A multicultural look at space and form

If we are talking about a particular picture, say Mu Ch’i’s famous ink painting of persimmons, then we can say certain things about the space, and about the forms in it.. Space may be t

With Representation,” is forthcoming in a book on the artist Vik Muñiz

Portions not required for “Issues in Visual and Critical Studies” are in red

This text was originally posted on www.jameselkins.com

Please send all comments, etc., to jelkins@artic.edu

This text should be read onscreen; there are embedded links to illustrations, marked

“(plate).” Some are noted as “not available.” I recommend skipping over those sections; the text is legible without them

Revised October 2005

The pages that follow are from a work in progress, a book called The Visual: How

It Is Studied The book is intended for first-year university courses, where I hope it will

be used in place of the usual “art appreciation” textbooks Those books, which proliferate

in all languages, are nearly always based on a rudimentary pedagogy of form, color, space, motion, and texture In such textbooks, linear perspective is inevitably introduced

as the centerpiece of the Western archievement in visual art It was perspective, so these textbooks say, that allowed artists to develop realism and to represent the physical world

in a quantitative, systematic fashion Although such rudimentary instruction is often ignored by professional art historians, it is compatible with much of what the discipline currently does Monographic accounts of the Renaissance continue to stress naturalism as

a sine qua non of the Renaissance, and textbooks of world art continue to emphasize

linear perspective at the expense of the many other representational forms developed worldwide.1

I do not think The Visual will correct that imbalance, and I am not even convinced

that it is correct to call it an imbalance Linear perspective is a unique project, and I do not believe that a lengthy, sympathetic description of some other denotative system can realistically hope to replace the interest that perspective continues to attract What I do

hope The Visual will do is show students, right from the beginning, that there is a

tremendous amount outside of normative Western scholarship that is genuinely interesting, and often more challenging than the familiar constructions and achievements

of linear perspective Perspective has a traditional group of “others”: marginal and

“incorrect” forms such as anamorphosis, “reverse” perspective, inverted perspective, curvilinear perspectives, “herringbone perspective,” stereoscopic perspective, anaglyphs, hyperbolic perspective, engineering drawing, and so forth Those “exotic” Others are actually the traditional accompaniments of the study of linear perspective, and they

seldom reach beyond the West, or outside of painting The Visual will revisit some of those, but my principal interest is simply to begin from a different dramatis personae,

and see what kind of drama develops. 2

A Multicultural Look at Space and Form

The word space is a bit abstract If we are talking about a particular picture, say Mu Ch’i’s

famous ink painting of persimmons, then we can say certain things about the space, and about the forms in it

The space in this painting, for instance, might be infinitely deep—perhaps it is a bright misty morning, hiding a view of blue mountains—or it may be paper-thin, no more than a film of dried ink on brittle silk The persimmons may be as spongy as they were when Mu Ch’i painted them eight centuries ago, as fluid as the ink and water he used to paint them Or they may be flat, fallen against one another like dried persimmon skins

This kind of indecisive meditation is part of what it is to look carefully at a picture Such thoughts on space and form may lead, as they often do, to more concrete questions—I might want to ask about the elusive nature of reality in Zen practice, or the Buddhist sense

of the transience and eternity of the world Thinking through space and form to other ideas

is a stock in trade in the interpretation of pictures, perhaps even interpretation’s most indispensable moment But instead of continuing down this path let me emphasize the strangeness of what I have just done: I have opened the discussion of the picture by talking about not persimmons, inkbrush painting, Mu Ch’i, Zen, or Buddhism in general, but

space and form Where did those ideas come from? Certainly not from the picture, which

says nothing about them And what do they mean? Are “space” and “form” so well understood, that I can just begin by naming them, without thinking them out first?

The more carefully you consider this problem, the more you will be dragged away from the picture and pushed up against basic philosophic problems: What is space in any picture, and what do we want to call “space” itself? And what is a thing, that can exist in such an imaginary space?3 How is the space in a picture “in” the picture? (And as for sculpture: perhaps the space around a sculpture an essential part of the sculpture, but what exactly is that space? How far does it extend? Does it envelop the viewer, or glue viewer to sculpture?4) Can you think about space without forms in it? (If you think of Euclidean axes

extending off to infinity, with nothing else around, then you are still thinking about forms

in space.) And if it is not possible to imagine space without forms, how do the two depend

on one another?

