[Greg Lynn] Folds, Bodies Blobs Collected Essa(BookFi.org)

Books-By-ArchLtects Series edited by Michele Lachowsky and Joel Benzakin Design: Greg Lynn FORM Coordination: Saffet Bekiroglu Copy editing: Stephanie C. Jaeger Type set in Platelet and Gill Sans All rights reserved. No part of this book may be reproduced in any form without the permission in writing from the publisher or author.

Depot legal: Bibliotheque Royale de Belgique 2e trimestre 1998 - D/1998/5636/2 ISBN 2-873 17-068-9

8ooks-8y-ArchLtects

Gre~ aodLes & aLoBs coLLected Essays

FoLds~

La Lettre voLee

These essays have previously appeared as:

MuLtLpLLCLtOUS and In-organLc BodLes "Multiplicitous and In-Organic Bodies" Assemblage 19 (December 1992). "Multiplicitous and In-Organic Bodies" Architectural Design I06 (November 1993). "Multiplizitare und inorganische Korper" Arch+ I 19/120 (December 1993).

The Renewed NoveLty of symmetry "The Renewed Novelty of Symmetry" Assemblage 26 (April 1995). "Das erneurte Neue der Symmetrie" Arch+ 128 (September 1995).

proBaBLe GeOmetrLes "Probable Geometries:The Architecture of Writing in Bodies" Any 0 (May/June 1993). "Wahrscheinlichkeitsgeometrien" Arch+ I 17 (june 1993).

DLfferentLaL GravLtLes "Differential Gravities" Any 5 (March/April 1994). "Leicht und Schwer" Arch+ 124/125 (December 1994).

The FoLded

J

the pLLant and the suppLe

"Architectural Curvilinearity: The Folded, the Pliant and the Supple" Architectural Design 102 (Marchi April 1993). "Das Gefaltete, das Biegsame und das Geschmeidige" Arch+ I3 I (April 1996).

Body Matters "Body Matters" Journal

ofPhilosophy and the Visual Arts 5

(1995).

BLoBS "Blobs" Journal of Philosophy and the Visual Arts 6 (1995). "Buros" Fisuras (1995).

why TectonLCs LS sQuare and TopoLogy LS Groovy "Blobs:WhyTectonics is Square and Topology is Groovy" Any 14 (May 1996).

a physLQue out of proportLon "A Physique Out of Proportion" Any I I (1995).

New varLatLons on the Rowe compLex "New Variations on the Rowe Complex" Any 7/8 (1994).

Forms of €XpreSSLon "Forms of Expression: The Proto-Functional Potential of Diagrams in Architectural Design" EJ Croquis 72/73 (1995). "Alles gebeurt als in een fJuidum" de Architect v.26 n.9 (September 1995). "Entsurfsprozesse" Arch+ 128 (September 1995).

contents

Amor(f)aL Archltecture

ay oLe Bouman

encore... BruxeLLes lnstaLLatlon MuLtlpLlc~tous

and In-organlc Bodles

The Renewed NoveLty of symmetry pro~a~Le

Geometrles

olfferentlaL Gravltles - The FoLded the pLlant and the suppLe l

9 15 33 63 78 95 10 9

Body Matters

135

BLo~s

157

why Tectonlcs ls sQuare and TopoLogy ls Groovy

169

A physlQue out of proportlon

187

New varlatlons on the Rowe compLex

199

Forms of £xpresslon

223

flgure credlts

235

Amor(f)aL archLtecture or ArchLtecturaL muLtLpLes Ln the post-humanLst a~e By oLe Bouman

When an architect manages to take time out from a busy career for a spot of reflection, it usually begins with a discourse on greater matters than architecture. Only at a later, riper age, are the eternal values of the profession discovered. In

der Beschrankung zeigt sich der Meister (Limitation is the hallmark of the master), said Goethe, who was himself the perfect example of this truth. But what if one shows signs of such masterdom early on in life? In that case one must be careful not to allow limitation to degenerate into megalomania. Greg Lynn is just such a person who knows early on in life how to limit himself. In his mid-thirties, he already displays a mature interest in the question of how things should be done in his profession and, more important still, what kind of assumptions underlie that 'how'. He seems to view commissions as opportunities to test fundamental scientific research in practice rather than the other way round. The research continues unabated. The work belies a passion for the meaning of architecture as an ancient discipline with a body of knowledge built up over thousands of years. This attitude is very rare, certainly for such a young architect. There is only a small group of like-minded architects: Ben van Berkel, Raoul Bunschoten, Martine de Maeseneer, Alejandro Zaera Polo, Christian Moller,Wiel Arets, Neil Denari... All in one way or another seek legitimation for their work, on the one hand by placing their labours in a historical theoretical tradition, on the other hand by justifying themselves vis-a-vis the relevant forces of their own age. This in itself is enough to make their work very valuable.

FoLds~

BodLeS

&

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In almost every text in this anthology, Greg Lynn refers somewhere to architecture as a 'discipline'. This consistency implies more than clarity of expression. It also indicates an unusual view of architecture as a body of knowledge requiring a certain disciplinary approach. Architecture is more than a liberal art, or a service provider, or a social orbit; it has its own intellectual mandate which must be respected by all those wishing to help it move forward. As such, each essay in this book is a conscientious confirmation of this mandate. Only by recognizing the disciplinary autonomy of architecture can Lynn contribute to its modernization. And that is precisely what he has in mind. Once having acknowledged the theoretical achievements of architecture, he is then able to introduce his own work as a break with these achievements. By demonstrating his continuing faith in the development of an fundamental architectural theory, he is able to give this theory a paradigmatic twist of his own. And there you have the first interesting feature of Lynn's remarkable oeuvre. It seldom happens that a young architect is not content with an interesting portfolio of commissions but is also bent on getting to the very heart of the theoretical meaning of his profession. What are those theoretical achievements, and what is the nature of break with them that Lynn envisages - that, of course, is the question. In addressing this question, I am careful not to use the same words and terminology as Lynn himself. Respect for the historical autonomy of the discipline of architecture may constrain Lynn to use a certain jargon intrinsic to that discipline, but that does not apply to anyone seeking to introduce a collection of his writings. Rather, my task is to act as mediator, to try to give the prospective reader a general idea of the research embodied in this book. Given the complexity of Lynn's thoughts, this is no sinecure. As befits pure scientific research, there is no irony in Lynn's writing, no populism, few metaphors and scarcely any criticism. For anyone taking up these essays, there looms a treatise worthy of the best architectural tradition. Step by step, essayby essay, Lynn pursues his attempts to furnish his curvilinear architecture with a convincing argument. His line of reasoning is one of anti-subjectivism. His architecture is no formalistic whim, but a logical step in a

Amor(f)aL archLtecture

post-humanist architectural theory. Which is to say,this step can be generalized. Anyone who is unprepared to accept this, is not only no follower of Greg Lynn but also, so his argument implies, like as not a theoretical laggard. Hardly surprising, since anyone prepared to accept a particular ceuvre as the next step in a two-and-a-half millennia-old architectural history, will be inclined to see marginalia as irrelevant details. There are marginalia and hence irrelevant details in abundance. By no means everyone accepts this work on the historical plane to which it lays claim. Lynn himself is public-spirited enough to take these reservations very seriously. I shall return to this anon. Respect for a discipline does not, of course, begin and end with the deployment of a legitimizing idiom. The important thing is to contribute to the grand tropes of architecture. The classic themes, the ostensibly eternal motives for erecting a building. In this Lynn is related both diachronically and synchronically to the great figures of his profession. As a mathematician, Lynn takes up a position in a line that runs from Pythagoras, via Vitruvius and Alberti, to Rudolph Wittkower and Colin Rowe. However different these thinkers may have been, they shared a common interest in geometrical an.d compositional ground rules. They were always looking for the underlying structures of external forms and relationships to which they subsequently attached metaphysical meanings. Conversely, they sought to externalize their metaphysics by regarding certain proportional systems as absolute and God-given. Through geometry, architecture can lay claim to a seemingly universal language that spans different eras and cultures. The philosophical idealism on which this approach rests also implies an organicism. When a design embodies the divine proportions, every addition and every omission detracts from the whole. The building is whole, represents wholeness. A composition and a grid according to the agreed rules of measurement are a necessary condition thereto. Anyone who tampers with the rules, also tampers with that wholeness. And this is precisely what Greg Lynn is about. On the assumption that this metaphysics is bankrupt, Lynn attempts to change the structure of the aforemen-

10

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tioned ground rules. As a child of his time, he is no longer prepared to accept architectural rules imposed from above. Besides, has he not exposed them as mere psychological props? Just as chaos theory drew attention to natural phenomena that were until recently excluded from the physics repertory, so architecture must start paying attention to forces that are by definition suppressed in a classical proportional system. For according to Lynn, "geometric exactitude tends to transform particularities into inexactitudes through mathematical reduction. Reducing architecture to a fixed and universal language of proportion in this way means simply that architecture reproduces itself. Organic types that are whole to the fullest extent are full to the point of exclusion." Inspired by the baroque thinking of Leibniz, Bergson and Deleuze, Lynn is trying to discover a different geometry; one that is no longer tied to a transcendent value system, but is an adequate expression of contemporary secular reality. Greg Lynn's criticism of the classic value system is nothing new of course. Many architects have preceded him in their efforts to be absolument moderne. Consequently, Greg Lynn is also busy clarifying his position vis-a-vis his contemporaries. Architects who still display a penchant for a lost paradise of wholeness and moral authority merit scarcely a mention. Those whose architecture is intended to compensate a historical loss get no credit from Lynn. Kindred spirits, however, receive far more attention. Among those named in this book are Robert Venturi, Peter Eisenman, Bernard Tschumi, Daniel Libeskind and Mark Wigley, all of whom have contributed, over the last thirty years, to a subtle anticlassical discourse on contradiction, complexity and multiplicity. Lynn reproaches them with a too direct metaphorical translation of differential thinking in their architectural vocabulary: "I can only suggest that the now dominant practice of eliding cultural difference with formal conflict as a method for writing in architecture is becoming suspect". For Lynn's'taste it is all too literal, too metaphorical, even too critical. Their architecture tries to represent the new cultural condition through symbols and language. Lynn prefers an experimental architecture in which concepts are developed and expressed through what Deleuze would

Amor(f)aL archLtecture

11

,~.~II

abstract machines. These are techniques that reveal the strengths of a given programme without immediately instrumentalizing them in a concrete design. Lynn:"neither the reactionary call for unity nor the avant-garde dismantling of it through the identification of internal contradictions seems adequate as a model for contemporary architecture and urbanism". Lynn himself has settled for 'post contradictory work', an architecture that has passed beyond the stage-management of tensions and, amoral and amorfal, incorporates the forces of reality. He calls this architecture 'smooth'. "Smooth mixtures are made up of disparate elements which maintain their integrity while being blended within a continuous field of other free elements." For Lynn this analysis means above all a new form. The work originates in the conviction that the supposed link between mathematics of form and transcendent architectural values is obsolete. This does not mean that the relation itself is obsolete. If classical form is obsolete, another form is needed, a form appropriate to non-transcendent values. What must remain, according to Lynn,is the unity of content and form. "What is necessary for a rigorous theorization of diversity and difference within the discipline of architecture (sic!) is precisely an alternative mathematics of form; a formalism that is not reducible to ideal villas or other fixed types but is in its essence freely differentiated. (... ) I would maintain that the dominant question today is in fact the question of the status of forms of order and organization in architecture." Lynn has applied himself to providing an answer to this question. "To disentangle the pact between organic bodies and exact geometric language that underlies architecture's static spatial types is a monumental task. (... ) any attempt to loosen this alliance must simultaneously 'deterritorialize' the autonomy of whole organisms and replace the exactitude of rigid geometry with more pliant systems of description:' Here then you have a few quotations from this book that seem to me to go to the heart of Lynn's ambitions. What Lynn means by 'more pliant systems of description' becomes clear when we take a closer look at his own architecture. One glance reveals that this work is

12

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not about volumetric clarity according to the laws of the simple, basic form. The classic dilemma of pure scientific research raises its head: the need to apply new insights. For an architect who is trying to avoid the transcendence of the static form and who strongly doubts the possibility of establishing forms for all time, this is naturally a life-size problem. Not so for Lynn,who sees it as a challenge: "The challenge to architecture, once geometry and the body enter into a new alliance, is to write - in form - a monument that is irreducible to any ideal geometric type." Referring to the biologist Gregory Bateson, Lynn finds a nice reversal of classical reductionism. Instead of regarding amorfal (building) volumes as a primitive first stage of a mathematical architecture, Lynn argues that the disappearance of symmetry "and formal homogeneity is a sign that more information can be incorporated into a symbolic system: "symmetry breaking is not a loss but an increase in organization within an open, flexible and adaptive system." What is more, the desire for moving architecture need not lead to physical movement. As far as the construction of buildings is concerned, it means rather that 'one can conceive of lighter compositions where weight is carried through many different vectors that are not subject to the right-angle pull of the earth's gravity'. The architectural outcome of this approach is just starting to become visible in the first realized projects. But as yet Lynn's intentions are much clearer in the computer animations he makes of this projects. These are curvilinear indeed! In fact it is impossible to describe Lynn's designs, for language also is too much tied to the rules that this architecture is bent on undermining. Only meta-concepts can convey something of the principles on which this architecture is based: curves, folds, blobs. For an explanation, read this book. The whole idea is to create forms that are resistant to every attempt to understand architecture once again as a higher, metaphysical order. They are forms to which idealism will not stick, that cannot be reproduced and thereby universalized. Greg Lynn'sgreatest passion is form. But from the vantage point of that passion he makes arnorfal architecture. Up to this point, the word computer has been mentioned only once. Anyone familiar with Greg Lynn's work will find this rather strange. After all, his work is

Amor(f)aL archLtecture

13

known primarily for the use it makes of all kinds of advanced 'non-architectural" software. Internationally, Lynn's work makes a big impression because of the way-\ he visualizes his designs with the aid of animation programs borrowed from,

:'1

among others, the film industry. At the very least this leads to design presenta- . tions that would not be feasible using conventional resources. His images radiatean unmistakable fascination. Unfortunately, this fascination often stands in the way of an evaluation of the underlying research. The spectacle of the form, courtesy of the software engineers, narrows the focus to the shock of the new. For those who are more au fait with animation industry, this spectacle quickly becomes a facile trick in a discipline which, compared with industrial design, advertising, film and virtual reality environments, is technologically backward. Which is why the computer, however attractive it may seem, is actually an unproductive point of access to Lynn's work. While each new update of Lynn's vocabulary of forms is eagerly awaited, no attention is paid to the development of the architectural theory that drives this vocabulary. Before you know it, Lynn will have become a globetrotting lecturer showing off his latest update. His audience will consist only of those who want to be seduced rather than convinced. In the long run this could serve to hamper the development of his theory. Worse still, that theory would become simply a legitimizing spiel. And that would be a great pity for there are a number of questions awaiting Lynn's response. I shall conclude this introduction by listing one or two: - Given that your aim is to arrive at a dynamic architecture, what precisely are the forces that go to make up this dynamism? Are they only quantifiable forces, or others as well? - When you give examples of new knowledge in the field of biology, informatics, chaos theory and the like, you end up dragging architecture out of the mechanistic paradigm that has for so long been the source of its authority. The only problem with this recontextualization of architecture is that it does not admit of prescriptions for the future. And yet surely that is just what the emancipatory character of this architecture implies. - Can the consequences of this architectural theory be visibly extended to other matters besides form? Does it have any implications for the organization of the discipline for example, or better still, for the definition of this discipline?

FoLds~

aodLes & aLoBs

Which brings me back to where I started: the position of Greg Lynn vis-a.-vis his own discipline. His theoretical work opens up new paths in a way that emphasizes just how long those paths are. His prototypical architectural works are but the beginning of a genuine architecture of the blob. The important thing in the coming years is to continue to regard this work as a promise. Only then will the abiding curiosity necessary for the fulfilment of this promise be assured.

Encore . . 8ruxeLLes rnstaLLatLon

Although there could never be a direct correlation between the concepts developed in these collected essays and any architectural design, there are many preoccupations common to the site specific installation at "encore... Bruxelles" and

Folds, Bodies and Blobs. Both engage the relationship between geometry and various models of the organism. Both explore a mode of design based on a notion of growth and mutation free from reductive typologies. Both locate discussions of form and shape within a field of external influencing forces, including motion and gravity.

Both define organization in terms of combinatorial exchanges

between multiple, complex and intricate systems that interact and evolve in time. Both embrace teratological processes where order and identity emerge from differential variation and mutation. Designed for a mobile spectator rather than for a.fixed eye, the installation is constructed as a swept flow of motion translated into curves.

Rather than

approaching the existing gallery as a frame, the site for the installation is reconceived as a soft mutable envelope shaped by the motion around and through it. This flexible continuous surface is torqued and reconfigured by a virtual random walk that is introduced into the gallery interior. The gallery space is animated by this gesture that loops from the entry vestibule through the gallery.' The movement of the visitors through the installation echoes the virtual path from which the surfaces precipitated. A translucent fabric on which moving images are projected is stretched across a fluid steel frame producing a lightweight ghost of the original space.

16

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Endnote I. For an extended discussion of the implications and applications of concepts and techniques of "animation" to architectural theory and design see the introductory essay to my book Animate FORM (New York, 1998).

The three surfaces were divided into four bays. In each of these bays a single surface was swept from one surface to anotherto another. The result is four surfaces that transform across theirwidth from the first surface, to the second,to the third. These four bays of were subdivided into three areas corresponding to the original floors, walls and ceiling of the site. The ceiling area of the surfaces is articulatedwith a series of steel cross bars. The wall area of the surface is articulated as a curvedtensile fabric that becomes a translucent screen forprojections. T.he floor area of the surface is articulated as a series of ribs that defines a new ground plane.

Encore ... BruxeLLes

I. Interior perspective

of installation.

2. Perspective of four bays divided into roor, walland ceiling areas.

FoLds, GodLes & GLoBS

15-20. Plan of frames 60-85.

Encore ... GruxeLLes

20

21-23. Plan of frames 0-10.

24-26. Plan offrames 15-25.

27-29. Plan of frames 30-40.

FoLds, BodLes

&

BLoBS

The existing floor, walls and ceiling of the site are defined as a soft continuous surface that is connected to the flexible joints of the skeleton.

Encore ... 8ruxeLLes

30-32. Perspective

of frames 0-10.

33-35. Perspective

of frames 15-25.

36-38.Perspeetive of frames 30-40.

21

The movement ofthe path bends the skeleton that is constrained to it and these undulations are translated into inreetions of the continuous surface.

FoLds,

22

39-41. Plan

of frames 45-55.

42-44. Plan offrames 60-70.

45-47. Plan offrames 75-85.

Godles & GLoGS

Encore ... 8ruxeLLes

48-50. Perspective

of frames 45-55.

5/-53. Perspective

of frames 60-70.

54-56. Perspective

of frames 75-85.

23

FoLds)

57-6/. Perspe.ctives

ofthree surfaces.

62-66. Perspectives

ofthree surfaces.

67-7/. Perspectives

ofthree surfaces.

GodLes

&

GLoBS

£ncore ... eruxeLLes

Three instances in the deformation of the surface were recorded and superimposed on one another. This resulted in three time portraits ofthe surface at one moment.

26

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oLo8s

encore ... 8ruxeLLes

73. Roof plan ofinstallation.

74. Longitudinal elevation 75.Transverse elevation

ofinstallation.

ofinstallation.

27

2~

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GLOBS

76-77./nstollotion photographs.

II

'.

. I'irom abave. ofinstallation. 78. Perspective

Encore ... aruxeLLes

79-81. Installation photograph.

FoLds)

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oodLes

&

oLo8s

82. Installation photograph.

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'\ ,._~~_: ..--'It

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MuLti.pLi.ci.tous and Inor~ani.c Bodi.es

Types of spatLaL aodLes tilt is obvious, moreover, that mathematical organization imposed on stoneis none other than the completion of an evolution of earthly forms, whose meaning is given, in the biological order, by the passage ofthe simian to the human form, the latter already presenting all the elements ofarchitecture. In morphological progress men apparently represent only an intermediate stage between monkeys and great edi~ces. Forms have become more and more static, more and more dominant The human order from the beginning is, just as easily, bound up with architectural order, which is no more than its development." Georges Bataille I In 1949, Rudolf Wittkower systematized a theory of harmonic proportion by uncovering a single spatial type in the domestic architecture of Andreas Palladio. Indeed, he discovered Palladio, one might say,by inventing an origin for his work. 2 Wittkower's theory continues to provide a general rule for the definition of essential architectural structure: the nine-square grid. The exact geometry of this type guarantees its universal applicability. Wittkower exploits the differences between eleven of Palladio's villas for their ability to cancel each other out. The cancellation of disparate elements manifests a hidden typological order while through a return inquiry the nine-square grid emerges as the universal origin of each of the vlllas.: For Wittkower, the type is not merely a constellation of

First published in Assemblage. no.19.

34

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mathematical correspondences, but further, a system of spatial organization that functions as a unified and self-regulating body. Through harmonic proportion, the nine-square grid type makes each villa in particular, and the eleven villas in general, whole. Two years earlier, in The Mathematics of the Ideal Villa, Colin Rowe used the same nine-square grid type to crossbreed two pairs of twins: Le Corbusier's Villa Savoye and Andreas Palladio's Villa Rotunda, and Le Corbusier's Villa Stein with Palladio's Villa Malcontenta:' Both progeny seem less than natural kin to the villas (the type relying on variations between villas and never fully present in any villa in particular but present in all villas in general). It is, nevertheless, the proportional correspondence of these often contradictory spatial organizations that lays the groundwork for a single cubic spatiality from which a lineage of villas is born.: For Rowe, the proportional harmony of the spatial body founded on the ninesquare grid evoked a "Virgilian tranquility." 6

1-2-3. Statue ofUberty armature construction details through shoulders.

Rather than continue this logic of burial and recovery of origins for architecture, there might be another way to respect particularities and differences without returning our inquiry to universal types. Today we confront a different but related problem: What is the nature of the interior of architecture? What lies hidden within this interior? These questions are already thematized within architecture through the erection of boundaries that establish the difference, and degree of autonomy, between the inside and outside. Yet before determining where to begin with architectural

MuLtLpLLcLtous and InorganLc BodLes

35

interiority - which is a problem of finding an entry we have to question the origin of the interior. In the work ofVitruvius we find the first clue as to the problem of the type and content of this interior space. He identified an internal "proportional balance which results

from principles of symmetry in architecture." Vitruvius

• I

expressed remorse that, like a living body, the breast of architecture could never be opened to reveal the secrets of its interior. 7 But the architectural orders of proportion and symmetry are not simply already present within architecture; according to Vitruvius, they

4. Statue ofUberty armature during construction.

have been intentionally concealed so that questions of interiority can be posed only within a closed harmonic system. This geometric system of proportion, as Wittkower, Rowe and Vitruvius have argued, is itself a whole. This description of architecture as a harmonic, naturally proportioned organism is indebted to the operation of two purloined secrets within an inviolate interior: geometry and the body. 8

The unLty of the organLsm and the €LdetLc Language of Geometry "The design of a temple depends on symmetry, the principles of which must be most carefully observed by the architect. They are due to proportion, in Greek. Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. Without symmetry and proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members, as in the case of those of a well shaped man." Vitruvius 9

"Pure geometry and kinematics (and all the associated sciences for which they are the example here), then, will be material eidetics, since their purpose is the thingly, and thus

FoLds} aodLes &

5.Villa Stein at Garche, by Colin Rowe.

6.Villa Malcontenta,

aLo~s

the corporeal, determination of objeas in general. But they are abstract material sciences, because they only treat certain eidetic components of corporeal things in general, disregarding their independent and concrete totality, which also comprises the 'material' (stofflich), sensible qualities and the totality oftheir predicates. Spatial shapes, temporal shapes, and shapes of motion are always singled out from the totality ofthe perceived body. Byitselfalone, then, a static analysis could a priori and rigorously recall for us that the protogeometer always already had at his disposal anexaa spatiotemporal shapes and essentially 'vague' morphological types, which can always give rise to a pregeometrical descriptive science. This could be called geography. For such a subject, the rigor of eidetic assertions (like that for determining vague essences) is not at all undermined bythe necessary anexaaitude of the perceived object. We must indeed beware of scienti~c naivete, which causes this anexaaitude of the object or concept to be considered as a 'defeet,' as an inexactitude." Jacques Derrida 10

. by Colin Rowe.

7.Villa Malcontenta, by RudolfWittkower.

In architecture, structure is drawn within things. As Bataille has suggested, architecture is the locale where the universality of geometry binds the base matter of temporal bodies. The regulating lines of architectural orders make a connection to the world as a whole, but also to the specific morphological characteristics of forms. Spatial types are involved in the practice of originating families of form (as in the constitution of species such as Wittkower's brood of villas). II

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37

Architectural types organize amorphous matter. Architectural proportion, moreover, achieves the transcendental status of an abstract, holistic and organic body.

It adopts the logic of an organism,

which is above and beyond either mathematics or matter.

What distinguishes harmonic proportion

from mathematical measure is the value granted to specific ratios based on the symmetrical unity of all

8.Villa Zeno at Cessalto, by Rudo/fWittkower.

parts to a whole. The terms. organic, organism and organization can be used interchangeably to the extent that they all delimit things which are

whole, that is, containing both a rigid external boundary "to which nothing can be added or subtracted without jeopardizing the balance of the composition," and an interior space closed to the unpredicted and contingent influences of external forces. 12 It is important to qualify these ideal bodies as whole to the fullest extent, complete to the point of exclusion.

This organic logic of proportion is already

embedded within architecture's interior.

9.Villa Poiana at Maggiore, by Rudo/fWittkower.

Architecture's provision for structure, use, and shelter necessitates an absolute and exact delimitation of internal volume from external forces. To signify this rigid sense of the interior, architecture frequently invokes the paradigm of the inviolate interior of a living body. Le Corbusier's Modular provides an obvious example of the alignment of the body with measure. Of course, the paradigmatic body is both docile and static; its particularities of culture, history, race, development, and degeneration are repressed in favor of a general model. Even the Husserlian notion

/ O. Villa Sarego at Miega, by Rudo/fWittkower.

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of "variation" places the particular in the service of the average or mean. 13 The typology of natural orders is always underwritten

by the variable measurement of difference

between and within species. For instance, the evolutionary transformation "From Frog to Apollo:' which appeared in the

1803 edition of Johann Casper

Lavater's Physiognomische Fragmente, exploited 1I.Villa Thiene at Cicogna, by RudolfWittkower.

both the constellation of particularities and differences between the frog and the ideal man and a continuous and general faciality that registers these differences. 14 Rather than

reducing the differential variations

between elements to a static type, Lavater employed a continuous, differentiated system of transformation. A similar method of Cartesian deformation was developed in 1917 by the morphologist D'Arcy 12.Villa Emo at Fanzolo. by RudolfWittkower.

Thompson to describe the transformations of natural form in response to environmental forces. 15 Thompson provisionally aligned bodies and measure in such a way that particular dissymmetries and disproportions were maintained as events within a deformable, supple, and irreducible geometric system of description. Geometry is no longer a static measure of invariant and unitary characteristics but what Gilles Deleuzeand Felix Guattari have referred to as a "plane

ofconsistency"

upon which differential

transformations and deformations occur. Type itself 13.Villa Rotunda, by RudolfWittkower.

is never present in a fixed state in an entire species. Thus a more fluid and dynamic system of measure

MuLtlpLlCltous and rnorganlc aodles

can be employed to describe ever-changing spatial bodies through their manifestations at singular moments. In Thompson's deformations, particular information influences and transforms a general grid, making geometry more compliant to the matter it describes. The enlargement of a fish's eye is registered in the deformation of its accompanying grid. The dimensional fluctuation became, for Thompson, an indication of light level and water depth influencing that particular species. In this manner, the type or spatial organism is no longer seen as a static, whole separate from external forces, but rather as a sensibility continuously transforming through its internalization of outside events. But within the pact of the organism and the geometric language with which it is exactly described, these fluid characteristics are generally reduced to fixed principles. 16 To understand this better we must look to the language of geometry with an eye toward those moments where it describes spaces and forms as whole bodies. It is in fact most likely not utility, economy or structure that fixes architecture statically but its prejudice in favor of geometric ideality. Geometry provides the apparently universal language with which architecture assumes to speak through history, across culture, and over time. Architecture tends to employ geometries that are eidetic: that it is, they are manifest visually as pure spatial coordinates; they are self-identical, signifying nothing other than themselves; they are repeatable identically; and they are absolutely translatable for all

39

.

