ORDER Introduction: Ideas o f O r d e r " ... Ranron Fernandez, tell me, i f y o u know, Why, when fir? singing ended a i l d rue turned Toward the town, tell why theglassy lights, Tke lights iirr tiltfishing boats nt airchor there, As rlight descended, tiltir~g in the air, Mastered the night and portioned out the sea, Fixing einblazoned zoiles and fiery poles, Arranging, deepening, enchailtiiig night ..." -WALLACE STEVENS The title of this book, Ideas of Order, comes from a poem by Wallace Stevens, "The Idea of Order at Key WesY'. Stevens' poem elegantly and compactly addresses issues which in this text are drawn out over three hundred pages. The poem recounts the tale of a woman singing by the shore. The words of her song and the natural rhythms of the sea mimic one another, yet the gulf between language and the grinding water keep them from ever forming a dialogue. Instead, the contrast be- tween the song and the sounds of the wind and sea provides a frame which reveals both with new clarity. When the singing ends, the sea still can- not be grasped as an autonomous, independent entity. Instead, a new frame emerges; the lights of the fishing boats mark out a visual structure which fixes a new order for the sea. The primary aim of ideas o f Order is to pro- v i d e conceptual a n d historical frames of reference which can be used to 'portion out' the order of architecture, a task that is by no means easy. Most of our training prepares us to deci- pher linguistic and numeric information. We have little training in making sense out of visual and graphic material. Ground rules in visual literacy are presented in this book in an attempt to demystify the study of architecture, a disci- pline which is so fraught with jargon a n d specialized argot that without a primer, the novice may become hopelessly muddled, or worse, indifferent to the built environment. The intent is not to develop an historical or art his- torical argument, but rather to provide insight into the way architects make decisions so that I D E A S C the reader may better appreciate the rich- ness of the materlal world. We do not presume to divine the inten- tions of architects nor to understand the precise reasoning followed in their design processes. Instead, we shall examine objec- tive data: the physical forms of buildings a n d the interrelationships among the whole, the constituent p a r t s and the broader context. Formal analysis of build- ings a n d d r a w i n g s shall act as a springboard for our discussion, although excurses may range into more abstruse theoretical territory. Many complementary and contradictory readings may be prof- fered. That is why the book is called ldeas of Order, rather than The Idea of Order. In Stevens' poem, an interpretation of the sea which emphasizes its auditory structure is supported by the song; another interpreta- tion which emphasizes i t s s p.

1. ORDER
Introduction: Ideas o f O r d e r
" ... Ranron Fernandez, tell me, i f y o u know,
Why, when fir? singing ended a i l d rue turned
Toward the town, tell why theglassy lights,
Tke lights iirr tiltfishing boats nt airchor there,
As rlight descended, tiltir~g in the air,
Mastered the night and portioned out the sea,
Fixing einblazoned zoiles and fiery poles,
Arranging, deepening, enchailtiiig night ..."
-WALLACE STEVENS
The title of this book, Ideas of Order, comes
from a poem by Wallace Stevens, "The Idea of
Order at Key WesY'. Stevens' poem elegantly and
compactly addresses issues which in this text are
drawn out over three hundred pages. The poem
recounts the tale of a woman singing by the shore.
The words of her song and the natural rhythms of
the sea mimic one another, yet the gulf between
language and the grinding water keep them from
ever forming a dialogue. Instead, the contrast be-
tween the song and the sounds of the wind and
sea provides a frame which reveals both with new
clarity. When the singing ends, the sea still can-
not be grasped as an autonomous, independent
entity. Instead, a new frame emerges; the lights
of the fishing boats mark out a visual structure

2. which fixes a new order for the sea.
The primary aim of ideas o f Order is to pro-
v i d e conceptual a n d historical frames of
reference which can be used to 'portion out' the
order of architecture, a task that is by no means
easy. Most of our training prepares us to deci-
pher linguistic and numeric information. We
have little training in making sense out of visual
and graphic material. Ground rules in visual
literacy are presented in this book in an attempt
to demystify the study of architecture, a disci-
pline which is so fraught with jargon a n d
specialized argot that without a primer, the
novice may become hopelessly muddled, or
worse, indifferent to the built environment. The
intent is not to develop an historical or art his-
torical argument, but rather to provide insight
into the way architects make decisions so that
I D E A S C
the reader may better appreciate the rich-
ness of the materlal world.
We do not presume to divine the inten-
tions of architects nor to understand the
precise reasoning followed in their design
processes. Instead, we shall examine objec-
tive data: the physical forms of buildings
a n d the interrelationships among the
whole, the constituent p a r t s and the
broader context. Formal analysis of build-
ings a n d d r a w i n g s shall act as a

3. springboard for our discussion, although
excurses may range into more abstruse
theoretical territory. Many complementary
and contradictory readings may be prof-
fered. That is why the book is called ldeas
of Order, rather than The Idea of Order. In
Stevens' poem, an interpretation of the sea
which emphasizes its auditory structure is
supported by the song; another interpreta-
tion which emphasizes i t s s p a t i a l
characterist~cs is supported by the cadence
of lights and fishing boat masts. So too in
architecture, multiple orders can be found
and ambiguous, overlapping strata do not
diminish the interpretations, but rather cre-
a t e reverberations among them which
strengthen the whole. Apparent disorder
may yield a higher kind of order.
As Stevens suggested, order is discern-
ible only through contrast and framing; and
frames, by their nature, include some
things and exclude others. A theoretical
scaffold acts as a frame to sharpen critical
focus so that the structure of a verbal or
graphic idea is more easily discerned.
Meaning is conferred in many ways. In
language, the order of words, the choice of
I F O R D E R
vocabulary, the particularities of syntax
and tone signify more than the literal deno-
tation of a phrase. In architecture the most
straightforward function, that of making

4. shelter, carries only a small part of the
building's meaning. Architecture is not
just about shelter and accommodation; it
also conserves rituals and mediates be-
tween the condition of humankind and the
forces beyond our control.
The first five chapters of the book set forth
methods of examining buildmgs and provide
tools for formal analysis. Categories, vocabulary
and criteria are presented which identify some
organizing principles of architectural works.
With an understanding of how architectural
ideas are structured, it is hoped that the reader
will gain insight into why one choice was made
and not another, and how different arrange-
ments of form can shape their attendant
meanings.
The last ten chapters loosely follow an
historical time line, although the approach
in this book is not historical. Rather, an
historical sequence is used as a convenient
armature for the discussion of broader ar-
chitectural ideas. Our methodology
diverges from that of most architectural
histories in another way. Architectural his-
torians explore temporal chains of
relationship. Here, we shall concentrate on
the spatial, not the temporal context.
Buildings will not be looked at as autono-
mous specimens, responsible only to their
own logic and limited by their own bound-
aries, but as elements in dialogue with a
context. A building's design does not end
with its walls and roof but extends to en-

5. I N T R O D
age the entire site. Similarly, the true site
f a building does not end at the property
nes but includes a larger context of ele-
ents in the environment. Within this
xtended context, the building partakes in a
equence of events. Repetition, rhythm,
uxtaposition, patterns of light and dark-
ess, solid and void, large a n d small,
articulate an architectural procession a n d
construct a frame of reference in which a
building is seen and understood.
The scope of this book concentrates on
buildings but i s not limited to buildings
alone. Landscapes and cities are looked a t
as extensions of architectural ordering sys-
tems, for architecture comments upon and
makes intelligible the landscape a n d the
context. Another poem by Wallace Stevens,
"Anecdote of the Jar", deals with the theme of
context and the power of architectural interven-
tions to define place by calling out difference
and thereby instituting hierarchy:
" I placed a jar in Tennessee,
And round it was, upon a hill.
It made the slovenly wilderness
Surrozi~~d the hill .."
Sequence, time and memory set architec-

6. ture apart from other visual arts, such as
painting or sculpture. The painters' canvas
defines a frame which clearly circumscribes
their work from its surrounding environ-
ment. The entirety of a painting can be
apprehended in an instant. Moreover, the
two-dimensionality of painting calls it out
as alien and artificial in the three-dimen-
sional world we inhabit. Sculptors work in
three-dimensions, but their creations a r e
usually independent objects which can be
U C T I O N
bought, sold and moved to any site. As ob-
jects i n e n v i r o n m e n t s , p a i n t i n g s a n d
sculptures engage in a dialogue with their
surroundings, but unlike the architect, the
sculptor and t h e painter are usually n o t
able to control these relationships.
As in poetry and music, no single part
of a n architectural work can be considered
except in relation t o that which immedi-
ately precedes it. To quote an old adage,
'architecture is frozen music'. As such, ar-
chitecture is a pure art; architecture is
about architecture; its task is to formulate
a n internal o r d e r which gives i t signifi-
cance, a l t h o u g h i t s m e a n i n g m a y b e
inaccessible to the general public. At the
same time architecture h a s a public nature.
Every architectural act is a civic gesture
loaded with political a n d social implica-
t i o n s . B u i l d i n g s d o n o t o n l y p r o v i d e

7. shelter for the simple functions of everyday
life, but they also act as repositories for the
collective history and memory of a culture.
An Egyptian pyramid evokes the grandeur
of the pharaonic age and the capabilities
and values of the society more powerfully
than a hieroglyphic inscription or any other
written text. Histories are constructed by
authors whose viewpoints may color the
material, but stones never lie. In examining
architectural artifacts we can make fresh as-
s e s s m e n t s of a c u l t u r e , f r e e f r o m t h e
interposed lens of the historian's vision.
Architecture i s a palimpsest, each built
layer inscribing its form and meaning o n
s u b s e q u e n t interventions, the assembled
whole mapping out the trajectory of a civi-
lization.
The Mathematics of the
Ideal Villa
First published in the Architectural Review,
1947.
2 The Mathematics of the Ideal Villa
There are two causes of beauty-natural and customary. Natural
is from geometry
consisting in uniformity, that is equality and proportion.
Customary beauty is

8. begotten by the use, as familiarity breeds a love for things not
in themselves love-
ly. Here lies the great occasion of errors, but always the true
test is natural or
geometrical beauty. Geometrical figures are naturally more
beautiful than irregu-
lar ones: the square, the circle are the most beautiful, next the
parallelogram and
the oval. There are only two beautiful positions of straight
lines, perpendicular
and horizontal; this is from Nature and consequently necessity,
no other than
upright being firm.
-Sir Christopher Wren, Parentalia
As the ideal type of centralized building Palladia's Villa Capra-
Rotonda (Plate
1) has, perhaps more than any other house, imposed itself upon
the imagination.
Mathematical, abstract, four square, without apparent function
and totally memo-
rable, its derivatives have enjoyed universal distribution; and,
when he writes of it,
Palladia is lyrical.
The site is as pleasant and delightful as can be found, because it
is on a small hill
of very easy access, and is watered on one side by the
Bacchiglione, a navigable
river; and on the other it is encompassed about with most
pleasant risings which

