Architectural Curvilinearity
Greg Lynn
ARCHITECTURAL CURVILINEARITY
THE FOLDED, THE PLIANT AND THE SUPPLE
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 in formal conflicts. When comparing Venturi's Complexity and Contradiction or Learning from Las Vegas with Wigley and Johnson's Deconstructivist Architecture it is necessary to overlook many significant and distinguishing differences in order to identify at least one common theme.
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 programmes. These disjunctions result from a logic which tends to identify the potential contradictions between dissimilar elements. A diagonal dialogue 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 programmes which are then represented in architecture as internal contradictions. The most paradigmatic architecture of the last ten years, including Robert Venturi's Sainsbury Wing of the National Gallery, Peter Eisenman's Wexner Center, Bernard Tschumi's La Villette park or the Gehry 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. In architecture, both the reaction to and representation of heterogeneity 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.
In response to architecture's discovery of complex, disparate, differentiated and heterogeneous cultural and formal contexts, two options have been dominant; either conflict and contradiction or unity and reconstruction. Presently, 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 defence 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 through fluid tactics of mixing and blending. Smooth mixtures are not homogeneous and therefore cannot be reduced. Deleuze describes smoothness as 'the continuous variation' and the 'continuous development of form’. Wigley's critique of pure form and static geometry is inscribed within geometric conflicts and discontinuities. For Wigley, smoothness is equated with hierarchical organisation: 'the volumes have been purified — they have become smooth, classical — and the wires all converge in a single, hierarchical, vertical movement.' 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 to neither 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 possible connections of 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.
If 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 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 neither homogenous, like whipped cream, nor fragmented, like chopped nuts, but smooth and heterogeneous. In both cooking and geology, there is no preliminary organisation 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 fibres obtained by fulling (for example, by roiling the block of fibres back and forth). What becomes entangled are the microscales of the fibres. 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 centre; it does not assign fixed or mobile elements but distributes a continuous variation).'
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. They are intricate, they affiliate local surfaces of elements with one another by negotiating 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.
Viscous Mixtures
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 favourable and unfavourable situations that occur by chance. Vicissitudinous events result from events that 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 A Thousand Plateaus, Spinoza's concept of 'a thousand vicissitudes' is linked with Gregory Bateson's 'continuing plateau of intensity' to describe events which incorporate unpredictable events through intensity. These occurrences are difficult to localise, 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 affiliation with external forces. In this sense, vicissitudinous mixtures become cohesive through a logic of viscosity.
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 organisation. Forms of viscosity and pliability cannot be examined outside of the vicissitudinous 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.
Curving away from Deconstructivism
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 valorisation of contradictions. Deconstructivism theorised 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 curved forms. However, many of the formal similitudes suggest a far richer ‘logic of curvilinearity' that can be characterised by the involvement of outside forces in the development of form. If internally motivated and homogeneous systems were to extend in straight lines, curvilinear developments would result from the incorporation of external influences. Curvilinearity can put into relation the collected projects in this publication, Gilles Deleuze's The Fold: Leibniz and the Baroque and René Thom's catastrophe diagrams. 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 organisation. 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 neighbourhood: sheds, chain-link fences, exposed plywood, trailers, boats and recreational vehicles. The house is described as an 'essay on the convoluted relationship between the conflict within and between forms ... which were not imported to but emerged from within the house.' The house is seen to provoke conflict within the neighbourhood due to its public representation of hidden aspects of its context. The Gehry House violates the neighbourhood 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 organisation 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 valorise the conflicts the house engenders, as has been done in both academic and popular publications, a more pliant logic would identify, not the degree of violation, but the degree to which new connections were exploited. A new intermediate organisation occurs in the Gehry House by vicissitude from the affiliation of the existing house and its addition. Within the discontinuities of Deconstructivism there are inevitable unforeseen moments of cohesion.
Similarly, Peter Eisenman's Wexner Center is conventionally portrayed as a collision of the conflicting geometries of the campus, city and armoury 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 armoury and grid. The armoury and diagonal grids are shown by Somol to participate in a hybrid L-movement that organises 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 schizo-analytic model is its ability to maintain multiple organisations 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 that are overlooked. Where Deconstructivist Architecture was seen to exploit external forces in the familiar name of contradiction and conflict, recent pliant projects by many of these architects exhibit a more fluid logic of connectivity.