14.Geometric pattern ofPalladio's villas, by RudolfWittkower.

o

2

a

4

15. Cartesian deformation of diodon into mola, by D'Arcy Thompson.

•

16. Cartesian deformation of diodon into mola, by D'Arcy Thompson.

8

I

FoLds, BodLes

&

BLoes

people, for all time. For example, geometry need posit only one sphere as a surface composed of an infinite number of points equidistant from a single radius. In effect, the sphere that existed for Plato has been handed down to us identically across cultures and through history. Vague objects that are merely round may be more or less spherical yet no two are ever absolutely identical. Roundness itself can be defined with probability but never ideally described with exactitude. Likewise, an ideal sphere can never be realized in matter. Certain things are believed to be spherical even though their specific matter

/ 7.Transformation

of frog intoApollo.

/8.Transformation

offrog intoApollo.

MuLtLpLLCLtous and rnorganLc aodLes

41

guarantees that they can never achieve pure form. Vague forms that do not repress the particular characteristics of matter are typically considered to be inexact. 17 Geometric exactitude, in other words, tends to transform particularities, no matter how precise they may be, into inexactitudes through mathematical reduction. It renders particularities and difference as mere variations beneath which subsists a more fixed and universal language of proportions. Proportional bodies are bound by geometric exactitude. These ideal spatial organisms are reducible and identically repeatable. They have the appeal of being stated "once and for all." In systems of proportion, architecture assumes a natural relationship between geometry, with its claims to exact measure, and the unified stasis of an organism, with its claims to wholeness. Because of its predilection for fixity and stasis, architecture has become the privileged site for the elision of eidetic geometry and holistic organization. Yet we should beware of any architecture described as wholesome or organic, for the logic of the organism is the logic of self-enclosure, self-regulation and self-determination. Organic types that are whole to the fullest extent are full to the point of exclusion. Buildings are not organisms but merely provisional structures that are already multiplicitous. Where the organic is internally consistent, the inorganic is internally discontinuous and capable of a multiplicity of unforeseen connections. To disentangle the pact between organic bodies and exact geometric language that underlies architecture's static spatial types is a monumental task. Any attempt to loosen this alliance must simultaneously deterritorialize the autonomy of whole organisms and replace the exactitude of rigid geometry with more pliant systems of description. 18 Like all forms of writing, architecture is neither exact nor inexact but anexact. A suppler geometric description of architectural form would necessarily loosen the connection to organic models of proportional harmony and stasis through a flexible compliance to particularities. Thompson's deformations subject the stasis of geometric types to dynamic transformation through the internalization of particular, vague or anexact, characteristics. With a less whole and wholesome

FoLds~

42

aodLes & aLoBs

paradigm of the body, not only do typologies become dispersed, but, moreover, their interiors open to productive alliances. That is to say, spatial bodies other than the ideal types are brought into affiliations with systems outside of their boundaries, where their determinacy at any point in time is dependent upon influence by external events. Deleuze and Guattari have proposed such a model for a "body without organization" where the organic, bound by a unified and internally consistent model of the organism, is reformulated as a multiplicity of affiliated organs without any single reductive organization. In architecture, the present static alliance between rigid geometry and whole organisms cannot be entirely overcome but may be made more flexible and fluid through the use of more suppler, deformable geometries. 19

Geometry resists the play of writing more than any other language. Bataille's idea of the "informe:' or formless, recognizes the capacity to both define and defer form within a practice of writing. This informal practice writes the anomalies in a manner that is amorphous. Denis Hollier, writing through Bataille in Against Architecture, implies that the practice of writing the "informe" can only be arrested in form by architecture. But rather than locating the refusal of form solely within philosophy, the formless might also be written within architecture by architects. The most transgressive moment of Bataille's"informe" occurs were the formless is found to be already within the "mathematical frock coat" of form. 20 Formless writing within architecture leads, as previously suggested, toward a different kind of alliance between geometry and the organism, resulting in anexact, multiplicitous, temporal, supple, fluid, disproportionate and monstrous spatial bodies. Unlike exact geometry, formless writing accommodates differences in matter by resisting any reductions to ideal form. Because of this hesitation to arrest forms once and for all,their descriptions become more compliant to the base matter they signify. 21

MuLtLpLLcLtous and InorganLc aodLes

43

MonumentaLLty and MuLtLpLLcLty "Ihe othertype ofmultiplicity appears in pure duration: it is an internal multiplicity ofsuccession, of fusion, oforganization, ofheterogeneity, of qualitative discrimination, or ofdifference in kind; it is a virtual and continuous multiplicity that cannot be reduced to numbers." Gilles Deleuze 22 Architecture reserves its strongest statements for the monument. The monument commemorates an event that is experienced through shared (particularly urban) histories, and thus it offers a unitary and repeatable space. As a result, the monument offers the strongest allegiance between exact geometries and organic models of the body. Hollier incriminates architecture for its monumental mode of discourse. He executes this judgement through a critical strategy similar to that which Derrida employed in his Husserl's Origin of Geometry, arguing that architecture's "origin is stUllacking at the beginning." 23 This argument repeats the idea that architecture unifies itself by continually originating ideal spatial bodies that can only be invoked after the fact of their variations. Hollier's, and Bataille's, rejection of architecture as a potential practice of writing depends on the assumption that proportional order originates in and is natural to architecture. In monuments, architecture arrests events in form by defining ideal urban spatial bodies in exact geometric terms. The challenge to architecture, once geometry and the body enter into a new alliance, is to write - in form - a monument

/9. Hedgehog flea withmites.

20. Hedgehog flea withmites.

2/. Hedgehog flea withmites.

44

FoLds~

aodles & aLoBs

that is irreducible to any ideal geometric type. To refuse the transcendence of static form, architecture must begin to describe the particular characteristics of incompletion rejected by the exactitude of geometry and the symmetry of proportion. 24 Deleuze and Guattari's "body without organs" suggests an alternative to the organic paradigm of the whole body. Such a multiplicitous body is always both less 22. Longitudinal cut through anterior end ofplanarian, or flatworm.

than a single organism and an affiliation of many organs. Their extension of Elias Canetti's paradigm of the pack, swarm or crowd is one model for engaging a less-than-whole building within a context that is an assemblage of often disparate morphologies rather than a continuous fabric. The behavior of the pack does not turn on the distinctions between part and whole, autonomous individual and collective.

To

become intensively involved with such an organization, an individual must enter into the affiliative alliances of the pack. There is a two-fold deterrito23. Two-headed planarian resulting from longitudinal cut

rialization in becoming a multiplicity: the loss of internal boundaries allows both the influence of external events within the organism and the expansion of the interior outward. This generates a body that is essentially inorganic. For instance, within a multiplicitous assemblage, each individual defers its internal structure to benefit, by alliance, from the fluid movements of the pack. As the proper limits of individual elements (multiplicity of, say, wolves) are blurred, the pack begins to behave as if it were itself an organism

24. Planarian whose head was repeatedly cut

(multiplicity of the pack). The pack itself is not regulated by or reducible to any single structure, as it is

MuLtlpLlCltoUS and Inorganlc aodles

continually, dynamically and fluidly transforming itself in response to its intensive involvement with both the external forces of its context and the internal forces of its members.

Multiplicity describes both the

assembly of a provisional group from disparate elements - which is less than a whole - and the already less-than-whole nature of each of those elements that are allied with the group. Multiplicitous bodies are always already entering into relations and alliances through multiple plications,> Structures such as these are not identically repeatable outside of the particularities of their internal elements or their external environments. In architecture, the multiplicitous connections of buildings to the particularities of context are typically repressed by the proportion of exact, unified, organic spatial types. One example that speaks to structural issues of multiplicity is the planarian, or flatworm. 26 Within the body of a single planarian is a very specific constellation of possibilities for the proliferation of a multiplicity of bodies. The limits of this development is determined both by the internal structure of the animal and by the lines of development imposed from outside its body. The developments that result along these lines can only be described by their affiliations.

45

t

1-1 ,

..1--' ,

25.Polarity in a planarian, a head growing from the anterior and a tail from the posterior.

I~' I~,

26. Competence for regeneration of a new head decreases from anterior to posterior.

~-t

I,--..

27. Small pieces of the planarian lack polarity as they regenerate symmetrically.

FoLds~

aodLes &

aLo~s

AffLLLatLve connectLons: The coLLossus

28. Grafting by taking a smallpiece from a donor and placing it on a wounded host

29.The graftgrows into a smallhead.

tWe still have something in common to them all; and using another mathematical term (somewhat loosely perhaps) we may speak of the discriminant charaders which persist unchanged, andcontinue to form the subjed of our transformation. But the method, far as it goes, hasits limitations. We cannot fit both beetle andcuttlefish into the same(famework, however we distort it; nor by any ccrordinate transformation can we turn either of them into one another or into the vertebrate type. They are essentially different; there is nothing about them which can be legitimately compared." D'ArcyThompson 27 "A unique plane of consistency orcomposition for the cephalopod and the vertebrate; for the vertebrate to become an OdOPUS or Cuttlefish, all it would have to do is fold itself.. Plication. It is no longer a question of organs and functions, and of a transcendent Plane thatcan preside over their organization only by means of analogical relations and types of divergent development" Gilles Deleuze 28

"There is in the colossal an attraction, a particular charm, to which the theories of ordinary art are hardly applicable." FredricAuguste Bartholdi 29 "It originally, the word '[kolossos] has no implication of size, it will come to have this implication later only by accident What about this accident, this one in particular, which brings cise to the colossus, notthe incisive cise which gives measure, not the moderating [moderat rice] cise but the dispropor-

MuLtLpLLcLtous and rnorganLc aDdles

47

tionate [demesurante] cise?" Jacques Derrida 30 use the word affiliative to describe a system of connections characteristic of a multiplicitous organism against the idea of the filiative. The latter implies the relations of a family, of proper parents and progeny. But the proper family values established through evolution often overlook the alliances of different species that develop along lines of involution. The distinction between the two strategies is aptly illustrated by the debate between D'Arcy Thompson, who favors essential unchanging species, and Deleuze and Guattari, who fold these species into each other. Thompson, as we have seen, situates essential differences on a fixed geometric plane of comparison. Deleuze and Guattari attack the essentialism of difference between these species by rendering this plane as a complex of folded connections between disparate species. Categories of form, such as the idea of species distinction, provide for a return to an original type from which subsequent spatial organizations develop. These types are reinvented each time they are invoked. Any evolutionary discourse that employs straight filial lines of development and pyramidal hierarchies of species is founded on the relations between families of forms. And these filial relations are weighted in favor of general principles. The prejudice toward fixed orders is achieved at the cost of repressing local differences of program, structure, form and culture. Affiliative relations, by contrast, typically exploit possible connections that occur

-

30. Copy of Statue of Uberty, with Eiffel Tower in the background.

3 I. Statue ofUberty, exterior view.

FoLds~

aDdLes

&

aLoBs

through vicissitude. They cannot be predicted by the global systems of organization present in any single unified organism. When whole systems of geometric description and organization break down, seemingly unnatural connections between disparate elements emerge. The introduction into architecture of forms that are proto-geometric, or without exact measure, presents such an opportunity. 32. Statue ofUberty, section looking West

33. Statue ofUberty, interior view.

RobertVenturi's paradigmatic duck is a possible multiplicitous body. The duck is founded on sculptural, not-yet-architectural figures, generally considered to be in conflict with structural and pragmatic requirements. The assumed natural contradiction of the pragmatic by the figural denies any possibility for a complicitous relationship between decoration and structure. Colossal statuary invites characterization as ducks: sculptures-becoming-buildings. The scale of colossal statuary requires architectural design despite the fact that the complex negotiations among figure, structure, and program are usually repressed in favor of an iconic and singular sculptural form. In the case of the Statue of Liberty, the enlargement of the oneto-one scale of the human figure to the monumental scale of the city meant that its sculptor, Frederic Auguste Bartholdi, had to collaborate with Viollet-leDuc and, later, Gustaf Eiffel. This collaboration, however, was not familial but unpredicted. The enlargement, "beyond theories of art," introduced an anomalous form that was neither sized nor incised before its entry into architecture. 31

MuLtlpLlCltous and rnorganlc aodles

The introduction of this particular amorphous figure, the Statue of Liberty, which did not originate in architecture, provokes new connections with the conventions of drawing, measurement, construction, use and context. By beginning with bodies of disproportionate matter rather than with spatial types, a suppler affiliation ensues between geometry and the thing described. No single proper filial line ever exists between amorphous or base matter and the mathematics of form. The description of these anexact morphological types can be precise yet will inevitably require empirical methods that are compliant to the matter with which they begin. Both Venturi's duck and the colossus, through size, introduce an alien form prior to the origination of an organic geometric system of proportion. This differs entirely from a more familiar anthropomorphism wherein the body forms a link between nature and architecture through geometric proportional correspondences of part to whole, microcosm to macrocosm. Colossal architecture instead introduces a disproportionate body that both precedes and resists geometric exactitude. Despite its singularity as a sculptural object, the Statue of Liberty's multiplicitous assembly of contingent and compliant substructures results from an internal resistance to any single proper form or type. Further, the compliancy between the designs of Bartholdi and Eiffel engenders unforeseen affiliations among pylons, trusses, tertiary grids, substructures, skins, ornaments, and their various interconnections without appealing to contradiction. Rather, it joins figural and structural systems symbiotically. The

49

T I

34. Statue of Uberty, plan of crown platform.

35. Statue ofUberty, plan ofLevel 9.

36. Statue ofUberty, plan ofLevel 8.

FoLds

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aodles & aLoBs

effects of the colossal scale, then, are visible not only in the enlargement of the singular body but, more importantly in the unpredicted local relationships of disparate building systems.

37. Statue ofUberty, plan ofLevel 7.

38. Statue ofUberty, plan ofLevel 6.

39. Statue ofUberty, plan ofLevel 5.

There is more than a dialectic relationship operating between Bartholdi and Eiffel. Although Bartholdi provided the original sculptural form that Eiffel was employed to structure, the work of each was altered in the bargain. The result of their combination is measured not by mere addition but by multiplication. On close examination, Liberty's body is found to be riddled with gridded fissures. Liberty is the site of a general topological gridding that flexibly coordinates the particu larities of the specific folds of the body and fabric that drape it. The rigid geometry of the hidden structural pylon infects the folded surface with a system of lines that seems arbitrary in this particular body.> Simultaneously, the pure structure of Eiffel's pylon has been deflected to one side to accommodate the nonsymmetrical posture of a woman with an arm raised. In contrast to the Eiffel Tower, the specific posture of the Statue of Liberty lacks general symmetry. The particular gestures across Liberty's surface causes differential torsional adjustments to proliferate locally throughout the steel structure. More significant than either the figural influences on the grid or the gridding of the figure is the development of fortuitous, contingent subsystems between them. The secondary network of connections between the trusswork and the inner surface - an

MuLtLpLLcLtous and rnorganLc BodLes

inner webbing of hundreds of flexible members exists only because of the affiliation between these disparate systems. The elements that negotiate between the trusses and the draped body could not be predicted within either the architectural or the sculptural discourse. There is a colossal disproportion of these parts to the whole. Neither the architectural nor the sculptural origin of the building can dominate the symbiotic network of affiliated subsystems that construct the seemingly singular iconic figure of the colossus. The alliance between Bartholdi and Eiffel thus produces not a singular organism but a multiplicity of organs. In the architectural drawings, or incisings, of the colossus, the iconic structure of the statue is diffused. Each specific cutting plane is oblique to the figure of the particular body since there is no single plane on which to project its form. The colossus is irreducible to any single measure or geometric description - apart from its size. For a multiplicitous body is generated from an interaction of internal logics with external events. Nevertheless, when comparing the plans,a nine-square grid more or less seems to span from the central pylon to the skin. Yet the nine-square bay system introduced by the structural tower varies in response to the contours of the folded skin. Eiffel's structure is provisional rather than an essential organizational type like the nine-square of Rowe and Wittkower. This resistance of amorphous matter to incisement

51

40. Statue ofUberty, plan

ofLevel 4.

41. Statue ofUberty, plan

ofLevel 3.

42. Statue ofUberty, plan ofLevel 2.

52

43. Statue ofLiberty, plan of colonnade.

FoLds~

aodles & aLoes

or reduction to proportional measure is characteristic of the colossus. Unlike sculpture, the discipline of architecture is founded on the drawing of a thing before its existence. It is the secondary, or what Robin Evans refers to as the alterior, status of architectural description that is resisted in the Liberty's plans and sections. 33 Its geometric coordinates come after, and are thus compliant to, the thing they describe. The geometries that incise the colossal are therefore pliant and supple. The colossus is a body that cannot be reduced to its original size or simplicity, a body that resists the proportional coordination of an anthropomorphic organism. In the Statue of Liberty, the architectural quality (other than firmness or structure) that distinguishes the colossus from sculpture is an aleatory commodiousness within the interior. The occupation of the folds of the dress, the blades of the crown, the strands of the hair, the muscular contours of the outstretched arm, and the profiles of the lips, nose, eyes, ears, chin and forehead is neither accidental nor anthropomorphic, but results from unpredicted affiliations between a network of disparate subsystems that make contingent connections between a multiplicity of spaces.

stranded sears Tower I have applied this alternative alliance between a suppler geometry and a body without a single organization to an architectural project first developed in response to an ideas competition for the city of Chicago in September of 1991; the project should be

MuLtLpLLCLtoUS and

Inor~anLc

BodLes

53

seen as a preliminary experiment and not as the full realization of the ideas presented here. The Stranded Sears Tower attempts to generate a multiplicitous urban monument that internalizes influences by external forces while maintaining an interior structure that is provisional rather than essential.

In

Chicago and cities throughout the United States, the corporate office tower has been the primary vehicle for innovations in urban monumentality. This project attempts to reformulate the image of the American monument by reconfiguring the

44. Statue of Uberty, typical armature diagram of secondary structure of skin.

existing dominant icon on the Chicago skyline and the tallest free-standing building in the world: the Sears Tower. The iconic status of the existing Sears Tower arises from its disassociation from its context. The building establishes itself as a discrete

c

and unified object within a continuous and homogeneous urban fabric. My project, by contrast, affiliates the structure of the tower with the heterogeneous particularities of its site while preserving aspects of its monumentality: laying the structure into its context and entangling its monolithic mass

45. Statue of Uberty, typical shapes of horizontal bars.

with local contextual forces allows a new monumentality to emerge from the old forms. 34 In "The Orders

ofSimulacra" Jean Baudrillard described

a new paradigm for the contemporary office tower in the United States." The old paradigm of competitive verticality has been supplemented with a desire not only for excessive size but also for excessive numbers. The double identity of the twin towers of the World Trade Center in New York innaugurated this

• • • • 46. Statue of Uberty, typical shapes of vertical bars.

54

FoLds, aodLes & aLoBs

tendency toward multiplicity. The duplication of the towers reinforced the self-identity of the whole, as the identical twins merge into a singular monumental structure. The response of the Sears Tower to this new paradigm was not only to exceed the height of the twin towers but to exceed their duplicity. The Sears Tower internalizes its multiplication by dividing itself into a nine-square tower that its engineer, Fazlur Kahn, has termed the "bundled tube." Where the identical twin towers duplicate, the differentiated Sears Tower proliferates. 36

47. Sears Tower, plan ofLevel I.

48. Sears Tower, exterior view.

The 225-foot square footprint is made up of nine 75foot square tubes, or towers; two of these tubes are 650 feet long, two are 860 feet long, three are 1,170 feet long and the remaining two are a record 1,450 feet long. Each tube is striated into five structural bays yielding another 25 tubes per tower. Each of these 225 independent structural bays is subdivided into three five-foot-square window bays yielding another ninesquare tube within each structural bay, for a total of 2,025 tubes. These nine-square tubes are the essential structure of the Sears Tower and the spatial type of the bundled tube. In the reformulation of the bundled tube, the whole organization of the tower (the ninesquare type) undergoes a two-fold deterritoriallzation as the Stranded Sears Tower internalizes particularities and extends its influence outward into the city. The nine-square persists merely as an organ, a provisional structure within a multiplicity of structures. The tower acts as if it were a strand: a collection of fibers or filaments twisted, plaited, or laid par-

MuLtlpLlCltous and rnorganlc aodles

55

allel to form a unit. This strand is both a system of interwoven filaments and a singularity capable of further twisting or plaiting into a larger or more complex yarn, thread, rope, or cordage. The project reformulates the vertical bundle of tubes horizontally along a strand of land between Wacker Drive and the Chicago River adjacent to the existing Sears Tower. The nine contiguous tubes accommodate themselves to the multiple and often discontinuous borders of the site.

The relations between

tubes are not exactly parallel but more or less parallel. These supple deflections engender affiliations with particular local events - adjacent buildings, landforms, sidewalks, bridges, tunnels, roads and river's edge - that would have been repressed by a more rigid and reductive geometric system of description. Although the increments of the floor plates are generally oriented perpendicularly to the surface of the drawings, the particularities of the site often deflect any single ideal orientation in favor of multiple oblique orientations. The deformations of twisting, plaiting and bending are not accidental but unpredicted, as they result from the combination of over two thousand bundled tubes with local conditions. The resulting image is neither monolithic nor pluralistic but belongs to the now supple and flexible internal order of the bundled tube that is differentiated by the

external forces of the river's edge, the city grid, and the vectors of pedestrian and transportation movement. The bundled tube is a possible paradigm for a multiplicitous monument.

It is an assembly of

49. Stranded SearsTower, view

ofmodel.

FoLds

l

aodles

&

aLobs

microsystems that constructs an icon that is provisional. Examined closely, the unified image of the monument unravels into heterogeneous local events. Irreducibility to any single type and the potential to participate with external systems are the characteristics of a stranded urbanism. The Stranded Sears Tower is neither discrete nor dispersed, but rather turns from any single organizational idea toward a system of local affiliations outside itself.

50 - 52. Stranded Sears Tower, view ofmodel.

MuLtlpLlCltous and rnorganlc aodles

endnotes I. Georges Bataille, "Architecture," Documents 2 (May 1929): 53. 2. RudolfWittkower, Architectural Principles in the Age of Humanism (New York, 1962). Peter Eisenman's discovery and subsequent invention ofTerragni employs a similar strategy. The instant that these architects speak secrets for Rowe and Eisenman is the precise moment when new spatial and theoretical types originate. 3.Wittkower invents a new origin, after the fact, for the Palladian villas: "Once he had found the basic geometric

pattern for the problem 'villa: he adapted it as clearly and as simply as possible to the special requirement of each commision. He reconciled the task at hand withthe 'certain truth' of mathematics which is final and unchangeable. The geometrical keynote is, subconsciously rather than consciously, perceptible to everyone who visits Palladio's villas and it is thisthat gives hisbuildings theirconvincing quality." See Wittkower, Architectural Principles, 72. Return inquiry or question en retour was developed by Jacques Derrida to describe the founding of an origin for geometry after the fact of its beginning. "UkeRuckfrage, return

inquiry is asked on the basisof a first positing. From received and already readable document, the pOSSibility is offeredme of askingagain, and in return, aboutthe primordial and final intention of what has been given me by tradition." See Jacques Derrida, Edmund Hussserl's Origin of Geometry: An Introduction, trans. John P. Leavey, Jr. (Lincoln, Neb., 1989), 50. 4. Colin Rowe, "The Mathematics of the Ideal Villa," in The Mathematics of the Ideal Villa and Other Essays (Cambridge, Mass., 1976). 5.A similar system of variation to underlies the definition of species in morphological discourse. Perhaps the most interesting example is William Bateson's argument, published in the I980s, that evolutionary development proceeds through both continuous and discontinuous variation. He held that variations precede adaptive developments or any single line of morphological progress - a position that contributed to his characterization by his Darwinian critics as a "theorist of monstrosities." See William Bateson, Materials for the Study of Variation:Treated with Especial Re&ard to Discontinuim' in the Origin of Species (Baltimore, 1992) first published in London and New York in 1894.

6. "Perhaps these werethe dreams of Virgil. . . And it is pos-

57

sibly the fundamentals of this landscape, the poignancy of contrast between the disengaged cube and the appearance of unimpaired nature, which lie behind Le Corbusier's Roman allusion." Rowe, Mathematics of the Ideal Villa, 3. 7."Thehuman breastshouldhavebeen furnished withopen windows, so that men might not keep their feelings concealed, but have them open to view... However, since they are not so constructed, but are as naturewilled them to be, it is impOSSible formen,while natural abilities are concealed int the breast, to forma judgementon the quality of the arts which is thus deeplyhidden." Vitruvius, The Ten Books of Architecture, trans. Morris Hickey Morgan (New York, 1960),69.

8. "Every organism consists of a highly ordered complex of structures, the majority of which are hidden in its interior .. . This exclusion of the interior of my system from direct investigation is an operational limitation to all research. In biology it means,that the interior of any organism can not be investigated without prior destruction of that organism." Ewald R.Weibel and Hans Elias, Quantitative Methods in Morphology (Berlin, 1967), I. 9.Vitruvius, The Ten Books of Architecture, 72. 10. Derrida, Husserl's Qrigin of Geometry, 123. I I. Denis Hollier, analyzing Bataille, argues that "architecture, consequently, has no "created" model; it must create this. It follows an archetype, but one that does not exist independent of itself. Far more importantly, it must itself produce this archetype. Which is how the unity of plan between architecture and nature is guaranteed. By constituting itself as a microcosm, architecture delineates the world and projects the shadowof the greatarchitect behind it Without architecture the world would remain illegible. Natureisthe archetype of architecture onlyinsofar as architecture is the archetype of nature. It is less that architecture is cosmic than that the cosmos itselfis architectured." See Denis Hollier, Against Architecture:The Writings of Georges Bataille (Cambridge, Mass., 1989), 35. 12.Vitruvius, The Ten Books, 70. 13. In conversation, Jeffrey Kipnis has described a formal strategy for phenomenological reduction through variation in the search for the ideal proportion of a nose. If multiple photographs of faces, at the same scale, were placed one upon the other and all of the variations between the particular noses were cancelled, only the form of the ideal nose would remain.The ideal pro-

FoLds, aodles

53. Stranded Sears Tower, plan and section of tube A.

56. Stranded Sears Tower, plan and seaion of tube D.

54. Stranded Sears Tower, plan and section of tube B.

57. Stranded Sears Tower, plan and seaion of tube £

55. Stranded Sears Tower, plan and seaion of tube C.

58. Stranded Sears Tower, plan and seaion of tube F.

&

aLoBs

MuLtLpLLcLtous and rnorganLc eodLes

59

59. Stranded Sears Tower, plan and section oftube G.

62. Stranded Sears Tower, plan of ground level.

60. Stranded Sears Tower, plan and section oftube H.

63. Stranded Sears Tower, plan of subterranean level.

6/. Stranded Sears Tower, plan and section oftube I.

60

portions of the nose would never exist in any single nose, yet they would become the transcendent order hidden in all noses in general. This is very similar to the photographic technique of "composite photography developed by Francis Galton. For further discussion of phenomenological reduction, see Derrida, Husserl's Origin of Geometry, 123-127. 14. Jurgis Baltrusaitis, Aberrations: An Essay on the Legend of Forms. trans. Richard Miller (Cambridge, Mass.. 1989), I-57. 15. D'Arcy Wentworth Thompson, On Growth and Form (Cambridge. 1961). 268-325. 16. Luce Irigaray describes how static characteristics are given precedence in science over characteristics of fluidity. This inattention to fluids is linked with the proposition of "formal types" and other "symbols of universality, whose modalities of recourse to the geometric still have to be examined." She argues that "one must know

howto listen otherwise than in good formes) to hear what it says. That it is continuous, compressible, dilatable, viscous, conductible, diffusible ... That it is unending, potent, and impotent owing to its resistance to the countable, that it enjoys and suffers from a greater sensitivity to pressures; that it changes - in volume or in force, forexample- according to the degree of heat; that it is, inits physical reality, determined by friction between two infinitely neighboring entities - dynamics of the near and not of the proper, movements coming from the quasicontactbetween two entities hardly definable as such (incoefficient of viscosity measured in poises, from Poiseulle [sic], and not energy of a finite system." Luce Irigaray. This Sex Which is not One (Ithaca, 1985), III.