9. look like a very great theatre and are all cultivated about with
most excellent
fruits and most exquisite vines; and therefore as it enjoys from
every part most
beautiful views, some of which are limited, some more
extended, and others
which terminate with the horizon, there are loggias made in all
four fronts.'
When the mind is prepared for the one by the other, a passage
from Le Cor-
busier's Precisions may be unavoidably reminiscent of this. No
less lyrical but
rather more explosive, Le Corbusier is describing the site of his
Savoye House at
Poissy (Plate 2).
Le site: une vaste pelouse bornbee en dome aplati. La rnaison
est une boite en
"air ... au milieu des prairies dominant Ie verger Le plan est
pur.... II it sa
juste place dans l'agreste paysage de Poissy .... Les habitants,
venus ici parce que
cette campagne agreste etait belle avec sa vie de campagne, ils
la contempleront,
maintenue intacte, du haut de leur jardin suspendu qu des quatre
faces de leurs
fenetres en longueur. Leur vie domestique sera inseree dans un
reve virgilien.?
The Savoye House has been given a number of interpretations.
It may indeed be
a machine for living in, an arrangement of interpenetrating
volumes and spaces, an

10. emanation of space-time; but the suggestive reference to the
dreams of Virgil may
put one in mind of the passage in which Palladia describes the
Rotonda. Palladio's
landscape is more agrarian and bucolic, he evokes less of the
untamed pastoral, his
scale is larger; but the effect of the two passages is somehow
the same.
Palladia, writing elsewhere, amplifies the ideal life of the villa.
Its owner, from
3 The Mathematics of the Ideal Villa
within a fragment of created order, will watch the maturing of
his possessions and
savor the piquancy of contrast between his fields and his
gardens; reflecting on
mutability, he will contemplate throughout the years the antique
virtues of a sim-
pler race, and the harmonious ordering of his life and his estate
will be an analogy
of paradise.
The ancient sages commonly used to retire to such places,
where being oftentimes
visited by their virtuous friends and relations, having houses,
gardens, fountains
and such like pleasant places, and above all their virtue, they
could easily attain to

11. as much happiness as can be attained here below."
Perhaps these were the dreams of Virgil; and, freely interpreted,
they have
gathered around themselves in the course of time all those ideas
of Roman virtue,
excellence, Imperial splendor, and decay which make up the
imaginative recon-
struction of the ancient world. It would have been, perhaps, in
the landscapes of
Poussin-with their portentous apparitions of the antique-that
Palladio would
have felt at home; and it is possibly the fundamentals of this
landscape, the poi-
gnancy of contrast between the disengaged cube and its setting
in the paysage
agreste, between geometrical volume and the appearance of
unimpaired nature,
which lie behind Le Corbusier's Roman allusion. If architecture
at the Rotonda
forms the setting for the good life, at Poissy it is certainly the
background for the
lyrically efficient one; and, if the contemporary pastoral is not
yet sanctioned by
conventional usage, apparently the Virgilian nostalgia is still
present. From the
hygenically equipped boudoirs, pausing while ascending the
ramps, the memory
of the Georgics no doubt interposes itself; and, perhaps, the
historical reference
may even add a stimulus as the car pulls out for Paris.
However, a more specific comparison which presents itself is
that between Pal-
ladio's Villa Foscari, the Malcontenta of c. 1550-60 (Plates 3,
4), and the house

12. which in 1927 Le Corbusier built for Mr. and Mrs. Michael
Stein at Garches
(Plates 5, 6).
These are two buildings which, in their forms and evocations,
are superficially
so entirely unlike that to bring them together would seem to be
facetious; but, if
the obsessive psychological and physical gravity of the
Malcontenta receives no
parallel in a house which sometimes wishes to be a ship,
sometimes a gymnasium,
this difference of mood should not be allowed to inhibit
scrutiny.
For, in the first case, both Garches and the Malcontenta are
conceived of as
single blocks (Plates 7, 8); and, allowing for variations in roof
treatment, it might
be noticed that both are blocks of corresponding volume, each
measuring 8 units
4 The Mathematics of the Ideal Villa
in length, by 5Yz in breadth, by 5 in height. Then, further to
this, there is a com-
parable bay structure to be observed. Each house exhibits (and
conceals) an alter-
nating rhythm of double and single spatial intervals; and each
house, read from
front to back, displays a comparable tripartite distribution of
lines of support

13. (Figure 1).
But, at this stage, it might be better to introduce an almost.
Because, if the dis-
tribution of basic horizontal coordinates is, in both cases, much
the same, there
are still some slight and significant differences relating to the
distribution of those
lines of support which parallel the facades; and thus at Garches,
reading from
front to back, the fundamental spatial interval proceeds in the
ratio of Yz : 1% :
1Yz : 1% : %, while at the Malcontenta we are presented with
the sequence 2 : 2 :
1Yz. In other words, by the use of a cantilevered half unit Le
Corbusier obtains a
compression for his central bay and thereby transfers interest
elsewhere; while
Palladio secures a dominance for his central division with a
progression towards
his portico which absolutely focuses attention in these two
areas. The one scheme
is, therefore, potentially dispersed and possibly equalitarian and
the other is con-
centric and certainly hierarchical; but, with this difference
observed, it might sim-
ply be added that, in both cases, a projecting element-extruded

14. terrace or at-
tached portico-occupies 1Yz units in depth.
Structures, of course, are not to be compared; and, to some
extent, both archi-
tects look to structure as a justification for their dispositions.
Thus Palladio em-
ploys a solid bearing wall; and of this system he writes:
It is to be observed, that those (rooms) on the right correspond
with those on the
left, that so the fabric may be the same in one place as in the
other, and that the
walls may equally bear the burden of the roof; because if the
walls are made large
in one part and small in the other, the latter will be more firm to
resist the weight,
by reason of the nearness of the walls, and the former more
weak, which will pro-
duce in time very great inconveniences and ruin the whole
work."
Palladio is concerned with the logical disposition of motifs
dogmatically ac-
cepted, but he attempts to discover a structural reason for his
planning symme-
tries; while Le Corbusier, who is proving a case for structure as
a basis for the
formal elements of design, contrasts the new system with the
old and is a little

15. more comprehensive.
[e vous rappel Ie ce "plan paralyse" de la maison de pierre et
ceci aquoi nous
sommes arrives avec la maison de fer ou de ciment arrne.
plan libre
facade libre
5 The Mathematics of the Ideal Villa
Figure 1 Malcontenta and Garches. Analyti-
~ i .:':.-- cal diagrams.
-1 I
I I
I I
I I
I I
I I
I I
- I
I
I
I
I
1
I
iI
I
I

16. I
I
I,
L _
I-------r--l--------r---I-------]I t I
I I I I
I I I I
r-------T---T-------;-----+-------l
------1---~------_t----~-------
I I " I I: I j' . . II I I I I
r-------1-----------r-- r--- ----
t I I I
~--~-==-~-~+~~~l===~-__-J~~-=r-~~-~~=~
I I
I I
I I
I I
I IL J
6 The Mathematics of the Ideal Villa
ossature independante
fenetres en longueur ou pan de verre
pilotis
toit-jardin
et l'interieur muni de "casiers" et debarrasse de I'encombrement
des meubles."
Palladio's structural system makes it almost necessary to repeat
the same plan
on every level of the building, while point support allows Le

17. Corbusier a flexible
arrangement; but both architects make a claim which is
somewhat in excess of the
reasons they advance. Solid wall structures, Palladio declares,
demand absolute iiHiii
symmetry; a frame building, Le Corbusier announces, requires a
free arrangement: ,.
but these must be, at least partly, the personal exigencies of
high style-for asym-
metrical buildings of traditional structure remain standing and
even frame build-
ings of conventional plan continue to give satisfaction.
In both houses there is a piano nobile one floor up, which is
linked to the gar-
den by a terrace or portico and a flight (or flights) of steps. At
the Malcontenta
this main floor shows a cruciform hall with, symmetrically
disposed about it, two
suites of three rooms each and two staircases; but at Garches
there is nothing so
readily describable. At Garches there is a central hall and there
are two staircases;
but while one of the staircases occupies a similar position to
those of the Malcon-
tenta, the other has been turned through an angle of ninety
degrees. Further, the
entrance hall has been revealed from th is level by an asym
metrical cutting open of
the floor; and the terrace (which corresponds to the
Malcontenta's portico) has
become partly a reentrant volume obliterating a line of support,
placed in distinct-
ly less perceptible relationship to the principal room. Thus, at
Garches, the cruci-
form shape survives only vestigially (perhaps it may be thought

18. to be registered by
the apse e>! the dining room?); and therefore, instead of the
centrality of Pal-
ladio's major space, a Z-shaped balance is achieved which is
assisted by throwing
the small library into the main apartment. Finally, while at the
Malcontenta there
is a highly evident cross axis, at Garches this transverse
movement which is inti-
mated by the central voids of the end walls is only allowed to
develop implicitly
and by fragments.
The wall at the lVIalcontenta comprises the traditional solid
pierced by vertical
openings with a central emphasis in the portico and subsidiary
accents in the
outer windows placed toward the extremities of the facade. The
double bay in the
center of the building which carries the upper pediments of the
roof is expressed
on the one front by a single door, on the other by a 'Roman
baths' motif; and,
horizontally, the wall also falls into three primary divisions:
base; piano nobile,
corresponding to the Ionic order of the portico; and
superimposed attic. The base
7 The Mathematics of the Ideal Villa
plays the part of a projecting, consistently supporting solid
upon which the house
rests; but, while the piano nobile and attic are rusticated, the
base is treated as a

19. plain surface and a feeling of even greater weight carried here is
achieved by this
5
highly emotive inversion of the usual order.
Again the situation at Garches is more complex; and there the
exploitation of
the structural system has led to a conception of the wall as a
series of horizontal
strips-a strategy which places equal interest in both center and
extremity of the
facade and which is then maintained by Le Corbusier 's
tendency to suppress the
wider spans of the double bays. By these means any system of
central vertical
accent and inflection of the wall leading up to it is profoundly
modified; and the
immediate result in the garden elevation of Garches shows itself
in the displacing
of the elements which may be considered equivalent to the
Malcontenta's portico
and superimposed pediment. These become separate; and,
transposed as terrace
and roof pavilion, the one occupies the two (or three) bays to
the left of the fa-
cade, the other a central position in the solid but an
asymmetrical one in the
whole elevation.
On the other hand, the entrance front at Garches retains what
could be regarded
as the analogue of Palladio's upper pediment. This is the central
element of the
upper story; but then it is also noticeable, in spite of its
symmetrical position,

20. that the further development of this element within itself is not
symmetrical. Nor
does it promote symmetry in the facade as a whole; and, though
it is responded to
by the large central window of the entrance hall, since the
horizontal gashes of
the windows act to prohibit any explicit linking of these two
manifestations,
there ensues in the elevation something very like that
simultaneous affirmation
and denial of centrality which is displayed in the plan. Thus a
central focus is
stipulated; its development is inhibited; and there then occurs a
displacement and
a breaking up of exactly what Palladio would have presumed to
be a normative
emphasis.
Another chief point of difference lies in the interpretation of the
roof. At the
Malcontenta this forms a pyramidal superstructure which
amplifies the volume of
the house (Plate 9); while at Garches it is constituted by a flat
surface, serving as
the floor of an enclosure, cut out from-and thereby diminishing-
the house's
volume. Thus, in the one building the behavior of the roof might
be described as
additive and in the other as subtractive; but, this important
distinction apart, both
roofs are then furnished with a variety of incident, regular or
random, pediment
or pavilion, which alike enter into important-though very
different-relationships
with the vertical surfaces of the walls below.