Immersed in 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 complexity and contradiction arose previously from inherent contextual conflicts, present attempts are being made to fold smoothly specific locations, materials and programmes into architecture 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 characterisation 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 internalisation and incorporation of external influences into a pliant system. Distinct from a whole organism — to which nothing can be added or subtracted — intensive organisations continually invite external influences within their internal limits so that they might extend their influence through the affiliations they make. A two-fold deterritorialisation, such as this, expands by internalising 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 Las Vegas 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 generalised 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 are neither in deference to nor in defiance of their contexts but exploit them by turning them within their own twisted and curvilinear logics.
The Supple and Curvilinear
1 supple \adj [ME souple, fr OF, fr L supplic-, supplex submissive, suppliant, lit. bending under, fr sub + plic- (akin to plicare to fold) - more at PLY] 1a: compliant often to the point of obsequiousness b: readily adaptable or responsive to new situations 2a: 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.
At an urban scale, many of these projects seem to be somewhere between contexturalism 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 rigour necessary for measurement.
Anexact geometries, as described by Edmund Husserl, are those geometries which are irreducible yet rigorous. 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 repeat identically an anexact geometric figure outside of the specific context within which it is situated. In this regard, anexact figures cannot be easily translated.
Jeffrey Kipnis has argued convincingly that Peter Eisenman's Columbus Convention Center has become a canonical model for the negotiation of differentiated urban fringe sites through the use of near figures. Kipnis identifies the disparate systems informing the Columbus Convention Center including: a single volume of inviolate programme of a uniform shape and height larger than two city blocks, an existing fine grain fabric of commercial buildings and network of freeway inter- changes 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, programmes and pedestrian and automotive circulation of a highly differentiated urban context. Kipnis' canonisation 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 connection between intervals within its context; where the Wexner Center destabilises through contradictions the Convention Center does so by subterfuge.
In a similar fashion Frank 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. Akin to the Vitra Museum, the curvilinear roof forms of the Bilbao Guggenheim 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 programmes require conciliatory, complicit, pliant, flexible and often cunning tactics. Presently, numerous architects are involving the heterogeneities, discontinuities and differences inherent within any cultural and physical context by aligning formal flexibility with economic, programmatic and structural compliancy. A multitude of pli based words — folded, pliant, supple, flexible, plaited, pleated, plicating, complicitous, compliant, complaisant, complicated, complex and multiplicitous to name a few — can be invoked to describe this emerging urban sensibility of intensive connections.
The Pliant and Bent
Pliable \adj [ME fr plier to bend, fold - more at PLY] 1a: 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.
John Rajchman, in reference to Gilles Deleuze's book Le Pli, has already articulated an affinity between complexity, or plex-words, and folding, or plic-words, in the Deleuzian paradigm of 'perplexing plications' or 'perplication'. 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 complex, intricate connections. Where Post-Modernism and Deconstructivism resolve external influences of programme, 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 multi-plicity in that 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 with one another through various manipulations of bending, twisting, pleating, braiding and weaving through external force. In RAA Um's Croton Aqueduct project a single line following the subterranean water supply for New York City is pulled through multiple disparate programmes 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 20 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 programmatic elements. The implications of Le Pli 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 organisation. 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 co-ordinates for dynamic relations across surfaces.
Alternative types of transformation
Discounting the potential of earlier geometric diagrams of probability, such as Buffon's Needle Problem, D'Arcy Thompson provides perhaps the first geometric description of variable deformation as an instance of discontinuous morphological development. 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 Rudolf Wittkower — in his analysis of the Palladian villas of 1949 — and Rowe — in his comparative analysis of Palladio and Le Corbusier of 1947 — uncover a consistent organisational type: the nine-square grid. In Wittkower's analysis of 12 Palladian villas the particularities of each villa accumulate (through what Edmund Husserl has termed variations) to generate a fixed, identical spatial type (through what could best be described as phenomenological reduction). The typology of this 'Ideal Villa' is used to invent a consistent deep structure underlying Le Corbusier's Villa Stein at Garche and Palladio's Villa 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 internalisation of heretofore external forces within the system. For instance, the enlargement of a fish's eye 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. 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 aIternative 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.
The morphing effects used in the contemporary advertising and film industry may already have something in common with recent developments in architecture. These mere images have concrete influences on space, form, politics and culture; for example, 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 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 homogenising 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 which aggressively reconstructs his own physical form. Neither the theory, the geometry or 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 with probability 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 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 is the roof of Shoei Yoh's roof structures, but they can deflect to the contours and context of the site, similar to Peter Eisenman's Columbus Convention Center and RAA Um's Croton Aqueduct 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 René Thom. Gehry's supple geometry is capable of smooth, heterogeneous 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 internalise cultural and contextural 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 deformed by their environment.