17."Husserl speaks of protogeometry that addresses vague, in other words, vagabond or nomadic, morphological essences. These essences are distinct from sensible things, as well as from ideal, royal, or imperial essences. Protogeometry, the science dealing withthem,is itselfvague, but anexact yet rigorous (essentially and not accidentally inexact). The circle is an organic, ideal, fixed essence, but roundness is a vague and fluent essence, distinct both from the circle and things that are round (a vase, a wheel, the sun). A theorematic figure is a fixed essence, but its transformations, distortions, ablations, and augmentations, all of its variations, form problematic figures that are vague yet rigorous, 'lens-shaped', 'umbilliform' or 'indented." Gilles Deleuze and Felix Guattari, A Thousand Plateaus: Caj;>italism and Schizoj;>hrenia, trans. Brian Massumi (Minneapolis, 1987),367.

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18.The idea of deterritorialization resonates with Elias Canetti, Deleuze and Guattari, and Rene Thom as it is a method of stabilizing a collection of individual elements or intensities that remain open to influence through dynamic interactions and exchanges. Canneti's descriptions of crowds and packs developing behaviors (growth, movement. protection) that are irreducible to anyone of the individual members, Deleuze and Guattari's description of symbiotic, coevolutionary and involutionary development. and Thorn's concept of retroactive smoothing. all perform a kind of expansion of territory and stability by opening a heretofore internal system to external forces. See Elias Canetti, Crowds and Power (New York. 1984), Deleuze and Guattari, A Thousand Plateaus, and Rene Thorn, Structural Stability and Morj;>hogenesis, trans. D.H. Fowler (Reading. Mass.• 1975). 19. Deleuze and Guattari propose that a body is merely an affiliation of organs (what in other contexts they refer to as "free intensities") that lacks a global organization capable of unifying the disparate elements harmoniously. Such an assemblage is constructed by vicissitude: unpredicted external events put these free elements into a multiplicity of possible relations. (Hence the play in the title of their book on Spinoza's idea of "one-thousand vicissitudes.") See their "November 28. 1947: How Do You Make Yourself a Body without Organs?" in A Thousand Plateaus. 149-166.

20. "In fact, for academic men to be happy, the universe would have to take shape. All of philosophy has no other goal: it is a matter of giving a frock coat to what is, a mathematical frock coat." Georges Bataille, "Formless," in Visions of Excess: Selected Writings. 1927-1939, trans. and ed. Alain Stoekl (Minneapolis, 1985). 3 I. 21. The suppler "protogeometries" of geology, geography, morphometry, anatomy, fluid dynamics and other sciences that model particular, temporal and incomplete bodies that cannot be wholly reduced are examples of such "anexact yet rigorous" descriptions. Sanford Kwinter posits the best example to my knowledge of a particularly geologic methodology for analyzing architectural systems of organization in his essay on Peter Eisenman's Aronoff Center. Sanford Kwinter, "The Genius of Matter." in Peter Eisenman Frank Gehry (New York, 1991). 22. Gilles Deleuze, Bergsonism (New York, 1991), 38. 23. Hollier, Against Architecture, 5.

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24. What Hollier will not allow is that architecture might provide a sensuous sign for commodity and firmness; that structural and functional materiality is signified by architecture in its orders, outside of itself already; or that structure and shelter are not natural to architecture but are signified by it. See Hollier, Against Architecture, 10.

32. We might look to Erwin Panofsky's description of the arbitrary, more or less architectural gridding of the Egyptian body as compared to the humanist practice of modular measure. See Erwin Panofsky "The History of the Theory of Human Proportions as a Reflection of the History of Styles," in Meaning in the Visual Arts (Chicago, 1955),64-68.

25. Plication describes the proliferation of new structures either by the division of a single organism into multiple organisms, as in the example of the flatworm, or by the combination of two or more disparate organisms into a composite organism, as in symbiosis.

33. Robin Evans, "Architectural Projections," in Drawing as Idea (Cambridge, Mass., 1990).

26. R. Chandebois, "Histogenesis and Morphogenesis in Planarian Regeneration," in Monograj;>hs in Develoj;>mental Biology, vol. 2 (Basel, 1976). 27. D'Arcy Thompson, On Growth and Form, 321. 28. Deleuze and Guattari, A Thousand Plateaus, 255. 29. Cited in Marvin Trachtenberg, The Statue of LibertY:The Centenary Edition of a Classic History and Guide (New York, 1986),44.

34. Here, the relations to contexts imply connections by vicissitude and alliance. The building becomes involved with adjacent particularities. This differs from a familiar argument of contextual ism that is based on the evolution of a building from the general characteristics of an urban fabric. For a further discussion, see my "The Folded, the Pliant and the Supple" in this collection.

35."Buildings are no longer obelisks, but lean one uponthe other, no longer suspicious one ofthe other, like a statistical graph. This new architedure incarnates a system that is no longer competitive, but compatible, and where competition has disappeared for the benent of the correlations." Jean Baudrillard, Simulations (New York, 1983), 135-136.

30. Jacques Derrida, The Truth in Painting (Chicago, 1987),120. 31. Derrida distinguishes between two kinds of lines in proportion. Cise describes the form of a line or "incisement" and size describes the measure of that form. In the case of the colossus, there is initially neither an implication of incisement (it is amorphous or formless) nor an implication of size (it is vast). See Derrida, The Truth in Painting.

36. "The basis ofthe Sears Tower is the bundled tube. In the Sears Tower, ninecontiguous tubes,in essence ninetowers seventy-nve-feet square, make up the nfty storybase of the building. Their tubes are interlocked; thus each tube helpsto support its neighbor." Fazlur Kahn, cited in David P. Billington, The Tower and the Bridge:The New Art of Structural Engineering (Princeton, 1983), 246.

The Renewed Novelty of symmetry

The title of this text attempts to combine two familiar architectural concepts in a slightly unexpected way. I While symmetry has usually been understood in architecture as an underlying organization upon which variations are ordered, it will intead be argued here that novelty is the organizer of symmetry. 2 Rather than criticize reductive theories of eidetic types, this text will outline a generative theory of complex variation involving a reappraisal of vague organizations and anexact yet rigorous geometries. Similarly, idealization and differentiation have been understood as the constituents of any concept of organization based on repetition and previous theories of variation have structured their relationship around the concept of iterative reduction to ideal essences. The design for the Cardiff Bay Opera House will, in contrast, be described through processes of repetition that are evolutionary, flexible, and proliferating. Alfred North Whitehead has described evolution as the "creative advance into

novelty." The opera house project develops techniques of repetition that incorporate two kinds of evolutionary differentiation: endogenous (the unfolding of unmotivated internal directives toward diversity) and exogenous (the infolding of external constraints towards adaptability). This dynamic combination of internal directed indeterminacy and external vicissitudinous constraint leads to organizations that cannot be reduced to any ideal form or single cause. Complexity is an integral, generative, and stabilizing characteristic of these twofold systems of organization. In order to theorize these differential organizations, new con-

First published in Assemblage. no. 26.

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cepts of order and difference must be developed that are distinct from received notions of typology and variation.

I. Human (inger mutation analysis by William Bateson, 1894. This is one of two possibilities for mutations of the human hand at the site of the thumb. What is both disturbing and beautiful about this example is that the mutation replaces the asymmetry of the opposed thumb with a higher level of symmetry. In place of the thumb, the four (ingers are mirrored by an additional four (ingers.

Novelty, rather than some extnnsic effect, can be conceived as the catalyst of new and unforeseeable organizations that proceed from the interaction between freely differentiating systems and their incorporation of external constraints. Novelty and order are related in an autocatalytic rather than binary manner, as they are simultaneously initiated from a constellation of vicissitudes. 3 This regime of dynamical organizations should be understood as neither neo-Platonist nor neo-Darwinist since it is not merely reducible to external or internal constraints. The resistance to both fixed types and random mutation makes flexible, adaptable, emergent, and generative systems a provocative basis for. contemporary techniques of organization and explorations of dynamic architectural concepts of symmetry. The competition brief for the Cardiff Bay Opera House was explicit about two expectations: first, that the project have a symmetrical horseshoe opera hall and, second, that the primary urban concern be a strong yet innovative relationship to the historic site of the Oval Basin. Initially, it seemed odd that in 1994, the authors of the,competition would both ask for a new architecture and legislate formal symmetry. The dilemma inherent to these seemingly contradictory constraints became the catalyst for the project. After rejecting both the revolutionary potential of refusing

The Aenewed NoveLty of symmetry

these requests and the reactionary possibilities of supplicating to a predefined catalogue of Beaux-Arts partis, our design team decided to take a monstrously evolutionary position by incorporating both oval forms and symmetry so thoroughly that they could proliferate wildly in unexpected ways.

In other

words, the competition brief's strange coupling of requests for newness and symmetry initiated the present discussions of novelty and symmetry. The project became an experiment in the development of new concepts and techniques for contextualism. The competition organizers were emphatic in their desire for an institution that could be understood as absolutely continuous with its context while having a distinctly new identity. They hoped to reconfigure the defunct industrial waterfront as a cultural and recreational center while maintaining the urban fabric and atmosphere of the shipyards. We therefore attempted to evolve a new identity that could be understood as emerging from its urban, institutional, temporal and cultural setting.

To avoid the mere

reproduction of the existing context, unification was approached through processes of differentiation rather than simplification, through mutation rather than duplication. We defined the new in architecture as being unattributably different yet continuous - an architecture that cannot be localized within any previous context but has been sponsored nonetheless by existing orders.

Like a monstrosity that,

despite its difference, can still be understood as inhabiting the familiar class of the normal, the project

2. Human thumb mutation analyses by Bateson, 1894. This is the second of two possibilities for mutation about the human thumb due to a loss in information. In this case, the mutation exhibits a higher level of symmetry than the norm. Within the asymmetry of the hand, the thumb is symmetrically mirrored by an extra opposed thumb, adding a second level of local symmetry.

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3. Coleoptera beetle leg mutation analysis by Bateson, 1894. A fused condition of a normal right leg bearing an extra pair of right and left legs.

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attempted to turn the indigenous information of its context into an alien novelty. In the design, the context was understood as a gradient field of generalized and unorganized information rather than as a repository of fixed values, rules and codes. Our tactic was to treat the rusting technological husks of the shipbuilding industry, such as the Oval Basin, as the chrysalis for the incubation of a new urban structure. The maintenance of the Oval Basin and a compulsion for symmetry became the directives for differential growth. The progressive assimilation of differences within this system led to an emergent organization that was unpredictable at the outset and irreducible at its conclusion to either the external constraints of its context or the internal parameters of the competition program. After determining that the judges and authors of the project were very serious in their desires for symmetry, we specified a series of organizational guidelines for the project. The parameters of the project involved an adherence to rules of symmetry at all scales. Directed indeterminate growth became the motto for this approach, where a series of intuitions about abstract organizations (such as predilection for oval basins and the symmetrical disposition of forms) were formulated as directives that would be triggered and guided by external constraints. We combined these intuited parameters with the contingencies of the unorganized context and began to study the generative fields that ensued as we organized the context. These generative fields emerged from the dou-

The Aenewed NoveLty of symmetry

ble constraints of internal directives and external vicissitudes. During the design of the project, we became increasingly interested in theories of symmetry and discontinuous variation developed by William Bateson in 1894. 4 What we found most striking about Bateson's Rule is the relationship between order and variation and homogeneity and heterogeneity. Bateson's insight, which has since been reaffirmed by his son Gregory, is that a loss of information is accompanied by an increase in symmetry. This seems quite plausible given that "iterative reduction through phenomenological

variation" involves the elimination of difference (or more technically, what would be referred to as"alterations of deformation") toward a reduced "eidetic type." Here, the terms information and difference are almost interchangeable. Homogeneity is understood as sameness or lack of difference, while disorganization is associated with an absence of difference (information) and therefore of symmetry. In this way, difference, information, and organization are related. Gregory Bateson has gone so far as to define information as "the difference that makes the difference." 5 William Bateson did not arrive at this theory of symmetry through classical reduction to types but rather by attempting to theorize processes of variation outside of their defective relationship to a norm." His views on symmetry are explanatory rather than taxonomic. For Bateson, monstrosities and mutations are specific polymorphic expressions of growth and

4. Coleoptera beetle leg mutation analysis by Bateson, 1894. Examples of mirror symmetry in limb appendages such as this are the foundation for what is now referred to as "Bateson's Rule." The additional legs are aligned in a cascading relationship based on planes of mirror symmetry orientation between duplicate limbs. The normal limb is opposed along a mirror plane by an extra right limb, which is then opposed along a mirror plane by an extra left limb.

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variation responding to particular temporal and environmental conditions. This theory, along with Francis Galton's "multiple positions

oforganic stability,"

is tem-

poralized by Conrad Waddington's concept of the epigenetic landscape. 7 Against Darwin, Bateson postulated a theory of "essential diversity" rather than

"random mutation" and organization through "discontinuous variation" rather than "gradualism." As a teratologist, he realized that even monstrosities 5. Machine constructed by Bateson, 1894. A mechanical device showing the relations of secondary symmetry of normal right (R), extra left (SL), and extra right (SR) legs. The normal right leg is attached to the circular base about which it rotates on center. The orientation of the normal leg is registered in relationship to the beetle's body using a wedgeshaped block. The extra left and extra right legs rotate at the center of this block. At the base of each leg is a gear that translates the rotation of the normal leg through each of the extra legs. For example, if the normal right leg is rotated counterclockwise forty degrees off perpendicular to the body (using the wedge-shaped dial), that rotation will be translated through the gears into a fortydegree clockwise rotation in the extra left leg and a fortydegree counterclockwise rotation in the extra right leg.

adhere to recognizable forms of those classified as normal and they therefore might lead to a theory of order that does not treat the variant as merely contingent or extraneous. He argued that variant forms are as definite and well formed as typical forms. The variations of monstrosities led him to a two fold theory of diversity and differentiation. Like the earliest experimental morphology studies of Hydra and Planaria by Abraham Tremblely, Bateson looked for typicality in the atypical.8 In his classic example of the two possible mutation of the thumb, Bateson demonstrated that the monstrosities display higher degrees of symmetry than do normal hands. On one hand, the normal asymmetry between four fingers and the thumb is replaced by two groups of four fingers reflected along a mirror axis. On another hand, nested within the normal asymmetry of the thumb and four fingers is a second level of mirror symmetry between the normal thumb and an extra thumb. The existence of mutations that exhibit higher degrees of symmetry than the norm led to contradictory explanations. The taxonomic

The Aenewed NoveLty of symmetry

hypothesis locates extra information at the point of mutation in order to explain the increase in symmetry and the decrease in heterogeneity. Bateson proposed an alternative explanation whereby the decrease in asymmetry and the increase in homogeneity was a result of a loss of information. He argued that where information is lost or mutated, growth reverts to simple symmetry. Thus symmetry was not an underlying principle of the essential order of the whole organism, but was instead a default value used in cases of minimal information. Organisms are not attributed to any ideal reduced type or single organization; rather, they are the result of dynamic non-linear interactions of internal symmetries with the vicissitudes of a disorganized context. These contexts become

"generative fields" once they are organized by flexible and adaptable systems that integrate their differences in the form of informational constraints. For these types of morphological processes Bateson invented the term "genet-

ics." Genes are not generators but modifiers or regulators that are intermittently applied during growth and regeneration. In the case of Bateson's Rule, information regulates simple mirror symmetries by introducing heterogeneity and difference as a form of organization. Gregory Bateson qualifies the idea of

"information selecting asymmetry" as "information preventing symmetry." Genetic information excludes potential default positions of stability, like a governor or rheostat that excludes alternative possible states through feedback. Genes do not provide a blueprint in this theory but rather guide development at critical junctures by excluding simple default organizations. By differentiating in this manner, predetermined potentials are replaced with novel possibilities that are initiated by general external information and integrated within specific internal parameters. The modifying information that generates heterogeneity was explained as a specific response to perturbations that could be either environmental or genetic. Symmetry breaking is therefore a sign of the incorporation of information into a system from the outside in order to unfold its own latent diversities. Contexts lack specific organization and the information that they provide tends to be gen-

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eral. In this regard, contexts might be understood as entropic in their homogeneity and uniform distribution of differences. Adaptive catalysts configure this information by breaking their own internal symmetry and homogeneity in order to differentiate heterogeneously.

Gregory Bateson gives the example of an

unfertilized frog's egg that develops a plane of bilateral symmetry as an embryo depending on the point of entry of a spermatozoon. Bateson substituted this point of entry by pricking the egg's surface with a camel's hair, along which a plane of bilateral symmetry grew. In this example, the message from the context is relatively general, while the internal context into which his indefinite information is received must be exceedingly complex. While the external information is general, the response that it triggers is specific. The egg initially exhibits a high degree of simplicity and radial symmetry. As it unfolds in an open relationship with its environment, it breaks symmetry, differentiates, and becomes more complex and heterogeneous because of its feedback with exigencies and constraints outside of its control. Symmetry breaking is not a loss but an increase in organization within an open, flexible, and adaptive system.

Symmetry breaking from the exact to the anex-

act is the primary characteristic of supply systems. These flexible economies index the incorporation of generalized external information through the specific unfolding of polymorphic, dynamic, flexible and adaptive systems. Symmetry is not a sign of underlying order but an indication of a lack of order due to an absence of interaction with larger external forces and environments. Given this complex conceptualization of endogenous and exogenous forces, deep structure and typology are just what they seem to be: suspect, reductive, empty and bankrupt. An alternative is an internal system of directed indeterminate growth that is differentiated by general and unpredictable external influences, producing emergent, unforeseen, unpredictable, dynamic and novel organizations.

The Aenewed NoveLty of symmetry

€ndnotes I. I would like to thank Jesse Reiser for coining this term in reference to the design of the Cardiff Bay Opera House Project. 2. I have dealt with the relationship between order (of which symmetry is perhaps a primary example) and variation in more detail elsewhere. See my "New Variations on the Rowe Complex" and "Multiplicitous and Inorganic Bodies" in this collection.

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See Gregory Bateson, "A Re-examination of Bateson's Rule" in SteRs to Art Ecology of Mind (New York, 1972), 379-396.

6. "This much alone is clear, that the meaning of cases of complex repetition will not be found in the search for an ancestral form, which, itself presenting the same character; may be twisted into the representation of its supposed descendant. Such forms may be, but in finding them the real problem is not even resolved a single stage; for from whence was their repetition derived? The answer to this question canonlycomein a fuller understanding ofthe laws ofgrowth and ofvariations which are as yet merely terms."

3. See my "Architectural Curvilinearity: The Folded, the Pliant and the Supple in Architecture" in this collection.

William Bateson, "The Ancestory of the Chordata," in The Scientific PaRers of William Bateson, 2 vols. (Cambridge, 1928).

4. William Bateson, Materials for the Study of Variation: Treated with ESRecial Regard to DiscontinuitY in the Origin of SRecies (Baltimore, 1992; 1894).

7. Gerry Webster, "William Bateson and the Science of Form," in William Bateson, Materials for the Study of Variation (Cambridge, 1928), xlvii.

5. I would like to thank Mark Rakatansky for bringing to my attention Gregory Bateson's text that describes the connections between William Bateson's theories of symmetry and genetics and more recent concepts of feedback, cybernetics, negative entropy, and complexity.

8. Sylvia Lenhoff and Howard Lenhoff, Hydra and the Birth of EXRerimental Biology - 1744: Abraham Trembley's Memoirs Concerning the Natural History of a TYRe of Freshwater PolYR with Arms ShaRed Like Horns (Pacific Grove, Ca., 1986).

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The Renewed NoveLty of symmetry

6-1I.Waters edge. The site's adjacency to the Oval Basin and the waterfront's history of boat building and repair suggested that this edge be a critical feature of the projea. The coastline was analyzed at various scales forself-similarit and repetition. At numerous scales, a pattern of gastrulations was discovered whrethe water's edge was captured by the land as rivers, bays, and harbors. Thesecascading shiftsin scale include the Atlantic Ocean, Cardiff Bay, the innerharbor; the gravingberths, and the Oval Basin.

12.One generation of oval branching. The site's proximity to the northeastern edge of the Oval Basin allowed the water's edge to be brought intothe site through the differential repetition of the Oval Basin. The generative diagram forthe proliferation of ovals was a twothirds-scale oval aligned on centerwiththe given site area. A secondary branch was located perpendiculary at one-third scale.

13.Two generations of oval branching. A secondgeneration with branches following the same rules of decreasing scale

and mirror symmetry.

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14.Oval branching within site. This internally linear system wsa controlled or modified by general information from the context Ovals werestretched, turned, and aligned in order to exploit any near connections. Oncealigned, they were frozen in terms of future branching. This strategy allowed for an internally directed system (the branchingovals) to be modified and regulated by a generalized context so that the resulting configuration was attributable neither to the contextitself(as it was introduced as a set of internal directives) nor to the system itself(as it was modified by the unrelated, external parameters of the context). Ovals were stretched, turned, and aligned to connect with adjacent streets, building edges, and views. Oncealigned, each connection was frozen in terms of future branching. The perimeter of this figure became a new waterline, wherethe surface of the site was flooded by a swamplike waterfront space.

15.Program alignments. The realignment and deformation of the initial volumes are based on the programmatic adjacencies of the foyers, opera hosue, stages, shops, loading, dressingrooms, and rehearsal rooms.

16.Lathing and smoothing of oval plan forms. The branching system of ovals are lathedabouttheirindividual axes into volumes. These volumes are smoothedand realigned to reflect the programmatic constraints of operahall, main stage, rearand sidestages, rehearsal rooms, and foyers. Both the adjustment to program and the differential faceting based on scale are reflected here.

The Renewed NoveLty of symmetry

17.Four polyp types: four-sided, six-sided, eight-sided, and twelve-sided. The complexity of the faceting of the volums is related to theirsurface area. The smaller volumes are four-sided and simpler than the largest volumes that are twelve-sided so that they can remain relatively smoothand be deformed more uniformly.

18.Structure & Surface. Uke a ship's hull, the volumes are structured on theirsurface withtransfer beams and ridge beams that extend along theirlength. The ridge beams are supported by columns on center at each end of the volume. The transfer beams allow the volumes to be supported at arbitrary alignments to the portalized walls that supportthem. The volumes are enclosed with a continuous surface that is faceted in one direction and open at both ends. The skin is constructed of metal panels similar to steel ship-building techniques.

19.Model.

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20. Sitestriations. A structure of ~n walls was developed to supportthe Opera House volumes above the sunken area of the site. This IIswampll edge was rakedwith perpendicular lines that followed several existing site alignments, including the light rail line, the building of the edge of the Oval Basin, the existing edge of buildings, and the highway underpass.

21.Alternating alignments across four striation patterns. The structural ~ns werealigned along these intersecting striation patterns on ten-meterintervals. The walls followed an alignement until an intersection, at which pointthey branched. On crossing an alignment parrallel to a previous orientation a secondary branch was originated.

22. Boatdry dock section. Due to the affinity that was developing between the polypII-like -volumes and the steel-hulled boatsthat historically occupied the site,the analogy of the "graving dockll was adopted for the relationship of the building to the ground. This section diagram was abstracted and exploited both urbanistically and structurally. The Opera House interior is contained in the oval volumes that are analygous to the hull, which is supported by a provisionaillcradiell-like structure. This entire systemis partially sunkeninto the site where the three-hundrd-ear parking garage is located half in and half out of the ground. The Opera House volumes are approached by a series of ramps.

The Renewed NoveLty of symmetry

23. Perspective ofpolyp volumes. Showing the oval volumes ofthe Opera House interior to be cladin metal sheeting. The steel-clad volumes are the only environmentally closed spacesin the project

24. Perspeaive ofportalized ~n walls. Showing the sloping ofthe ground lane down intothe sunken parking area; the sloping ofthe struaurolportalized ~n walls from the Oval Basin to the height ofthe contextbuildings.

25. Perspective ofroofmembrane. Showing the lightweight fabric structure that stretches across the buildable site area. The buildable site area as de~ned by the briefis covered by a translucent tensile membrane that would protea the spacesbetweenstruaural ~ns from rain and snow. This membrane would also diffuse direa sunlight during the day and glow in the evening.

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prOBaBle GeOmetrLes· The ArchLtecture of wrLtLng Ln 80dLes In the last decade the attention of architectural designers and theorists has been primarily directed toward the descriptive geometries with which architectural space is written. To the extent that geometry is the preferred language for architectural communication, its interrogation has become the dominant form of writing in architecture. More precisely, the majority of both spatial and theoretical innovations in architecture have become increasingly dependent on geometric conflicts. These developments are superlatively described by Mark Wigley in his introduction to the Deconstructivist Architecture exhibition and publication as a conflict within and between forms.

I

Wigley's essay on architectural form

depends on the belief that geometric conflict presents a new form of writing. Architecture's recent investment in geometric conflicts can be seen as an internal response to the critique, by philosophy, that writing is essentially an "antiarchitectural gesture" defined against geometric purity. The interest in formal conflict positions Wigley and others on a common trajectory inaugurated by Robert Venturi with the publication of Complexity and Contradiction in Architecture in 1966. 2 Of the many similarities and significant differences between these theorists of formal conflict, the most important suggests that the now dominant practice of eliding cultural difference with formal conflict as a method for writing in architecture is becoming progressively suspect. Yet the exclusion of architecture from writing persists, demanding a further interrogation of geometry. If indeed geometric conflict is becoming bankrupt as an urban organizational model, what are the alternatives to the transgression of geometric order available to archi-

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tecture? First, an adequate definition of a practice of writing in architecture must be formulated, one capable of engendering the urban, cultural, and programmatic differences that have been previously exploited for their ability to generate geometric conflicts and contradictions. Architecture is described by philosopher Denis Hollier in Against Architecture as the discipline that resists the play of writing more than any other. Hollier opposes the ideal proportions of architectural order to the indeterminate, heterogeneous, and undecidable characteristics of "writing" as practiced by philosopher Georges Bataille.

HWriting in this sense would be a profoundly antiarchitectural gesture, a nonconstructive gesture, one that, on the contrary, undermines and destroys everything whose existence depends on edifying pretensions. . . . We propose to read Bataille here starting from this refusal, a refusal that produces the heterogeneity, in contrast to the continuity pursued by discourse as its ideal, that will be indicated by the term writing." 3 For Hollier, architecture's resistance to writing arises from two linked ideas inherent in any logic of proportion: the whole organism and exact measure. Hollier confirms that these two components of architectural proportion underwrite static, fixed forms in that "tne greatest motive for Bataille's aggressivity toward architecture is its anthropomorphism."4 Bataille locates in geometric proportion an anthropomorphism that is in essence architectural.

J. Shell structure aggregations

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Hit is obvious, moreover, that mathematical organization imposed on stone is none other than the completion of an evolution of earthly forms, whose meaning isgiven, in the biological order, by the passage of the simian to the human form, the latter already presenting all the elements of architecture. In morphological progress men apparently represent only an intermediate stage between monkeys and great edifices. Forms have become more and more static, more and more dominant. The human order from the beginning is, just as easily, bound up with architectural order, which is no more than its development." 5 The mathematics that underwrites such an exact classical geometry is impartial: no number is more or less ideal than any other. In response to that dilemma, architecture has historically identified pure forms that can be made to correlate with ideal bodies through symmetry and proportion. The moments where geometric exactitude is most vital to architecture are the instances where buildings are described as ideal, whole, complete, autonomous, and unified bodies. This tradition began with Vitruvius's description of proportion and symmetry in "Book III" of the Ten Books of Architecture.

"Proportion is a correspondence among the measures of the members of an entire work, and of the whole to a certain part selected as standard. From this result the principles of symmetry. Without symmetryand proportion there can be no principles in the design of any temple; that is, if there is no precise relation between its members, as in the case of a well shaped man'"

2. Le Corbusier's Maison Dom-ino typology.

3. Le Corbusier's Maison Citrohan typology.

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Since that time, the logic of the whole organism has been linked with the complete, pure forms of exact geometries in architecture. The static proportions of these forms are rejected by Bataille and Hollier in favor of a transgressive practice of writing against form. As writing is indeterminate, nonideal, heterogeneous, and undecidable, it is implicitly resisted by exact geometries. Exact geometries may render only those characteristics that can be reduced to ideal proportions. They promise a universally translatable and therefore absolutely fixed language for architecture, as their pure forms are written "once and for all." For instance, there is only one sphere for all cultures for all time: an infinite number of points on a shared surface equidistant from a single radius point. Ideal forms such as these must be reducible to eidetic mathematical statements. Eidetic forms are (I) exact in measure and contour, (2) visually fixed, and (3) identically repeatable. Architecture, as described by Bataille and Hollier, is eidetic: it is reducible, static, exact, fixed, proportional, and identically reproducible. This monumental characterization of architecture through its geometric conventions allows for the dialectical opposition of decidable geometric bodies and undecidable bodily matter. Hollier and Bataille are predominantly interested in architecture as a discipline against which writing can be defined. For their philosophy, architecture is refused as an ideal style of discourse constructed of arrested, static, complete forms against which writing stands. The best definition of writing that Bataille and Hollier can provide is that it is defined Against Architecture. The anti-architectural practice of writing does not arrest matter in fixed proportions; it respects and maintains 4. Random sections.