21. ......5
8 The Mathematics of the Ideal Villa
That mathematics and musical concord were the basis of ideal
proportion was a
common belief of the circles in which Palladio moved. Here
there was felt to be a
correspondence between the perfect numbers, the proportions of
the human fig-
ure and the elements of musical harrnonv ;" and Sir Henry
Wotton, as British am-
bassador to Venice at a slightly later date, reflects some part of
this attitude when
he writes:
The two principal Consonances that most ravish the Ear are, by
the consent of all
Nature, the Fifth and the Octave; whereof the first riseth
radically, from the Pro-
portion between two and three. The other from the double
Interval, between one
and two, or between two and four, etc. Now if we shall transport
these Propor-
tions, from audible to visible Objects, and apply them as shall
fall fittest ... ,
there will indubitably result from either, a graceful and
harmonious Contentment
to the Eye."
It was not, in fact, suggested that architectural proportions were
derived from
musical harmonies, but rather that the laws of proportion were
established mathe-

22. matically and everywhere diffused. The universe of Platonic and
Pythagorean
speculation was compounded of the simpler relationships of
numbers, and such a
cosmos was formed within the triangle made by the square and
the cube of the
numbers 1, 2, 3. Also, its qualities, rhythms, and relationships
were established
within this framework of numbers up to 27; and if such numbers
governed the
works of God, it was considered fitting that the works of man
should be similarly
constructed, that a building should be a representative, in
microcosm, of the pro-
cess exhibited at a larger scale in the workings of the world. In
Alberti's words:
"Nature is sure to act consistently and with a constant analogy
in all her opera-
tions";8 and, therefore, what is patent in music must also be so
in architecture.
Thus, with proportion as a projection of the harmony of the
universe, its basis-
both scientific and religious-was quite unassailable; and a
Palladio could enjoy
the satisfactions of an aesthetic believed to be entirely
objective.
Le Corbusier has expressed similar convictions about
proportion. Mathematics
bring "des verites recontortantes," and "on ne quitte pas son
ouvraqe qu'avec la
certitude d'etre arrive ala chose exacte'l i' but if it is indeed
exactness which Le
Corbusier seeks, within his buildings it is not the
unchallengeable clarity of Pal-
ladio's volumes which one finds. It is, instead, a type of planned

23. obscurity; and,
consequently, while in the Malcontenta geometry is diffused
throughout the in-
ternal volumes of the entire building, at Garches it seems only
to reside in the
block as a whole and in the disposition of its supports.
The theoretical position upon which Palladio's position rested
broke down in
the eighteenth century when proportion became a matter of
individual sensibility
9 The Mathematics of the Ideal Villa
and private inspiration;'? and Le Corbusier, in spite of the
comforts which math-
ematics afford him, simply in terms of his location in history
can occupy no such
unassailable position. Functionalism was, perhaps, a highly
Positivistic attempt to
reassert a scientific aesthetic which might possess the objective
value of the old,
and the ultimately Platonic-Aristotelian critique. But its
interpretation was crude.
Results may be measured in terms of process, proportions are
apparently acci-
dental and gratuitous; and it is in contradiction to this theory
that Le Corbusier

24. imposes mathematical patterns upon his buildings. These are the
universal "verites
recon fortantes. "
Thus, either because of or in spite of theory both architects
share a common
......t standard, a mathematical one, defined by Wren as
"natural" beauty; and, within
limitations of a particular program, it should therefore not be
surprising that the
two blocks should be of corresponding volume or that both
architects should
choose to make didactic advertisement of their adherence to
mathematical formu-
lae. Of the two-and, perhaps, characteristically-Le Corbusier is
the more aggres-
sive; and at Garches he carefully indicates his relationships by
an apparatus of
regulating lines and figures and by placing on the drawings of
his elevations the
ratio of the golden section, A: B = B : (A + B) (Figure 2).
But, if Le Corbusier 's facades are for him the primary
demonstrations of the
virtues of a mathematical discipline, with Palladio it would
seem that the ultimate
proof of his theory lies in his plan. Throughout his Quattro
libri, Palladio consist-

25. ently equips both his plans and elevations with their numerical
apologetic (Plate
8); but the cryptic little figures which he appends to his
drawings seem always ~o
be more convincing, or at least more comprehensible, when they
relate to the
plan. And this is, possibly, to be understood, for in a house such
as the Maicon-
tenta the plan may be seen as an exhibition of 'natural' beauty,
as the pure thing,
abstract and uncomplicated; but the facades are, of necessity,
adulterated (though
scarcely to their detriment) by an intrusion of 'customary'
material. The facades
become complicated, their strict Platonic rationale may be
ultimately vitiated by
the traditional presence, in this case, of the Ionic order which
possesses its own
rationale and which inevitably introduces an alternative system
of measurement
(Plate 11).
The conflict between the 'customary' demands of the order and a
series of 'nat-
ural' relationships might be assumed to be the source from
which the facades of

26. the Maicontenta derive. They are suggestive, evocative, but they
are not easily or
totally susceptible to mathematical regulation; and, therefore, it
is again toward
Palladio's plan that one reverts. Provided with explanatory
dimensions, the two
10 The Mathematics ofthe Ideal Villa
Figure 2 Garches, elevations.
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11 The Mathematics of the Ideal Villa
suites comprising three rooms each can be read as a progression
from 3 : 4 to a
2 : 3 relationship. They are numbered 12 : 16, 16 : 16 and 16 :
24.
And here, on the part of Le Corbusier and Palladio, we have to
recognize, if not
duplicity, at least wishful thinking; but, if the ratio of 3 : 5 = 5 :
8 is only an ap-
proximation to that of the golden section, and if the ideal
measurement of Pal-
ladio's rooms does not concur with what is their actual size,!l
this is to be ex-
pected and it should not be considered useful to enlarge upon
these inconsis-
tencies. Instead it should be considered much more opportune to
examine Pal-
ladio's preference for the triple division and Le Corbusier's

28. propensity to divide
by four.
At the Malcontenta, as already noticed, the facades are divided
vertically into
three principal fields, those of the portico and the flanking
walls, and horizontally
the same situation prevails in the sequence, basement, piano
nobile, attic; but at
Garches, in spite of the comparable structural parti, it is always
a situation if not
of one, at least of two or, alternatively, offour fields of interest
with which we
are presented. Thus in the entrance elevation, it is a business of
four and one
which prevails; and, in the garden facade, this breakdown
becomes a matter of
four and two.
But, in both houses, there are elaborations in detail of the
dominant schema
which becomes complicated by its interplay with a subsidiary
system. That is: it is
by vertical extension into arch and vault, diagonal of roof line
and pediment that
Palladio modifies the geometrical asperities of his cube; and
this use of the circu-
lar and pyramidal elements with the square seems both to
conceal and to amplify
the intrinsic severity of the volumes. However, the arch, the
vault, and the pyra-
mid are among the prerogatives of solid wall construction. They
are among the
freedoms of the traditional plan, the "plan paralyse"; and the
introduction of
arched forms and pitched roofs is a liberty which at Garches Le

29. Corbusier is un-
able to allow himself. For in the frame building it is obviously
not, as in the solid
wall structure, the vertical planes which predominate. Rather it
is the horizontal
planes of floor and roof slabs (Plate 12); and, therefore, the
quality of paralysis
which Le Corbusier noticed in the plan of the solid wall
structure is, to some ex-
tent, transferred in the frame building to the section. Perforation
of floors, giving
a certain vertical movement of space, is possible; but the
sculptural quality of the
building as carving has disappeared and there can be nothing of
Palladio's firm
sectional transmutation and modeling of volume. Instead,
following the predom-
inant planes of the slabs, in the frame building extension and
elaboration must
occur horizontally. In other words, free plan is exchanged for
free section; but the
12 The Mathematics of the Ideal Villa
limitations of the new system are quite as exacting as those of
the old; and, as
though the solid wall structure has been turned on its side, with
the former com-
plexities of section and subtleties of elevation now transposed
to plan, there may
be here some reason for Palladio's choice of plan and Le
Corbusier's choice of
elevations as being the documents, in each case, most
illustrative of elementary

30. mathematical regulation.
The spatial audacities of the Garches plan continue to thrill; but
it may some­ •times seem to be an interior which is acceptable
to the intellect alone-to the in-
tellect operating from within a stage vacuum. Thus there is at
Garches a perma-
nent tension between the organized and the apparently
fortuitous. Conceptually,
all is clear; but, sensuously, all is deeply perplexing. There are
statements of a
hierarch ical ideal; there are cou nter statements of an egal
itarian one. Both houses
may seem to be apprehensible from without; but, from within, in
the cruciform
hall of the Malcontenta, there is a clue to the whole building;
while, at Garches, it
is never possible to stand at any point and receive a total
impression. For at
Garches the necessary equidistance between floor and ceiling
conveys an equal
importance to all parts of the volume in between; and thus the
development of
absolute focus becomes an arbitrary, if not an impossible,
proceeding. This is the
dilem ma propounded by the system; and Le Corbusier responds
to it. He accepts
the principle of horizontal extension; thus, at Garches central
focus is consistently
broken up, concentration at anyone point is disintegrated, and
the dismembered
fragments of the center become a peripheral dispersion of
incident, a serial instal-
lation of interest around the extremities of the plan.
But it is now that this system of horizontal extension which is

