Singles & Multiples

Erik G. L’Heureux

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Centre for Advanced Studies in Architecture

Department of Architecture, School of Design and Enviroment, National University of Singapore

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© Assistant Professor

Erik G. L’Heureux AIA, LEED

Singles And Multiples

Single

From Middle English, via old French: From Latin singulus,relatedtosimplus;simple Adjective:onlyone;notoneofseveral,consistingof onepart

Verb:tochoosesomeoneorsomethingfromagroup forspecialtreatment,toreducetoasingleline

Multiple

From seventeenth-century French: From Latin, multiplus,analterationofmultiplex

Adjective: having or involving several parts, elements,ormembers

Noun:anumberthatmaybedividedbyanothera certainnumberoftimeswithoutaremainder

Why Care About Form?

Form as a field of study appears old fashioned. It refers to an age in which geometry was celebrated by Sebastiano Serlio in his first book of architecture, Architettura, in which he states “how needful and necessary the most secret Art of Geometrie is”. This was in 1537. Philibert Delorme held geometry as a virtue in architectural thinking throughout his Nouvelles Inventions Pour Bien Bastir et à Petits Frais and Le Premier Tome de L’Architecture published in 1561 and 1567 respectively.

Form, however, is not geometry, nor is shape the same as form. They can be defined as distinct categories. They share interrelated attributes, though each has a different profile. Geometry is the mathematical study of lines, planes, surfaces and solids. Shape is the appearances of such geometries specific to external descriptions. Form comes from the Latin “forma”, meaning a mold. It is also the outward appearance of geometries as in shape. But in architectural discourse, form is also an internal organization typically understood within a logical (or linguistic) framework. When we say that a building has a nice shape, we are referring to its exterior composition. When we say that architecture is a product of form, what we really mean is that the architecture is thoughtfully considered inside and out in terms of both its shape and its geometry. This “thoughtfulness” is aesthetics, as Serlio indicates by calling geometry an “Art”. Geometry alone is mathematics. But geometry that becomes observable as visible and spatial phenomena rendered through a thoughtful ambition becomes art, the aesthetics of geometry. It then follows that architecture is the transformation and intensification of geometry, shape and form into a system that holds our attention, a special kind of shape and geometry that is in contrast to ordinary geometry found around us. Of course any building is geometric and has a shape, but this alone does not make architecture. This book is about this intensification and the systems that hold our architectural attention on geometry that becomes form.

Considering the current milieu of crisis that confrontsurbanenvironmentsand,toasmaller degree, architecture today; from political turmoil to environmental deterioration; from climate change to economic disparity and poverty; the study of form—the study of formal intensification—appears isolated at best, or entirely self-indulgent at worst.

Though we can find a more contemprary axis of architects speaking on form. Colin Rowe spoke of form in great detail during his career as an educator and theorist. Peter Eisenman, mentored by Rowe, begins his career on form with his 1963 PhD dissertation, The Formal Basis of Modern Architecture.1 Likewise, Greg Lynn, a student of Eisenman and later an educator, continues writing about form through digital tools and the diagram. In Southeast Asia, and in Singapore in particular, from where this book springs, this important work is hardly understood, nor is the impact great.

Form takes on secondary and tertiary roles in a Singapore atmosphere of practicality in which architecture’s role is relegated to positivistic social or technological ambitions. If the assumed larger and “more important” social and technological forces drive architecture, then architecture’s role is one of service. Indeed, in Singapore, architectural attention is firmly oriented toward the solving of problems. The assumption follows suit that “to make a better society one makes better architecture”. This is not a new relationship to architecture; rather, it emerges out of thinking put forth by CIAM decades earlier, when modern architecture was a vehicle for the benefit of larger social and developmentalist ambitions, and serving those ambitions was its aim. And indeed, Singapore’s urban environment is planned almost entirely under CIAM principles to create “solutions” for the nation’s housing and development agendas. The convenient adages “form follows function” and “form follows finance”, subjugating form to second place, emerge in the context of such thinking. These are misguided. Form has never entirely followed function, nor has it been a direct product of structure, culture or society. Form can never be viewed as a legitimate mode of architectural research if architecture’s role as service is already predetermined. Likewise, architecture cannot have any ability to shift society if its ambitions are only to serve.

In this context, Le Corbusier, a founding member of CIAM, spoke of form in service to society, yet produced his formal invention in architecture not from these social agendas but from a formal and painterly tradition emerging out of Purism. His compositional logic of shape, geometry and form guided the architecture not only of his villas but also of his urban planning propositions.

Form, I firmly believe, operates between its ownautonomouslogicandthecurrentlogicsof society, culture and the performance criteria required of it. At specific moments, form is a uniquedisciplinewithinarchitecture.Atother moments, form is influenced by symbolism, program, finance, technology, atmosphere and climate. A symbiosis between those two spheres—form’s own autonomous logic and the environment in which it functions—is what makes form so compelling, fascinating and wrought with continual debate.