Do we know what space or form are? Do we know what they are in pictures? These are the kinds of questions that sound simple, or vague—but they lie at the heart of everyone’s ideas of what visual art is about Artists, critics, and historians continually use words like form, object, shape, and space, but the abstract tenor of the questions I have just asked sounds a little eccentric because those words are normally used

to talk about particular artworks Yet behind the great majority of descriptions of artworks there are assumptions about what space and form are and how they are related, and those ideas silently guide peoples’ thinking and writing For that reason alone it may be worthwhile to pause try to think about the words themselves and how we want to put them

to work

I find it is a good generalization to say that, in the twentieth century at least, space tends to come before form Space may be the great topic of modern art, and it is difficult to find writing on architecture, photography, painting, or sculpture that does not depend heavily on the idea that space is what makes visual art possible Buildings are said to construct space, pictures to depict it, and sculptures to mold it Artworks are said to create and interact with space, so when it comes to thinking about art people tend to begin by positing some ideal empty space, and then they try to say what the artwork has done with that space Space is a natural first term in many discussions on art

Yet there are reasons to wonder about this (Notice, for example, I just used the phrase “empty space.” But isn’t space empty by definition?)) It can be shown that the

preoccupation with space is typical of the twentieth century In past centuries critics didn’t need to bring up space as frequently as twentieth-century writers did The architectural historian Peter Collins has made an important observation about this: “it is a curious fact,”

he writes, “that until the eighteenth century no architectural treatise ever used the word” space.5 Today, I think, it would be literally inconceivable to write a book on buildings, sculpture, painting, photography, or any other medium of art, without mentioning space

“Space” is a relatively new word, but it is taken to be both universal and unproblematic

So it seems best to be cautious about space, especially when it comes to studying artworks made before the twentieth century In this chapter I will go at this problem first by

making an eclectic survey of kinds of space in visual art, trying not to emphasize what

seems to be common or proper The single most important and universal kind of space in visual art, perspectival space, is a kind of roadblock to seeing other kinds of space By

largely avoiding it, I am going to try to see the possibilities of the concept space in a

slightly new light I want to widen the question and show how perspectival space does not have hegemony over the concept of space—and how spaces, in the plural, are more involved and less understood than they might seem

Toward the end of the chapter I will have two further points to make: one is that all such talk about space is flawed, since it does not present space and form as coeval partners, equally involved in the creation and meaning of art; and the other is that no matter how

reflective we are about spaces and forms, there is no adequate way of addressing space or

form in artworks, since artworks spill out uncontrollably into the world The whole subject,

in this sense, is refractory Space and form are not at all easy to talk about, unless you ignore what you do not know about them and simply begin, as I did here, with some particular painting

picture is in correct perspective The great majority of photographs, movies, billboards, and

magazine advertisements are in correct perspective.)

Art historians tend to say that a fundamental turning point in Western art came when linear perspective was invented five and a half centuries ago.6 Pictures made before the adoption of perspective in the Renaissance, or in cultures that did not use perspective, tend to look flat, while perspective pictures tend to look like they possess depth

Perspective was originally a series of methods painters used to give their pictures a quality that we now call “photographic” or “realistic.” To get that effect, perspective makes use of a particular kind of space Linear perspective is based on the idea that space has four qualities: it is three-dimensional (two-dimensional surfaces like paper do not count as

“space”), infinite (it extends in every direction without limits), isotropic (twelve inches is the same length whether it is measured vertically or side-to-side), and homogeneous (space

is smooth and continuous, it has no lumps) If space is this way, then it is possible to construct perspective pictures, make photographic cameras, design video games that take place on infinite grids, and in general do everything that depends on three-dimensional, infinite, isotropic, homogeneous space: navigate the Atlantic to find the New World, measure the landscape of Venus, and image fetuses with ultrasound In visual art terms like perspective space are used to what the rules of linear perspective produces, and scientifically-minded authors tend to call space based on the four characteristics I have named “Euclidean space” or “rational space.” It is a powerful conception, and it underlies virtually every book on art history—but it is not the only available sense of space

Space is also something less formal and geometric, more like “an area provided for

a particular purpose” such as sitting or walking around.7 It is simplest to call this second kind of space room or everyday space Everyone needs a certain amount of room to stand

or sit That is different from the space occupied by an ocean or the solar system, because in order to measure such great distances you need some concepts of geometry, surveying, and astronomy Everyday space is intuitive, untechnical, and local—its limits are more or less those of the human body It gives us our sense of whether we can squeeze between two people in an elevator, or jump over a little stream Ergonomics is the study of everyday space in and around cars, machines, furniture, and workplaces