31. conceptually
logical comes up against the rigid boundary of the block which,
almost certainly,
is felt to be perceptually requisite;'? and, consequently, with
horizontal exten-
sion checked, Le Corbusier is obliged to employ an opposite
resource. That is, by
gouging out large volumes of the block as terrace and roof
garden, he introduces a
contrary impulse of energy; and by opposing an explosive
moment with an im-
plosive one, by introducing inversive gestures alongside
expansive ones, he again
makes simultaneous use of conflicting strategies.
8y its complexities, the resultant system (or symbiosis of
systems) throws into
intense relief the elementary, geometrical substructure of the
building; and, as a
sequel, the peripheral incident which substitutes for the
Palladian focus can also
become compounded with the inversions (of terrace and roof
garden) which rep-
resent an essentially analogous development to Palladio's
strategy of vertical ex-
tension.
13 The Mathematics of the Ideal Villa
Finally, a comparable process to that which occurs in plan takes
place also in
the elevations, where there is the same regular diffusion of
value and irregular
development of points of concentration; and here, with the

32. horizontal windows
conveying an equality to both the center and verge of the
facades, a disintegration
of focus which is never complete causes a brisk oscillation of
attention. Here, as in
the plan, there is nothing residual, nothing passive, nothing
slow moving; and the
extremities of the block, by this means, acquire an energetic
clarity and tautness,
as though they were trying to restrain the peripheral incident
from flying out of
the block altogether.
A detailed comparison is less easy to sustain between the two
houses which,
initially, seemed to invite their linking together: the Savoye
House and the Villa
Rotonda; and, conceivably, this is because neither of these
buildings is so entirely
condensed in its structure and its emotional impact as are,
respectively, the earlier
Garches and the later Malcontenta. The Savoye House and the
Rotonda are both
more famous; but they are also, in each case, more obviously
Platonic and easy to
take. Possibly this is because they are both in the round; and
that, therefore, what
is concentrated in two fronts at Garches and the Malcontenta is
here diffused
through four, resulting in far greater geniality of external effect.
But, if there is a
noticeable easiness and lack of tension to be found in these
facades, there are
analogous developments to those in the other houses. Such are
Palladio's concern,
both in plan and elevation, with central emphasis and Le

33. Corbusier's determined
dispersal of focus. At Poissy, just possibly, the complicated
volumes of the upper
roof garden replace the Palladian pitched roof and cupola; and
again, just possi-
bly, Palladio's four projecting loggias are subsumed within the
block as the en-
closed terrace which, alternatively, as the dominant element of
the piano nobile,
could also be considered to correspond to the domed salon of
the Rotonda.
But, symbolically and in the sphere of 'customary' beauty,
Palladio's and Le
Corbusier's buildings are in different worlds. Palladio sought
complete clarity of
plan and the most lucid organization of conventional elements
based on sym-
metry as the most memorable form of order, and mathematics as
the supreme
sanction in the world of forms. In his own mind his work was
essentially that of
adaptation, the adaptation of the ancient house; and, at the back
of his mind were
always the great halls of the Imperial thermae and such
buildings as Hadrian's villa
at Tivoli. He had several schemes of archaeological
reconstruction of Greek and
Roman domestic buildings, based on Vitruvius and Pliny,
incorporating elements
which in Greek and Roman practice would have been found only
in public build-
14 The Mathematics of the Ideal Villa

34. ings, but which he regarded as general. Indeed, Rome for him
was still supremely
alive; and, if the ancients had adapted the temple from the
house, their large scale •
planning was, no doubt, similarly reflective. •
Notoriously, Le Corbusier has an equal reverence for
mathematics and he would
appear also, sometimes, to be tinged with a comparable
historicism. For his plans
he seems to find at least one source in those ideals of
convenance and commodite
displayed in the ingenious planning of the Rococo hotel, the
background of a
social life at once more amplified and intimate. The French,
until recently, pos-
sessed an unbroken tradition of this sort of planning; and,
therefore, one may
often discover in a Beaux Arts utilization of an irregular site,
elements which if
they had not preceded Le Corbusier might seem to be curiously
reminiscent of his
own highly suave vestibules and boudoirs. Le Corbusier admires
the Byzantine
and the anonymous architecture of the Mediterranean world; and
there is also

35. present with him a purely French delight in the more overt
aspects of mechanics.
The little pavilion on the roof at Garches is, at the same time, a
temple of love
and the bridge of a ship. The most complex architectural
volumes are fitted with
running water.
Geometrically, both architects may be said to have approached
something of
the Platonic archetype of the ideal villa to which the fantasy of
the Virgilian
dream might be supposed to relate; and the realization of an
idea which is repre-
sented by the house as a cube could also be presumed to lend
itself very readily to
the purposes of Virgilian dreaming. For here is set up the
conflict between the
absolute and the contingent, the abstract and the natural; and the
gap between
tydeal world and the too human exigencies of realization here
receives its most
pathetic presentation. The bridging must be as competent and
compelling as the

36. construction of a well-executed fugue; and, if it may be
charged, as at the Malcon-
tenta with almost religious seriousness, or, as at Garches,
imbued with sophisti-
cated and witty allusion, its successful organization is an
intellectual feat which
reconciles the mind to what may be some fundamental
discrepancies in the pro-
gram.
As a constructor of architectural fugues, Palladio is the
convinced classicist with
a sixteenth century repertory of well-humanized forms; and he
translates this
received material with a passion and a high seriousness fitting
to the continued
validity that he finds it to possess. The reference to the
Pantheon in the superim-
posed pediments of the Malcontenta, to the thermae in its
cruciform salon, the
ambiguity, profound in both idea and form, in the equivocal
conjunction of tem-
ple front and domestic block; these are charged with meaning,
both for what they

37. 15 The Mathematics of the Ideal Villa
are and what they signify; and their impression is poignant. By
such apparatus the
ancient house is not recreated, but something far more
significant is achieved: a
creative nostalgia evokes a manifestation of mythical power in
which the Roman
and the ideal are equated.
By contrast Le Corbusier is, in some ways, the most catholic
and ingenious of
eclectics. The orders, the Roman references, were the traditional
architectural
clothing of authority; and, if it is hard for the modern architect
to be quite so
emphatic about any particular civilization as was Palladio about
the Roman, with
Le Corbusier there is always an element of wit suggesting that
the historical (or
contemporary) reference has remained a quotation between
inverted commas,
possessing always the double value of the quotation, the
associations of both old
and new context. In spite of his admiration for the Acropolis
and Michelangelo,
the world of high classical Mediterranean culture on which
Palladio drew so ex-
pressively is largely closed for Le Corbusier. The ornamental
adjuncts of human-
ism, the emblematic representations of the moral virtues, the
loves of the Gods
and the lives of the Saints have lost their former monopoly; and
as a result, while
allusion at the Malcontenta is concentrated and direct, at

38. Garches it is dissipated
and inferential. Within the one cube the performance attempts
the Roman; but,
within the other, no such exclusive cultural ideal is entertained.
Instead, as the
sponsors of his virtuosity, Le Corbusier largely selects a variety
of hitherto undis-
criminated phenomena. He selects the casual incidents of Paris,
or Istanbul, or
wherever it may be; aspects of the fortuitously picturesque, of
the mechanical, of
objects conceived to be typical, of whatever might seem to
represent the present
and the usable past; and all those items, while transformed by
their new context,
retain their original implications which signify maybe Platonic
ideality, maybe
Rococo intimacy, maybe mechanical precision, maybe a process
of natural selec-
tion. That is, one is able to seize hold of all these references as
something known;
but, in spite of the new power with which they become invested,
they are only
transiently provocative. Unlike Palladio's forms, there is
nothing final about any
of their possible relationships; and their rapprochement would
seem to be af-
fected by the artificial emptying of the cube in which they find
themselves lo-
cated, when the senses are confounded by what is apparently
arbitrary and the
intellect is more than convinced by the intuitive knowledge that,
despite all to the
contrary, here problems have been both recognized and
answered and that here
there is a reasonable order.

39. The neo-Palladian villa, at its best, became the picturesque
object in the English
park and Le Corbusier has become the source of innumerable
pastiches and of
16 The Mathematics of the Ideal Villa
tediously amusing exhibition techniques; but it is the
magnificently realized qual-
ity of the originals which one rarely finds in the works of neo-
Palladians and ex-
ponents of 'Ie style Corbu.' These distinctions scarcely require
insistence; and no
doubt it should only be sententiously suggested that, in the case
of the derivative
works, it is perhaps an adherence to 'rules' which has lapsed.
Addendum 1973
Though a parallel of Schinkel with late Corbu might not be so
rewarding as the
comparison of early Corbu and Palladio, much the same
arguments as those sur-
facing in this article might quite well be found developing
themselves if, for the
Villa Malcontenta, one were to substitute the Berlin Altes
Museum and, for
Garches, the Palace of the Assembly at Chandigarh.
Illustrations (Plates 13-16)
might suffice to make the point: a conventional classical parti
equipped with tra-
ditional poche and much the same parti distorted and made to
present a competi-

40. tive variety of local gestures-perhaps to be understood as
compensations for tra-
ditional poche.
A criticism which begins with approximate configurations and
which then pro-
ceeds to identify differences, which seeks to establish how the
same general motif
can be transformed according to the logic (or the compulsion)
of specific analyti-
cal (or stylistic) strategies, is presumably Wolflinian in origin;
and its limitations
should be obvious. It cannot seriously deal with questions of
iconography and
content; it is perhaps over symmetrical; and, because it is so
dependent on close
analysi~ if protracted, it can only impose enormous strain upon
both its con-
sume(and producer. However, if one would not like to imagine
oneself con-
fronted with the results of an intensive critical workout on the
materiel provided
by the Altes Museum and the Palace of the Assembly, this
reservation should not
be understood as depreciating the limited value of such an
exercise. For the two
buildings incite comparison and can also, both of them,
stimulate further parallel
with certain productions of Mies van der Rohe. But, if normal
intuition might
suggest so much, a Woltlinlan style of critical exercise (though
painfully belonging
to a period c. 1900) might still possess the merit of appealing
primarily to what is
visible and of, thereby, making the minimum of pretences to
erudition and the

41. least possible number of references outside itself. It might, in
other words, possess
the merits of accessibility-for those who are willing to accept
the fatigue.
17 The Mathematics of the Ideal Villa
qual-
ex-
ative
Notes
1 Isaac Ware, The Four Books of Palladia's
Architecture, London, 1738, p. 41.
2 Le Corbusier, Precisions sur un etat pre-
sent de l'architecture et de l'urbantsme,
Paris, 1930, pp. 136-38.
3 Ware, p. 46.
4 Ware, p. 27.
5 Le Corbusier, Precisions, p. 123.
6 For these particular observations I am
highly indebted to Rudolf Wittkower, Archi-
tectural Principles in the Age of Humanism,
London, 1949.
7 Sir Henry Wotton, The Elements of Archi-