Folding and other catastrophes for architecture
3 fold vb [ME folden, fr. OE foaldan; akin to OHG faldan to fold, Gk di plasios twofold] vt1: 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.
Philosophy has already identified the displacement presently occurring to the Post-Modern paradigm of complexity and contradiction in architecture, evidenced by John Rajchman's Out of the Fold and Perplications. Rajchman's text is not a manifesto for the development of new architectural organisations, but responds 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 Peter Eisenman's architectural practice through an explication of Le Pli 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 of René Thom's catastrophe diagrams in the design process.
Despite potential protestations to the contrary, it is more than likely that Thom's catastrophe nets entered into the architecture of Carsten Juel-Christiansen's Die Anhalter Faltung, Peter Eisenman's Rebstock Park, Jeffrey Kipnis' Unite d’Habitation at Briey installation and Bahram Shirdel's Nara Convention Hall as a mere formal technique. Inevitably, architects and philosophers alike would find this in itself a catastrophe for all concerned. Yet, their use 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 Thom 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.
'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. Where one would expect that an architect looking at catastrophes would be interested in conflicts, ironically, 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. Thom's morphogenesis engages seemingly random events with mathematical probability.
Thom'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 co-ordinates. Like any simple graph, Thom's diagrams deploy X and Y 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 Y co-ordinates. The supple topological surface of Thom'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 organises disparate forces in order to describe possible types of connections.
If there is a single dominant effect of the French word pli, it is its resistance to being translated into any single term. It is precisely the formal manipulations of folding that are capable of incorporating manifold external forces and elements within form, yet Le Pli undoubtedly risks being translated into architecture as mere folded figures. In architecture, 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 organisation of disparate elements within continuous spaces. Yet, these smooth systems are highly differentiated by cusps or zones of co-presence. The catastrophe diagram used by Eisenman in the Rebstock Park project destabilises 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 project, and Shirdel in the Nara Convention Hall, develop an interstitial space 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 dematerialise and differentiate the massive homogeneous volumes dictated by commercial development in order to bring them into relation with finer grain heterogeneous urban conditions. 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.
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 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. The contours between an object and its context are obfuscated 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 'building board' which 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 difference 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. This disappearance into the fold is neither insidious nor innocent but merely a very effective tactic.
Like Henry Cobb, Peter 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 typologies of housing and office buildings are initially deployed on the site in a more or less functionalist fashion; then a topological net derived from Thom's Butterfly 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 manifestation of the fold is in the incorporation of 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 organisations that were seemingly given to the architect — office tower and siedlung — with the figure of a fold. The shared principle of folding identified by both Eisenman and Cobb, evident in their respective texts, is the ability to differentiate the inherited homogeneous organisations of both Modernism (Eisenman's siedlung) and commercial development (Cobb's tower). This differentiation of known types of space and organisation has something in common with Deleuze's delimitation of folding in architecture within the Baroque. Folding heterogeneity into known typologies renders those organisations 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 organisation. 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 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.
So far in architecture, Deleuze's, Cobb’s, Eisenman's and Hoberman's discourse inherits dominant typologies of organisation into which new elements are folded. Within these activities of folding it is perhaps more important to identify those new forms of local organisation and occupation which 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 organisation. Folding can occur in both the organisations of old forms and the free intensities of unrelated elements, as is the case with Shirdel's project. Likewise, other than folding, there are several manipulations of elements engendering smooth, heterogeneous and intensive organisation.
Despite the differences between these practices, they share a sensibility that resists cracking or breaking in response to external pressures. These tactics and strategies are all compliant to, complicated by, and complicit with external forces in manners which are: submissive, suppliant, adaptable, contingent, responsive, fluent, and yielding through involvement and incorporation. The attitude which runs throughout this collection of projects and essays is the shared attempt 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 Gilles Deleuze's book Le Pli. 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 which do not internally cleave or shear but through which they connect, incorporate and affiliate productively. Cunning and viscous systems such as these gain strength through flexible connections that occur by vicissitude. If the collected projects within this publication do have certain formal affinities, it is as a result of 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. The formal affinities of these projects result from their pliancy and ability to deform in response to particular contingencies. What is being asked in different ways by the group of architects and theorists in this publication is: How can architecture be configured as a complex system into which external particularities are already found to be plied?