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incompletness, undecidability, amorphousness, and other vague characteristics. Therefore, any writing in architecture must begin with a geometry that does not reduce matter to ideal forms. Geometries that not only maintain but measure amorphousness in some form resist the definition of writing against architecture. Recently themes of writing in architecture have engendered an anti-architectural, transgressive bias for formal juxtapositions, collisions, fragmentations, and contradictions. The measurement and description of amorphous, fluid, flexible, open, non-ideal, non-eidetic, provisional, incomplete, indefinite, and irreducible effects is an alternative to the mere arrest of these qualities in conflicting forms. In "The

Mechanics

of Fluids,"

Luce Irigaray points to a distinct lack of attention to the

description of vital matter and fluids in the sciences and mathematics, as the exact measure of these kinds of matter is precluded by their mobility, fluidity, and mutability. 7 Bataille's proclivity for "base matter" along with his rejection of pure forms explains his definition of writing as an anti-architectural gesture; the exact, proportional, fixed, and static geometries, seemingly natural to architecture, are incapable of describing corporeal matter and its undecidable effects. This rejection may be taken as an invitation: rather than violating the inadequate stasis of exact geometries, writing in architecture must begin with an adequate description of amorphous matter through "anexaet yet rigorous" geometries. Since the publication of Edmund Husserl's Origin of Geometry in 1917 there has been considerable philosophical speculation surrounding the definition of anexact forms. Jacques Derrida and Gilles Deleuze and Felix Guattari in A Thousand Plateaus have articulated the characteristics of various proto-geometries that are 5. Sectioning randomly orientedobjectswith a single plane.

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neither exact nor inexact but "anexaa yet rigorous." 8 Without rehearsing the extensive philosophical discourse surrounding the development of the term an exact it is possible to describe its operative characteristics briefly. The distinctions between exact, inexact, and anexact geometries, although seemingly esoteric, are becoming critical to any discussion of new spatial organizations. Husserl distinguishes exact forms as those that can be reduced eidetically. Like the form of a sphere, they are not only precise but can be reduced completely. Conversely, inexact forms are described as those figures that cannot be fixed or reduced because their contours cannot be described. In interrogating Husserlian exact geometries, Irigaray, Derrida, and Deleuze locate in many of the "vague essences" of science both a measurable rigor and a resistance to ideal reduction. These "anexaet yet rigorous" forms can be described with local precision yet cannot be wholly reduced. These irreducible but precise geometries are typically associated with disciplines that are forced to develop models that must remain incomplete. For example, the geologic sciences of the earth cannot develop a single fixed model for the continuous transformation of matter. Therefore geologists employ what Husserl has referred to as "anexaa proto-geometries." Protogeometries are used to measure various contours before they are reduced to eidetic statements. These descriptions are rigorous, yet many resist being reduced to exact forms and are referred to as anexact. These proto-geometries are employed to describe local effects with a clarity not possible in alternative global systems, which would reduce these effects to inexactitudes. These descriptions are rigorous and precise (they are not inexact) yet lack unity and completion (they are not totalizing). Disciplines dedicated to the study of vital 6. OMA,Bibliotheque de France, axonometric, /989.

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matter (embryology, virology, biology, and geology to name a few) have recently been the first to develop convincing geometric descriptions of vague forms. Most importantly, the development of stochastic and probable geometries by these disciplines indicates that all geometries are not exact. The ability for these anexact systems to measure undecidable, mobile, and fluid behaviors without arresting their effects in reduced, fixed forms describes an open practice of writing that exists within the horizon of geometric rigor. As a consequence of recent biomedical image-processing technologies, biometrics, the measurement of biological objects, has recently developed the ability to accurately measure shapes and shape changes. Analyses of biometric shape changes typically employ irreducible, supple, deformable geometries to describe the incorporation of unpredicted external forces in the continuous morphogenetic development of form. The probable geometry of the biometric "random section" model will provide a specific example of supple measurement that already exists as an architectural device. As this essay focuses on only one of a manifold collection of techniques, I would suggest for further reading not only the canonic works of D'Arcy Thompson and Rene Thom but also Fred Bookstein's The Measurement of Biological Shape and Shape Change, which provide an extensive description of various other anexact and diffeomorphic geometries and their applications to organic matter. 9 A case study of the random section model of probable geometry will provide architecture with the possibility of writing volumetric indeterminacy within a 7. OMA, Bibliotheque de France, superposition

8. OMA, Bibliotheque de France, diagram

ofpublic space.

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precise and rigorous system of measurement: a system of serial transections along with related coefficients of size, shape, and orientation. In architecture this particular model first came to my attention in an essay by Kas Oosterhuis, adjacent to a seemingly unrelated series of Oscar Niemeyer sketches. 10 The use of this scientific diagram by an architect, in close proximity to Niemeyer's sketches, suggested a latent connection between orthographic rigor and amorphous organic forms. Upon further research I found that this system shared with architecture a practice of stereometric projection: as stereology (a term first developed by Hans Elias in 1961) is tithe study of three-dimensional structures of speci-

mens by examination of various two-dimensional images, usually of sections through it." II The difference between the orthographic techniques of architecture (which provide two-dimensional anterior descriptions of objects before their construction) and two-dimensional histological descriptions of the human body (which provide ex post facto two-dimensional measurements of shape and size to existing matter), is that architecture prefers to begin with ideal forms whereas materials science, food science, geology, astronomy, and the life sciences begin with the amorphous. A close examination of one of these probable or stochastic geometric models reveals that architecture's predilection for eidetic, exact forms precludes the description of flexible, fluid, or mutable programs and spaces. It is important to observe that these probable geometries occupy a provisional relationship to the matter they describe; they do not embody or symbolize anything. Geometry has classically occupied a foundational position in architecture,

9. Buffon's Needle Problem.

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and this tradition must certainly be overcome in order to exploit the effects of geometric probability. Architecture's orthographic plan and section projections are identical to the parallel serial transections employed in probable geometry, yet in the study of matter the events described between these sections are variable, indeterminate, and not reducible to ideal forms. Perhaps the first attempt by an architect to develop a provisional system of geometric transections to describe the unrelated contours of spatial, structural, and programmatic contents was by Le Corbusier in the I920s. In the serial parallel plan cuts of the Maison Dom-ino and the serial parallel section cuts of the Maison Citrohan, Le Corbusier attempted to develop structural and geometric systems that would be completely independent of the organization and functions of the buildings. In the biological practices of stereology these provisional cuts are referred to as "ran-

dom seaions." The geometric principle of Le Corbusier's Maison Citrohan is a series of parallel lateral sections. These lateral load-bearing walls allow for greater freedom in openings since they eliminate fixed columns and beams. Accompanying this freedom in penetrating the walls is the ability to place the floor slabs at virtually any level and slope. Inter-sectional volumetric possibilities multiply as the necessity for fixed columnsand beams is removed by these lateral parallel walls. The provisional deployment of rigid parallel transections increases the possible orientation, shape, and size of internal volumes. The planimetric freedom of the Domino and the sectional freedom of the Citrohan multiply the structural and pro-

I I. Estimating the volume to surface ratio from a point and intersection count

12. Estimation of curve length from the number of intersections with a grid of parallel lines.

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grammatic possibilities and combinations within the house. Le Corbusier revolutionized the architectural plane by arguing that it supported only one moment of the contiguous space that passed through it. Previously, architecture strove to represent all essential spatial characteristics on a transcendent, reduced plane. Erwin Panofsky, in the chapter "History

Reffection

of the History of Styles"

of the Theory of Human Proportions as a

in Meaning in the Visual Arts, poignantly

describes this architectonic logic: "Egyptian representations are planar because

Egyptian art renders only that which can de facto be presented in the plane; ... the Egyptians positively excluded the three-quarter profile and oblique directions of the torso or limbs." 12 Where Panofsky's reduced "geometrical plan" conveys information "incompletely yet in one image," Le Corbusier suggests an incompleteness that proliferates between images. In the Citrohan and Dom-ino types the two-dimensional intersections with the parallel walls are fixed while the spaces between those contours can only be described with probability. The flexibility and adaptability of structure and program in the Citrohan and Dom-ino organizations are intricately connected to this geometry of sectional regulation and inter-sectional probability. The urban, political, structural, programmatic, and spatial effects of the extension of the principles of the random section and random plan since their invention by Le Corbusier are suggested by the library projects of Rem Koolhaas. The development of the random section model, as it is known now in biometric science, originated with the development of the 'Needle Problem' by the celebrated naturalist Comte de Buffon in 1777. 13 The Needle Problem is a geomet13.Intersection of a spacecurve by planes.

14.linear analysis.

proBaBLe GeOmetrLes

ric model used to describe the probability of chance events. As the Citrohan and Dom-ino types multiplied the possibilities for programmatic and volumetric events between lateral walls, Buffon's Needle Problem describes a multiplicity of probable occurrences without reducing them to any single rule. Probability theory is typically attributed to the mathematicians Blaise Pascal (1623-62) and Peirre de Fermat (1601-65). But Jackob Bernoulli was the first to publish a treatise on probability theory in 1713, in which he described two types of probability, discrete and continuous. An example of discrete probability is the toss of a coin, whose symmetry permits one to state in advance that it will always land on one of two sides. Continuous systems, due to configurations of shape, may not state the possible positions of an object in advance. Therefore, an experimental series must be performed to establish the frequency of possible positions. With the assistance of a professional gambler, Buffon developed a twodimensional model of continuous probability capable of describing the occurrence of a needle intersecting a parallel series of lines when thrown on a horizontal surface. Given a striped surface with a consistent band width (d) and a needle length (L) dropped at random onto the surface, the probability that the needle will intersect the boundary is 2U?d. This geometric technique was revised by EwaldWeibel in 1966 in the form of the Multipurpose Test Grid. 14 In 1847, Buffon's Needle Problem was adapted by French geologistAchilie Delesse for the analyses of the volume areas of minerals in rock samples. 15 Delesse's Principle states that the volume fraction of a component tissue can be estimated 15.Point analysis.

16.Diameter of the area of an equivalent circle by the random caliper diametermethod.

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by measuring the area fraction of a random section occupied by that volume's transection. The Principle of Delesse demonstrates that the areas occupied by different components in a single section approximate closely the ratios between the volumes occupied by those components in three-dimensional space. The Principle allows an estimation of volume from the area analysis of random transections. With this technique Delesse was able to polish a single surface and estimate the internal mineral content of specific specimens. In 1898 Rosiwal adapted Delesse's principles to Buffon's linear analysis and used it as a transectional device. The profile areas in two dimensions are estimated from the proportion of objects lying on the test grid. In the following linear example, the total length of intersection with these lines is 25 percent of the total length of the test lines. According to the Principle of Delesse, the area volume of these objects is then .25 +- .024 of the total volume. A test grid of points can also be used, as proven by Nil Aleksandro Glagolev in 1933, where, for instance, a grid of 81 points cutting a section through nine objects with a total of 36 intersections yields: 81 / (9 x 36) = 0.25. It is only recently that these geological techniques were employed by biologists (primarily Weibel, Elias, and Underwood) for the reconstruction of actual shape rather than mere statistical area. The plane contour analysis of Buffon, along with the projection of this information into three dimensions using the Delesse Principle, has recently been applied to the serial transections of biological description, such as vivisection, CaT: PET: and X-ray imaging. 16 Histology and all other biological descriptions have been plagued by two linked problems: the human body conceals its contents within an opaque and fragile I 7. Profile radius "r"depends on the level at which each sphereis sectioned.

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91

interior, and the dimensional integrity of its size and shape is contingent upon the fluidities, movements, and pressures of living in time. Stereometry attempts to describe the shape, size, area, and volume of organs in a manner that is indirect, rapid, flexible, versatile, and "founded upon ideas and procedures drawn from geometric probability" in order to describe the fluidity of dynamic bodies prone to geometric instability and deformation. As Weibel states: "The tissues of biologic organisms are built ofsolid structures, three-dimensional bodies which arecharacterized by a certain volume, a surface area and some geometric properties which are often difficult to define in precise terms." 17 It is the resistance of biological structures to geometric exactitude that determined "how two such apparently disparate subjects as geometry and probability came to be associated." In the description of the area diameter of a transection of muscle fiber, for instance, the shape is "more or less" circular but cannot be reduced to an actual circle. The transection's roundness results from the fluctuations of shape due to adjacent pressures, distension, and the compression of outside forces on the body. These contingent pressures that deform the fiber are more important than any reduction to a pure eidetic form. Stereometric serial transections, as developed by Buffon and Delesse, have in the last two decades been adapted, with the addition of coefficients for the reconstruction of shape,to maintain deformations, particularities, and differences as the registration of meaningful events. The simplest coefficients of shape are used to determine the degrees of randomness in shape and orientation of volumes. Any collection of randomly oriented

18.Frequency distribution of the various profile sizes based on the level of sectioning.

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spheres, when sectioned, will yield circles of varying sizes. A coefficient of shape based on the number of sectional elements and their mean diameter is used to determine whether or not the varying circles result from similarly or randomly sized spheres. Thickened lines, ellipses, and circles indicate the presence of more or less cylindrical strands of varying orientations, such as those of the large and small intestines. The reconstruction of the orientation and continuities of these loops as they pass randomly through the transections is vital, and coefficients for tubular volumes have been developed to model these relationships with high degrees of probability. From the areas and shapes of these sectioned lines, ellipses, and circles as they appear in two or more transections, the length, diameter, orientation, and quantity of tubular elements can be described. Unlike architecture - which is more or less anistropic, or regularly structured and aligned to an orthogonal descriptive grid (conventionally the surfaces of buildings correspond exactly to the drawn planes of orthogonal projection) - in cases of anistropic linear tissue, stereometry achieves greater accuracy by maximizing the random alignment of cutting planes or probing points. Moreover, the degree of accuracy of these sections relates to their randomness. In anistropic tissues, where matter is organized in nonrandom recursive patterns, a higher degree of accuracy is achieved as the orientation of the random section differs from that of the tissue itself. Anistropic tissues display different characteristics in different axes and assume different positions in response to external stimuli. A system of rotational coefficients has already been developed to locate the most random orientations for these sections. Random section analyses exploit the obliqueness and particularities of organs, in reference to parallel transections and orthogonal grids. I 9. Convex, non-convex and topologicalelements yieldingcircles.

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The case study of the probable geometry of Buffon, Delesse, and Weibel, among others, moves architecture's fixed orthogonality through the disciplines of professional gambling, geology, and biology and closer to the behavior of vital matter while retaining a rigorous system of measure. In these stereometric examples, possible three-dimensional areas and shapes are projected from two-dimensional transections through a radical orthogonal technique that seems to be already natural to architecture. These indeterminate forms are not fixed, although they are are written between known contours. The elision of geometry with probability, along with the provisional, rather than essential alignment of these systems to matter, allows varying degrees of amorphousness to be measured between local exactitudes. The possibilities of this random section technique were explored by Le Corbusier in his Citrohan and Dom-ino types and extended by Koolhaas in his recent library competition projects. Anexact geometries such as these may supply architecture with the ability to measure amorphousness and undecidability in a manner conventionally associated with writing rather than architecture.

20.Tubular anistropic elements.

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Endnotes

10. Kas Oosterhuis, "Space, Time, Volume," Wiederhall 12 (1990): 5-8.

I. Mark Wigley,"DeconstructivistArchitecture," in Mark Wigley and Philip Johnson, Deconstructivist Architecture (New York, 1988), 10-20.

I I. Ewald R. Weibel and Hans Elias, Ouantitative Methods in Morphology (Berlin, 1967).

2. Robert Venturi, ComplexitY and Contradiction in Architecture (New York, 1966). 3. Denis Hollier, Against Architecture: The Writings of Georges Bataille, trans. Betsy Wing (Cambridge, Mass., 1989) 23. 4. Denis Hollier, Against Architecture. 5. Georges Bataille, "Architecture," Documents 2 (May 1929): 171-72. 6. Vitruvius, The Ten Books of Architecture, trans. Morris Hickey Morgan (New York, 1960). 7. Luce Irigaray, This Sex Which Is Not One, trans. Catherine Porter with Carolyn Burke (Ithaca, N.'f., 1985). 8. See Jacques Derrida, Edmund Husserl's Origin of Geometry: An Introduction, trans. by John P. Leavey,Jr. (Lincoln, Nebraska, 1989) and Gilles Deleuze and Felix Guattari, A Thousand Plateaus: Capitalism and Schizophrenia, trans. Brian Massumi (Minneapolis, 1987). 9. Fred Bookstein, The Measurement of Biological Shape and Shape Change (Berlin and New York, 1978).

12. Erwin Panofsky, Meaning in the Visual Arts (Chicago, 1955). 13. See Geometrical Probability and Biological Structures: Buffon's 200th Anniversary: Proceedings, ed. R. E. Miles and J. Serra (Berlin and New York, 1978). 14. For a discussion of the technique of the random section model see E. R.Weibel, G. S. Kistler and W. R. Scherle, "Practical Stereological Methods for Morphometric Cytology," lournal of Cellular Biology Ouly, 1966):23-38. For related discussions of the applications of the random section model, see John C. Russ, Practical Stereology (New York, 1986) and P. N. Gaunt and WA. Gaunt, Three Dimensional Reconstruction in Biology (Baltimore, 1978). 15.Achille Delesse, Procede Mecanique pour determiner la Composition des Roches (Paris, 1847). 16. For applications of these techniques to contemporary bio-medical imaging see Barbara Maria Stafford, Imaging the Body: From Fragment to Total Display (Chicago, 1992). 17.Weibel and Elias, Morphology.

2 I. Variable profile sections of an irregular solid.

DLfferentLaL GravLtLes

The image of the burrow is one of the countless abstract spatial types developed by Rudolf Arnheim in The Dynamics of Architectural Form. I In the context of discussions of architectural lightness, such a literally and conceptually massive structure must seem counterintuitive. But there is a lightness to the way the mole-hill is grounded, a lightness that defines itself not against, but in relation to mass, material, gravity and ground. More importantly, this new lightness is an effect linked to the multiplication of orientations, positions and movements. Labyrinthine organizations such as the burrow are light because they are essentially ungrounded, or rather they are not grounded by the single gravitational force of the earth's horizon. Because these structures are both mounded and subterranean, gravity's influence in the organization of the burrow does not mandate any single or essential plane of organization. Subterranean organizations are massive, yet the density of the surrounding matter provides a thickened, over-structured ground within which a multiplic-

First published in Any Magazine. no.s.

I. Burrow by RudolfArnheim

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ity of potential passages can be developed. Because these various orientations, positions, and movements are not regulated or reducible to a single orientation, position, or movement, the burrow floats below the ground. The labyrinth or burrow models a lightly grounded architectural space that is light because and not in spite of its massive subterranean location. Within the labyrinth, vertical and horizontal movement are separated by degrees of gravitational force rather than by right angles. In this way there are as many gravities and grounds for such structure as there are potential orientations and vectors of movement. In order to develop these complex, lightly grounded structures, it is necessary first to develop an architectural concept of multiple and differential gravities that diverges from the normative, singular concept of the earth's one gravity. Most discussions of architectural weight have involved two linked and seemingly matter-of-fact assumptions: first, that there is one and only one architectural gravity, that of the earth; and second, that this singular gravitational force mandates that, in order to provide shelter, buildings must stand up. In order to avoid an equally simple concept of lightness, one that is defined as a resistance to a simple concept of gravity (this will be described later as a theory of the immaterial or lightweight), it is necessary not only to develop a more complex idea of gravity, but also to establish architectural relationships to these gravities that are not reducible to an ideal point or line of resistance. Lightness is an idea that can make architecture's assumptions about the simplicity of gravity more complex. It is important to acknowledge that resistance to gravity would be the most conservative and familiar architectural response to questions regarding weight or weightlessness., Unlike these normative views based on a resistance to weight, the concept of differential gravities is based on a more flexible notion of the ground and grounding. Rather than weighing down architectural thinking with the concept of the resistance of a single gravitational force perpendicular to the earth's surface, lightness offers us the concept of grav-

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97

itational forces that proliferate between masses and can never be fixed in any single ground form. Gravity, understood as an unchanging, singular and universal force, is perhaps the only convention in architecture that has been agreed upon as an unassailable truth - this, in spite of the fact that a theory of gravity has only developed relatively recently in the history of architecture. One could argue that gravity and its simple resistance is the dominant principle upon which architectural thinking has been grounded. The idea that buildings must stand up to gravity has become a constant in architecture - in the literal sense of vertical structuring, bearing and transfer of loads, and, perhaps even more so, in the theoretical and conceptual grounding that gravity provides architecture. The conventional assumption that buildings should be made to stand up is rarely questioned, and as a result it has become more an intractable truth than a convention. Nonetheless, there are many ways of structuring matter, only one of which is standing it up. The architectural predilection toward verticality, and the linked preference for the horizontal datum of the earth as an absolute ground, can be traced to a conception of gravity as a single, constant force that brings things down to the earth in a simple and direct manner. The structuring of architecture on the horizontal datum or ground of the earth gives architecture its distinct, vertical identity. Moreover, the concept of gravity as a singular universal force (which should be distinguished from the phenomenon of things falling toward the earth, as gravity is indeed a concept and does not

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properly exist) is intimately connected with the identity of shelter and standing up through resistance to the elements. Gravity provides architecture with a source of grounding. In order to explore the possibility of developing a multiplicity of groundings, however, it is necessary to distinguish several different types of gravities. Architecture can become weighted with radically different qualities depending on our understanding of gravity. Buildings do not, after all, have to be structured as standing up, as they can be, and have been structured on principles of bridging, hanging, stretching, squatting, leaning, lying and floating among others. For example, Lina Bo Bardi's Museo de Arte de Sao Paolo of 1957-68 is structurally sound despite the fact that it floats over the coffee mansions that once stood on the site. It would be inaccurate to characterize the museum's spanning as gravity defying, since the building is merely suspended at two ends in a rather unheroic fashion. Bo Bardi's project floats because it has a loose and complex relationship with the ground, not because it is lightweight-it is, in fact, quite brute. The building floats not because it is immaterial; on the contrary, it floats because its immense mass is suspended as a beam, making the project unexpectedly light. With Bo Bardi's M.A.S.~ project a certain presence of materiality and mass becomes integral to lightness. Lightness can thus be seen to emerge when materials are not grounded coincident with the horizon of the surface of earth, but are instead multiply or obliquely grounded. If weight is conventionally understood as a resistance to the earth's gravity, we can begin to define lightness by reconsidering the ways in which mass is structured as something other than an absolute and direct grounding by the earth alone. Bo Bardi's project offers us the example, of a kind of architectural suspension that has a complex, rather than a simple, relation to the ground. This is not to imply that all relations to the earth should be jettisoned. When the gravity of the earth is understood as one force among many, matter no longer has a primary but rather a secondary, or tertiary relationship to the ground form of

DLfferentLaL GravLtLes

the earth.

99

With lightness more dynamic, multiple,

complex and differential forms of stability emerge. Before developing alternative light grounds for architecture, it is important first to differentiate the concept of lightness from earlier notions that were defined through resistance to gravity. Previous definitions of lightness in architecture, whether couched in the rhetoric of modern architecture or in the more recent discussions of architecture in the context of electronic technologies, have depended on either the innovation of increasingly lightweight structural systems of suspension and support, or the dematerialization of building materials toward a state of ideal immateriality. The former innovation is dependent on and in fact defines a theory of the lightweight, while the latter is dependent on and defines a theory of antigravity. These two dominant definitions of lightness merely oppose gravity and therefore constitute an architecturally conservative position of resistance. Both the lightweight and the antigravitational depend on a literal elimination of mass through dematerialization. Immateriality - the latest in a long history of theories of gravitational resistance - offers a conservative response to the problems posed by the traditional understandings of gravity, and most recently through innovations in electronic technology. Within the discipline of architecture, immateriality is as conservative a concept as the earlier ideas of grounded, rooted and regional

architecture

it

claims

to

oppose.

Dematerialization invokes an ideal state defined as an

3. Hong Kong Peak Club by Zaha Hadid.

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absolute minimum condition of ethereal space - cyberspace in the parlance of the theorists of electronic architectures. Transparent materials and minimal structures are the signifiers of this frustrated project that aspires to an ideal, immaterial space. In the case of either an antigravitational levitation or immaterial cyberspace, absolute lightness can only be understood as a resistance to an absolute gravity. An ideal atmosphere of zero gravity is common to both immateriality and antigravity. But lightness is not an absence of materiality and it is therefore not simply opposed to the weight and fixi~y of the earth. This dialectical and oppositional definition of lightness and gravity encourages the rather simplistic speculation that soon the material architectures of the earth will be eclipsed by the new, immaterial technological architectures of cyberspace. Such an argument discriminates between two ideal Cartesian worlds: one of absolute weight and the other of pure immateriality. Both are based on simple concepts of the earth, matter and gravity: as there is only one gravity there can be only one lightness. This rather limited understanding of architecture's grounds - as either absolutely earthly and tectonic or absolutely ethereal and electronic makes it impossible to develop concepts of differing degrees of gravity and different conceptions of the earth. John Rajchman's call (through Nietzsche) for a reconceptualization of the earth as light opens the way for many different gravities and therefore for a multiplicity of grounds. 2 Rather than liberating lightness from the pull of gravity, what is required is a liberation of lightness from the understanding of gravity as a single force emanating from the earth. From the simple gravitational force of the earth, and the vertical grounding of architecture upon it, lightness moves the concept of gravity in many directions. When defined by the qualitative relations between particularities of matter rather than by the relation of various masses to a single ground form, a multiplicity of potential architectural gravities emerge. One such departure from an earthly architecture based on vertical structures and horizontal grounds occurs through the multiplication of alignments and grounds and therefore a multiplication of ground forms. Such a proliferation of

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potential alignments to gravity was present in Rem Koolhaas's characterization of Zaha Hadid's work as planetary. 3 Hadid's planetary architecture announced an orientation of "89 degrees" in relation to questions of gravity. Her suggestion of less-than-vertical alignments to the earth invokes at least two possibilities: first, that buildings might be seen singularities, or planets, with their own degrees of gravitational force; and secondly, that relations between these planetary masses will be regulated by the particularities and adjacencies of the elements themselves rather than by the relation of each of the elements to a single, uniform gravitational force of the earth. This allows for a multiplicity of gravitational vectors through, along and across objects, where loads are transmitted through a network of propped, sloped, cantilevered, sandwiched, and skewered solids. In Hadid's most recent work, the transmission of loads through a network of differential connections, has become even more acute. Her comments on the frustrations of attempting weightlessness in the projects should be compared to the successes of her projects in realigning themselves to the ground and to gravity in many oblique ways. Two strategies appear to be at work here. The first attempts a heroic, modernist antior zero-gravity, while the second attempts to complicate architecture's alignment to the ground. This later strategy, in which the term "planetary urbanism" suggests not the weight of a disembodied celestial light, but a network of intricate relationships between a constellation of somewhat free elements with differ-

4. Glass Video Gallery in Gronigen by Bernard Tschumi.

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ent gravitational characteristics, is the more sucessful and interesting of the two. Hadid's project for the Peak Club in Hong Kong is intricately grounded as it reconfigures the surface on which it is embedded as a series of interrelated plates. The project is an aggregate of elements resting one on the other rather than a simple perpendicular transferal of mass to the ground. Defined by various fields of attraction between free elements, lightness here is neither gravitational indifference nor gravitational resistance, but a condition of gravity in difference. Where gravity and weight are thought in complex, differential terms, lightness is distinguished as the complication, not the simple loss, of ground. Lightening the manner in which architectures can be grounded escapes the necessity to think through the problem of support and weight in terms of structural efficiency and dematerialization. It is critical to maintain the distinction between lightness and the lightweight as the second term involves, yet again, an ideal conception of weight and a conservative mode of resistance. In this way a critical distinction emerges between existing theories of antigravity and this proposal for differential gravities.

Instead of continuing to resist a single gravity,

architects must reformulate the question of weight through lightness understood as a more complex and intricate question of relationships between surfaces and grounds that are multiple and loosely connected. Through a more general formulation of new gravitational paradigms, lightweight structural systems and nearly invisible building materials can be developed in conjunction with lightly grounded architectural and urban organizations. With lightness, forms of dynamic stability and differential loading emerge that are qualitatively different from the stasis implicit in the singular, perpendicular grounding of the earth.Without appealing to literal movement, one can conceive of lighter compositions where weight is carried through many different vectors that are not subject to the right-angle pull of the earth's gravity.