42. tecture, published in John Evelyn, Parallel of
the Ancient Architecture with the Modern,
3rd ed., London, 1723, p. xv.
8 Giacomo Leoni, Ten Books on Modern
Architecture by Leon Battista Alberti, 3rd
ed., London, 1755, p. 196.
/ __ 9 Le Corbusier and Pierre Jeanneret, Oeuvre
complete 7970-7929, 3r·d ed., Zurich, 1943,
p. 144. These remarks refer to Garches.
10 "The break away from the laws of har-
monic proportion in architecture" is exten-
sively discussed in Wittkower (see n. 6), but
the parallel disintegration of the Platonic-
Aristotelian critical tradition is somewhat
more laconically observed by Logan Pearsall
Smith: "There are great youths too whose
achievements one may envy; the boy David
who slew Goliath and Bishop Berkeley who
annihilated, at the age of twenty five, in
1710, the external world in an octavo vol-
ume; and the young David Hume, who, in
1739, by sweeping away all the props of the
human understanding, destroyed for ever
and ever all possibility of knowledge." Lo-
gan Pearsall Smith, All Trivia, London,
1947,p.159.
11 For the actual rather than the ideal in-
ternal measurements of the Malcontenta see
Ottavio Bertotti Scamozzi, Les batiments et
les desseins de andre palladia Vicenza
1776-83. "

43. 12 It is possible to suppose that the rigid
boundaries of Garches were considered to be
perceptually necessary. The house is pre-
sented as one of 'the four compositions' in
Oeuvre complete 7970-7929, p. 189; and, in
Precisions, p. 73, Le Corbusier writes of
Garches: "Pour s'imposer it I'attention, pour
occuper puissament I'espace, il fallait
d'abord une surface premiere de forme par-
faite, puisune exaltation de la platitude de
cette surface par l'apport de quelges saillies
ou de trous faisant intervenir un mouvement
avant-arriere. "
18 The Mathematics of the Ideal Villa
19 The Mathematics ofthe Ideal Villa
Plate 1 Villa Capra-Rotonda, Vicenza.
Andrea Palladia, c. 1550.
Plate 2 Villa Savoye, Poissy. Le Corbusier,
1929-31.
Plate 3 Villa Malcontenta (Villa Foscari),
Malcontenta di Mira. Palladio, c. 1550-60.
Plate 4 Villa Malcontenta.
20 The Mathematics of the Ideal Villa

44. 21 The Mathematics of the Ideal Villa
Plate 5 Villa Stein, Garches. Le Corbusier,
1927.
Plate 6 Villa Stein.
Plate 7 Villa Stein. Plan.
DPlate 8 Villa Malcontenta. Plan.
22 The Mathematics of the Ideal Villa
Plate 9 Villa Malcontenta. Aerial view.
Plate 10 Villa Stein. Axonometric view.
Plate 11 Villa Malcontenta. Facade.
,
view.
e.

45. 24 The Mathematics of the Ideal Villa
Plate 12 Project, Maison Domino. Le
Corbusier, 1914.
Plate 13 Altes Museum, Berlin. Karl
Friedrich Schinkel, 1823.
25 The Mathematics of the Ideal Villa
Plate 14 Altes Museum. Plan. ..... .... .... .... --- .... --- .... --~ .,
., ,... .. .. .. .. .. ..
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26 The Mathematics of the Ideal Villa
Plate 15 Palace ofthe Assembly, Chand i-
garh, Le Corbusier, 1953- .

46. 27 The Mathematics of the Ideal Villa
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GROUND - FLOOR- PlAN
Plate 16 Palace of the Assembly. Plan.
Sculpture in the Expanded Field
Author(s): Rosalind Krauss
Source: October, Vol. 8 (Spring, 1979), pp. 30-44

47. Published by: The MIT Press
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ress
Mary Miss. Perimeters/Pavillions/Decoys. 1978.
(Nassau County, Long Island, New York.)
Sculpture in the Expanded Field
ROSALIND KRAUSS
Toward the center of the field there is a slight mound, a
swelling in the earth,
which is the only warning given for the presence of the work.
Closer to it, the large
square face of the pit can be seen, as can the ends of the ladder
that is needed to
descend into the excavation. The work itself is thus entirely
below grade: half
atrium, half tunnel, the boundary between outside and in, a
delicate structure of
wooden posts and beams. The work,
Perimeters/Pavilions/Decoys, 1978, by Mary
Miss, is of course a sculpture or, more precisely, an earthwork.
Over the last ten years rather surprising things have come to be
called
sculpture: narrow corridors with TV monitors at the ends; large
photographs
documenting country hikes; mirrors placed at strange angles in
ordinary rooms;
temporary lines cut into the floor of the desert. Nothing, it
would seem, could
possibly give to such a motley of effort the right to lay claim to

49. whatever one
might mean by the category of sculpture. Unless, that is, the
category can be made
to become almost infinitely malleable.
The critical operations that have accompanied postwar
American art have
largely worked in the service of this manipulation. In the hands
of this criticism
categories like sculpture and painting have been kneaded and
stretched and
twisted in an extraordinary demonstration of elasticity, a
display of the way a
cultural term can be extended to include just about anything.
And though this
pulling and stretching of a term such as sculpture is overtly
performed in the
name of vanguard aesthetics-the ideology of the new-its covert
message is that
of historicism. The new is made comfortable by being made
familiar, since it is
seen as having gradually evolved from the forms of the past.
Historicism works on
the new and different to diminish newness and mitigate
difference. It makes a
place for change in our experience by evoking the model of
evolution, so that the
man who now is can be accepted as being different from the
child he once was, by
simultaneously being seen-through the unseeable action of the
telos-as the
same. And we are comforted by this perception of sameness,
this strategy for
reducing anything foreign in either time or space, to what we
already know and
are.

50. OCTOBER
No sooner had minimal sculpture appeared on the horizon of the
aesthetic
experience of the 1960s, than criticism began to construct a
paternity for this work,
a set of constructivist fathers who could legitimize and thereby
authenticate the
strangeness of these objects. Plastic? inert geometries? factory
production?-none
of this was really strange, as the ghosts of Gabo and Tatlin and
Lissitzky could be
called in to testify. Never mind that the content of the one had
nothing to do with,
was in fact the exact opposite of, the content of the other. Never
mind that Gabo's
celluloid was the sign of lucidity and intellection, while Judd's
plastic-tinged-
with-dayglo spoke the hip patois of California. It did not matter
that constructiv-
ist forms were intended as visual proof of the immutable logic
and coherence of
universal geometries, while their seeming counterparts in
minimalism were
demonstrably contingent-denoting a universe held together not
by Mind but by
guy wires, or glue, or the accidents of gravity. The rage to
historicize simply swept
these differences aside.
Richard Serra. 5:30. 1969.

51. 32
Sculpture in the Expanded Field
Of course, with the passing of time these sweeping operations
got a little
harder to perform. As the 1960s began to lengthen into the
1970s and "sculpture"
began to be piles of thread waste on the floor, or sawed
redwood timbers rolled into
the gallery, or tons of earth excavated from the desert, or
stockades of logs
surrounded by firepits, the word sculpture became harder to
pronounce-but not
really that much harder. The historian/critic simply performed a
more extended
sleight-of-hand and began to construct his genealogies out of
the data of millenia
rather than decades. Stonehenge, the Nazca lines, the Toltec
ballcourts, Indian
burial mounds-anything at all could be hauled into court to bear
witness to this
work's connection to history and thereby to legitimize its status
as sculpture. Of
course Stonehenge and the Toltec ballcourts were just exactly
not sculpture, and
so their role as historicist precedent becomes somewhat suspect
in this particular
demonstration. But never mind. The trick can still be done by
calling upon a
variety of primitivizing work from the earlier part of the
century-Brancusi's
Endless Column will do-to mediate between extreme past and
present.

52. But in doing all of this, the very term we had thought we were
saving-
sculpture-has begun to be somewhat obscured. We had thought
to use a
universal category to authenticate a group of particulars, but the
category has now
been forced to cover such a heterogeneity that it is, itself, in
danger of collapsing.
And so we stare at the pit in the earth and think we both do and
don't know what
sculpture is.
Yet I would submit that we know very well what sculpture is.
And one of the
things we know is that it is a historically bounded category and
not a universal
one. As is true of any other convention, sculpture has its own
internal logic, its
own set of rules, which, though they can be applied to a variety
of situations, are
not themselves open to very much change. The logic of
sculpture, it would seem,
is inseparable from the logic of the monument. By virtue of this
logic a sculpture
is a commemorative representation. It sits in a particular place
and speaks in a
symbolical tongue about the meaning or use of that place. The
equestrian statue
of Marcus Aurelius is such a monument, set in the center of the
Campidoglio to
represent by its symbolical presence the relationship between
ancient, Imperial
Rome and the seat of government of modern, Renaissance
Rome. Bernini's statue
of the Conversion of Constantine, placed at the foot of the

53. Vatican stairway
connecting the Basilica of St. Peter to the heart of the papacy is
another such
monument, a marker at a particular place for a specific
meaning/event. Because
they thus function in relation to the logic of representation and
marking,
sculptures are normally figurative and vertical, their pedestals
an important part
of the structure since they mediate between actual site and
representational sign.
There is nothing very mysterious about this logic; understood
and inhabited, it
was the source of a tremendous production of sculpture during
centuries of
Western art.
But the convention is not immutable and there came a time
when the logic
began to fail. Late in the nineteenth century we witnessed the
fading of the logic of
33
OCTOBER
the monument. It happened rather gradually. But two cases
come to mind, both
bearing the marks of their own transitional status. Rodin's Gates
of Hell and his
statue of Balzac were both conceived as monuments. The first
were commissioned
in 1880 as the doors to a projected museum of decorative arts;
the second was

54. commissioned in 1891 as a memorial to literary genius to be set
up at a specific site
in Paris. The failure of these two works as monuments is
signaled not only by the
fact that multiple versions can be found in a variety of museums
in various
countries, while no version exists on the original sites-both
commissions having
eventually collapsed. Their failure is also encoded onto the very
surfaces of these
works: the doors having been gouged away and anti-structurally
encrusted to the
point where they bear their inoperative condition on their face;
the Balzac
executed with such a degree of subjectivity that not even Rodin
believed (as letters
by him attest) that the work would ever be accepted.
With these two sculptural projects, I would say, one crosses the
threshold of
the logic of the monument, entering the space of what could be
called its negative
condition-a kind of sitelessness, or homelessness, an absolute
loss of place.
Which is to say one enters modernism, since it is the modernist
period of
sculptural production that operates in relation to this loss of
site, producing the
monument as abstraction, the monument as pure marker or base,
functionally
placeless and largely self-referential.
It is these two characteristics of modernist sculpture that
declare its status,
and therefore its meaning and function, as essentially nomadic.
Through its