Singles and Multiples

Consider single and multiple elements in architecture. Those two categories are basic, even reductive. They are both clearly autonomous from politics, technology and society. What are the differences between single objects and multiple objects beyond a numerical counting? In what context can we speak of those differences?

When considering a singular element in a pictorial two-dimensional configuration, a conversation can be had about its own proportion: its width to length, its total area, and its organization. Is it composed of poche (the blacked-in portions of plans) or constructed of an enclosing line?

What is the thickness of that enclosing line in relationship to the interior body? In this example, the elemental form is Euclidean, assumed to be two-dimensional and perpendicular to the line of sight. Its poche might be solid, lined or stippled; it could operate as a pocket and contain internal organs, as Bernhard Hoesli described.2 The conversation is primarily interior to the rectangle itself; that it is understood as an autonomous object with its own internal organization independent of its surrounding.

Placing a singular rectangle on a table shifts the conversation to the relationship of the rectangle to the table’s size, the table’s perimeter, and the orientation between the rectangle and its frame. The juxtaposition changes the conversation about the rectangle itself as an autonomous construct to one of relationships, of context. As Fumihiko Maki writes in Investigations of Collective Form (1964), two elements form a compositional arrangement.3 Is that relationship between the two elements axial or asymmetrical? Do the two elements create a third space?

Multiple elements—more than two— establish primary relationships between each of the constituent pieces. Questions of proximity, distance, orientation, location and position arise between each of the pieces. Parallel to the single rectangle positioned on another rectangle (represented by a table in Figure 2), a discussion of multiple elements is primarily one of externality and relationship. The space among and between each of the elements is primary. The proportions of the singular element are secondary.

Maki makes the urban argument that the organization of multiple elements may be categorized as compositional, megastructural, or group-form. Compositional form describes a discernible order among the elements separated in space. The megastructure category is produced by the aggregation of smaller elements into a larger structural framework. Group-form, or the collective, implies that the elements are similar in proportion and size and yet have an organization that is not entirely fixed or predetermined.

In Figure 3, a compositional organization illustrates rectangles organized about a Euclidean grid with clear spacing between each of the edges. Elements are positioned in parallel or perpendicular relationships. A negative space is produced between the four solid elements as cohesive glue. The elements themselves are all rectilinear and in orthogonal proximity to one another. The proportion of the elements, the resulting negative space, areas of solidity, and clear structure of organization are visible. The single element is articulated and remains autonomous, though in precise position to its neighbors.

The linking of a series of smaller elements to a larger whole, as illustrated in Figure 4 through the spine- or mega-structure, utilizes proximity, overlap and adjacency to construct a larger entity. The single is repressed into a mega-framework where the coherence of the whole outweighs the articulation of the singular. The coherence of the larger agglomeration supersedes that of the individual elements of its fabrication.

Group form in Figure 5 is organized along a latitudinal structure; however, the position of each of the elements has no immediately discernible organization. A semi-spine separates two elements on the left from three on the right, though the spine is neither precisely positioned nor clearly visible. Likewise, a general massing of the elements keeps them in relative proximity, though the specifics of their internal aggregation are not evident. The multiple elements—the collective group-form—assert aggregation over order, informal over formal, and the pile over the structural. In that example, sequential order is favored over compositional order and the elements dissolve into the entire whole.

The compositional and mega-structural forms are closed-form organizations. Modifications to those organizations must explicitly follow the rules of composition or mega-structure; without considering those rules, the organization becomes highly incoherent and illogical.

By contrast, group-form organizations are [Figure open-form organizations where additions and subtractions are tolerated in the overall structure. The openness of that formal system enables change and adaptability as long as the modifications are of similar size and scale.

Compositional form is based on positional logic while mega-structure is founded on hierarchal logic. Group-form organization, however, is an adaptable logic, more closely related to the urban field rather than the singular object itself.

A fourth organizational structure, one based on transparency as presented by Colin Rowe and Robert Slutzky in Transparency: Literal and Phenomenal (1963), constructs an argument for multiple interpretations of form at the same time.4

Multiplicity in architecture is accomplished by overlapping forms to create new and indeterminate organizations. An example of multiplicity, as shown in Figure 6, illustrates an orthogonal organization of elements, latitudinally displaced, yet overlapping.

In this figure, the elemental rectangle is multiplied, overlapped and transposed. Time is introduced if we imagine moving through the layers physically, or through the process of creating one layer placed over another. The overlapping of each element creates secondary and tertiary elements (smaller and larger rectangles and squares) that demand alternative readings of the organization. Those overlaps undermine the purity of the primary elements. Alignments and equivalent areas produce sub-structures, super-structures or mega-elements that emerge out of the overlapped elements. Indeed, more than one organizational logic may be read.

