virgin, dandling her pomegranate child. Everything (behind her, below her, in her lap) is a peculiar dream to which she gives no special credence. But then we know from our (skewy, apocryphal) Biblical history that the predicaments of the various individuals in the hyper-imagined spaces beyond are her own predicaments; they seem, even, to be generated, pictorially, or perhaps sustained by the multi-dimensional tangle of her hair and hair piece and the halo spinning at near-light speeds; she is, despite her apparent poise and lightness, a swirling gravitational mass, a spatial sorceress, a Circe.

In other words, if we try to understand this picture as a conception unified by known principles of orderly recession it is deeply perplexing; if instead we understand it as organised around the considerable asymmetrical pictorial weight of the Virgin - if we lean, in other words, towards an iconic reading of it as a devotional object - it is, I hardly know, excusably beautiful.

In its asymmetrical weight it is, in other words, closer to this:

ejected from an airlock

... where Joachim seems about to be ejected, not from the temple, but from an airlock, than to this:

spozalizio

... where everyone seems to know precisely where they stand.

 

 

Lippi’s composition is determined by the shape of the field. Linear perspective on a circle was always going to be a challenge.

The picture hangs in the Palazzo Pitti in Florence, and I cannot remember, and cannot tell from reproductions, if the panel on which it is painted is given to convexity or concavity or neither. My perceptual apparatus, the more I stare, is thrown into crises of uncertainty. And then, this is a large object – 1.38 metres across. Perhaps, when you stand in front of it, it would all make sense. There is no way of knowing, and I don't remember.

There will be no more standing in front of it.

Perhaps for our purposes the best map after all is the Isolarion; as though Clarke up there on Madingley Tower with his monster cameras could spy out the places on my map for me; Venice, let’s say, and Florence; and Urbino and Arezzo; and for himself, Rome; and for Kelley, San Francisco. When you are young you look at maps and see the names of places dotted over them; and then, as you live out your life, you visit some of them, live in others, have friends here, or there, fall in love in this one, or that – a random set taking on different valencies, different weights. Some – perhaps, Tokyo, for example, or Sydney, or Jerusalem – will be forever known to me as a medieval composite: bullet trains, neon signs, opera houses, harbour bridges, wailing walls and temple mounts; others will be known and frequented mental spaces.

This woman in the Bartolini tondo is a virgin with a child. Perhaps no wonder it is strange. A desco da parto full of virginal mother and immaculate conceptions. I do not know the circumstances under which such a painting would have been presented to a Florentine mother; but I suppose it is unlikely that they would have nailed it to the wall as she lay there, in a far corner of a great stone palace, pummelled with childbirth, laden with sweat and blood and a swaddled infant, surrounded by the men of the House congratulating themselves on the birth of an heir and conspiratorial womenfolk to whose conspiracy she is not party but temporarily subject; it could not have taken place like that - the presentation - unless the household were undergoing a narrative collapse analogous to that occurring the painting.

However, I find myself wondering what she must have made of it, this luxury object in a world of few luxuries. Would it have helped her to locate herself on her personal map, insofar as that map overlapped with the rituals and roles of her people? Would she have understood, in other words, what it meant?

Or would she have misunderstood? Would she have lain there glaring at it, asking herself whether, on her private map, the genealogy of her joy and satisfaction now overlay (with little humpback bridges) the linear descent of her suffering and failure (so many nodes or elements common to both); or the other way around?