55. fetishization of the base, the sculpture reaches downward to
absorb the pedestal
into itself and away from actual place; and through the
representation of its own
materials or the process of its construction, the sculpture
depicts its own auton-
omy. Brancusi's art is an extraordinary instance of the way this
happens. The base
becomes, in a work like the Cock, the morphological generator
of the figurative
part of the object; in the Caryatids and Endless Column, the
sculpture is all base;
while in Adam and Eve, the sculpture is in a reciprocal relation
to its base. The
base is thus defined as essentially transportable, the marker of
the work's homeless-
ness integrated into the very fiber of the sculpture. And
Brancusi's interest in
expressing parts of the body as fragments that tend toward
radical abstractness
also testifies to a loss of site, in this case the site of the rest of
the body, the skeletal
support that would give to one of the bronze or marble heads a
home.
In being the negative condition of the monument, modernist
sculpture had a
kind of idealist space to explore, a domain cut off from the
project of temporal and
spatial representation, a vein that was rich and new and could
for a while be
profitably mined. But it was a limited vein and, having been
opened in the early
part of the century, it began by about 1950 to be exhausted. It
began, that is, to be
experienced more and more as pure negativity. At this point

56. modernist sculpture
appeared as a kind of black hole in the space of consciousness,
something whose
positive content was increasingly difficult to define, something
that was possible to
locate only in terms of what it was not. "Sculpture is what you
bump into when
34
Auguste Rodin. Balzac. 1897.
Constantin Brancusi. Beginning of the World.
1924.
Robert Morris. Green Gallery Installation. 1964.
Untitled (Mirrored Boxes). 1965.
you back up to see a painting," Barnett Newman said in the
fifties. But it would
probably be more accurate to say of the work that one found in
the early sixties
that sculpture had entered a categorical no-man's-land: it was
what was on or in
front of a building that was not the building, or what was in the
landscape that
was not the landscape.
The purest examples that come to mind from the early 1960s are
both by
Robert Morris. One is the work exhibited in 1964 in the Green
Gallery-quasi-

57. architectural integers whose status as sculpture reduces almost
completely to the
simple determination that it is what is in the room that is not
really the room; the
other is the outdoor exhibition of the mirrored boxes-forms
which are distinct
from the setting only because, though visually continuous with
grass and trees,
they are not in fact part of the landscape.
In this sense sculpture had entered the full condition of its
inverse logic and
had become pure negativity: the combination of exclusions.
Sculpture, it could be
said, had ceased being a positivity, and was now the category
that resulted from
the addition of the not-landscape to the not-architecture.
Diagrammatically
expressed, the limit of modernist sculpture, the addition of the
neither/nor, looks
like this:
not-landscape not-architecture
/
sculpture
Now, if sculpture itself had become a kind of ontological
absence, the
combination of exclusions, the sum of the neither/nor, that does
not mean that
the terms themselves from which it was built-the not-landscape
and the not-

58. Sculpture in the Expanded Field 37
architecture-did not have a certain interest. This is because
these terms express a
strict opposition between the built and the not-built, the cultural
and the natural,
between which the production of sculptural art appeared to be
suspended. And
what began to happen in the career of one sculptor after
another, beginning at the
end of the 1960s, is that attention began to focus on the outer
limits of those terms
of exclusion. For, if those terms are the expression of a logical
opposition stated as
a pair of negatives, they can be transformed by a simple
inversion into the same
polar opposites but expressed positively. That is, the not-
architecture is, according
to the logic of a certain kind of expansion, just another way of
expressing the term
landscape, and the not-landscape is, simply, architecture. The
expansion to which
I am referring is called a Klein group when employed
mathematically and has
various other designations, among them the Piaget group, when
used by structu-
ralists involved in mapping operations within the human
sciences.* By means of
this logical expansion a set of binaries is transformed into a
quaternary field which
both mirrors the original opposition and at the same time opens
it. It becomes a
logically expanded field which looks like this:
, %

59. landscape- >architecture ........... complex
not-landscape< >not-architecture ........... neuter
-% 4
sculpture
" The dimensions of this structure may be analyzed as follows:
1) there are two relationships of
pure contradiction which are termed axes (and further
differentiated into the complex axis and the
neuter axis) and are designated by the solid arrows (see
diagram); 2) there are two relationships of
contradiction, expressed as involution, which are called
schemas and are designated by the double
arrows; and 3) there are two relationships of implication whichti
are called deixes and are designated by
the broken arrows.
For a discussion of the Klein group, see Marc Barbut, "On the
Meaning of the Word 'Structure'
in Mathematics," in Michael Lane, ed., Introduction to
Structuralism, New-York, Basic Books, 1970;
for an application of the Piaget group, see A.-J. Greimas and F.
Rastier, "The Interaction of Semiotic
Constraints," Yale French Studies, no. 41 (1968), 86-105.
x ? ? '~~~~~~~~~~~~~4
* /f
*%*%4 - **
4.4.4.,??~
sculpture~~~~~~~~~~4

60. ? The imensins of his stucturemay beanalyed as ollows 1) thre
aretwo reationsips o
pure~~~~~~ * o taito whc r emdae ad ute ifrnitdi. o tecmlxai n h
neuter~~~~~~ * xs an r eintdb h oidarw sedarm;2
heeaetorltosiso
contadicion .xrse asivlto,wihaecle*cemsadaedsgae ytedul
OCTOBER
Another way of saying this is that even though sculpture may be
reduced to
what is in the Klein group the neuter term of the not-landscape
plus the not-
architecture, there is no reason not to imagine an opposite term-
one that would
be both landscape and architecture-which within this schema is
called the
complex. But to think the complex is to admit into the realm of
art two terms that
had formerly been prohibited from it: landscape and
architecture-terms that
could function to define the sculptural (as they had begun to do
in modernism)
only in their negative or neuter condition. Because it was
ideologically prohibited,
the complex had remained excluded from what might be called
the closure of post-
Renaissance art. Our culture had not before been able to think
the complex,
although other cultures have thought this term with great ease.
Labyrinths and
mazes are both landscape and architecture; Japanese gardens are

61. both land-
landscape and architecture; the ritual playing fields and
processionals of ancient
civilizations were all in this sense the unquestioned occupants
of the complex.
Which is not to say that they were an early, or a degenerate, or
a variant form of
sculpture. They were part of a universe or cultural space in
which sculpture was
simply another part-not somehow, as our historicist minds
would have it, the
same. Their purpose and pleasure is exactly that they are
opposite and different.
The expanded field is thus generated by problematizing the set
of opposi-
tions between which the modernist category sculpture is
suspended. And once this
has happened, once one is able to think one's way into this
expansion, there are-
logically-three other categories that one can envision, all of
them a condition of
the field itself, and none of them assimilable to sculpture.
Because as we can see,
sculpture is no longer the privileged middle term between two
things that it isn't.
Sculpture is rather only one term on the periphery of a field in
which there are
other, differently structured possibilities. And one has thereby
gained the "permis-
sion" to think these other forms. So our diagram is filled in as
follows:
site-construction
- %

62. landscape4 >,architecture ........... complex
/. '*..
marked sites ** ' axiomatic
"~~ //* structures
........... neuter
38
Robert Smithson. Spiral Jetty. 1969-70. (Photo Gianfranco
Gorgoni.)
Robert Morris. Observatory. 1970.
Alice Aycock. Maze. 1972.
Carl Andre. Cuts. 1967.
Sculpture in the Expanded Field
It seems fairly clear that this permission (or pressure) to think
the expanded
field was felt by a number of artists at about the same time,
roughly between the
years 1968 and 1970. For, one after another Robert Morris,
Robert Smithson,
Michael Heizer, Richard Serra, Walter De Maria, Robert Irwin,
Sol LeWitt, Bruce

63. Nauman . . . had entered a situation the logical conditions of
which can no longer
be described as modernist. In order to name this historical
rupture and the
structural transformation of the cultural field that characterizes
it, one must have
recourse to another term. The one already in use in other areas
of criticism is
postmodernism. There seems no reason not to use it.
But whatever term one uses, the evidence is already in. By
1970, with the
Partially Buried Woodshed at Kent State University, in Ohio,
Robert Smithson
had begun to occupy the complex axis, which for ease of
reference I am calling site
construction. In 1971 with the observatory he built in wood and
sod in Holland,
Robert Morris had joined him. Since that time, many other
artists-Robert Irwin,
Alice Aycock, John Mason, Michael Heizer, Mary Miss, Charles
Simonds-have
operated within this new set of possibilities.
Similarly, the possible combination of landscape and not-
landscape began to
be explored in the late 1960s. The term marked sites is used to
identify work like
Smithson's Spiral Jetty (1970) and Heizer's Double Negative
(1969), as it also
describes some of the work in the seventies by Serra, Morris,
Carl Andre, Dennis
Oppenheim, Nancy Holt, George Trakis, and many others. But
in addition to
actual physical manipulations of sites, this term also refers to
other forms of

64. marking. These might operate through the application of
impermanent marks-
Heizer's Depressions, Oppenheim's Time Lines, or De Maria's
Mile Long
Drawing, for example-or through the use of photography.
Smithson's Mirror
Displacements in the Yucatan were probably the first widely
known instances
of this, but since then the work of Richard Long and Hamish
Fulton has focused
on the photographic experience of marking. Christo's Running
Fence might be
said to be an impermanent, photographic, and political instance
of marking a site.
The first artists to explore the possibilities of architecture plus
not-
architecture were Robert Irwin, Sol LeWitt, Bruce Nauman,
Richard Serra, and
Christo. In every case of these axiomatic structures, there is
some kind of
intervention into the real space of architecture, sometimes
through partial
reconstruction, sometimes through drawing, or as in the recent
works of Morris,
through the use of mirrors. As was true of the category of the
marked site,
photography can be used for this purpose; I am thinking here of
the video
corridors by Nauman. But whatever the medium employed, the
possibility
explored in this category is a process of mapping the axiomatic
features of the
architectural experience-the abstract conditions of openness and
closure-onto
the reality of a given space.