'

These new, qualitatively different stabilities involve an alternative relationship to ground and site that is not merely the loss of specificity or location. The light effects of hovering, levitation, and floating depend on an intricate relationship of

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equalization between a body and the environment in which it is immersed. Dynamic structural principles of walking, flying, floating, skimming, and swimming are not grounded by any single environment but are relational structures that exist between bodies and environments. Insects can only skim across liquids when their mass is supported by surface tension as lizards can run only across the water's surface when their mass is propelled at an appropriate speed. Floating can be achieved by massive land mammals such as hippopotami once their mass is equalized with that of water. Likewise fish that fly in the air and devilfish that fly in the water suggest to us that qualities of lightness and support are dependent not just on the mass of a body but on its relationship to some larger field. Lightness and gravity are relational not absolute terms. To evaluate a building's lightness is therefore not simply a matter of disentangling it from its context and weighing it.

Levitation, floating, and suspension are

achieved when a body occupies multiple positions of stability. Flotation is a quality that emerges from the particular relationships between things: it occurs when the mass and density, or gravitational attraction, between things equalizes.With this equalization emerges new dynamics and new movements. Characteristic of lightness are several types of flotation, three of which can be developed here. The first type of flotation is aviary and involves the dematerialization of an object to the point at which it begins to float in the air. Bernard Tschumi's GlassVideo Gallery in Groningen, The Netherlands, is

5. Rem Koo/haas, Urban Ring Exhibition, Yokohama.

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perhaps the most radical in this regard. The transparency of the envelope, along with the structuring of the mass itself with glass-bearing elements, dematerializes the mass of the pavilion. This dematerialization is linked to the elevation and sloping of the ground plane from the horizontal datum of the site. In fact, the weightlessness of the gallery is not nearly as evocative of flotation as is the slope of the building's base. Similarly, the dematerialization of the structure through the use of glass materials does not displace the normative gravity of the building, at least to the extent that the inclination of the ground is capable of reconfiguring the gravity of the space. In the case of aqueous environments, weight is reduced or displaced through the equalization of a body's mass and that of the environment in which it is immersed. Flotation, or the condition of weightlessness, is an effect generated by the equalization. For instance, it is possible for the human body to float when it is immersed in an environment that has the same weight as our bodies. At the moment our bodies begin to float we lose our mostly vertical posture and enter into a new relationship with the ground and thus the earth. The potential for movement and structure are shifted and multiplied with the differing relations between bodies and environments; in this way there are as many gravities as there are bodies. This principle of suspension-surrounding an object with a diffused field of structure that is roughly equivalent to its mass and density-suggests that in order to become light, structures need not be increasingly dematerialized (becoming lightweight) but must instead become more diffuse. The deployment of diffused structuring offers an alternative to floating achieved by the use of increasingly lightweight structures. In architecture, diffused structuring can be achieved by employing a dense field of small columns or some other structure that diminishes each individual point of support by multiplying the number of support points. Where Bo Bardi's M.A.S.~ project floats on two points of support there is only one possible siting for the mass;if those two massive points of support were diffused to form a field across the site, the number of positions for the mass would multiply exponentially. The proliferation and dif-

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fusion of microstructural elements would therefore multiply the potential for objects to float within fields. With these more diffuse structures the air would literally become heavy with support, and massive objects could begin to float in a more equalized environment of structural fluidity. The seemingly weightless flotation of a whale offers an analogy for this diffuse structure.When grounded or beached the whale is anything but light; but in water, where its body mass is equalized with its aquatic context, the whale moves almost effortlessly. In this way, these massive creatures are practically weightless. The leviathan's levitation within water is similar to the levitation of a bird in the air, the primary difference being the weight of the bodies in reference to the earth, the primary similarity being the ratio or relation of the weight of the bodies to the weight of their environment. In comparison to the ground of the earth, the gravity of the whale is heavy and the gravity of a bird is not. In relation to the grounds within which these bodies are immersed, their gravity is similarly equalized, allowing each to float. In both cases the gravitational attraction of bodies to the earth - what is thought of in architecture as a single gravitational force - is lightened, allowing us to explore in a more open and multidimensional way the gravities between bodies. Between these two extremes there are seemingly endless variations of light relations between bodies and the environments in which they are immersed. Once the air is thought of as potentially heavy enough to bear the weight of objects and the earth is conceived of as a porous mass capable of supporting objects not only on its surface

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6. Coincidental ground withdematerialized lightness. (Note: the angle Signifies a provisional relationship to the ground only.)

r - .. ---- ..... - , I I

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but also burrowing and floating within its mass,then a new sense of ground has been established and a new mobility is achieved. We witness the possibilities for these kinds of thickened ground conditions in Rem Koolhaas's two library projects in Paris and his Urban Ring Exhibition in Yokohama,Japan.ln the Yokohama project, the fact that the surface of the site and the surfaces of the floors and roof are malleable and deformable allow this project to develop a thickened ground throughout that supports various spaces,programs and passages. This project suggests a return to Arnheim's diagram of the burrow, whose labyrinthine structure seems to be the least grounded and the lightest type of architecture imaginable. The hypothetical moles that might inhabit these spaces would indeed float in the thickened and multiple grounds of the burrow, rather than remain fixed on the ideal plane of the earth's surface. In his discussions of spatial mobility,Arnheim opposes the abstract type of the "shelter" to that of the "burrow." He did this by arguing that there is no plan regulation in the burrow as there is in the shelter. Arnheim speculates that the primary consideration of the shelter is the resistance to gravity, where in the case of the burrow there is only a desire for connectivity and movement. The shelter is initially geometric, exact and structured vertically while the burrow is in some way proto-geometrical, anexact and grounded neither horizontally nor vertically. In Arnheim's model of the subterranean burrowing into a labyrinthine space, there is a condition of weightlessness that develops from the density of matter in which one is burrowing. The relationship of the burrow to the ground is light because there is no single gravitational force that fixes the space of the labyrinth: almost any direction or orientation is gravitationally and structurally possible. The burrow occupies the earth not as a horizon or ground but as a field of potential spaces, orientations and positions.

'

Lightness is not the elimination of gravity but is instead an equalization of gravities.

Immersion implies that the boundaries between figures and grounds

become blurred and envelopes become negotiable. There are countless possi-

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bilities for architectural grounds once the simple concepts of weightlessness and dematerialization give way to a more complex and open concept of differential gravities. This type of lightness does not ascend to an ideal, immaterial space, but instead descends into questions of matter, support and burrowing. This fall into the dynamics of gravity opens the way for more than one lightness and the possibility for masses to float within mass, as in the labyrinth. As a result, floating is transformed from an idealized state of immateriality to an immersion and suspension of masses in material contexts with particular qualities and characteristics - shifting from an ideal space in which bodies are grounded by fixed points to dynamic fields with multiply configured supports.

7. Coincidental ground with diffused structure. (Note:the angle signifies a provisional relationship to the ground only.)

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Architecture," Any Magazine 5 (Mar.-April 1994):5-7 and "Light Matters," Any Magazine 5 (Mar.-April 1995): 28-29.

Endnotes I. Rudolf Arnheim, The Dynamics of Architectural Form (Berkeley, 1977). 2. See John Rajchman,

&

"Lightness:

8. Coincidental ground with subterranean burrowing. (Note: the angle signifies a provisional relationship to the ground only.)

A Concept in

3. See Zaha M. Hadid, Planetary Architecture: Projects 1977-1981 (New York, 1981) and Planetary Architecture Two (London, 1983).

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For the last two decades, beginning with Robert Venturi's Complexity and Contradiction in Architecture, and Colin Rowe and Fred Koetter's Collage City,and continuing through Mark Wigley and Philip Johnson's Deconstructivist Architecture, architects have been primarily concerned with the production of heterogeneous, fragmented and conflicting formal systems. These practices have attempted to embody the differences within and between diverse physical, cultural and social contexts through formal conflicts. Although Venturi's Complexity and Contradiction or Learning from LasVegas differ significantly from Wigley and johnson's Deconstructivist Architecture and are normally thought of as incomparable, the importance of their shared interest in formal conflict cannot be overemphasized. I Both Venturi and Wigley argue for the deployment of discontinuous, fragmented, heterogeneous and diagonal formal strategies based on the incongruities, juxtapositions and oppositions within specific sites and programs. These disjunctions result from a logic which tends to identify the potential contradictions between dissimilar elements. A diagonal relationship between a building and its context has become an emblem for the contradictions within contemporary culture. From the scale of an urban plan to a building detail, contexts have been mined for conflicting geometries, materials, styles, histories and programs which are then represented in architecture as internal contradictions. The most paradigmatic architecture of the last ten years, including Venturi's Sainsbury Wing of the

First published in Architectural Design. no. 102.

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National Gallery, Peter Eisenman's Wexner Center, Bernard Tschumi's LaVillette park or Frank Gehry's House, invests in the architectural representation of contradictions. Through contradiction, architecture represents difference in violent formal conflicts. Contradiction has also provoked a reactionary response to formal conflict. Such resistances attempt to recover unified architectural languages that can stand ..../ against heterogeneity. Unity is constructed through one of two strategies: either by reconstructing a continuous architectural language through historical analyses (Neo-Classicism or Neo-Modernism) or by identifying local consistencies resulting from indigenous climates, materials, traditions or technologies (Regionalism). The internal orders of Neo-Classicism, Neo-Modernism and Regionalism conventionally repress the cultural and contextual discontinuities that are necessary for a logic of contradiction. Despite their differences, both the reaction to and representation of hetero-..: geneity in architecture have shared an origin in contextual analysis. Both theoretical models begin with a close analysis of contextual conditions from which . they proceed to evolve either a homogeneous or heterogeneous urban fabric. Neither the reactionary call for unity nor the avant-garde dismantling of it through the identification of internal contradictions seems adequate as a model for contemporary architecture and urbanism. Instead, an alternative smoothness is being formulated that may escape these dialectically opposed strategies. Common to the diverse sources of this post-contradictory work - topological geometry, morphology, morphogenesis, catastrophe theory or the computer technology of both the defense and Hollywood film industry - are characteristics of smooth transformation involving the intensive integration of differences within a continuous yet heterogeneous system. Smooth mixtures are made up of disparate elements which maintain their integrity while being blended within a continuous field of other free elements. Smoothing does not eradicate differences but incorporates free intensities

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through fluid tactics of mixing and blending. 2 Smooth mixtures are not homogeneous and therefore cannot be reduced. Deleuze describes smoothness as the

"continuous variation" and the "continuous development ofform." 3 Wigley's critique of pure form and static geometry is inscribed within geometric conflicts and discontinuities. For Wigley, smoothness is equated with hierarchical organization:

"the volumes have been purified - they have become smooth, classical - and the wires all converge in a single, hierarchical, vertical movement." 4 Rather than investing in arrested conflicts, Wigley's "slipperiness" might be better exploited by the alternative smoothness of heterogeneous mixture. For the first time perhaps, complexity might be aligned with neither unity nor contradiction but with smooth, pliant mixture. Both pliancy and smoothness provide an escape from the two camps which would either have architecture break under the stress of difference or stand firm. Pliancy allows architecture to become involved in complexity through flexibility. It may be possible neither to repress the complex relations of differences with fixed points of resolution nor arrest them in contradictions, but sustain them through flexible, unpredicted, local connections. To arrest differences in conflicting forms often precludes many of the more complex ways of connecting the forms of architecture to larger cultural fields. A more pliant architectural sensibility values alliances rather than conflicts between elements.

Pliancy

implies first an internal flexibility and second a dependence on external forces for self-definition. Ylf there is a single effect produced in architecture by folding, it will be the ability to integrate unrelated elements within a new continuous mixture. Culinary theory has developed both a practical and precise definition for at least three types of mixtures. The first involves the manipulation of homogeneous elements; beating, whisking and whipping change the volume but not the nature of a liquid through agitation. The second method of incorporation mixes two or more disparate elements; chopping, dicing, grinding, grating, slicing, shredding and mincing eviscerate elements into fragments. The first method agitates a single uniform

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ingredient, the second eviscerates disparate ingredients. Folding, creaming and blending mix smoothly multiple ingredients "through repeated gentle overturnings

without stirring or beating" in such a way that their individual characteristics are maintained." For instance, an egg and chocolate are folded together so that each is a distinct layer within a continuous mixture. Folding employs neither agitation nor evisceration but a supple layering. Likewise, folding in geology involves the sedimentation of mineral elements or deposits which become slowly bent and compacted into plateaus of strata. These strata are compressed, by external forces, into more or less continuous layers within which heterogeneous deposits are still intact in varying degrees of intensity. A folded mixture is not homogeneous, like whipped cream, but smooth and heterogeneous. In both cooking and geology, there is no preliminary organization which becomes folded but rather there are unrelated elements or pure intensities that are intricated through a joint manipulation. Disparate elements can be incorporated into smooth mixtures through various manipulations including fulling:

"Felt is a supple solid product that proceeds altogether differently, as an anti-fabric. It implies no separation of threads, no intertwining, only an entanglement of fibers obtained by fulling (for example, by rolling the block of fibers back and forth). What becomes entangled are the microscales of the fibers. An aggregate of intrication of this kind is in no way homogeneous; nevertheless, it is smooth and contrasts point by point with the space of fabric (it is in principle infinite, open and uninhibited in every direction; it has neither top, nor bottom, nor center; it does not assign fixed or mobile elements but distributes a continuous variation)." 6 The two characteristics of smooth mixtures are that they are composed of disparate unrelated elements and that these free intensities become intricated by an external force exerted upon them jointly. Intrications are intricate connections that affiliate local surfaces of elements with one another by negotiating

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interstitial rather than internal connections. The heterogeneous elements within a mixture have no proper relation with one another. Likewise, the external force that intricates these elements with one another is outside of the individual elements control or prediction.

vLscous MLxtures Unlike an architecture of contradictions, superpositions and accidental collisions, pliant systems are capable of engendering unpredicted connections with contextual, cultural, programmatic, structural and economic contingencies by vicissitude. Vicissitude is often equated with vacillation, weakness and indecisiveness but more importantly these characteristics are frequently in the service of a tactical

cunning." Vicissitude is a quality of being mutable or changeable in response to both favorable and unfavorable situations that occur by chance. Vicissitudinous events are neither arbitrary nor predictable but seem to be accidental. These events are made possible by a collision of internal motivations with external forces. For instance, when an accident occurs the victims immediately identify the forces contributing to the accident and begin to assign blame. It is inevitable, however, that no single element can be made responsible for any accident as these events occur by vicissitude; a confluence of particular influences at a particular time makes the outcome of an accident possible. If any element participating in such a confluence of local forces is altered the nature of the event will change. In the title of Gilles Deleuze and Felix Guattari's book, A Thousand Plateaus, Spinoza's concept of "a thousand vicissitudes" is linked with Gregory Bateson's "continuing plateaus

of

intensity" to describe events which incorporate unpredictable events through intensity." These occurrences are difficult to localize, difficult to identify. Any logic of vicissitude is dependent on both an intrication of local intensities and the exegetic pressure exerted on those elements by external contingencies. Neither the intrications nor the forces which put them into relation are predictable from within any single system. Connections by vicissitude develop identity through the exploitation of local adjacencies and their affiliations with external forces. In this sense,vicissitudinous mixtures become cohesive through a logic of viscosity.

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Viscous fluids develop internal stability in direct proportion to the external pressures exerted upon them. These fluids behave with two types of viscidity. They exhibit both internal cohesion and adhesion to external elements as their viscosity increases. Viscous fluids begin to behave less like liquids and more like sticky solids as the pressures upon them intensify. Similarly, viscous solids are capable of yielding continually under stress so as not to shear. Viscous space would exhibit a related cohesive stability in response to adjacent pressures and a stickiness or adhesion to adjacent elements. Viscous relations such as these are not reducible to any single or holistic organization. Forms of viscosity and pliability cannot be examined outside of the viscissitudinous connections and forces with which their deformation is intensively involved. The nature of pliant forms is that they are sticky and flexible. Things tend to adhere to them. As pliant forms are manipulated and deformed the things that stick to their surfaces become incorporated within their interiors.

curvLng away from oeconstructLvLsm Along with a group of younger architects, the projects that best represent pliancy, not coincidentally, are being produced by many of the same architects previously involved in the valorization of contradictions. Deconstructivism theorized the world as a site of differences in order that architecture could represent these contradictions in form. This contradictory logic is beginning to soften in order to exploit more fully the particularities of urban and cultural contexts. This is a reasonable transition, as the Deconstructivists originated their projects with the internal discontinuities they uncovered within buildings and sites. These same architects are beginning to employ urban strategies which exploit discontinuities, not by representing them in formal collisions, but by affiliating them with one another through continuous flexible systems. Just as many of these architects have already been inscribed within a Deconstructivist style of diagonal forms, there will surely be those who would enclose their present work within a Neo-Baroque or even Expressionist style of

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curved forms. _However, many of the formal similitudes suggest a far richer logic of curvilinearity that can be characterized by the involvement of outside forces in the development of form. 9

If internally motivated and homogeneous systems

were to extend in straight lines, curvilinear developments would result from the incorporation of external influences. Curvilinearity can relate many contemporary architectural projects to Deleuze's The Fold: Leibniz and the Baroque and ReneThom's catastrophe diagrams. 10 The smooth spaces described by these continuous yet differentiated systems result from curvilinear sensibilities that are capable of complex deformations in response to programmatic, structural, economic, aesthetic, political and contextual influences. This is not to imply that intensive curvature is more politically correct than an uninvolved formal logic, but rather, that a cunning pliability is often more effective through smooth incorporation than contradiction and conflict. Many cunning tactics are aggressive in nature. Whether insidious or ameliorative these kinds of cunning connections discover new possibilities for organization. A logic of curvilinearity argues for an active involvement with external events in the folding, bending and curving of form. Already in several Deconstructivist projects are latent suggestions of smooth mixture and curvature. For instance, the Gehry House is typically portrayed as representing materials and forms already present within, yet repressed by, the suburban neighborhood: sheds,chain-link fences, exposed plywood, trailers, boats and recreational vehicles. The house is described as an "essay on the convoluted

relationship between the conffiet within and between forms ...which were not imported to but emerged from within the house." II The house is seen to provoke conflict within the neighborhood due to its public representation of hidden aspects of its context. The Gehry House violates the neighborhood from within. Despite the dominant appeal of the house to contradictions, a less contradictory and more pliant reading of the house is possible as a new organization emerges between the existing house and Gehry's addition. A dynamic stability develops with the mixing of the original and the addition. Despite the contradictions between elements, possible points of connection are exploited. Rather than valorize the conflicts the house engenders, as both academic and popular publications have

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done, a more pliant logic would privilege degrees of connection rather than violation. A new intermediate organization occurs by vicissitude from the affiliation of the existing house and its addition.

Within the discontinuities of

Deconstructivism there are inevitably unforeseen moments of cohesion. Peter Eisenman's Wexner Center is similarly conventionally portrayed as a collision of the conflicting geometries of the campus, city and armory which once stood adjacent to the site. These contradictions are represented by the diagonal collisions between the two grids and the masonry towers. Despite the disjunctions and discontinuities between these three disparate systems, Eisenman's project has suggested recessive readings of continuous non-linear systems of connection. Robert Somol identifies such a system of Deleuzian rhizomatous connections between armory and grid.

12

The armory and diagonal grids are shown

by Somol to participate in a hybrid "L-movement" that organizes the main gallery space. Somol's schizophrenic analysis is made possible by,yet does not emanate from within, a Deconstructivist logic of contradiction and conflict. The force of this Deleuzian schizoanalytic model is its ability to maintain multiple organizations simultaneously. In Eisenman's project the tower and grid need not be seen as mutually exclusive or in contradiction. Rather, these disparate elements may be seen as distinct elements co-present within a composite mixture. Pliancy does not result from and is not in line with the previous architectural logic of contradiction, yet it is capable of exploiting many conflicting combinations for the possible connections they overlook. Where DeconstructivistArchitecture was seen to exploit external forces in the familiar name of contradiction and conflict, recent pliant projects exhibit a more fluid logic of connectivity.

Immersed Ln context The contradictory architecture of the last two decades has evolved primarily from highly differentiated, heterogeneous contexts within which conflicting, contradictory and discontinuous buildings were sited. An alternative involvement with heterogeneous contexts could be affiliated, compliant and continuous. Where com-

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plexity and contradiction arose previously from inherent contextual conflicts, attempts are presently being made to fold specific locations, materials and programs into architecture smoothly while maintaining their individual identity. This recent work may be described as being compliant; in a state of being plied by forces beyond control. The projects are formally folded, pliant and supple in order to incorporate their contexts with minimal resistance. Again, this characterization should not imply flaccidity but a cunning submissiveness that is capable of bending rather than breaking. Compliant tactics, such as these, assume neither an absolute coherence nor cohesion between discrete elements but a system of provisional, intensive, local connections between free elements. Intensity describes the dynamic internalization and incorporation of external influences into a pliant system. Distinct from a whole organism - to which nothing can be added or subtracted - intensive organizations continually invite external influences within their internal limits so that they might extend their influence through the affiliations they make. A two-fold deterritorialization, such as this, expands by internalizing external forces. This expansion through incorporation is an urban alternative to either the infinite extension of international modernism, the uniform fabric of contextualism or the conflicts of post-modernism and Deconstructivism. Folded, pliant and supple architectural forms invite exigencies and contingencies in both their deformation and their reception. In both Learning from LasVegas and Deconstructivist Architecture, urban contexts provided rich sites of difference. These differences are presently being exploited for their ability to engender multiple lines of local connections rather than lines of conflict. These affiliations are not predictable by any contextual orders but occur by vicissitude. Here, urban fabric has no value or meaning beyond the connections that are made within it. Distinct from earlier urban sensibilities that generalized broad formal codes, the collected projects develop local, fine grain, complex systems of intrication. There is no general urban strategy common to these projects, only a kind of tactical mutability. These folded, pliant and supple forms of urbanism neither defer to nor defy their contexts but

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exploit them by turning them within their own twisted and curvilinear logics.

The suppLe and curvLlLnear "supple \adj [ME souple, fro O~ fro L supplic-, supplex submissive, suppliant, lit., bending under, fro sub- + plic- (akin to plicare to fold) - more at PLY] I a: compliant often to the point of obsequiousness b: readily adaptable or responsive to new situations 2 a: capable of being bent or folded without creases, cracks or breaks: PLIANT b: able to perform bending or twisting movements with ease and grace: LIMBER c: easy and fluent without stiffness or awkwardness." 13 At an urban scale, much contemporary architecture seems to be somewhere between contextualisrn and expressionism. Their supple forms are neither geometrically exact nor arbitrarily figural. For example, the curvilinear figures of Shoei Yoh's roof structures are anything but decorative but also resist being reduced to a pure geometric figure. Yoh's supple roof structures exhibit a logic of curvilinearity as they are continuously differentiated according to contingencies. The exigencies of structural span lengths, beam depths, lighting, lateral loading, ceiling height and view angles influence the form of the roof structure. Rather than averaging these requirements within a mean or minimum dimension they are precisely maintained by an anexact yet rigorous geometry. Exact geometries are eidetic; they can be reproduced identically at any time by anyone. In this regard, they must be capable of being reduced to fixed mathematical quantities. Inexact geometries lack the precision and rigor necessary for measurement. Anexact geometries, as described by Edmund Husserl, are those geometries which are irreducible yet rigorous. 14 These geometries can be determined with precision yet cannot be reduced to average points or dimensions. Anexact geometries often appear to be merely figural in this regard. Unlike exact geometries, it is meaningless to identically repeat an anexact geometric figure outside of the specific context within which it is situated. In this regard, anexact figures cannot be easily translated.

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Jeffrey Kipnis has convincingly argued that Eisenman's Columbus Convention Center has become a canonical model for the negotiation of differentiated urban fringe sites through the use of near-figures. 15 Kipnis identifies the disparate systems informing the Columbus Convention Center including, a single volume of inviolate program of a uniform shape and height larger than two city blocks, an existing fine grain fabric of commercial buildings and network of freeway interchanges that plug into the gridded streets of the central business district. Eisenman's project drapes the large rectilinear volume of the convention hall with a series of supple vermiforms. These elements become involved with the train tracks to the north-east, the highway to the south-east and the pedestrian scale of High Street to the west. The project incorporates the multiple scales, programs and pedestrian and automotive circulation of a highly differentiated urban context. Kipnis's canonization of a form which is involved with such specific contextual and programmatic contingencies seems to be frustrated from the beginning. The effects of a pliant urban mixture such as this can only be evaluated by the connections that it makes. Outside of specific contexts, curvature ceases to be intensive. Where the Wexner Center, on the same street in the same city, represents a monumental collision, the Convention Center attempts to disappear by connecting between intervals within its context; where the Wexner Center destabilizes through contradictions the Convention Center does so by subterfuge. In a similar fashion Gehry's Guggenheim Museum in Bilbao, Spain covers a series of orthogonal gallery spaces with flexible tubes which respond to the scales of the adjacent roadways, bridges, the Bilbao River and the existing medieval city. Just as in the Vitra Museum, the curvilinear roof forms of the Guggenheim Museum integrate the large rectilinear masses of gallery and support space with the scale of the pedestrian and automotive contexts. The unforeseen connections possible between differentiated sites and alien programs require conciliatory, complicit, pliant, flexible and often cunning tactics. Presently, numerous architects are intensively investigating the heterogeneities, discontinuities and differences inherent within any cultural and physical context

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by aligning formal flexibility with economic, programmatic and structural compliancy. A multitude of pli based words - folded, pliant, supple, flexible, plaited, pleated, plicating, cornplicitous, compliant, complaisant, complicated, complex and multiplicitous to name a few - can be invoked to describe this emerging urban sensibility of intensive connections.

The pLLant and Bent "pliable \adj [ME fro plier to bend, fold - more at PLY] I a: supple enough to bend freely or repeatedly without breaking b: yielding readily to others: COMPLAISANT 2: adjustable to varying conditions: ADAPTABLE syn see PLASTIC ant obstinate." 16 John Rajchman, in reference to Deleuze's book The Fold, has already articulated an affinity between complexity, or plex-words, and folding, or pli-words, in the Deleuzian paradigm of "perplexing plications" or "perplication." 17 The plexed and the plied can be seen in a tight knot of complexity and pliancy. Plication involves the folding in of external forces. Complication involves an intricate assembly of these extrinsic particularities into a complex network. In biology, complication is the act of an embryo folding in upon itself as it becomes more complex. To become complicated is to be involved in multiple, intricate connections. Where post-modernism and Deconstructivism resolve external influences of program, use, economy and advertising through contradiction, compliancy involves these external forces by knotting, twisting, bending and folding them within form. Pliant systems are easily bent, inclined or influenced. An anatomical plica is a single strand within multiple plicae. It is a multiplicity because it is both one and many simultaneously. These elements are bent along with other elements into a composite, as in matted hair(s). Such a bending together of elements is an act of multiple plication or multiplication rather than mere addition. Plicature involves disparate elements connecting with one another through various manipulations of bending, twisting, pleating, braiding and weaving through external force. In RAAUm's Croton Aquaduct project a single line following the subterranean water

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supply for New York City is pulled through multiple disparate programs which are adjacent to it and which cross it. These programmatic elements are braided and bent within the continuous line of recovered public space which stretches nearly twenty miles into Manhattan. In order to incorporate these elements the line itself is deflected and reoriented, continually changing its character along its length. The seemingly singular line becomes populated by finer and finer programmatic elements. The implications of The Fold for architecture involve the proliferation of possible connections between free entities such as these. A plexus is a multi-linear network of interweavings, intertwinings and intrications; for instance, of nerves or blood vessels. The complications of a plexus - what could best be called complexity - arise from its irreducibility to any single organization. A plexus describes a multiplicity of local connections within a single continuous system that remains open to new motions and fluctuations. Thus, a plexial event cannot occur at any discrete point. A multiply plexed system - a complex - cannot be reduced to mathematical exactitude, it must be described with rigorous probability. Geometric systems have a distinct character once they have been plied; they exchange fixed coordinates for dynamic relations across surfaces.