Some artists and periods are more sensitive to everyday space than others Here there is room enough in the doorways and apertures for each of the figures to enter the

manger—even the ox and the ass could jump in if they wanted—but if they were all in the manger, it would be apparent that perspective has given them too much room The angel and the human figures would not be able to link hands, since the perspective has made the space too large That is extra space, supernumerary room, produced unthinkingly as the artist kept adding blocks to his perspective construction This picture is typical of the early years of linear perspective: the constructions, and the infatuation with space, have gotten the better of the artists Other pictures from this period, which are not in perspective, have just the right amount of room for their figures In Giotto’s pictures, people walk around in tiny rooms and walk in and out of small buildings; but if you do not think of Giotto’s work as failed perspective, then the “tiny” architecture seems just right

Everyday space can sometimes be measured If you are thinking of squeezing into a crowded elevator, you can mentally compare your width to someone in the elevator, and estimate your changes of fitting in Linear perspective space is the very epitome of measurement: a space isn’t in perspective at all if it cannot be quantitatively measured Two other kinds of space cannot be measured at all One is psychophysiological space, which is the subjective sense we have of the larger world we live in Part of psychophysiological space is the space we sense, even though we can never touch it; I will call that visual space

It is said that the moon never looks like it is more than one-half mile away (I think it looks more like five or six miles) If you look at a perfectly blue sky, on a day when there are no clouds, and if you forget whatever you know about the stratosphere, the ionosphere, and

outer space, then the sky will appear as a dome, slightly flattened on top.8 The same kind of thing can happen at night, when the stars suddenly seem to be perforations in a vast hemisphere Visual space is an everyday fact of perception The oversize term

“psychophysiological” is meant in part to describe those subjective, body-oriented guesses

when they apply to objects that we can touch A book may look larger than the empty place

in the bookshelf that fits it perfectly The distance to the top of the stairs may look longer than the same distance when you get to the top and look back down This kind of space is three dimensional, but not homogeneous or isotropic: that is, it changes depending on how far away things are People can judge distances fairly well when things are close by, but much less accurately when things are farther away (Think of the difference between judging the separation of two piles of sand in a sandpile, and judging the separation of two mountains in the distance.) Psychophysiological space is partly psychological, and partly physiological (to do with the motion of our bodies), and for that reason it is sometimes called kinesthetic space.9 If the staircase looks longer from below, it might be because your perception is influenced by the memory of the effort of climbing; and if it looks longer from above, perhaps you are thinking of the possibility of falling.10 The Japanese concept of ma may also be useful here; ma is used to speak of the space between two objects, but also between two sounds, or two events in time Ma is similar to what modern Western critics

call negative space, the emptiness between figures in a painting or forms in a sculpture Negative space is a kind of opposite of what is painted—it is what is left over when the painted parts are mentally subtracted—and so it is elusive and intriguing to modernist eyes

Ma is even less like distances in perspectival space: it does not distinguish very crisply between distances in space and time The mixture of memory and sensation conjured by ma

might be a little closer to psychophysiological experience than to geometric space.11

And there is at least one other major kind of space It is our innate imaginary space, the sense we are all given that things have distance from one another People who are blind from birth understand imaginary space: they know that objects are separate, that one thing can be between another, and so forth.12 Some people think that infants are born with the idea of three dimensions, and others think they learn their sense of space by looking around and reaching for things The enigma of the inner sense of space is related to the mystery of the inner sense of time: if you are asked to close your eyes and count thirty seconds, you will probably be accurate to within five seconds But how did you do it? Assuming humans

have something like an inner clock, you might say that you have learned by experience what a second is, and how to count thirty seconds; but that still leaves a deep mystery: how did you count that first second? How do you know what an interval of time is?13 The philosophers who claim that we are born with a sense of time and three-dimensional space—such as Immanuel Kant—would say that all we have to do is adopt out inner clocks and rulers to the scales we use in our society Other philosophers would say we know nothing when we’re born, and we gradually learn about time and space from our infantile experience Luckily I don’t have to decide that conundrum here; it’s only important that there is an inner sense of space that complements and perhaps also directs the more outward kinds of space Perhaps imaginary space should be called the idea of space itself