65. The expanded field which characterizes this domain of
postmodernism
possesses two features that are already implicit in the above
description. One of
these concerns the practice of individual artists; the other has to
do with the
41
OCTOBER
question of medium. At both these points the bounded
conditions of modernism
have suffered a logically determined rupture.
With regard to individual practice, it is easy to see that many of
the artists in
question have found themselves occupying, successively,
different places within
the expanded field. And though the experience of the field
suggests that this
continual relocation of one's energies is entirely logical, an art
criticism still in the
thrall of a modernist ethos has been largely suspicious of such
movement, calling
it eclectic. This suspicion of a career that moves continually and
erratically
beyond the domain of sculpture obviously derives from the
modernist demand for
the purity and separateness of the various mediums (and thus
the necessary special-
ization of a practitioner within a given medium). But what
appears as eclectic

66. from one point of view can be seen as rigorously logical from
another. For, within
the situation of postmodernism, practice is not defined in
relation to a given
medium-sculpture-but rather in relation to the logical operations
on a set of
cultural terms, for which any medium-photography, books, lines
on walls,
mirrors, or sculpture itself-might be used.
Thus the field provides both for an expanded but finite set of
related positions
for a given artist to occupy and explore, and for an organization
of work that is not
Robert Smithson. First and Seventh Mirror
Displacements, Yucatan. 1969.
42
Sculpture in the Expanded Field
dictated by the conditions of a particular medium. From the
structure laid out
above, it is obvious that the logic of the space of postmodernist
practice is no
longer organized around the definition of a given medium on the
grounds of
material, or, for that matter, the perception of material. It is
organized instead
through the universe of terms that are felt to be in opposition
within a cultural
situation. (The postmodernist space of painting would obviously
involve a

67. similar expansion around a different set of terms from the pair
archi-
tecture/landscape-a set that would probably turn on the
opposition unique-
ness/reproducibility.) It follows, then, that within any one of the
positions
generated by the given logical space, many different mediums
might be employed.
It follows as well that any single artist might occupy,
successively, any one of the
positions. And it also seems the case that within the limited
position of sculpture
itself the organization and content of much of the strongest
work will reflect the
condition of the logical space. I am thinking here of the
sculpture of Joel Shapiro,
which, though it positions itself in the neuter term, is involved
in the setting of
images of architecture within relatively vast fields (landscapes)
of space. (These
considerations apply, obviously, to other work as well-Charles
Simonds, for
example, or Ann and Patrick Poirier.)
Richard Long. Untitled. 1969. (Krefeld, Germany.)
43
44 OCTOBER
I have been insisting that the expanded field of postmodernism
occurs at a
specific moment in the recent history of art. It is a historical
event with a

68. determinant structure. It seems to me extremely important to
map that structure
and that is what I have begun to do here. But clearly, since this
is a matter of
history, it is also important to explore a deeper set of questions
which pertain to
something more than mapping and involve instead the problem
of explanation.
These address the root cause-the conditions of possibility-that
brought about
the shift into postmodernism, as they also address the cultural
determinants of the
opposition through which a given field is structured. This is
obviously a different
approach to thinking about the history of form from that of
historicist criticism's
constructions of elaborate genealogical trees. It presupposes the
acceptance of
definitive ruptures and the possibility of looking at historical
process from the
point of view of logical structure.
Joel Shapiro. Untitled (Cast Iron and Plaster Houses).
1975.
:: i:::: -: V~~~~~~~~~~~~~~~~~~l ~ ~ ~ :s: -
Article Contentsp. [31]p. [30]p. 32p. 33p. 34p. [35]p. [36]p.
37p. 38p. [39]p. [40]p. 41p. 42p. 43p. 44Issue Table of
ContentsOctober, Vol. 8 (Spring, 1979), pp. 1-125Front Matter
[pp. 1 - 2]Lecture in Inauguration of the Chair of Literary
Semiology, Collège de France, January 7, 1977 [pp. 3 - 16]The
Forms of Violence [pp. 17 - 29]Sculpture in the Expanded Field
[pp. 31 - 44]From Americans on the Move [pp. 45 - 57]Stuart
Sherman: Object Ritual [pp. 59 - 74]Pictures [pp. 75 -
88]Seven Prolegomenae to a Brief Treatise on Magrittian
Tropes [pp. 89 - 110]About Snow [pp. 111 - 125]Back Matter

69. Fighting in Las Vegas, I thought the fight on the ground was
boring. Gradually it revealed itself to me in all its subtle
urgency.
One night, I realized that, like Glengarry Glen Ross, the fight
on the
ground is the true metaphor of how we live today. Down at the
office, the university, or the plant, we rarely have the
opportunity
to stand up and punch it out. On the job, in the bureaucracy,
we grapple forever on the ground, seeking tiny advantages, bits
ofleverage, and the occasional clean shot. Herein lies the true
satisfaction of the standing knockout.
So why fight this kind offight now? I attribute it to the
enormous tectonic forces alive in America today, where we have
never been so safe and in so much peril. We live in a filigree of
perfectly interconnected safety nets with helmet laws, seat
belts,
infant seating, low cholesterol, no-smoking signs, playdates,
cell

70. phones, and e-mail. All this coddles people trying to work on
the
precipice of absolute disaster. One merger, one outsourced job,
one bad decision, one deceptive mortgage, one religious idiot,
one accident, one gun nut or illness, and we are falling forever,
and we can't even scream lest we disturb the peace. So you
ask: Why fight? I say, Why not? Don't we need a little space, an
octagon, perhaps, where no self-serving lies need be spoken,
where we know exactly what's going down?
1 Sam Sheridan, A Fighter's Heart: One Man's Journey through
th e World
o/Fighting, Atlantic Monthly Press, New York, NY, 2007.
82 FIRST WE FIGHT
Formalism
SAW my first Chinese opera in the early 1970s, in
Manhattan, on a whim, because a Blue Oyster Cult
concert had been canceled. I loved the whole thing. l[t
The performers were beautiful. The makeup was
beautiful. The costumes made Liberace look like Dick Cheney,

71. and the music sounded like Blue Oyster Cult falling down
stairs.
I didn't understand anything, but I walked out ofthe theater very
excited. I told my companion that ifI saw four more Chinese
operas, knowing nothing more than I did then, I could tell which
was the best one, once I identified the parts. Four was
optimistic.
There are 360 regional forms ofChinese opera, according to
one playbill I read, and they can only be understood against the
backdrop ofChinese history, so, in my case, it took six or seven.
I saw my last Chinese opera in April 2006 at La MaMa down on
4th Street, The Dragon-Princess and the Scholar.
I still knew nothing beyond my experience ofseeing six or
seven performances, but even so, in 2006, I could feel the shape
of
the piece, the logic of the spectacle. I recognized infelicities
and
corners cut. I reveled in bravura moments and exquisite details,
and, most critically, I felt in tune with the predominantly Asian
audience, most ofwhom, I suspected, were hardcore New
Yorkers

72. no more erudite about the 360 forms than I. This was important
83
to me because, during the period of my Chinese Opera Project,
modernists like Picasso and Degas were being called to the bar
for "plundering" Asian and African sources and exploiting the
cultural integrity of these sources. This tribal proposition, as
I pointed out at the time, neglects the fact that Velazquez and
Ribera lived in the wake ofa Moorish culture. Spain was awash
in North African influences and that the French Rococo, thanks
to plantations in Indochina , was inundated by Oriental tropes,
thus an Oriental predisposition was already part of being
French.
Africa was already a part of being Spanish. Scolding Picasso for
grooving on Yoruba artifacts and degrading Degas for his
Oriental
tropes, is like indicting me for speaking English instead of
Zuni.
The fatwa against cultural borrowing, however, was only a

73. tactical feint. My real adversary was the escalating jihad against
formalism in contemporary art criticism. At that time,
professors
were attacking formalism at the very moment that iconic
theorists
like Jacques Derrida, Noam Chomsky, and Gilles Deleuze were
arguing in its defense . This seemed a willful turning away from
difficulty-as if the American art world, given the chance to
watch
Michelangelo Antonioni's Red Desert, had opted for Elvis
Presley's
Blue Hawaii. So I started calling myself a formalist critic
because
everyone was calling Clement Greenberg a formalist critic. He
wasn't. He never really addressed the shape ofanything and was,
I suspect, color-blind. He was a literate Marxist, so, obviously,
the
formalist job was still open.
When people asked me why I was embracing the f-word,
I would ask them this: " When Jacques Derrida asserts that
there is no meaning outside the text, do you think it's a fact

74. or a problem? If you think it's a fact, you're a formalist. If you
think it's a 'problem' that might befixed, you are a reactionary
idealist." I would always remind my inquisitors that human
beings
do not express themselves telepathically. Everything goes Out
into the physical world in tangible patterns. It comes back in
84 FORMALISM
through our hard-wired capacity to detect patterns and report
any anomalies to our consciousness through blips or floods of
emotion. So a lot comes in of which we are not consciously
aware
that JUSt stays in storage, at the ready, awaiting its cue.
Chomsky
proposes that human beings express themselves by manipulating
a finite vocabulary of tangible signs through a finite number of
transformations to create an infinite array of utterances.
These patterns are internally meaningful-color to color, word
to word, mark to mark, noise to noise. Their relationship to the
world beyond is always flimsy because, as Deleuze argues, the
meaning and reference that we derive from any utterance or text

75. is inextricable from the tangible "logic ofsensation" that
governs
our expression and perception of it. How else could we enjoy
the
atmospheric nonsense of Lewis Carroll's "Jabberwocky," which
is
rife with hints but otherwise devoid of real-world referents?
My first conscious experience with the logic ofsensation
took place in the Ransom Library at the University ofTexas in
Austin where I sat, wearing white gloves, in a beige carrel and
read a fair copy manuscript ofD. H. Lawrence's Women in Love
straight through, foolscap sheet by foolscap sheet. By the time
I had finished, the steady, curving logic of Lawrence's insistent
handwri ting [no mark OutS, no interlinear revisions] had so
totally infected the narrative that, even today, I can't look at
a printed page of Women in Love without feeling the terrible
absence of Lawrence 's brown cursive, drawn across a page
nearly
a century ago. This experience [especially with the white
gloves],

76. contributed to my becoming an art critic and set me offin search
of the intimate bang of The Dragon-Princess and the Scholar,
which
I enjoyed as a child delights in the/abberwocky.
If Chomsky's overarching theory is anywhere near right [and
he is wrong sometimes, about personal pronouns] the whole of
human utterance can be experienced without translation-ifwe
can identify the finite number of tangible "parts" in an
expression.
85
Formalists analyze events that have already happened. They
don't
teach us how to "enjoy" art. They investigate the consequences
of
parts [words, notes, colors) that usually remain un-recognized
to
us. If we tease out the finite sums of each part and the
proportion
of each part to another, we are on our way to having a shape.
When we learn the curves-the frequencies with which the parts

77. and their redundancies occur-we have some sense of its various
tempos. [In literature phonemes, go faster than sentences.)
When
we know enough about the genre ofexpression to recognize the
parts and frequencies that don't occur, we know a great deal.
The problem is that most critics are more fluent in philosophy
than arithmetic, Boolean algebra, and calculus, but the numbers
are there. We usually know them before we even count, but we
should count. The triumphant formalist study of music, I should
note, is Leonard Meyer's The Rhythmic Structure ofMusic. To
analyze
a literary text, we should begin with a total vocabulary-a list of
units and sums oftheir redundancies. We should know how
many parts are important-the proper nouns, verbs, phonemes,
consonants, tenses, adverbs, adjectives, pronouns, demon-
stratives, and their redundancies. Ifwe know what doesn't
occur and the frequencies at which the parts that do occur
occur, we have a great deal ofapplicable information about the
conformation of the object's vocabulary.