ALternatLve types of transformatLon Discounting the potentials of earlier geometric diagrams of probability, such as Buffon's Needle Problem, D'ArcyThompson provides perhaps the first geometric description of variable deformation as an instance of discontinuous morphological development. 18 His Cartesian deformations, and their use of flexible topological rubber sheet geometry, suggest an alternative to the static morphological transformations of autonomous architectural types. A comparison of the typological and transformational systems of Thompson and Rowe illustrates two radically different conceptions of continuity. Rowe's is fixed, exact, striated, identical and static, where Thompson's is dynamic, anexact, smooth, differentiated and stable. Both RudolfWittkower - in his analysis of the Palladian villas of 1949 - and Rowe

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- in his comparative analysis of Palladio and Le Corbusier of 1947 - uncover a consistent organizational type: the nine-square grid.

19

In Wittkower's analysis of

twelve Palladian villas the particularities of each villa accumulate (through what Husserl termed variations) to generate a fixed, identical spatial type (through what could best be described as phenomenological reduction). The typology of this 'IdealVilla' is used to invent a consistent deep structure underlying Le Corbusier's Villa Stein at Garche and Palladio'sVilla Malcontenta. Wittkower and Rowe discover the exact geometric structure of this type in all villas in particular. This fixed type becomes a constant point of reference within a series of variations. Like Rowe, Thompson is interested in developing a mathematics of species categories, yet his system depends on a dynamic and fluid set of geometric relations. The deformations of a provisional type define a supple constellation of geometric correspondences. Thompson uses the initial type as a mere provision for a dynamic system of transformations that occur in connection with larger environmental forces. Thompson's method of discontinuous development intensively involves external forces in the deformation of morphological types. The flexible type is able to both indicate the general morphological structure of a species while indicating its discontinuous development through the internalization of heretofore external forces within the system." For instance, the curvatures that result from the flexing of a grid are compared to alternative positions of the transformational type. Changes in the organism correspond to environmental data curves. For example, water depth and light intensity correlate with differences in the forms of fish, such as eye position and size. The flexing grid of relations cannot be arrested at any moment and therefore has the capacity to describe both a general type and the particular events which influence its development. Again, these events are not predictable or reducible to any fixed point but rather begin to describe a probable zone of co-present forces, both internal and' external. Thompson presents an alternative type of inclusive stability, distinct from the exclusive stasis of Rowe's nine-square grid. The supple geometry of Thompson is capable of both bending under external forces and folding those forces internally. These transformations develop through discontinuous involution rather than continuous evolution.

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The morphing effects used in the contemporary advertising and film industry may already have something in common with recent developments in architecture. These images have concrete influences on space, form, politics and culture. A good example is the physical morphing of Michael Jackson's body, including the transformation of his form through various surgeries and his surface through skin bleaching and lightening. These physical effects and their implications for the definition of gender and race were only later represented in his recent video Black & White. In this video, multiple genders, ethnicities and races are mixed into a continuous sequence through the digital morphing of video images. It is significant that Jackson is not black or white but black and white, not male or female but male and female. His simultaneous differences are characteristic of a desire for differentiated smoothness to become heterogeneous yet continuous. Physical morphing, such as this, is monstrous because smoothness eradicates the interval between what Thompson refers to as discriminant characteristics without homogenizing the mixture. Such a continuous system is neither an assembly of discrete fragments nor a whole." With Michael Jackson, the flexible geometric mechanism with which his video representation is constructed comes from the same desire that aggressively reconstructs his own physical form. Neither the theory, the geometry nor the body proceed from one another. Rather, they participate in a desire for smooth transformation. Form, politics and self-identity are intricately connected in this process of deformation. A similar comparison might be made between the liquid mercury man in the film Terminator 2 and the Peter Lewis House by Frank Gehry and Philip Johnson. The Hollywood special effects sequences allow the actor to both become and disappear into virtually any form. The horror of the film results not from ultra-violence, but from the ability of the antagonist to pass through and occupy the grids of floors, prison bars, and other actors. Computer technology is capable of constructing intermediate images between any two fixed points resulting in a smooth transformation. These smooth effects calculate the interstitial figures between fixed figures. Furthermore, the morphing process is flexible enough that multiple between states are possible. Gehry's and Johnson's Peter Lewis

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House is formulated from multiple flexible forms. The geometry of these forms is supple and can accommodate smooth curvilinear deformation along their length. Not only are these forms capable of bending to programmatic, structural and environmental concerns, as are Shoei Yoh's roof structures, but they can deflect to the contours and context of the site, similar to Eisenman's Columbus Convention Center and RAAUm's Croton Aquaduct project. Furthermore, the Lewis House maintains a series of discrete figural fragments - such as boats and familiar fish - within the diagrams of D'Arcy Thompson, which are important to both the morphing effects of Industrial Light and Magic and the morphogenetic diagrams of Rene Thorn. Gehry's supple geometry is capable of smooth, heterogeneous and continuous deformation. Deformation is made possible by the flexibility of topological geometry in response to external events, as smooth space is intensive and continuous. Thompson's curvilinear logic suggests deformation in response to unpredictable events outside of the object. Forms of bending, twisting or folding are not superfluous but result from an intensive curvilinear logic which seeks to internalize cultural and contextual forces within form. In this manner events become intimately involved with particular rather than ideal forms. These flexible forms are not mere representations of differential forces but are themselves deformed by their environment.

FoLdLng and other catastrophes for archLtecture "fold vb [ME fa/den, fro OE fea/dan; akin to OHG fa/dan to fold, Gk di p/asios twofold] vt I: to lay one part over another part 2: to reduce the length or bulk of by doubling over 3: to clasp together: ENTWINE 4: to clasp or em-brace closely: EMBRACE 5: to bend (as a rock) into folds 6: to incorporate (a food ingredient) into a mixture by repeated gentle overturnings without stirring or beating 7: to bring to an end." 22 I

Philosophy has already identified the displacement presently occurring to the post-modern paradigm of complexity and contradiction in architecture, as is suggested by Rajchman's"Out ofthe Fo/d" and "Perplications." Rajchman's texts are not

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manifestos for the development of new architectural organizations as much as they are responses to the emergence of differing kinds of complexity being developed by a specific architect. His essays inscribe spatial innovations developed in architecture within larger intellectual and cultural fields. Rajchman both illuminates Eisenman's architectural practice through an explication of The Fold and is forced to reconsider Deleuze's original argument concerning Baroque space by the alternative spatialities of Eisenman's Rebstock Park project. The dominant aspect of the project which invited Rajchman's attention to folding was the employment of one ofThom's catastrophe diagrams in the design process. Despite potential protestations to the contrary, it is likely that Thom's catastrophe nets were first introduced into architecture as a mere formal technique more or less simultaneously by Carsten Jule-Christiansen in Die Anhalter Faltung project, Eisenman in the Rebstock Park, Kipnis in the Unite de Habitation at Briey Installation, and Bahram Shirdel in the Nara Convention Hall. Inevitably, architects and philosophers alike would mistakenly find this in itself a catastrophe for all concerned. Yet, this event illustrates that at least four architects simultaneously found in Thom's diagrams a formal device for an alternative description of spatial complexity. The kind of complexity engendered by this alliance with Thorn is substantially different than the complexity provided by either Venturi's decorated shed or the more recent conflicting forms' of Deconstructivism. Topological geometry in general, and the catastrophe diagrams in particular, deploy disparate forces on a continuous surface within which more or less open systems of connection are possible. This diagram is catastrophic because it can represent abrupt transformation across a continuous surface. Topology considers superficial structures susceptible to continuous transformations which easily change their form, the most interesting geometric properties common to all modification being studied. Assumed is an abstract material of ideal deformability which can be deformed, with the exception of disruption. These geometries bend and stabilize with viscosity under pressure. Ironically,

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where one would expect that an architect looking at catastrophes would be interested in conflicts, architects are finding new forms of dynamic stability in these diagrams. The mutual interest in Thom's diagrams points to a desire to be involved with events which they cannot predict. The primary innovation made by those diagrams is the geometric modelling of a multiplicity of possible co-present events at any moment. Thorn's morphogenesis engages seemingly random events with mathematical probability. Thorn's nets were developed to describe catastrophic events. What is common to these events is an inability to define exactly the moment at which a catastrophe occurs. This loss of exactitude is replaced by a geometry of multiple probable relations. With relative precision, the diagrams define potential catastrophes through cusps rather than fixed points. Like any simple graph, Thom's diagrams deploy X andY forces across two axes of a gridded plane. A uniform plane would provide the potential for only a single point of intersection between any two X and Ycoordinates. The supple topological surface ofThom's diagrams is capable of enfolding in multiple dimensions. Within these folds, or cusps, zones of proximity are contained. As the topological surface folds over and into itself multiple possible points of intersection are possible at any moment in the Z dimension. These co-present Z-dimensional zones are possible because the topological geometry captures space within its surface. Through proximity and adjacency various vectors of force begin to imply these intensive event zones. In catastrophic .events there is not a single fixed point at which a catastrophe occurs but rather a zone of potential events that are described by these cusps. The cusps are defined by multiple possible interactions implying, with more or less probability, multiple fluid thresholds. Thom's geometric plexus organizes disparate forces in order to describe possible types of connections. The dominant effect of the French word pli derives from its resistance to translation by any single term. Nevertheless and despite folding's capacity to incorporate manifold external forces and elements within form, The Fold undoubtedly risks being translated into architecture through mere folded figures. In archi-

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tecture, folded forms risk quickly becoming a sign for catastrophe. The success of the architects who are folding should not be based on their ability to represent catastrophe theory in architectural form. Rather, the topological geometries, in connection with the probable events they model, present a flexible system for the organization of disparate elements within continuous spaces. These smooth systems, however, are highly differentiated by cusps or zones of co-presence. The catastrophe diagram used by Eisenman in the Rebstock Park project destabilizes the way that the buildings meet the ground. It smooths the landscape and the building by turning both into one another along cusps. The diagrams used by Kipnis in the Briey Installation project, and Shirdel in the Nara Convention Hall, develop an interstitial space which is contained simultaneously within two folded cusps. This geometrically blushed surface exists within two systems at the same moment and in this manner presents a space of co-presence with multiple adjacent zones of proximity. Before the introduction of either Deleuze or Thom to architecture, folding was developed as a formal tactic in response to problems presented by the exigencies of commercial development.

Henry Cobb has argued in both the

Charlottesville Tapes and his "Note on Folding" for a necessity to both dematerialize and differentiate the massive homogeneous volumes dictated by commercial development in order to bring them into relation with finer grain heterogeneous urban conditions. 23 His first principle for folding is a smoothing of elements across a shared surface.

The facade of the John Hancock Tower is

smoothed into a continuous surface so that the building might disappear into its context through reflection rather than mimicry. Any potential for replicating the existing context was precluded by both the size of the contiguous floor plates required by the developer and the economic necessity to construct the building's skin from glass panels. Folding became the method by which the surface of a large homogeneous volume could be differentiated while remaining continuous. This tactic acknowledges that the existing fabric and the developer tower are essentially of different species by placing their differences in mixture, rather than contradiction, through the manipulation of a pliant skin.

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Like the John Hancock Building, the Allied Bank Tower begins with the incorporation of glass panels and metal frames into a continuous folded surface. The differentiation of the folded surface, through the simultaneous bending of the glass and metal, brings those elements together on a continuous plane. The manipulations of the material surface proliferate folding and bending effects in the massing of the building. The alien building becomes a continuous surface of disappearance that both diffracts and a reflects the context through complex manipulations of folding. In the recent films Predator and Predator II, a similar alien is capable of disappearing into both urban and jungle environments, not through cubist camouflage but by reflecting and diffracting its environment like an octopus or chameleon.

24

The contours between an object and its context are obfus-

cated by forms which become translucent, reflective and diffracted. The alien gains mobility by cloaking its volume in a folded surface of disappearance. Unlike the "decorated shed" or "buildingboard" that mimics its context with a singular sign, folding diffuses an entire surface through a shimmering reflection of local adjacent and contiguous particularities.

For instance, there is a significant dif-

ference between a small fish which represents itself as a fragment of a larger fish through the figure of a large eye on its tail, and a barracuda which becomes like the liquid in which it swims through a diffused reflection of its context. The first strategy invites deceitful detection where the second uses stealth to avoid detection. Similarly, the massive volume of the Allied Bank Tower situates itself within a particular discontinuous locale by cloaking itself in a folded reflected surface. Here, cunning stealth is used as a way of involving contextual forces through the manipulation of a surface. The resemblance of folded architecture to the stealth bomber results not from a similarity between military and architectural technologies or intentions but rather from a tactical disappearance of a volume through the manipulation of a surface. 25 This disappearance into the fold is neither insidious nor innocent but merely a very effective tactic. Like Cobb, Eisenman introduces a fold as a method of disappearing into a specific context. Unlike Cobb, who began with a logic of construction, Eisenman aligns the fold with the urban contours of the Rebstock Park. The repetitive

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typologies of housing and office buildings are initially deployed on the site in a more or less functionalist fashion; then a topological net is aligned to the perimeter of the site and pushed through the typological bars. This procedure differentiates the uniform bars in response to the global morphology of the site. In this manner the fold incorporates differences - derived from the morphology of the site - into the homogeneous typologies of the housing and office blocks. Both Eisenman's local differentiation of the building types by global folding and Cobb's local folding across constructional elements, which globally differentiates each floor plate and the entire massing of the building, are effective. Cobb and Eisenman 'animate' homogeneous organizations that were seemingly given to the architect - office tower and siedlung - with the figure of a fold. The principle of folding shared by Eisenman and Cobb, evident in their respective texts, enables one to differentiate the inherited homogeneous organizations of both modernism (Eisenman's siedlung) and commercial development (Cobb's tower). This differentiation of known types of space and organization has something in common with Deleuze's delimitation of folding in architecture within the Baroque. Folding heterogeneity into known typologies renders those organizations more smooth and more intensive so that they are better able to incorporate disparate elements within a continuous system. Shirdel's use of Thom's diagrams is quite interesting as the catastrophe sections do not animate an existing organization. Rather, they begin as merely one system among three others. The convention halls float within the envelope of the building as they are supported by a series of transverse structural walls whose figure is derived from Thom's nets. This mixture of systems, supported by the catastrophe sections generates a massive residual public space at the ground floor of the building. In Shirdel's project the manipulations of folding, in both the catastrophe sections and the building envelope, incorporate previously unrelated elements into a mixture. The space between the theatres, the skin and the lateral structural walls is such a space of mixture and intrication. With structure itself, Chuck Hoberman is capable of transforming the size of

13 0

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domes and roofs through a folding structural mechanism. Hoberman develops adjustable structures whose differential movements occur through the dynamic transformation of flexible continuous systems. The movements of these mechanisms are determined both by use and structure. Hoberman's structural mechanisms develop a system of smooth transformation in two ways. The iris dome and sphere projects transform their size while maintaining their shape. This flexibility of size within the static shape of the stadium is capable of supporting new kinds of events. The patented tiling patterns transform both the size and shape of surfaces, developing local secondary pockets of space and enveloping larger primary volumes. The architectural discourses of Deleuze, Cobb, Eisenman and Hoberman inherit dominant typologies of organization into which new elements are folded. Within these activities of folding it is perhaps more important to identify those new forms of local organization and occupation that inhabit the familiar types of the Latin cross church, the siedlung, the office tower and the stadium, rather than the disturbances visited on those old forms of organization. Folding can occur in both the organizations of old forms and the free intensities of unrelated elements. There are similarly several manipulations of elements which engender smooth, heterogeneous and intensive organization. Despite differences between many contemporary architectural practices, some share a sensibility that resists cracking or breaking in response to external pressures. They use tactics and strategies that are compliant to, complicated by,and complicit with external forces in manners that are submissive, suppliant, adaptable, contingent, responsive, fluent, and yielding through involvement and incorporation. Architects who fold seek to place seemingly disparate forces into relation through strategies which are externally plied. Perhaps, in this regard only, there are many opportunities for architecture to be effected by Deleuze's book. The formal characteristics of pliancy - anexact forms and topological geometries primarily - can be more viscous and fluid in response to exigencies. They maintain formal integrity through deformations that do not internally cleave or shear but through which they connect, incorporate and affiliate productively. Cunning and

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viscous systems such as these gain strength through flexible connections that occur by vicissitude. The formal affinities of some contemporary projects result from a folding out of formalism into a world of external influences. Rather than speak of the forms of folding autonomously, it is important to maintain a logic rather than a style of curvilinearity through which pliancy and the ability to deform are responses to particular contingencies. With this logic, the question then becomes how can architecture be configured as a complex system into which external particularities are already found to be plied.

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Endnotes

the animal lines of beasts of burden. See Catherine Ingraham, Burdens of linearitY (New York, 1998).

I. Both Venturi and Rowe argue for collage strategies of formal conflict and complexity. Two additional ideas were introduced in Rowe and Koetter's text that are relevant to contemporary architecture: typological deformation and the continuity between objects and contexts. Both of these concepts receded when compared with the dominant ideas of collision cities and the dialectic of urban figure-ground relationships. Curiously, Rowe and Koetter illustrate typological deformations in both Baroque and early modern architecture. See Robert Venturi, Comj;>lexity and Contradiction in Architecture (New York, 1966) and Colin Rowe & Fred Koetter, Collage CitY (Cambridge, Mass., 1978) and Mark Wigley and Philip Johnson, Deconstructivist Architecture (New York, 1988).

10. Gilles Deleuze, The Fold: Leibniz and the Baroc;jue, trans. Tom Conley (Minneapolis, 1993).

2. See Sanford Kwinter and Jonathan Crary,"Foreword," in Zone 6: Incorj;>orations. ed. Sanford Kwinter and Jonathan Crary (New York, 1992), 12-15.

II.Wigley and Johnson, DeconstructivistArchitecture, 22. 12. Robert Somol, "0-0," in Architectural Design: Wexner Center for the Visual Arts (London, 1990). 13. Webster's New Collegiate Dictionary (Springfield, Mass., 1977), I 170. 14. See Jacques Derrida, Edmund Husserl's Origin of Geometry: An Introduction trans. john P. Leavey, Jr. (Lincoln, Neb., 1989). 15. jeffrey Kipnis, "Freudian Slippers," in Fetish ed. Sarah Whiting, Edward Mitchell and Greg Lynn (New York, 1992), 158-173. 16. Webster's, 883.

3. Gilles Deleuze and Felix Guattari, A Thousand Plateaus: Caj;>italism and Schizoj;>hrenia trans. Brian Massumi (Minneapolis, 1987), 478. 4. Wigley, Deconstructivist Architecture, 15. 5. Marion Cunningham, The Fannie Farmer Cookbook. 13th edition (NewYork, 1990),41-47. 6. Deleuze, A Thousand Plateaus 475-476. 7. An application of vicissitude to Kipnis' logic of undecidability and weak form might engender a cunning logic of non-linear affiliations. This seems apt given the reference to both undecidabilty and weakness in the definition of vicissitudes. See Ann Bergren's discussions of the metis in architecture for another example of cunning manipulations of form. Similarly, for a reading of metis tactics in Greek art see Jean-Pierre Vernant and Marcel Detienne, Cunning Intelligence in Greek Culture and Society, trans. janet Lloyd (Atlantic Highlands, Nj, 1978). 8. Deleuze, A Thousand Plateaus 256. 9.This concept was developed by Leibniz and has many resonances with Sanford Kwinter's discussions of biological space and epigenesis as they relate to architecture and Catherine Ingraham's logic of the swerve and

17. John Rajchman identifies an inability in contextualism to "index the complexifications of urban space" in his "Perplications: On the Space and Time of Rebstock Park," in Unfolding Frankfurt, ed. judy Greib and Sabu Kohsu (Berlin. 1991). 21. 18. For a more elaborate discussion of probable and anexact geometries, see my "Probable Geometries: The Architecture of Writing in Bodies" in this collection. 19. Rudolf Wittkower, Architectural Princij;>les in the Age of Humanism (New York, 1971) and Colin Rowe, Mathematics of the Ideal Villa and Other Essays (Cambridge. Mass.• 1976). 20. For an earlier instance of discontinuous development based on environmental forces and co-evolution. in reference to dynamic variation, see William Bateson, Materials for the Study of Variation: Treated with ESj;>ecial Regard to DiscontinuitY in the Origin of Sj;>ecies (Baltimore. 1894). 21. Erwin Panofsky has provided perhaps the finest example of this kind of heterogeneous smoothness in his analyses of Egyptian statuary and the Sphinx in particular: "three different systems of proportion were employed - an anomaly easily explained by the factthat the organism in question ;s not a homogeneous but a heteroge-

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neous one." See Erwin Panofsky, Meaning in the Visual Arts (New York, 1955). 62, note 10. 22. Webster's, 445. 23. See Henry Cobb, "First Interstate Bank Tower: A Note on the Architectonics of Folding" in Architectural Design Profile: Folding in Architecture, no. I02 (London, 1993), 94-96 and his contributions in The Charlottesville Tapes: Transcripts of the Confere~ Held at the University of Virginia School of Architecture. Nov. 12-13 1982 (Rizzoli,1985). 24.Analyzing the work of Douglas Garofalo, the editors of assemblage describe a strategy of camouflage that invests surfaces with alternatives to the forms and volumes they delimit. The representation of other known

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figures is referred to as a logic of plumage. For instance, a butterfly wing representing the head of a bird invites a deceitful detection. This differs from the disappearance of a surface by stealth which resists any recognition. See Douglas Garofalo, "The Camouflage House," assemblage 21 (August, 1993):72-81. 25. This recalls Michael Hays's text on the early Mies van der Rohe Friedrichstrasse Tower as a tactic of disappearance by proliferating cacophonous images of the city. Hays's work on Hannes Meyer's United Nations Competition Entry is perhaps the most critical in the reinterpretation of functional contingencies in the intensely involved production of differentiated, heterogeneous yet continuous space through manipulations of a surface.

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Matters

Since the time ofVitruvius, the whole concept of architecture has been dependent on the model of a unified body. Only the characteristics of whole bodies are described in terms of architecture: any particular body is rejected in favor of all bodies in general. There are many variations of ideal or whole bodies in architecture, all of which result from a search for a universal model of symmetry and proportion for the regulation of whole bodies. I Because of its desire for a holistic model of the body - one that is essentially static - only bodies that can be ideally reduced through a process of division to whole numbers are acknowledged in architecture. The proportional correspondence between a temple and a well shaped man are based first on a single organization regulating all parts to the whole and second on the presence of a common module. This formulation of the body as a closed system in which all parts are regulated by the whole is organized from the top down. Proportional orders impose the global order of the whole on the particular parts. This whole architectural concept ignores the intricate local behaviors of matter and their contribution to the composition of bodies. An attention to the matters out of which bodies are composed suggests a reformulation of the concept of the whole. An acknowledgment of base matI. David Reed, No.276 (for Nick), detail, /987-88, 63.5x259.08cm.

First published in lournal of Philosoj;>hy and the Visual Arts. 1993.

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ter does not necessarily lead to a transgression of the concept of the body itself (as has been the recent reaction to the repression of differences by the logic of the whole) but could engender a more open and dynamic conceptualization of how bodies are composed. Bodies can emerge through local intricate connections, alliances, aggregations and affiliations of base matter. These bodies can not be reduced to any single, general, universal or ideal organization as they result from the complex interactions of disparate systems. In order to define a body without appealing to the proportional logic of a whole organism, it is necessary to develop new categories of stability and unity. A reformulated concept of the body, which is composed from the bottom up through a process of continuous differentiation and multiplication, mandates "anexaa yet rigorous" topological descriptions that are neither ideal nor reducible. Edmund Husserl developed the category of the .anexact yet rigorous in the Origin of Geometry in 1936, to describe forms which are neither exact (they cannot be reduced to mathematical statements) nor inexact (they cannot be measured with precision). The necessity of these vague descriptions to any ideal geometry has been developed more extensively by Jacques Derrida in Edmund Husserl's Origin of Geometry: An Introduction of 1962. 2 This category of the anexact is capable of describing the vague characteristics of bodies that are not fixed statically," These geometries are capable of describing the architectural characteristics of bodies that are both "more and less" than whole.

composLtLon Through DLfferentLatLon An alternative model for architectural organization is based on the behavior of local particularities (base matter) as they contribute to the composition of provisional unities (bodies) from the bottom up, describing various degrees of cohesiveness and unity within bodies. Questions of composite bodies seem intimately related to questions of urban and architectural composition. Within such a base approach, any body's provisional unity depends on the stabilities and

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alliances between local elements. The manner in which bodies are composed and diffused from the motions of differential forces differs from the more familiar modeling of ideal bodies and wholes against which variations can be measured and reduced from the top down. This base procedure can inform new compositional sensibilities toward the development of dynamic, incorporative stabilities. An interest in non-static but stable bodies is utterly distinct from an interest in the decomposition of the concept of the body. The practices in architecture associated with philosophical deconstruction typically operate from the top down beginning with the model of the body as a whole, which is then dismantled through the identification of necessary internal differences which are seen as contradictory to the organization of the whole. Without an appeal to internal contradictions, differentiation can playa constructive role in the composition of stable bodies that are capable of continuous transformation and mutation. The now apparent failure of deconstruction to develop an adequate theory of composition in architecture (apart from its interpretation through strategies of decomposition) is most likely due to its proclivity for arresting internal differences in forms of contradiction and conflict. Rather than displacing stability and unity through difference, a continuous process of differentiation can be seen as the very possibility for the composition of an always incomplete and provisional unity. Bodies emerge through processes of differentiation, yielding varying degrees of unity based on specific affiliations and mutations. By beginning with bodily matter the possibility for singular bodies is not to precluded, but rather, bodies are sedimented, aggregated, unified and stratified through differential forces and the continual fusion of matter. An architectural model of bodily matter such as this exists as a fluid interface. Difference in this bottom up approach is the basis for a compositional sensibility that rejects the transgressive project of what has come to be called deconstructivism in architecture.

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parasLtLc Exchanges The concept of the parasite has recently and frequently been invoked by several deconstructivist architects and theorists as a model for a necessary supplement that internally destabilizes an existing structure. Mark Wigley has identified the integrity of internal difference to any stable structure in his description of "a sub-

versive alien, a foreign body that already inhabits the interior and cannot be expelled without destroying its host."" Wigley is careful to articulate this deconstruction of the whole as a displacement of a still intact structure rather than as a dismantling, decomposition or demolition. Yet in his description of Coop Himmelblau's Rooftop Addition it is clear that the parasite is seen as a surplus to the existing "form that houses it," displacing the relationship between interior and exterior necessary to the reading of the house as a body. 5 Likewise, in the recent projects of Diller+Scofidio, including the Para-Site installation at the Museum of Modern Art, the model of the parasite operates as a critical armature for the deconstruction of previously whole constructions. This critical method uses difference as an other that has been excluded or repressed from an already extant whole. These uses of difference to produce discontinuity and disjunction rely on a stable frame against which they operate as a critique of unity. Alternatively, the cybernetic paradigm proposed by Michel Serres in The Parasite suggests that the parasite has to configure the possibility for its own existence.

"The parasite invents something new. Since he does not eat like everyone else, he builds a new logic." 6 For Serres, parasitism is the only possibility for the definition of any body in the first place. The parasite discovers unity and stability within an entropic system through connectivity. A parasite does not attack an already existing host but invents a host by configuring disparate systems into a network within which it becomes an integral part. There is no interior before the parasite, the parasite is the active agent of unification. Such a sensibility configures difference as a

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compositional, rather than decompositional force. Rather than a threat to unity, difference becomes the very possibility for stability and order. Countless instances of parasitism, symbiosis, codependencies and mutualism illustrate that the differential processes of involution and coevolution bind disparate bodies into integral unities. The concept of the "body without organs" and the corresponding example of the wasp and orchid cited by Gilles Deleuze and Felix Guattari is just one such example of a composite body that emerges through parasitism." Friedrich Barth discovered that in the case of orchids (Ophrys inseetifera) and digger wasps (Gorytes mystaceaus and Gorytes campestris) there is not a mutualism but the inverse of the typical relations of insects and flowers: a parasitism of orchids on the wasps through "pseudocopulation." 8 The orchid becomes what Barth calls a "false female" that sexually attracts the wasp through pheromone-scented hair follicles on the thick appendage of its labellum, on which the wasp rubs its abdomen with the copulatory organs extended. As the wasp flutters on the orchid, pollinia become entangled on the wasp's head. Unsatisfied, the wasp eventually tires and repeats this behavior on other orchids fertilizing their stigma with the transported pollen from previous orchid contacts. By becoming a surrogate sexual partner to the wasp the orchid gains mobile genitalia in the wasp. The multiple orchids and wasps unify to form a singular body. This propagating unity is not an enclosed whole but a multiplicity: the wasps and orchids are simultaneously one and many bodies. What is important is that there is not a pre-existing collective body that was displaced by this parasitic exchange of sexual desire but rather a new stable body is composed from the intricate connections of these previously disparate bodies. Difference is in the service of a fusional multiplicity that produces new stable bodies through incorporations that remain open to further influence by other external forces. This formulation of bodies whose interiors are both produced by and are openly continuous with their external surroundings does not require a displacement of the oppositions between inside and outside as those categories are merely degrees of intensity located along a continuity. The familiar utilization of the model of the parasite as

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a deconstructive tool for the displacement of already existing orders overlooks the ability for parasitic exchanges to actually compose new bodies and new orders where none existed previously. These composite aggregations of new stabilities proceed through the continuous differentiation of matter.