Perspectival space, everyday space, psychophysiological space, and imaginary space are slippery concepts Each of them has been debated at length, and there is disagreement over their number and meaning The philosopher Henri Lefebvre, for example, has expanded elements of each of these four into politics and history, by talking about “social space.”14 The fourfold arrangement I have given here is only a starting place for discussion Almost everything that has to do with art theory depends on perspectival space, with things that go wrong with perspective, and with schemes for producing pictures that look something like linear perspective (in addition to the canonical linear perspective, there is “herringbone,” “reverse,” and “curvilinear” perspectives, among many others15) It

is a good idea to bear in mind that perspective is often at odds with other more intuitive or inner senses of space as well as with rival theories

W H A T I S L I N E A R P E R S P E C T I V E ?

It is easy enough to say what the basics of linear perspective are The picture plane

is usually just the surface of the picture, and then there is the viewer’s eye (the center of projection) and the object There are a dozen or so other terms in textbooks on linear perspective, but the important fact here is that a perspective picture behaves like a tracing on

a glass pane, exactly reproducing the contours that one eye sees The salient feature of the woman’s picture is that some lines converge to vanishing points, which are often lined up

on a horizontal line that runs across the picture at eye level (the horizon line).16 Perspective

space or fictive space is what seems to happen “in” the picture—that is, “behind” the picture plane

(Linear perspective needs to be firmly distinguished from aerial or color perspective The latter has nothing to do with lines, architecture, or geometry It is the study

of atmosphere: what things look like in fog or rain, how sunlight casts bluish shadows It is illogical that linear and aerial perspective have traditionally been mentioned and studied together.)

Here is an interesting example of linear perspective at work In the 1920’s there was

a stage show in which the audience sat facing a gauze screen.17 Each person in the audience was given a pair of red and green glasses, like the ones that are handed out in some 3-D movies They saw shadows of boys throwing balls, and it looked like the balls were coming through the screen and flying directly at them (notice that the artist has drawn the balls flying through the theater) Each observer would have thought all the balls were coming directly at his or her own eyes This is a complex case of perspective, in which the perspective space seems to burst out in front of the picture plane In almost all perspective pictures, everything seems to happen behind the picture plane Still, the whole stage show obeys the same basic rules of linear perspective Linear perspective is like this—extremely versatile, and apt to break its own conventions

(Fenanrdo Gallego: this picture is similar to the one mentioned in the text, with

ostentatious displays of perspectival skil.)

Perspective has always goaded artists into trying more and more complex constructions In the first half-century after perspective was discovered in the Renaissance,

artists got carried away by what perspective could do In Fernando Gallego’s Nativity, the

standard perspective construction outshines the Child himself, and all but the most important figures are kept out in order to emphasize its geometric perfection.18 The chinks are drawn as dark lines, probably in imitation of the artist’s preparatory drawing, and their jointings are done with as much care, and more authority, than the divine drama The glowing Christ child serves to illuminate the linear masonry, which is itself a showcase for the painter’s skills Religion is in trouble here, since linear perspective is undercutting the viewer’s attention: perspective partly replaces the worshipper’s desire to pray, and it promotes an inappropriate sense of wonder about the painting itself

Perspective was born from the seeds of its own self-destruction The corrosive experimentation that began in early pictures like Gallego’s continued with increasing force and guile in succeeding centuries Today linear perspective is both ubiquitous and ignored:

it’s ubiquitous in photography, movies, and the mass media, and it’s ignored in fine art Yet even in contemporary art, linear perspective remains the standard by which other kinds of fictive spaces are understood There is no easy escape from linear perspective: it is not possible to simply ignore it and study other kinds of space as if it did not exist.19 Our expectations and assumptions about what pictures are have become too deeply ingrained to let us do that, but at least we can attempt to distinguish among perspectives and pictures that are not perspectives

First would be non-perspective, pictures that are something other than perspective, and which were done without knowledge of perspective They present various problems,

because it’s very hard to see a picture made in a non-Western culture without thinking of all

the things it is not Mayan pictures are not in perspective, but it is not easy to look at them and say exactly what kind of space they actually have This bas-relief, for example, seems

to show a flat frieze of figures But how flat are they? Bodies come out of snakes’ mouths, and come forward from a background and recede into deeper space There is no treatise on Mayan space—either written by Mayans, or by modern historians—so it is not at all simple

to say what this space is.20

http://www.misericordia.edu/users/davies/maya/codex2.htm

(This site, of images by Justin Kerr, is copyrighted On this particular page, you can see

some amazing figural work by an unknown Mayan painter.)