78. Ifwe learn the frequency at which new information is fed
into the work, we have another usable curve. A text with mostly
"new" words is virtually unreadable, so the curve of new words
invariably flattens then rises at the volta. To cite a couple of
instances: The proportion and redundancy of adverbs and
adjectives should remind us that even their appearance in
literary
prose is problematic, that synonyms ofany son rarely appear
in memorable writing except as jokes. We learn that a flat line
of sentence lengths is euphonic suicide. We learn that the
redundancy of, say, Hemingway's prose, improves its velocity.
86 FORMALISM
We learn that his routinely incorrect usage of"which" over
"that"
makes his art more eloquent by suppressing subordination.
Clement Greenberg always insisted that one's sense ofa work's
quality, virtue, or intensity is as instantaneous as the mind's
ability to sense patterns and to infer their "on-purpose-ness"
without knowing that purpose. For once, I agree with Clement.

79. We can processes massive arrays of patterns [as in a Chinese
opera], without being able to sort them out, define them, isolate
them, or even identify them. This ignorance does not impair
their
effectiveness, however. Stochastic patterns and sequences ofany
sort elicit responses. Total ignorance of thoroughbreds does not
mitigate the pleasures ofthe horse race, although eventually one
learns that art, music, and literature are founded on obbligatos
of redundancy and moments ofeccentricity. These make the arts
memorable. They live in memory. Sorting out the parts that
make
the whole is what formalism does. In music we start with the
parts
and adduce the whole; in art we start with the whole and adduce
the parts to our satisfaction.
In art criticism and music criticism, there is no dictionary,
and in literary prose there shouldn't be. The virtue of not having
a dictionary is that patterns present themselves to us that are
unaccounted for in "correct" readings, and this increases the
works' longevity, because all expressions contain secondary and

80. tertiary patterns that contribute to the work's conscious purpose,
but the parts can change. First we love the picture, then we love
the paint, then we love the arrangement. The primary virtue of
formalism is that it allows you to see and hear patterns that
were
not put there-that only ended there as a side effect ofsome other
pattern more urgently desired by the artist. Formalist readings
can
reverse their hierarchy. Because ofthis, Jackson Pollock could
look
at Thomas Hart Benton'S folksy murals in Jefferson City,
Missouri,
upon which he was assisting, and see Autumn Rhythm (1950).
Jerome Robbins could look at Autumn Rhythm and see a dance.
87
Sadly, the attacks against formalism in the early 70S had little
to do with fact or philosophy. The jihad was a radical maneuver
designed to "Iiberalartsify" contemporary art. Professors needed
a way of talking about contemporary art that was adapted to

81. their
Clockwork Orange (eyes-clamped-open) classroom procedures.
They needed something to say while student brains were washed
with "art history." In these chambers of horror, children were
coerced into looking at pictures of pictures they did not care
about and to which they did not respond. Pictures ofart provided
the texts. Professors provided the dictionary. This evil practice
has
been long since discontinued , I'm sure, but I want to emphasize
the fact that formalism doesn't do dictionary, darling; it doesn't
do answers; it doesn't do pictures of art; and it doesn' t do
coerced
looking. Formalism speculates on the intensity and possible
longevity of tangible art that elicits an instantaneous visual or
emotional confirmation.
We try to isolate the critical frequencies, ask the right
questions, and never gain knowledge or truth. Sometimes, we
come up with little Aesopian morals, but nothing major. Jasper
Johns's flag suggests that its value derives from the people who

82. salute it, not from the man who made it. Richard Serra's work
reminds us that we never stand alone, that we muSt lean against
the world, against one another, or curve to abeyance to the god
ofgravity. My favorite moral is found in Joan Mitchell's
painting.
Joan reminds us that she can do it and we can' t. She is the
Monica
Vitti of art, pure neurosis. So formalism doesn't do answers
because answers, would conclude the endless dance of inquiries
that keeps the work alive.
I remember looking at Jasper Johns's Target with Faces (1955)
in his retrospective at the Museum ofModern Art in New York
thinking that a half-century of intelligent speculation had
brought
us no closer to decoding its mysteries-and that this didn't matter
at all. It had been a long romance, and we always had Paris, or
88 FORMALISM
wherever Jasper's Target first became the target ofour gaze.
This is
a testament to Johns as an artist but also a reminder that art
leaves

83. questions unanswered, and I could not help but feel, standing
there in the MOMA, that we might do well to stop mooning over
the targets for a while and let them freshen up. Then, one day
in the future, in Brussels or Newport Beach, some youngster
might come upon them, and the song would begin again. That
mysterious aura ofon-purpose-ness would take hold, and offwe
go into the sunset.
So formalism begins with an instantaneous sense ofalien,
patterned complexity. We stand before a work ofart with no
hope of understanding it and no choice but to try. We reenact
the
primal cosmopolitan moment-the first time a human being stood
face to face with a stranger from a strange place with a strange
language, "sizing things up" without a dictionary. I met my first
genuine strangers of this SOrt in the 1960s, when I had the
benefit
of taking courses from the great writer Jorge Luis Borges, the
new
journalist Tom Wolfe, the French avant gardiste Nathalie
Sarraute,

84. and the great classicist Bill Arrowsmith. I don't remember a
word
they said. I remember that Borges wore a cape and fedora, that
Wolfe was a smartass, and Arrowsmith a show-off. I remember
that Nathalie Sarraute had a mind as exquisite and strange as a
Chinese opera. What I learned from these strangers was
something
like what I learned from D. H. Lawrence's manuscript. I learned
just exactly how high eloquence manifests itself, what it feels
like
to be around, how it moves in its mortality. This turned out to
be
a good thing to know.
89
http://www.jstor.org
Plato and the Simulacrum
Author(s): Gilles Deleuze and Rosalind Krauss
Source: October, Vol. 27 (Winter, 1983), pp. 45-56
Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/778495
Accessed: 28/08/2008 15:10

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ress
Plato and the Simulacrum*
GILLES DELEUZE
translated by ROSALIND KRAUSS
What is meant by the "overthrow of Platonism"? Nietzsche thus
defines
the task of his philosophy, or more generally, the task of the
philosophy of the
future. The phrase seems to mean abolishing the world of
essences and the
world of appearances. Such a project would not, however, be
Nietzsche's own.
The double objection to essences and appearance goes back to
Hegel, and fur-
ther still, to Kant. It is unlikely that Nietzsche would have
meant the same
thing. Further, this way of formulating the overthrow has the
drawback of be-
ing abstract; it leaves the motivation for Platonism obscure. To
overthrow
Platonism should, on the contrary, mean bringing this
motivation to light,
"tracking" it down-as Plato hunts down the Sophist.
In very general terms, the motive for the theory of Ideas is to be
sought in
the direction of a will to select, to sort out. It is a matter of
drawing differences,
of distinguishing between the "thing" itself and its images, the
original and the

87. copy, the model and the simulacrum. But are all these
expressions equal? The
Platonic project emerges only if we refer back to the method of
division, for this
method is not one dialectical procedure among others. It
masters all the power
of the dialectic so as to fuse it with another power and thus to
represent the
whole system. One could initially say that it consists of
dividing a genus into
opposing species in order to place the thing under investigation
within the cor-
rect species: thus the process of continuous specification in the
search for a
definition of the angler's art. But this is only the superficial
aspect of the divi-
sion, its ironic aspect. If one takes this aspect seriously,
Aristotle's objection is
clearly applicable; division is a bad and illegitimate syllogism,
because it lacks
a middle term that could, for example, lead us to conclude that
angling belongs
to the arts of acquisition and of acquisition by capture, and so
forth.
The real goal of division must be sought elsewhere. In the
Statesman one
finds an initial definition: the statesman is the shepherd of men.
But all sorts of
* "Platon et le Simulacre" is an excerpt from Logique du Sens
by Gilles Deleuze to be translated
and published by Columbia University Press.

88. OCTOBER
rivals - the doctor, the merchant, the laborer- come forward to
say, "I am the
shepherd of men." In the Phaedrus it is a matter of defining
madness, and more
precisely, of distinguishing well-founded madness, or true love.
There, too,
many rush forward to claim, "I am the possessed, I am the
lover." Division is
not at all concerned, then, to divide a genus into species, but
more fundamen-
tally with selection from among lines of succession,
distinguishing between the
claimants, distinguishing the pure from the impure, the
authentic from the in-
authentic. Hence the repeated metaphor which likens division to
the testing for
gold. But Platonism is the Odyssey of philosophy. The Platonic
dialectic is not a
dialectic of contradiction nor of contrariety, but one of rivalry
(amphisbetesis)-
a dialectic of rivals or claimants. Division's essence appears not
in breadth - in
the determination of the species of a genus - but in depth - in
the selection of
the lineage: the sorting out of claims, the distinguishing of true
claimant from
false.
To accomplish this, Plato proceeds once again by means of
irony. For,
when division arrives at this actual task of selection, everything
occurs as

89. though the task has been abandoned and myth has taken over.
Thus, in the
Phaedrus, the myth of the circulation of souls seems to interrupt
the effort of
division; so, in the Statesman, does the myth of archaic times.
Such is the second
trap of division, the second irony, this evasion, this appearance
of evasion or of
renunciation. For the myth really interrupts nothing. On the
contrary, it is an
integrating element of division itself. It is the property of
division to transcend
the duality of myth and of dialectic and to join, internally, the
power of dialec-
tic with that of myth. The myth, with its constantly circular
structure, is really
the narrative of foundation. It allows the construction of a
model according to
which different claimants can be judged. In effect, that which
must be founded
is always a claim. It is the claimant who appeals to foundation,
and it is on
the basis of his appeal that his claim is seen to be well or poorly
founded, not
founded. Thus in the Phaedrus the myth of circulation reveals
what souls, prior
to their incarnation, could see of Ideas, thereby giving us a
selective criterion
by which well-founded madness, or true love, belongs to those
souls who have
seen much and thus have many dormant but revivable memories;
while sen-
sual souls, forgetful and narrow of vision, are denounced as
false claimants. It
is the same thing in the Statesman. The circular myth shows that
the definition