Continuity and differentiation are the two conditions by which any collection of animate matter can be described as a body. Conventionally, architecture describes itself as an inanimate, modular, divisible, universal and static body. An alternative model of the body in architecture involves processes of continuous,

indivisible differentiation. Where divisibility is extensive, differentiation is intensive. Extensive systems obey an internal order that expands without changing its nature. Intensive systems follow a provisional internal order that adapts to, while influencing, its surroundings. Architecture has configured itself as an extensive system apart from exigencies and contingencies. An intensive model of the body is defined through the internalization of external, differential, disparate forces such that a stability emerges that is greater than the constituent elements. In this instance, no body can be absolutely coherent, cohesive, singular or unified as there are no pure unities apart from their specific contexts and the matter from which they are composed. Intensive bodies measure degrees of continuity within heterogeneous matter rather than the consistency of homogeneous modules. Composite organizations of base matter exhibit varying degrees of unity and bodiliness based on the influence of external forces. For example, when drinking a glass of water one often ingests e-coli bacteria. These external organisms are introduced into the interior of our bodies. The bacteria become integrated with the operations of our bodies as they enter the digestive system and begin to breed with other existing e-coli bacteria. These colonies of bacteria are both outside of the body's influence and also integral to its existence. They are bodies in themselves and, at the same time, they are organs of a more extensive human body. They are both free bodies and part of a composite body that they will eventually decompose and disperse from the inside out. The concept of multiplicity allows for the theorization and modeling

eody Matters

of such bodily matters that are folded continuously between the one and the multiple, between organs, free bodies and composite bodies. This multiplicitous insight into bodies is only possible when unity has been loosened from the concept of the whole and can be considered as a stability that emerges from differential forces that move from the bottom up rather than from the top-down.

Monstrous aodLes 2. Pseudocopulation between Gorytes mystaceus wasp and Ophrys orchid flowers.

3. Distribution ofhairson the Ophrys insectifera fly orchid (frontal and side views) compared withthe distribution ofhairson its pollinator, the Gorytes mystaceus wasp.

Monstrosities are those bodies which seem to "deviate from nature." 9 Erwin Panofsky, in The History of the Theory of the Proportions as a Reflection of the History of Styles, has provided an overtly architectural example of such a monstrous deviation from the natural proportions of architecture. His example of Egyptian sculpture is related to architecture in that the Egyptians inscribed profiles on the faces of stone blocks before carving them. The profiles consisted of a geometric network of squares of an equal size th~t regulated the proportion of the figure. Unique to the Berlin Sphinx Papyrus drawing are three different regulating networks, since that particular sphinx was composed of three heterogeneous parts: the body of a lion, the human

FoLds

head, and the small goddess. The proportions were prescribed by each figure: the canon for the lion, the canon of the Royal Heads and the canon of twenty-two squares for a complete body. The sphinx was assembled from three disparate components, each of which was conceived and proportioned as if it was standing alone. Through the composition of unrelated disparate free elements that lacked any common module the sphinx is seen as an

"anomaly easily explained by the fact that the organism in question is not a homogeneous but a heterogeneous one." 10 The lack of transcendent modularity leads, Panofsky maintains, to monstrous, hybrid, recombinant and heterogeneous bodies. The sphinx is not a mere collage of fragments as the three disparate networks are fused to produce the body of the sphinx. II Bodies produced through combinatorial differentiation are not divisible by any single module; they are both irreducible unities and collections of heterogeneous elements; they are simultaneously a unified whole and freely associated parts.

J

Bodles & BLoBS

4. Regnault, The Deviations of Nature 1775:'Double Child', used to illustrate Georges Bataille's text published in Documents (1930) (from the Cabinet des Medailles, collection, in Paris Bibliotheque Nationale).

5. Smooth sponge (suberites) growing on a hermit crabs adoptedshell.

6. Egyptian sculptor's working drawing (papyrus).

FUSLon and DLffusLon From processes of continuous differentiation, heterogeneous bodies emerge.

Body Matters

143

Bodies are capable of both gathering stability through alliances and dispersing matter freely in the same gesture. The seemingly opposed movements of cohesion and dispersion can be understood as a continuous movement.

Deleuze and

Guattari have formulated the model of the "body without organs" to describe this 7.Differences among species andsubspecies in ordinaryandspedalavicularia ofMetrarabdotos bryozoans.

double

gesture

of

"two-fold

deterritorialization." The motion of diffusion and fusion continuously redefines the boundaries between interior and exterior.

Internal territories are inten-

sively influenced from forces outside of their control while bodies extend their interiors outward to extend and reconfigure their territory.

Deterritorialization

not only disperses interiors outward but simultaneously unifies a constantly shifting interior through the internalization of external forces.

These negotiations

encompass both the laws of involution 8.Typical zooidmodule

ofbryozoan structure.

9.Hypothetical morphospace de~ned by varying degrees ofclimb axis between the colony axis andthe lateral angle branch systems, with constant branch spadng. These arethe internal undifferentiated axes ofgrowth apartfrom innuences by currents andotherforces.

and evolution. Evolution is the external selection

of

internal

mutations.

Involution is the internal selection of mutations due to intensive alignments with external forces. Rather than deconstructing the organic whole of humanism this logic of continuous differentiation constructs a fluid semi-permeable boundary between interior and exterior. A provisional unity is established both through

144

FoLds~

aodles & aLoBs

expansion and intensity. Such a model for the body is capable of describing the composition and stratification of unity while allowing the dispersal of those same characteristics through a continual process of differentiation. Deleuze and Guattari's concept of two-fold deterritoriali-zation owes much to Elias Canetti and Rene Thom, both of whom have described stable compositions of elements that remain open to influence through dynamic interactions and exchanges. Canetti's categories of "packs" (hunting, war, lamenting and increasing), "crowds" (open, closed, destructive, slow, baiting, flight, prohibition, reversal, feast and double) and "crowd crystals" (the unities that exist within crowds such as police and monks) all describe instances where multiple individuals enter into alliances from which new unities fuse and diffuse. 12 These composite entities develop behavior and traits that cannot be reduced to anyone of the individual members but result from the differential alliances of a composite, aggregate organization. Interiors and exteriors become folded into one another, yielding the continuous multiplicity of the pack-body, crowd-body or crowd-crystal-body. Canetti's psychoanalysis of crowds uncovers the emergence of composite body organizations, at the scale of the city, from free elements. Due to a crowd's desire for expansion and incorporation, its behavior is continually, dynamically and turbulently transforming from dispersion and disappearance to coherence and stability. Crowds are organized by neither one body nor multiple free bodies but through bodily alliances that stabilize and disperse. The hundreds of thousands of perceptions that contribute to the organization of the crowd are capable of both entrainment, to develop unity, and free movement, to produce dispersion. Similarly,Thom's concept of "retroactive smoothing" in insect swarms describes the stabilization of free elements after. a territorial expansion.

13

The elements of

a swarm are given over to free motion where they are dispersed by external forces, only later to be reconstituted through a retroactive gesture that emerges from within and between the elements. What is most startling about these pack, crowd, crystal and swarm bodies is that they interact with their environment intensively. Unlike a familiar contextualism

Body Matters

145

or functionalism, which is based on form's ability to passively result from contingencies and exigencies, an intensive sensibility turns external forces and contingencies to its own devices. By anticipating and reacting to external forces, supple and flexible provisional orders are able to incorporate vicissitudes and contingencies within their internal order. Supple bodies are shaped by an internal order capable of flexibly responding to vague external forces through smooth

retroactive gestures.

vLscous aodLes Conventional architectural description lacks the clarity necessary for the measurement of the behaviors and characteristics of matter, as those effects are not static and cannot be fixed with proportional exactitude. As Luce Irigaray has argued in "The Mechanics

of Fluids,"

this inattention to the dynamic and fluid is

not accidental but a symptom of the "precedence

ofthe solid and static."

14

The fluid model of viscosity is the condition where the cohesive characteristics of a body are determined by the external frictions, pressures and heat exerted upon it. Viscosity is a quality of being mutable or changeable in response to both favorable and unfavorable situations that occur by vicissitude. Vicissitudinous events are neither arbitrary nor predictable but are made possible by a confluence of internal motivations with external forces. For instance, when a seemingly accidental event occurs the victims immediately identify the forces contributing to the accident and begin to assign blame. It is inevitable, however, that no single element can be made responsible for any accident as these events occur by vicissitude; particular influences at a particular time make the outcome of an accident possible. If any element participating in such an intricate network of local forces is altered the nature of the event will change. A viscous sensibility depends on both an intrication of local intensities and the exegetic pressure exerted on those elements by external contingencies. Neither the intrications nor the forces which put them into relation are predictable from within any single system. Connections by vicissitude develop identity through the incorpora-

FoLds

tion of local adjacencies and their affiliations with external forces. In this sense, vicissitudinous mixtures become cohesive through a logic of viscosity. Irigaray defines the viscous as the model for relations of the "near and not the proper."

Viscous fluids develop internal stability in proportion to the external pressures exerted upon them. Fluids behave with two types of viscidity: they exhibit both internal cohesion and adhesion to external elements as their viscosity increases. Viscous fluids begin to behave less like liquids and more like sticky solids as the pressures upon them intensify. Irigaray refers to these gelatinous forms as nearsolids. Viscous forms are capable of yielding continually under stress so as not to shear, exhibiting both a cohesive stability in response to adjacent pressures and an adhesive stickiness to adjacent elements. The nature of pliant forms is that they are sticky and flexible. Things tend to adhere to them. As pliant forms are manipulated and deformed the things that stick to their surfaces become incorporated within their interiors. Forms of viscosity and pliability cannot be examined outside of the vicissitudinous connections and forces with which their deformation is intensively involved.

J

BodLes &

BLo~s

10-15.Gelgolfdemonstrates the ability of an intelligent gel to ad on its surroundings.

eody Matters

16-20.Gellooper device that moves by repeatedly curling and straightening itself as its surfactant moleculesrespond to the influence of an electric field with alternating polarity.

147

Viscosity and vicissitude characterize organizations

that

emerge

through

processes of differentiation. Recently

much

attention

has

been

focused on the potential development of a new kind of viscous machine. These gelatinous machines have been termed

"wet" and "intelligent." They are wet because they are fluid, supple, flexible and viscous in their development of varying degrees of stability, strength and coherence. They are intelligent because they exploit the vicissitudes of their surrounding environment for their own internal structuration.

15

They develop increasing

and decreasing degrees of viscosity in response to external stimulus. The relationships between their viscosity and their interactions with their environment is not determined by any factor or operator but develops out of a confluence of multiple forces. The gel-golf armature is an example of one such machine. It is a flexible arma-

i:II'·"rr ·'.-1 .til

ture that reacts to its environment through expansion and contraction based on the chemical content of the surrounding fluid in which it is immersed. When a ball with a specific chemical coating is dropped into the tank, the gel armature

FoLds, Bodles

&

BLoBS

reacts by expanding and bending toward the ball, striking it with sufficient force to move it. It will continue to swing at the ball until it is pushed out of reach. Due to this chemical feedback with its environment, this gelatinous matter is an open system. The gel is capable of responding to external forces and can therefore organize its environment through extensive gestures. Forces exerted on such an intensive body often instigate emergent gestures that are capable of reorganizing the context which initiated them. Deformation and curvilinearity are expressions of the dynamic, stable composition of bodies within a field of differential forces. Even the simple animal phylum of modular zooids internally mutates through the internalization of certain external influences.

16

As zooid modules become locally connected to form large

colonies - such as those of a sea weed - their individual organizations become specifically deformed. The more or less identical modules develop differing configurations, based on their alliances with one another, in response to exigencies. For example, as feeding must occur on the perimeter of the colony, and as the aggregate body increases its mass, sustenance is passed to the interior of the colony through specialized pores which develop only for this purpose. Long cilia mutate to clean the colony's surface and smaller, more powerful cilia develop to produce and funnel currents to increase the food supply to the interior of the colony. Reproductive functions are hypertrophied in specific zooids and atrophied in others as the colony begins to form specialized reproductive organs through alliances within particular sub-colonies of individuals. The modules differentiate into a more complex, particularized organism, due to an intensive relationship with the currents of the marine environment in which these colonies are immersed. The zooids are configured by their context and then begin to influence and reconfigure that context to maximize their own performance. An attention to the dynamic deformation of the module through local interstitial alliances and connections to evolving larger provisional unities can describe these forms of polymorphism.

Body Matters

149

curvLLLnear Gestures Gestures are always intensively curvilinear. Curvilinearity signifies the principled deformation of a line while organizing many disparate elements continuously. Astrology provides perhaps the best example of an intensively curvilinear gesture. Any given constellation of disparate points or stars arrives at its respective position through differential forces. An astrological gesture will unify those elements with a curvilinear line that both locates their particularities and places those particularities within a continuum. These gestures might take the form of a crab, ram, lion, fish, dipper, etc. More important than what these figures signify is that they are always continuous, always curvilinear and always gestural. Gestures, such as these, are highly principled flexibleconnectivenetworks, The

~

gesture maintains openness through an attention to the particular characteristics of the disparate elements which constitute it and give the continuous shape its particular curvilinear form.

17

The ~~~stract forces of their constituent, dis-

parate elements and the retroactive unity by which those points are placed into a relation are expressed along a continuous line. There is no propriety to the gesture, yet the possibilities are partially determined by the contingent differences with which the gesture begins. The curvilinear gesture is capable of maintaining many different and particular influences within its provisional unity. The primary characteristic of the gesture is its provisional ~~!fication_ through a P!:~ss of differentiation and the curvilinearity of its lines based on this same

deformation and differentiation. The simultaneity of the one and the many in these models renders any gestural organization a multiplicity, capable of dispersing into the constellation of the many or calcifying into the singularity of the one. The gradual dispersal of constituent points in some gestures invites more open readings where the gradual condensation and alignment of elements leads to a greater degrees of unity and closure. Gestures emerge from thousands of tiny perceptions, of cells, proteins, enzymes, hormones, and other base matter. Matter becomes connected forming organs, organs are collected to form bodies, bodies begin to articulate gestures in response to a constellation of forces resulting from differential interactions across molecular, cellular, organic and bodily

.,i:

FoLds~

aDdles & BLobs

scales. Hunger, for instance, does not arise from any single organ's perception but rather occurs through a dynamic interaction of e-coli bacteria that construct a body of digestive perception, the impulses of the stomach and large and small intestines, hormones, glands and the other visual, oral, auditory, and olfactory ;.' stimuli from outside the body. - Hunger is a unifying gesture that renders thousands of tiny perceptions visible as an abstract expression. Gestures are rigorous, precise modes of organization that render imperceptibly minute and multiple desires as unified perceptions. Bodies are expressed, stabilized, organized and f unified through the play of a multiplicity of tiny forces. ....'":"-._-------

:~.

.

Architecture is one vector mingled with many other political, social, economic, institutional and cultural forces. Architecture is not capable of determining events but nonetheless participates in the formation of urban bodies and populations. These urban bodies may be strictly determined or they may occur spontaneously. For instance, a more or less closed urban body is composed within the architectural space of a soccer or football stadium with the occurrence of a wave. This is one example of a building organizing a unifying gesture across constituent elements. There is no single individual that determines the instant or location that a wave will begin, what the speed of the wave will be across the crowd, whether the wave will move in a clockwise or counter-clockwise direction around the stands, what percentage of the crowd will participate in the wave or what the duration of the wave will be. These events are determined by the proceedings of the game, the media and the constituent fans. Although the example of the wave is constrained within a closed architectural structure, it is still notreducible to the form of the object in which it is housed. No stadium is capable of determining or predicting with exactitude these urban gestures, although it is capable of organizing the "thousands of tiny perceptions" in such a way that a temporary unification is possible. 18 The impulses that contribute to the production of the wave effect are differential and multiple, leading to a singular unifying gesture that temporarily renders the stadium and its occupants as a provisional body. The waving body may persist, even expanding as more of its elements are excited into a state of waving, and as the hundred thousand tiny

eody Matters

impulses subsist so too does the provisional body dissipate. The composite body of the waving stadium does exhibit cognition at the scale of urbanism: it is excitable, it is prone to hunger, it can be angered, it is celebratory, it is responsive to images, it is capable of sustained attention and distraction from its internal motor (the game occurring at its center). The intricate connection of tiny events, of the most base kind imaginable, along with the monolithic structure of the stadium and the game itself are necessary to the formation of the wave. Particular gestures are sponsored by particular forms: the wave is a closed gesture circulating within a unified architectural volume. The challenge for architecture is the design of urban spaces in which-- a--- multiplicity of gestures ~r~ pos--- --- -. -.. . ~Ie. An alternative model of the body to that of the stadium, which is after all a closed holistic enclosure, is perhaps the beginning for such an architecture. Gestures, such as the wave, establish a system of circulation between the crowd singularity (the one) and free elements (the many). These gestures of unification and dispersal constitute and diffuse bodies continuously. The wave is a curvilinear gesture that circulates through the individual particles, within the monolithic structure, uniting disparate elements into a dynamic, temporal body. .-_.-

--

-.

~.-.

. -.

.

_ ..

-

.

.-

Gestures as Abstract ExpressLons of Forces Etienne-Jules Marey was interested in recording the movements, pulsations and flows of bodies directly as abstract gestures.

"The whole of his work had consisted in showing what one could learn from a curve, which was not merely a simple 'reproduaion'. It was from and with the curve that forces could initially be calculated. It was easy to obtain the mass of the body as well as the speed it was going (chronobio/ogy); from this one could induce the force that had set it in motion, the work expended to produce this action. This trajeaory always had to be questioned and interpreted. Not only were the slightest nicks and notches in the line due to certain faaors, but they enabled the determination of resistances as well as impulses." 19

.~;

FoLds, aodLes & aLoBs

The figure of an electrocardiogram reading of the heartbeat is not only a numeric representation but a gestural expression of an abstract flow that captures perceptions of excitability, anger, relaxation, truth, deception, etc. Likewise, Marey's connective lines between photographically arrested instances of motion were drawn retroactively to express the force and duration of a body, its mass, velocity, direction and gravity in a single gesture. The lines of frozen motion of his photographs are merely the instants through which motion circulates between intervals. The connective strokes drawn by Marey are highly differentiated lines that express temporal and corporeal forces. Most importantly, these lines organize manifold influences along a continuously differentiated line. The smoothing lines of Marey traverse intervals expressing a continuity that incorporates a constellation of disparate forces. These unifying figures begin to describe a dynamic fluid body as it is intensively influenced and organized by particular contingencies and movements. The curvilinearity of these abstract expressions results from the differential forces that those lines organize. These curvilinear gestures express a body in time, in motion, intensively involved with its context. To reduce these curvi-