Next would be anti-perspectives, pictures done in partial or full awareness of perspective, but incorrectly There are many varieties of anti-perspectives, because artists began to bridle at perspective’s authority as soon as perspective got underway Cubist

pictures are anti-perspective, since they are partly attempts not to make proper linear

perspective pictures Even the pictures done in the early Renaissance, just as perspective was being codified, which I will call pre-perspectives, can sometimes be seen as attempts to keep away from the impending orthodoxy A final entry would then be a-perspective, meaning pictures done in awareness of perspective, but also with more or less profound disinterest in it Contemporary pictures are commonly a-perspectival, since they are made

by artists who never studied perspective and never cared to

Non-perspectives are easiest to approach, but hardest to get right If I say, for example, that cave paintings tend to ignore the requirements of fictive space, I am already

seeing them through the lens of modern Western culture (All modern cultures are alien to

cave paintings There is no privileged viewpoint, no modern tradition that is closer to cave paintings than another.) At first it may seem possible to accept the idea that one animal

overlaps another without being behind or in front, but we haven’t really accepted that kind

of non-perspectical relation Here some of the heavy lines are animal contours, but many others are inexplicable Is this a picture with space in it? What kind of space does it show?

Contemporary viewers usually also find it hard to understand visual art that is not framed (either literally or by the page it’s drawn on) Cave paintings usually have no borders, which makes them difficult to understand as pictures that might have space Even though the idea of unframed, borderless, overlapping works is appealing, we tend to become confused when we look at such pictures, and sometimes we’re not even sure if we are seeing pictures, writing, or meaningless scribbles A fragment of a cave wall, flattened

for reproduction in a book and forced into an artificial rectangular format, is like a picture

with space, but that may be just projection on our part

P R E - P E R S P E C T I V E : “ N A Ï V E M I S T A K E S ”

Second on my informal list of things that are other than perspective is pictures that are done in partial awareness of perspective, but tending in some other direction Not all artists had a clear idea of what perspective is A particularly strange moment occurred when Italian painters seemed to be trying to work their way toward perspective, and produced buildings that look like they are suffering from earthquake tremors.21

( Painting by Agnolo Gaddi)

They are usually explained as pre-perspectives: pictures that are almost in linear perspective, but were made by artists who did not quite know or follow the rules Since the early nineteenth century, when historians first began large-scale comparisons of Western and non-Western cultures, Westerners have been a little chauvinistic about perspective, dividing the history of art according to who used perspective and who did not In the mid-twentieth century there were even studies that tried to show that non-Westerners cannot understand perspective, or at least that non-Westerners do not understand it as well as

Westerners.22 But it is not always obvious what Western viewers count as linear perspective, or when an artist knew it or didn’t know it

Giovanni di Paolo’s painting of St John setting out into the wilderness would normally be counted as a non-perspective picture It shows the saint twice, so it is not a unified scene The technique is called continuous narrative, and it is meant to be read something like two cells in a comic strip But it is more than that The saint appears smaller

in the background, so it is tempting to think of this double scene as a single landscape, observed at two different times like a photographic double exposure Because there is no frame between the saint’s two appearances it is not easy to tell where one scene ends and the other begins The fields get smaller in the distance, and the flat plain ends with a little hill town But just beyond that little town, surprisingly, is a single house that is larger than most of the town So perhaps the foreground scene ends in the little town, and the background scene begins with the house Strictly speaking, in a linear perspective picture the lines of the fields would converge toward the background Giovanni’s lines don’t really

do that, but they do change direction—so was he thinking of receding forms, or are the

“receding” lines just accidental effects of the motions of his hand and arm as he painted?

In a treatise written a half-century before Giovanni painted this image, painters are advised to make things darker to show that they are farther away It looks like Giovanni is following that rule, since his mountainscape is in darkness even though the sun is shining

on the plain It is usually thought that Giovanni did not follow the modern rules of aerial perspective, which would require that the mountains turn blue or grey in the distance instead of black But a close look at the picture shows he did modulate his colors in the distance: the farther fields are lighter and grayer than the nearby ones So was he thinking

of aerial perspective after all?

The more carefully you look, the harder it is to say what is linear or aerial perspective, what is fictive space, and even what is a scene or a picture

A N T I - P E R S P E C T I V E :

Pictures that are non-perspective are different from pictures that are anti-perspective

Artists worked against perspective from the moment it was introduced, and modern art would not have been possible without some kind of reaction against perspectival space But the nature of that reaction is not well known It was not just a matter of giving up perspective, or substituting something else for it Cézanne and Picasso did complicated things with and to perspective: they did not merely “overturn” it or “abandon” it, as some books say

The art historian Meyer Schapiro has described Cézanne’s landscapes as

“intraversible,” “inaccessible,” and “unapproachable.”23 L’Estaque, Melting Snow begins

with an abyss As Schapiro observes, “there is no foothold for the spectator”: if I were to step into the picture, I would tumble onto the house far below.24 There is not much level space in the painting, and even the far field slopes steeply upward, in the way that some Chinese, Korean and Japanese paintings do, or as if it were a scene from a bad dream (a dream about climbing and falling) So to be exact about it, we are not excluded from the picture but trapped in middle distance After falling down onto the house, we can neither clamber back up the slope nor climb all the way to the distant farmhouse Cézanne’s landscapes can present formidable challenges to uninvited ingress and movement They do not seem to be in the infinite, isotropic space of linear perspective—but they do not appear

to be entirely beyond it, either

The Suicide’s House is also difficult to enter: we begin on what appears to be a level path, which slopes down so precipitously it is lost to sight That abyss is then followed by an abrupt turn The town, to which the trail evidently leads, is pathless It forms a barricade in the distance, and it is impossible to imagine how it might be walked through The berm is the only clear platform in the painting, and it does not look like a spot

to relax I can’t walk through this painting in my imagination It does not seem to be isotropic or homogeneous, and it is certainly not infinite: space only works in fits and starts

It may seem as if Cézanne is playing games with his spaces, trying to undermine the perspectival convention that says a painting’s fictive space should be a continuation of the

viewer’s real space (The idea is that our infinite Euclidean space is continuous with the

space in the picture, provided the picture is in perfect linear perspective.) But there is more going on in these paintings than a war waged against linear perspective There are a number

of forms in these two paintings that cannot be explained as deliberate strategies to overthrow perspective I will name four traits of the paintings that are not obviously aimed

at linear perspective

The Suicide’s House has a splayed center: the three windows of the central house

tip to the left, and a moundlike house slips away to the right The center breaks open for us, like a tree split by lightning

Both paintings begin at the upper left with a wave, which dies away toward the right Melting Snow has a cascade of trees that begins at the left and sinks, toward the right, into a quiet hill Swollen foliage crowds the upper-left corner, of The Suicide’s House, it

gives way to a lower and gentler horizon toward the right

The distant town in The Suicide’s House gives the painting a fragmented center, a

place near the middle of the canvas that receives particularly intense attention and takes on

the look of a geode packed with small crystals In Melting Snow there is a less important

place just in the middle on the horizon, where the most complicated forms jostle with some trees

And last, both paintings have a weak right margin, as if the Cézanne’s interested

trailed off or went out of focus To see the weak margins, put a card over the paintings, leaving only narrow a strip at the right The margins are weak in detail, in color, in the

differentiation of forms, and in both aerial and linear perspective In The Suicide’s House,

the right margin is nothing more than a flattened sheet of sod, contrasting strongly with the forms and colors along the other three margins

What do these four phenomena mean? However we choose to interpret them, they are not just strategies for overturning the rational space of perspective They may be symptoms of some mental condition, or just quirks of draftsmanship It is challenging to explain them, but we should begin by allowing that perspective is not something that can merely be overturned once and for all Many things are at work in Cézanne, and some of them are at work against perspective

A - P E R S P E C T I V E :

W H E R E T H E R E I S N O S P A C E

The final category, a-perspective, describes those artists who do not care one way

or the other for perspective, and I will look an example of that in a moment But perspective also describes a more radical possibility: a-perspectival pictures might not have

a-to do with space at all

Some abstract painters have tried to make pictures that do not represent space, and it

is an ambition that has been around ever since people first painted false-marble patterns on walls to mimic real stone.25