2 I. Chronophotograph: jump from a chair, 1884.

22. Marey's drawn analysis during running.

ofthe positions ofa leg

Body Matters

153

linear gestures to ideal average lines would evacuate them of their particular content. Outside of the vagueness of particular influences bodies such as these do not exist. The most important principle here is that 23.Mareys drawn analysis ofthe positions ofthe front limb ofa horse galloping with smoothing connective lines (both taken from chronophotographs).

~~~s occur ~cross the interval~ between ....,

bodies.__ There is no flow ·within a whole, only stasis.

Networks of internal and

external forces are resolved through these dynamic exchanges. An architecture of static bodies rejects all contiguous, contingent forces, leaving the flows .-. between bodies unattended. The insight of D'ArcyThompson is that all bodies are always internally mutating in response to forces outside of their influence. This principle of involution intensifies the relationships between bodies and disperses the interiority of an ideal body into a differential network. The body is reterrito24. Marey's graphic notations

ofmuscular shocks.

rialized in a two-fold manner as the interior of the body flows out and external contingencies flows in. Thompson posits perhaps the first geometric technique for the analyses of duration as it applies to the morphogenetic composition of form. Differential forces are the sources and material for discoveries, inventions and new dynamic stabilities. These forces are mapped by a deformable body geometry.

f"

FoLds, aodles

154

aLoBs

Thompson shares a profound disinterest in the module, as did the Egyptians in Panofsky's analyses. Thompson locates discriminate characters in order to chart their reassembly, migration, development and mutation due to external pressures. Thompson uses the initial type as a mere provision for a dynamic system of transformation that occurs in connection with larger environmental forces. Thompson intensively involves external forces in the creation of new morphological types through combinatorial deformation. The flexible type is able both to indicate the general morphological structure of a species and indicate its discontinuous development through the internalization of heretofore external forces within the system. For instance, the enlargement of the eye of a fish is represented by the flexing of a grid. This fluctuation, when compared to a previous position of the transformational type, establishes a relation between water depth and light intensity as those conditions are involved in the formal differences between fish. These events are not predictable or reducible to any fixed point but rather begin to describe a probable zone of co-present forces; both internal and external. The geometric effects of these deformations become a map of an intensive interaction between a disinterested environment and a discrete body, such that these two groups of forces become inextricably and intricately connected. The supple geometry of Thompson is capable of both bending under external forces and folding those forces i!l~~.rn.aJly. These transformations "" . --develop through discontinuous involution rather than continuous evolution. A deformable geometry is capable of describing the flow of these forces by attending to the localized particular deviations of bodily matter. 20 These curvilinear gestures are the abstract expressions of an open organization or unity that arises from a dynamic network of differential forces. These gestures describe the continuous process of differentiation that both fuses matter into bodies and diffuses bodies into free matter. -.

-II

&

-

""'-.

-. .

.

.-

. -~.

Body Hatters

155

Endnotes I. For a discussion of the role of variation in the phenomenological reduction of particular bodies to ideal "eidetic" bodies in relation to the production of architectural types see my "Multiplicitous and Inorganic Bodies" in this collection. 2. See Jacques Derrida, Edmund Husserl's Origin of Geometry: An Introduction, trans. John P Leavey Jr. (Lincoln, Neb., 1989). 3. I develop a discussion of these geometries and their relationship to architecture in "Probable Geometries: The Architecture of Writing in Bodies" in this collection. 4. Mark Wigley, "Postmortem Architecture: The Taste of Derrida," Persj;>ecta,no.23 (1987): 160. 5. Mark Wigley and Philip Johnson, Deconstructivist Architecture (New York, 1988), 80. 6. Michel Serres, The Parasite trans. Lawrence R. Schehr (Baltimore, 1982), 35. 7. Gilles Deleuze and Felix Guattari, A Thousand Plateaus: Caj;>italism and Schizoj;>hrenia, trans. Brian Massumi (Minneapolis, 1987), 10. 8. Friedrich Barth, Insects and Flowers:The Biology of a Partnershij;>, trans. M. A. Biederman-Thorson (Princeton, 1991),237-249. 9.This term is taken from an essay by Georges Bataille. See Bataille's "The Deviations of Nature" in Visions of Excess: Selected Writings 1927-1939, trans. Alan Stoekl (Minneapolis, 1985), 53-56. 10. Erwin Panofsky, Meaning in the Visual Arts (Chicago, 1955),62. I I. Jeffrey Kipnis has recently escalated the distinction between collage - which he defines as discontinuous heterogeneity - and other practices of continuous heterogeneity. This difference from and subsequent dismissal of collage strategies is the hinge on which Kipnis

25. David Reed, No. 252, /987, 274.32 em x 9/.44 em.

FoLds, aodles & aLoBs

turns from the Post-Modern practices (including those of what has come to be called Deconstructivism) to more cohesive architectural practices. See jeffrey Kipnis, "Towards a New Architecture" in Architectural Design Profile: Folding in Architecture, no. I03, ed. Greg Lynn (London, 1993),40-49. For an alternative discussion of continuous yet heterogeneous systems of organization see my "Architectural Curvilinearity: Folded, Supple and Pliant Architecture" in this collection. 12. Elias Canetti, Crowds and Power (New York, 1984). 13. Rene Thorn, Structural Stability and Moq;>hogenesis trans. D. H. Fowler (Reading, Mass., 1975).

14. "Yet one must know how to listen otherwise than in goodformes) to hearwhatit says. Thatit iscontinuous, compressible, dilatable, viscous, conduaible, diffusible ... that it is unending, potent and impotentowing to its resistance to the countable; that it enjoys and suffers from a greater sensitivity to pressures; that it changes - in volume or in force, for example- according to the degree of heat;that it is,in its physical reality, determined by friaion between two infinitely neighboring entities - dynamics of the near and not of the proper, movements coming from the quasi comaa between two unities hardly definable as such (in a coefficientof viscosity measured in poises, from Poiseuille, sic), and not energy of a finite system; that it allows itself to be easily traversed by flow by virtue of its conductivity to currents coming from other fluids or exerting pressure through the walls of a solid; that it mixes with bodies of a like state, sometimes dilutes itselfin them in an almost homogeneous manner, which makes the distinaion between the one and the other problematical; and furthermore that it is already diffuse "in itself," which disconcerts any attempt at static identification . . ." Luce Irigaray, This Sex Which is not One, trans. Catherine Porter with Carolyn (Ithaca, 1985), I I I.

of muscle than is that of metallic machines. This pliant motion is usually seen onlyin biological systems, such as the wings of birds, which reshape themselves continuously to maximize lift. Because gels are soft,they can manipulate delicate materials without damaging them. Even more important, however, gelsare soft with respea to their environments. Machines made of metal or silicon operate as closed systems. Theydo not adapt to changes in theiroperating conditions unless a separate sensor system or a humanoperator is at the controls. Gels, in contrast, arethermodynamically "open": they exchange chemicals with the solvent surrounding them and altertheirmolecular state in the process of accomplishing work...these properties create self-sensing and self-regulating machines that respond intelligently to changes in theirsurroundings." Yoshihito Osada and Simon B. Ross-Murphy, "Intelligent Gels," Scientific American (May, 1993). 16. See Biology of Bryozoans, eds. Robert Woollacott and Russel Zimmer (New York, 1977), Woollacott, Bryozoans (London, 1970), and especially Frank McKinney and jeremy B. jackson, Bryozoan Evolution (Chicago, 1989). 17. For Panofsky,the gesture was the first problem to be overcome by systems of proportion: while the gesture implied both particularity and temporality according to Panofsky, symmetry and proportion assume static fixity. See Panofsky, Meaning in the Visual Arts. 18.This discussion of "thousands of tiny perceptions" in regard to the formation of singular perceptions (such as the desire that can be named hunger at a certain threshold) is elaborated by Gilles Deleuze in The Fold: Leibniz and the Baroque, trans. Tom Conley (Minneapolis, 1993).

Burke

15."Simple though it is,the gellooper exhibits the essential charaaeristics that set "soft" chemomechanical systems apart from mechanical devices made of more rigid materials. In contrast to conventional motorsand pumps,gelsare gentle and flexible, and theirmovementis more reminiscent

19. Francois Dagognet, A Passion for the Trace: Etienne-Iules Marey, trans. Robert Galeta with jeanine Herman (New York, 1992), 62. 20. See my "Multiplicitous and Inorganic Bodies" in this collection.

GLOBS

In the last three decades, if one word could be identified as having a primary effect on architectural- theory and design, that word would most likely be complexity. The meaning of the term complexity has varied widely, yet its use as a vehicle for launching new ideas in architecture has been consistent. A very provocative history of architectural theory since 1966 could no doubt be written around the phrase "complexity in architecture." In fact, the pathological necessity for architecture continually to announce its newfound interest in complexity is perhaps the most important feature of architectural theory and design since the climax of late-modernism.

I have elsewhere discussed the

differing uses of the term complexity by architectural theorists as divergent as Robert Venturi - in Complexity and Contradiction - and Mark Wigley - in Deconstructivist Architecture. I The use

First published in lournal of Philosophy and the Visual Arts. 1995.

FoLds

J

aodles &

aLo~s

of the term complexity in these architectural texts has been related to the conflict of multiple differences. Venturi's complex wholes are exemplary of complication and its requisite contradictions masquerading as complexity. Although the differences between complicated and complex organizations have been ill defined, and although their differences are not as discrete as they might seem, the primary characteristic unique to complexity is a provisional unification of disparate components without totality or wholeness. 2 Both Venturi's "difficult whole" and Wigley's "conflicting geometries" share an appeal to multiple systems in conflict. While it is important to articulate an alternative theory of complexity that is not founded upon some notion of the multiple and differential being initially defined in dialectical conflict or contradiction, the present backlash of wholism and organicism in architecture under the umbrella of complexity theory should be avoided. The Neo-Platonist epistemology of multiple interacting simple systems giving rise to complex, synthetic, and, in the parlance of the new sciences, emergent wholes is troubling because it reinforces a naturalistic wholism from the bottom-up. The previous challenges to totalization, synthesis and wholism need not be opposed by a theory of complexity, but instead those critiques of wholism might be incorporated into a theory of differential complexity that does not begin with the law of contradiction. The most difficult task for the moment is the development of a discourse of complexity that avoids an appeal to conflict and contradiction without drifting into the reactionary discourses of wholism and emergence. The perennial alternatives of either contradiction or wholism are presently both defining themselves through the use of the term complexity in two distinct yet dialectically dependent ways. As dogmatic defenders of contradiction and deconstruction square off against the new age accolytes of complexity, any discussion of difference that is not apriori dialectic will be squeezed out. The law of contradiction announces that two different statements, A and B for instance, cannot be identical, so that A cannot be identical to B without being B. This relation, that two statements cannot be both different and identical, announces that the foundation for identity is in fact the identification of differ-

BLoBS

159

ence. It is no surprise then that complexity is often defined as the contradiction between multiple systems that cannot be synthesized into a single unified system. Although this is an alternative to a simplistic understanding of identity, to define complexity as the contradiction of differences is to remain within a very classical epistemology, however

complex

and

undecidable identity becomes within such a relation.

Given this understanding of

complexity as contradictory, simplicity can be defined in one of two ways: either as the primitive components from which more complex assemblages are constituted, or as the single organization underlying a composite assemblage that is discovered through reduction. The differences at stake between these two understandings of simplicity and complexity are between theories of emergence, on the one hand, and theories of reduction, on the other. Common to both of these positions is the assumption that complexity is irreducible and multiple and simplicity is reducible and singular. The differences are based on the position from which order is seen to proceed; in the case of emergence, order emerges from the bottom-up, whereas in the case of reductivism, order is discerned from the top-

160

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down. In the popular press and science journals there has been a distinct shift from top-down concepts of order that begin with complexity and arrive at simplicity, to concepts of order that begin with the interaction of simple components aggregating higher degrees of complexity and organization, which produces a nagging feeling that a dialectical system has simply been inverted. This is compounded by the troubling affinity between theories of emergence and the various revivals of neo-Darwinism and free market economics. The fact that contemporary complexity theories of emergence are presently being used to underwrite free-market capitalism and programs of social Darwinism is troubling insofar as they implicitly assume invisible control and selection through combination. It is this theoretical blind SPfJt in the theories themselves that allows them to be adopted by conservative ideologies. Complexity is often described in a neo-Darwinian fashion as the gradual accumulation of differences that are in essence random in their combination and mutation. This explains combination and affiliation as an ad hoc process that is organized by some invisible hand - in the case of Darwinism the hand of external selection and in the case of free market capitalism the informed consumer. In effect, affiliations between systems are mere super-impositions without method that are later read by a system that is incapable of being theorized or understood; an external act of selection from outside of the system of differentiation. The parallels with certain architectural practices of the I 980s seem all too literal and obvious in relation to the use of superposition of information such as conflicting grids or figures - which are then read for their latent organization. Bernard Tschumi, Daniel Libeskind and Peter Eisenman would be the best example of these practices which even today remain the dominant mode for architectural experimentation in the universities and the profession. Any definition of complexity as primarily the contradiction of ~ultiple systems is doomed to being understood as a critique of Cartesian reductivism from within a Cartesian horizon. There is a counter tradition, however, that does not exclude a theory of combination from discussions of order but instead makes the act of combination the primary mode of relationships. If Cartesian ism is associated

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with isolation and the reduction of systems to their constitutive identities then Liebniz's Ars Combinatoria is an alternative epistemology founded on the systematic nature of combinatorial changes in identity that take place with greater degrees of complexity. In order to develop a theory of complexity that is not founded on the contradiction of differences it is necessary to reconceptualize identity as neither reducing toward

primitives

nor emerging

towards wholes. A theory of complexity that abandons either the single or the multiple in favor of a series of continuous multiplicities and singularities is one way of escaping the definition of identity through dialectic contradiction. In other contexts I have argued for the development of theories of multiplicitous organizations that are neither one nor many. Similarly, one approach to a theory of complexity might be to develop a notion of the composite or the assemblage which is understood as neither multiple nor single, neither internally contradictory nor a unified.

Complexity

involves the fusion of multiple and different systems into an assemblage which behaves as a singularity while remaining

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irreducible to any single simple organization. Such a state of organization would have to be distinguished from the merely contradictory or complicated as it is

organized as a singularity, yet it would be distinguished from the wholistic by its internal multiplicity. The terms multiplicity and singularity both describe a linked assemblage of discrete components, although in two ways. The first is a provisional composition that exhibits a collective identity or a singularity. The second is a provisionally unified composition that exhibits its own internal diversification or a multiplicity. Singularity and multiplicity are mutually constituative terms as one that is internally multiple is termed a multiplicity and many that are aggregated into an assemblage are termed a singularity. Both reductive and emergent theories of complexity contain geometric assumptions. A theory of iterative reduction through variation emerges from a top-down elimination of complexity towards a simple geometric type. On the other hand, the

formation of a higher level dynamical or structurally stable type through

emergence is implied by a bottom-up development of complexity from a simple collection of types. Both assumptions are inadequate to describe the relationships within a continuously differentiated multiplicity. Nevertheless, in order to develop a theory of complexity, it is necessary to develop an abstract model of its relations, a task for which geometry has been invoked throughout the history of philosophy. The question remains, if complexity and contradiction were characterized by the conflict of geometric systems, what is the implicit spatial model with which one can measure a complex relationship that is not reducible to either the contradiction of the many or the wholistic unity of one. The effects of geometry and proportion on architecture are much deeper and less localizable than other disciplines' relationships to signifying systems. The implicit limitations and built-in prejudices of both geometry and the organizational analogies upon which it depends, influence architectural design and theory at its foundations. Architecture is the discipline where systems of regulation and proportion are implicit and it is in the discipline of architecture that concepts of geometry and wholistic order are most inextricably joined together. Linked to this critical project is an assertion that alternative geometries imply alternative instrumentalities. I would argue, that

aLoBs

new systems of organization and geometric description are available for implementation in various ways. Rather than simply transgressing these systems of proportion and order, it is possible that interests in diversity, difference and discontinuity do not preclude formal and mathematical thought. What is necessary for a rigorous theorization of diversity and difference within the discipline of architecture is precisely an alternative system of complexity in form; a complex formalism that is in essence freely differentiated. A class of topological geometric types for modeling complex aggregates that exhibits the qualities of multiplicity and singularity outlined above has recently been developed. The most interesting example of these topological types are isomorphic polysurfaces or what in the special effects and animation industry are referred to as meta-clay, meta..ball or blob models. The explanation of the organization of these topological geometries actually outlines a working schema for a new typology for complexity. Perhaps if Leibniz had had the resources of these models available during his debate with Descartes over gravity and force we potentially might have avoided two centuries of reductive Cartesianism.

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In a software program by Wavefront Technologies, Inc, called Meta-Balls in their Explorer 3Design program, it is possible geometrically to model an organization whose singular characteristics are defined by an assemblage of interacting local forces. 3

For example, in their blob modeling package, objects are defined by

monad-like primitives with internal forces of attraction and mass. Unlike a conventional geometric primitive such as a sphere, these objects are defined with a center, a surface area, a mass relative to other objects and importantly by two types of fields of influence. These meta-ball primitives are surrounded by halos of influence. The inner volume defines a zone within which the meta-ball will connect with another meta-ball to form a single surface. The outer volume defines a zone within which other meta-ball objects can influence and inflect the surface of the meta-ball object. The surfaces are surrounded by two halos of relational influence - one defining a zone of fusion, the other defining a zone of inflection. When two or more meta-ball objects are related to one another, given the appropriate proximity of their halos, they can either mutually redefine their respective surfaces based on their particular gravitational properties or they can actually fuse into one contiguous surface that is defined not by the summation or average of their surfaces and gravities but instead by the interactions of their respective centers and zones of inflection and fusion. A meta-ball aggregate is defined as a single surface whose contours result from the interaction and assemblage of the multiple internal fields that define it. In this sense,an aggregate geometric object such as this is a multiplicity; it is simultaneously singular in its continuity and multiplicitous in its internal differentiation. From the perspective of the unified surface it is a singularity (as it is contiguous but not reducible to a single order) and from the perspective of the constituent components it is a multiplicity (as it is composed of disparate components that are put into a complex relation). Fusion and unity should be distinguished from concepts of totality and wholism. Because fusion, unity and duration are considered conservative and reactionary themes relative to the decompositional techniques that have dominated architecture for the last twenty-five years, they have been equated with wholism and understood as reactionary. Although these themes are potentially conservative, they are easily radicalized when linked with concepts of differentiation and multiplicity.

BLobs

Along with an abstract geometrical model or typology, the primary component of any complex organization is temporal development. Curiously, both iterative reduction through variation and the emergence of order through interaction assume a temporal development that is ceased or punctuated respectively by a generalizable type. The characteristics of these types are very different; reducible and fixed on the one hand as a Platonic form such as a sphere; and evolutionary and structurally stable on the other hand as a Neo-Platonic form such as an attractor. Both top-down reduction and bottom-up emergence, however, share the assumption that generalized types can describe both simplicity and complexity. Iterative differentiation is necessary for the development of a theory of complexity that integrates time, suggesting a repetition with difference, or iteration, that is proliferative rather than reductive. Such a theory of complex organization in architecture would incorporate temporal variation within the development of alternative geometric types. An iteration and differentiation that proliferates can provide a counter project to the antiquated and fixed theories of iterative reduction that architecture has adopted for its concepts of statics and proportion.

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Temporal development, manifest as both subtle and catastrophic movements and fluctuations within and between interacting components, results in varying degrees of singularity in more global or large-scale structures. In the case of the isomorphic polysurfaces, a low number of interacting components and/or a stable relationship of those components over time leads to a global form that is more simple and stable and less complex and unstable. The qualification of their organization as more or less simple - as opposed to reducible - and as more or less stable - rather than static - is a crucial distinction. A high number of components and/or a gradual or abrupt change in relative position of those components over time leads to a global form that is more complex and unstable and less simple and stable. Simplicity and complexity are separated by degrees along a continuum in this schema and there is no contradiction between systems but rather differing qualities of relative interactions and their transformation in time. According to this logic, there is no essential difference between a more or less spherical formation and a blob. The sphere and its provisional symmetries are merely the index of a rather low level of interactions where the blob is an index of a high degree of information in the form of differentiation between components in time. In this regard, even what seems to be a sphere is actually a blob without influence; an anexact form that merely masquerades as an exact form because it is isolated from adjacent forces.

Indeed, the sphere is exposed as a

blob when it demonstrates the capacity of fluid and continuous differentiation based on interactions with neighboring forces with which it can be either inflected or fused to form higher degrees of singularity and multiplicity simultaneously. Complexity, therefore, is not only always present as potential in even the most simple or primitive of forms; but, even more so, it is measured by the degree of both continuity and difference that are copresent at any moment. This measure of complexity (the index of which is continuity and differentiation) might best be described as the degree to which a system behaves as a blob.

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Endnotes I. See my "Architectural Curvilinearity: The Folded, the Pliant and the Supple" in this collection. See also RobertVenturi, ComRlexit)' and Contradiction in Architecture (New York, 1966) and Mark Wigley and Philip Johnson, Deconstructivist Architecture (New York, 1988). 2. The term wholeness is one to which I have a great aversion despite the nuanced discussions of wholes common to many examinations of complexity in the sciences. Brian Goodwin, GerryWebster and David Bohm are perhaps the most formidable defenders of wholism as it relates to theories of dynamical systems. See Brian Goodwin, Atuhiro Sibatani and Gerry Webster, Dynamic Structures in Biology (Edinburgh, 1989), Brian Goodwin and Peter Saunders, Theoretical Biology: ERigenetic and Evolutionary Order from ComRlex Systems (Baltimore, 1989) and Brian Goodwin, How the LeoRard Changed Its SR0ts: The Evolution of ComRlexit)' (New York, 1994). 3. These modeling programs are native to Silicon Graphics computer hardware and are part of the Wavefront 3Design, Dynamation and Kinemation software as well as the Alias PowerAnimator software.

BLoB TectonLcs or why TectonLcs LS sQuare and TopoLogy LS Groovy J

Historically, discussions of tectonics have involved the difficult task of combining the particular with the general. In this instance, the particular is understood to be contingent factors such as the highly localized techniques of construction and the spatial techniques associated with use and organization. The general, meanwhile, stands for universalized ideals which are embodied in spatial typologies. Discourses on tectonics inevitably attempt to negotiate, however uneasily, the contingent, local concerns of the present with generalized typologies considered to be essentially timeless. But the discourse of tectonics has never encountered the blob. Or should I say blobs. Many blobs, of all different sizes and shapes and irreducible typological essences. Blobs that threaten to overrun a terrorized and deterritorialized tectonics like a science fiction horror movie. Blobs constitute a formal intervention in contemporary discussions of tectonics. That is, blobs intervene on the level of form, but they promise to seep into those gaps in representation where the particular and the general have been forced to reconcile - not to suture those gaps with their sticky surfaces, but to call attention to the necessary existence of gaps in representation. Blobs suggest alternative strategies of structural organization and construction that provide intricate and complex new ways of relating the homogeneous or general to the heterogeneous or particular.

First published in Any Magazine. no. 14.

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Blobs enrich the discourse of tectonics by confounding the terms of tectonic discourse. Blobs cannot be reduced to a typological essence:no two blobs are identical, the form and organization of any given blob is contextually intensive and therefore dependent on exigent conditions for internal organization. Most importantly, blobs are simultaneously alien and detached from any place yet capable of melding with their contexts. In any definition of the architectonic, there is an implication of the arche as being an ideal global singularity where the tectonic involves a particular local identity. For these reasons, blobs promise to open up strategic spaces in tectonic discussions, precisely in the discursive spaces where the particular, the multiple, the contingent is conflated with the global singular. But first more about blobs. The image, morphology, and behavior of the blob present a sticky, viscous, mobile composite entity capable of incorporating disparate external elements into itself. Blobbiness will be treated in three regards: first, in the images of science-fiction horror films; second, in the philosophical definition of viscous composite entities; and last, in contemporary construction techniques. B

BLot3s

Perhaps the most direct route into any discussion of blobs is to invoke a few canonical Hollywood B film blobs. These films present a paradigm for an aqueous, alien structure that moves through the city absorbing materials. Blobs, in these horror films, are organisms that are topologically inverted. They do not ingest material into an interior cavity but, like a single-cell organism, stick to things that are then slowly incorporated through their surface. In all of the Blob films, from the 1958 original starring Steve McQueen to the 1988 remake with Kevin Dillon, the alien has no discrete mouth that swallows but instead is a digestive system turned inside out. The blob is all surface, not pictorial or flat, but sticky, thick, and mutable. In virtually every instance, a B-film blob is a gelatinous surface with no depth per se; its interior and exterior are continuous. The shock effect in these films is often generated through the display

sLob TectonLcs, or why TectonLcs LS sQuare and TopoLogy LS Groovy

17 1

of partially digested victims suspended within a gelatinous ooze. These blobs are neither singular nor multiple since they have no discrete envelope.

I

Essentially, a

blob is a surface so massive that it becomes

a proto-object. Gelatinous

organisms, like fluids, have no internally regulated shape, but depend on contextual constraints or containment for their form. Although they have minor shaping forces such as surface tension and viscosity, they possess neither a global form nor a single identity. The spatiality of these blob organisms, and the manner in which they slither, creep, and squirm, instigates disgust and queasiness in the movie audience. Three principles to this movement and spatiality that are characteristic of all blobs: I.

Blobs possess the ability to move through space as if space were aqueous. Blob form is determined not only by the environI. The Blob, 1988,(tIm still.

ment but also by movement. A "near solid," to borrow Luce Irigaray's term, has no ideal static form outside of the particular conditions in which it is situated, including its position and speed. 2 Gel solids are defined not as static but as tra-

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jectories. In no film, to my knowledge, does a blob ever return to some point of origin or point of rest. II.

Blobs can absorb objects as if they were liquified. These incorporated objects float in a deep surface without being ingested into an interior cavity. Often, ingested masses become individuated organs in a larger mutant whole, as in The Thing of 1951 starring James Arness, or the 1982 remake starring Kurt Russell.

2. Meta-balls in formation.

III.

The term blob connotes a thing which is neither singular nor multiple but an intelligence that behaves as if it were singular and networked but in its form can become virtually infinitely multiplied and distributed.

LeLenLz and the aLoe If postwar American visual culture provides architecture with a working knowledge of blob behavior and morphology, certain philosophical currents, dating back to Leibniz and reintroduced to architects by way of Gilles Deleuze and Michel Serres,

3. Meta-balls.

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help to clarify the logic of the blob's structural system." The mechanics of blobs, like Irigaray's "Mechanics

of Fluids,"

is characterized by complex incorporations

and becomings rather than by conflicts and contradictions." These fluid entities are described as being "quasi-solid," incomplete beings whose symbolization has been ignored due to their "specific dynamics" characteristic of real fluids. Leibniz's Ars Combinatoria of 1666 quietly innaugurated an alternative tradition, one that does not exclude a theory of combination from discussions of order but instead makes the act of combination the primary mode of both the composition and the differentiation of identity.While Cartesianism is associated with the isolation and reduction of systems to their constitutive identities, Liebniz's combinatorial universe is founded on the changes in identity that take place with greater degrees of complexity and connection. To develop a theory of complexity not founded on the contradiction of differences requires, then, a reconsideration of identity as neither reducing toward primitives nor emerging toward wholes. A theory of complexity that abandons both the single and the multiple in favor of a series of continuous multiplicities and singularities is one way of escaping dialectical definition of identity. This mandates the development of theories of multiplicitous organizations that cannot be attributable as one or as many. Likewise, one approach to a theory of complexity might be to develop a notion of the composite or the assemblage understood as neither multiple nor single, neither internally contradictory nor a unified. Complexity involves the fusion of multiple and different systems into an assemblage that. behaves as a singularity while remaining irreducible to any single simple organization. The next step involves the development of an abstract model of complexity. Throughout the history of philosophy, geometry has been invoked to accomplish this task. Previous systems based on complexity and contradiction took the representational form of conflicting geometric systems.The question remains:What spatial model can represent a complex relationship irreducible either to the contradiction of the many or the holistic unity of the one? A rigorous theorization

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of diversity and difference within the discipline of architecture requires an alternative system of complexity in form - a complex formalism that is in essence freely differentiated. Recently, a typology of topological geometries for modeling complex aggregates has been developed. The most interesting example is the development of isomorphic polysurfaces or what in the special-effects and animation industry is referred to as meta-clay, meta-ball, or blob models. The explanation of the organization of these topological geometries actually outlines a working schema for a new typology for complexity. In blob modeling, objects are defined by monad-like primitives with internal forces of attraction and mass.Unlike a conventional geometric primitive such as a sphere, which has its own autonomous organization, a meta-ball is defined in relation to other objects. Its center, surface area, mass,and organization are determined by other fields of influence. The inner volume defines a zone within which the meta-ball will connect with another meta-ball to form a single surface. The outer volume defines a zone within which other meta-ball objects can influence and inflect the surface of the meta-ball object.The surfaces are surrounded by two halos of relational influence, one defining a zone of fusion, the other defining a zone of inflection. When two or more meta-ball objects are related to one another, given the appropriate proximity of their halos, 'they can either mutually redefine thel;l"" respective surfaces based on their particular gravitational properties or they can : ) actually fuse into one contiguous surface defined not by the summation or aver-~, age of their surfaces and gravities but instead by the interactions of their respecv , tive centers and zones of inflection and fusion] A meta-ball aggregate is defined': as a single surface whose contours result from the interaction and assemblage of the multiple internal fields defining it. In this sense, an aggregate geometric object such as this is a multiplicity; it is simultaneously singular in its continuity and multiplicitous in its internal differentiation. From the perspective of the unified surface it is a singularity (as it is contiguous but not reducible to a single order) and from the perspective of the constituent components it is a multiplicity (as it is composed of disparate compo-

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J

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nents put into a complex relation).Temporal development manifest as both subtle and catastrophic movements and fluctuations within and between interacting components results in varying degrees of singularity in more global or large-scale structures. In the case of the isomorphic polysurfaces, a low number of interacting components and/or a stable relationship of those components over time lead to a global form that is more simple and stable and less complex and unstable. The qualification of their organization as more or less simple - as opposed to reducible - and as more or less stable - rather than static - is a crucial distinction. A high number of components and/or a gradual or abrupt change in relative position of those components over time result in a global form that is more complex and unstable and less simple and stable. Simplicity and complexity are separated by degrees along a continuum in this schema.There is no contradiction between systems but rather differing qualities of relative interactions and their transformation in time. This system of meta-ball modeling is not opposed to a reductive Cartesianism; rather, it incoprorates reductivism into a more subtle and complex set of relations. The difference between the reductive tendencies of Cartesianism and the unfolding logic of Leibniz is that reductivism is expedient and crude compared with the creative, vital elegance of combinatorial multiplicity.

aLoB construct Lon In a September 1995 panel discussion at Columbia University organized in conjunction with the Light Construction exhibition at the Museum of Modern Art, a group of preeminent tectonic practitioners once again argued that humans have always structured themselves as standing upright and by extension, so should buildings. This fallacy that buildings must stand erect is already discredited by two-hundred years of research into theories of gravity. Any student of structural stability knows that structural dynamics are far more complicated than merely the transmission of perpendicular loads down to the earth's surface and must consider the interaction of multiple loadings that range from the perpendicular to the oblique. As structural engineers have for centuries, architects might consider more complex analogies of support than the simplistic, bankrupt,

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and highly overrated notion that buildings should stand vertically. The reason that architects retreat into this Cartesian model of simple gravity is that it is expedient. Unlike structural engineers, architects are expected to be simple, crude and upright in their approach. Many architects have begun to investigate the possibilities of topological surface organizations as alternatives to Cartesian volumes. These explorations invite us to consider a new morphological analog of the body more akin to a single-cell blob than a symmetrically articulated upright man. These investigations are not confined to surface organizations or blob models. Mark Rakatansky's Adult Day Care Center, for instance, uses a network of linear handrail and frame elements that intervene and connect throughout an existing institutional building.This project is more akin to the Invasion of the Body Snatchers of 1956 & 1978 than to The Blob. Like the body snatcher's ovoid tubers that send proboscidal appendages into and around their victims, Rakatansky's project is an inflected bundle of vegetal tubes that infiltrates and reconfigures its context. Blob construction, it must be acknowledged, is only in its nascent stages of development in contemporary architecture culture. With few exceptions, the recent projects that make use of topological surfaces do so for the development of complex roof forms, and roofs, however programmatically complex, are still in the end just roofs. Many experiments in architecture begin with the problem of the long-span roof, however, because it is there that form, structure and tectonics are so intricately entwined. Nonetheless, the roof projects do invite the reactionary (and perhaps overly hasty) responses put forward by the editorial board of Assemblage: Isn't this just the 1960s all over again? Isn't this more or less Buckminster Fuller redux? 5 Until blob organizations develop beyond the prototype of the shed, they will remain open to such accusations. What is interesting about these roof projects is that like any long-span project, the structure is an initial question that must be asked in conjunction with questions of form. Therefore, tectonics and construction techniques are developed

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simultaneously with formal diagrams. Consider last year's competition entries for the Yokohama Port Terminal. Nearly all the submissions rethink the nineteenth-century construction dilemma of the long-span shed terminal with a new set of criteria: the programming and occupation of its outer surface. A comparison of two entries that experiment with flexible surface tectonics - the winning design by Alejandro Zaera-Polo and Farshid Moussavi and the proposal by Jesse Reiser and Nanako Umemoto - reveals both the limitations and the potential of blob forms as built forms. Zaera-Polo and Moussavi treat the flexible surfaces as slabs. Their Yokohama Port Terminal adheres to the plan symmetry in the deployment of its spaces and the organization of the site. The combination of flexible slabs and symmetrical program deployment yields a globally monolithic typology that is locally flexible in its transitions from slab to slab. The radical distinction, characteristic of the Beaux-Arts style, between a mechanistically symmetrical plan and a more or 4. Invasion

ofthe BodySnatchers, 1978, film still.

less free section where one could interchange between slabs, limits the topological effects to sandwich deformations of roof, ceiling or floor. Reiser + Umemoto make use of a truss and joist system that provides a spatial thickness within the

FoLds) BodLes &

trusses in addition to the undulating roof surface. Like Otto Wagner's Postal Bank, this project takes the nineteenth-century roof typology of the station and programs the thickness of the truss. Reiser + Umemoto then extend this concept by treating the roof structure as a volume that can be packed with program. The location of program in the roof thickness, along with the variegated location of programs below, allows their project to deflect assymmetrically across the site. The net result is a continuous surface that has both a changing thickness and a changing height due to the various pressures of progams located within and below its surface. Perhaps the most important investigations into the tectonics of topological roof typologies are those of Shoei Yoh. His Odawara Sports Complex, Galaxy Toyama Gymnasium, Glass Station, Naiju Community Center and Nursery School, and Uchino Community Center all possess a highly differentiated globular singularity. The gymnasium projects announce an emerging blob aesthetic that inventively responds to shifts in the economics and construction techniques of the contemporary building industry. These projects articulate an approach to standardization

5.Alejandro Zaera-Po/o and Farshid Moussavi, Yokohama Port Terminal, proposal, 1995.

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and repetition that combines a generic system of construction with slight variations in every member.The projects make use of both prefabricated steel components and site-fabricated bamboo and concrete. Through both manual construction and industrial fabrication, the economies of what is often referred to as "custom assembly-line production" is exploited.

7. Reiser + Umemoto, Yokohama Port Terminal, proposal, 1995.

The spatial theme evident in all of Yoh's recent work is the enclosure of a diverse group of programs under a single roof. The conventional approach to this problem would be to identify either a maximum or an average span for a roof height that could then be used for the entire structure. Rather than simplify the roof structure to an ideal module that would be repeated identically, Yoh respects the specificity of each program and develops a surface that continuously connects across all of these heights like a wet cloth. The structural members of this system are similar but not identical. This strategy uses both generic and particular approaches simultaneously. There is repetition, but each repetition of a homogeneous surface brings a slight fluctuation or differentiation.

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In this manner, Yoh's work subtly complicates the distinctions between a global system and local components, between the general structure and particular variations and even between industrialized fabrication techniques and indigenous construction. The variations in the global form result from local variations in the program, and these variations are taken up in a repetitive construction technique in which every element is slightly differentiated within a more or less continuous system. The forms are both continuous and heterogeneous in their shape and construction. They are intensively determined by slight variations in their context yet alien in their continuity and connectivity. This multiplicity of minor variations does not add up to a single, simple global structure but instead manifests a blobular singularity, or, if you will; a blob.

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8. Shoe; Yoh, Odawara Sports Complex, Odawara-Shi, Japan, 1992,computerrendering.

9. Shoe; Yoh, Glass Station, Oguni, Aso-Gun, Kumamotoprefecture, 1993.

Any discussion of flexible shell structures owes a debt to the innovative research of the recently deceased Sir Edmund Happold. As the engineer for Frie Otto, Happold perfected the use of lattice shell structures. Whereas Otto, a structural expressionist, generated rational forms out of monolithic constructional systems of blown or poured concrete, Happold introduced the use of assembled components and thus pioneered the use of standardized repetitive members joined differentially as a network. Admittedly, Happold's lattice shell systems are not a paradigm of structural efficiency and ideal form, but they do provide a model for flexibility and fluidity. Despite the recent popularity and widespread application of lattice shell systems, Happold's Mannheim Pavilion of 1986 remains one of the most simple and elegant uses of the lattice shell.

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Endnotes I. Possible exceptions include the liquid-metal monster in James Cameron's Terminator 2 (1991), and the underwater creature in an earlier film, The Abyss (1989). 2. On theories of proto-plasmic and liquid identities, see Luce Irigaray, This Sex Which Is Not One, trans. Catherine Porter (Ithaca: Cornell University Press, 1985), 106-1 18. 3. See Gilles Deleuze, The Fold: Leibniz and the Baro