In Jewish mysticism, there is a doctrine of the ten mystical outflowings of God (the

sefirot) Each of them is abbreviated by a single Hebrew letter They have no determined

relation in space, and yet they are shown as if they do In this illustration, the letters wrap around each other and form a kind of tunnel Perhaps we are looking down into a well, or peering up into heaven, or across level space into a deep hallway, what is normally called a perspective corridor (As in Gallego’s painting.) Or perhaps this diagram is like an aerial view of a maze, so that it is really flat No matter how it is visualized, it is a picture that has space, even though it not meant to represent space

Here is another book, which tries to depict the evolution of heaven and earth by symbolic diagrams In this image Adam has been thrown out of heaven He is symbolized

by the letter A, and “he lies as dead,” as the text puts it, on the dark sphere of the earth

Above him is a model of the solar system with the planets spinning in their orbits, casting their evil rays on his head (the author says “all the stars shoot their Influences upon him”)

Above that there is heaven, and inside heaven is wisdom, shown by the letter S (for

“Sophia”) Below, in the darkness is the “Belly of Satan”—a second letter S—about to

hook Adam and pull him under In one sense this is an extraordinary picture of ordinary

space: the planets and the stars shine down on Adam, and the wisdom of God resides in the middle of heaven Heaven is above the stars, and the stars are above the earth But in another way, there is no space here at all: the three spheres of earth, sky, and heaven are like three plates overlapping, and there is no up or down, no depth, no gravity The picture

is a spiritual map, more like a graph or a chart than a picture in perspective Yet our eyes still search for signs of perspectival space in order to understand the image This is a trait of a-perspective, that you continue trying to see perspective in it when there probably isn’t any

A - P E R S P E C T I V E :

A common way to avoid linear perspective is to ignore it That insouciant attitude is common in twentieth-century painting and drawing, and it stems partly from cubism but partly from German expressionism The German expressionists, who worked mainly from

1900 to 1930, were uninterested in many aspects of conventional art making, including linear perspective

(This painting by Kirchner is similar to the one discussed below.)

Ernst Ludwig Kirchner’s Girl Before a Mirror pays scant attention to naturalistic

color, the consistency of flesh, anatomy, the direction of light, the laws of gravity, or even the laws of mirror reflection (a similar plate here) Kirchner’s eye is impatient and flighty and that is apparent in every stroke: he glances, and seldom pauses to gaze at the model or the furniture Instead his look circulates around his composition, tumbling and whirling, in washing-machine fashion The unnatural colors and rough paint are evidence that the painting was done without patience The artist was annoyed, he painted with a furious haste Anger and disinterest are mingled Kirchner was master of this kind “sloppiness,” which is really a delicate mental state composed of condescension to previous art (which was nearly all perspectival) and intense interest in the model and her pose His interest kept sparking and going out If the picture were uniform, if it obeyed rules that could be listed, then it might fall into linear perspective This way it fights free of perspective or any other system

This is skittish seeing, and I think it pertains also to the way we see his paintings Kirchner did not spend enough time looking at details of his figure studies to notice or care that he had made paws instead of hands, or broken limbs instead of healthy ones It is

possible to linger long enough over the Girl before a Mirror to enumerate its departures

from normal, perspectival academic painting, but it would be an artificial way of seeing the work Parts of the girl’s figure are outlined or shadowed in red, parts in blue, and parts not

at all, and the places those three treatments meet are themselves sloppily handled

In a way even to notice that is to risk looking too analytically The proper way to view such paintings is rapidly and with joy in their laconic candor A large percentage of contemporary art is influenced in one way or another by the “careless seeing” in German

expressionism, which depended on not thinking about perspective and other rules of

academic painting Of the four options (non-perspective, pre-perspective, anti-perspective, a-perspective), this last is by far the most attractive for an age tired of perspective, and tired

or rebelling against perspective The question for the German expressionists, and for artists influenced by them, is how long it is possible to keep up this uncaring attitude After a while, some care creeps back, and the pictures become either deliberately anarchistic (breaking perspective’s rules, and breaking them in an obvious, consistent way) or else more accurate and “correct” (keeping to perspective’s rules, returning to the ways of older academic painting)

S T R E T C H I N G , S T R A I N I N G A N D S H E A R I N G R E L I E F

S P A C E S

For artists who wish to work against perspective, there is a remarkable collection of strategies Orthodox perspectival space can be sheared, folded, compressed, crushed, negated, and ultimately partly destroyed.26 Each possibility shows the acute difficulty of avoiding perspective; each time perspective is mutilated it leaves some remainder

Stone and metal reliefs are a good example They are usually shallow, and their space can seem airless and compressed Figures in bas-reliefs are normally only half-round

or less, and they are attached to the fondo, the flat background plane of the relief The

shallow space that is the typical trait of relief sculpture may be distorted by stretching (imagine a rubber sheet, held at either side, and pulled apart with both hands), compressing (the same, strained by pressing the hands together), or shearing (imagine pulling up with one hand and down with the other) The last happens when a strip of figures in relief is wound around a column like a barber’s pole: everything is strained up on one side and down on the other Compression occurs whenever there is a row of figures that is packed close together Here it looks as if space has been wrung out, leaving only wrinkled people packed together or airlessly compressed, so that one scenes jostles against the next Stretching pulls out a relief like taffy, and some reliefs of processions or battles are extremely long, much longer than anything we would recognize as a picture

(Section of the Parthenon frieze in the British Museum There is also a partial plaster copy

in the Art Institute.)

One such stretched-out relief wraps all around the Parthenon in Athens, just under the eaves, and because it is on all sides of the building, it cannot be seen all at once like a normal picture It does not seem to represent space very clearly, even though people who lived in Athens might have recognized it as a procession that went through the city—something like a stretched-out picture of an entire marathon run.27 When “pictures” like these are reproduced in books, they are cut into individual scenes, made into long fold-out plates, or packaged separately as scrolls.28

(Tabula Peutingeriana, discussed below This is a similar detail to the one I mention; in

this detail, Rome is at the center, Europe above, and Africa below.)

Stretching, compressing, and shearing can also be done with flat pictures The

tabula Peutingeriana is a Roman map.29 This is a detail, because the entire map is too thin

and long to reproduce in this book The tabula tells its viewers about roads in Europe and

the distances between rest stations, and it gives a fair idea about how far it is between towns But the map is compressed from top to bottom, so that a person reading it can only measure east-west distances In this detail, Ireland is at the top of the map, just above Spain, and Spain floats just above a flattened Africa North-South connections are so distorted they are practically useless This serves the map’s purpose, because it was meant to show the public roads leading from Europe in the west to India in the east; it was not for north-south travelling We see it some two thousand years after it was made In the interim linear perspective was invented and became the preeminent method of depicting space, and it is

impossible for us to see the tabula without thinking of it as a “compressed” version of something else: either a “normal” map (whatever that is) or as a perspectival view from

above, like a photo from space Linear perspective has forever changed the way we see the

world, and it has made images like the tabula Peutingeriana and the bas-relief into

“stretched” and “compressed” versions of infinite, isotropic, homogeneous Euclidean space

The perspective box is the simplest perspective construction: a square, with lines radiating out from its four corners It is like a simple sentence that moves directly to its conclusion Just as a sentence has subject, verb, and object, so the perspective box has its required components: a symmetric floor or pavement, walls (or houses, if it’s a street scene) receding at either side, all converging on one central vanishing point Perspective can

be simple like this, but it can also be intricate and perverse, like a twisting sentence like this one whose elaboration is much more than is necessary for the point at hand

Experiments with the perspective box began in earnest after the High Renaissance, when perspective had become a commonplace, in the sixteenth-century style known as Mannerism Another good analogy for the kinds of distortions that Mannerist painters began to impose is the views from different seats in a theater Imagine a painted stage backdrop depicting a street scene, with houses receding on either side and a view into the distance in the middle (A basic perspective box composition.) Such a scene will only appear symmetric from a seat along the middle axis of the theater, and it will only provide convincing and proportionate depth from a position somewhere near the middle, neither too far back nor too close Mannerist paintings sometimes give us what we would see if we had bad seats Either we are too low down, so that the proscenium steps tower overhead and the stage is lost to sight, or too far to one side, so that the receding houses on either side become either precipitous (on the nearer side) or sluggish (on the farther side) Or perhaps we are too far back, so that both scenery and actors seem flat, without appreciable depth (Try this with a photo of a street scene, or with a perspective box such as If you move your eye too far to the right, the left wall will look odd, and if you move too far down, the entire manger will seem to zoom upwards From too far away, the picture will look flat, and from below, it will look enormous.)30