In this case, the graphical arrangement of rectangles on a two-dimensional surface is projected into three dimensions, the implication being a collection of spatial layers in time that may be viewed by a moving eye, oscillating between two- and fourdimensions. The eye moves through the various layers as a camera lens might, focusing either on one layer or on the entire image at once.

Yet Rowe and Slutzky’s work is primarily about expanding the possibilities of the single architectural object through the complexities of internal organization. In effect, Transparency: Literal and Phenomenal extends the resonance of compositional and mega-structure form into the architectural object itself.

Digital Modifications

Maki’s group-form, rather than Rowe’s Phenomenal (or his later work on Collage City), has been extended most dramatically in recent architectural research.5 Digital tools including software that enhances simulation, modeling and fabrication, along with scripting and algorithms, have enabled more complex geometries and organization. Gradients, permutations, folds, surface mutations, stretching, torques, liquefy, drapes, swarms, emergent, distributive, interpolation and approximations are part of the architect’s vocabulary, another tool that enhances architects’ understanding.

Much contemporary digital research and exploration is now predicated on creating basic and elemental rules within scripts, which affects all subsequent geometry. Parallel to Maki’s predilection for group-form, there is presently a preference for the aggregate and cellular found among many architects. Aranda/Lasch, MOS and Sou Fujimoto come to mind, though today the cellular is manifest through digital tools.

Compositional: Closed-Form, Object-Oriented,Single

Mega-Structure:ClosedForm,Urban Oriented,Singlewith multipleinteriors

Group: Open-Form,Urban Oriented,Multiple, Aggregate

Phenomenal: Closed-Form,Object Oriented,Multiples withinspaceoftheSingle

Parametric: ClosedForm,Urban Oriented,Multiples

The aggregate vacillates between its own internal singular logic, and the logic of the larger combined collection. In essence, it is a merging of the phenomenal transparency identified by Rowe—the complexity within the single architectural object—and Maki’s group form with its complexity produced by aggregation. The merging of these categories produces a double legibility allowing geometry to operate on different scales and enabling different readings simultaneously. Geometry then oscillates between complexity and coherence. I have extended Maki’s categories by adding Phenomenal (even though it was published a year earlier) and by adding another category of the Parametric.

That double coding of the parametric creates the ‘double entendre’. In this case, the double entendre is not a product of creating specific postmodern allusions as found through proponents of Post Modernism (Venturi, Johnson, and Graves come to mind), but rather emerges out of the specific rules and configurations of geometry itself.

If the “single” relates to logics of interiority, exhibiting a disconnection from its context, then “multiple” relates to ideas of association based on exteriorities and represents collective ideas of combination in the context of urban forms. In short, singles are architectural objects, multiples are urban organizations. Today, in digital parametric circles, we find ambitions of combining the two.

Single and Multiple Lineages

The ambitions of the single and the multiple as found in this book have robust lineages. Design on the single—the architectural object—is found within the work of Giuseppe Terragni and the early studies of Peter Eisenman.

For Eisenman (and Rowe), the frontality, elevation and exterior surface of the singular form are primary: Le Corbusier, Terragni and Palladio all feature heavily as undercurrents, where the preference for the architectural object as a singular body is paramount. The multiple (urban) plays a secondary role to the singular as complexities are developed within and about the interiority—and autonomous nature—of architecture. For Eisenman, operations to and about the single architectural body drive his formal agenda.

Research on the multiple is found in the projects of Paul Rudolph (1918-1997), in which overhang, cellar multiplicity, stacking and aggregation are all evident. For Rudolph, geometric clarity merges with a preference for spatial complexity, combinatory planometric ingenuity, and legible formal logics. Rudolph produced a body of work more multiple than singular and more urban than object.

Traces of operative techniques found in Eisenman’s work are clearly evident in Rudolph’s work as well; multiplication, shearing, shifting and displacement are all highly visible. Yet Rudolph’s process is of aggregation related to heat, breeze and solar shading rather than the syntactical notations and internal referential displays of virtuosity in architecture evident in Eisenman’s work.

Rudolph’s early houses in Florida and his later work in Asia most clearly deploy combinations of multiple elements. The techniques of stacking techniques, both vertically and horizontally, and aggregation strategies created variegated arrangements of shade, terrace, volume and overhang.

Rudolph’s large-scale mid-career work in the United States embodies many of those formal ideas, though many seem inappropriate to the temperate northeastern states where much of his work was built. His preference for exterior spaces as a product of geometric operation has little relevance in the blustery winds of a New England winter, as we find in his University of Massachusetts Dartmouth campus. In Singapore, however, where Rudolph’s career later thrived, his work seemed to take on an ever-pressing relevance, where large overhangs, generous verandahs and covered exterior patios all make sense in areas of tropical heat and humidity. It is there that the geometrical manipulation of planar and volumetric elements produced unexpected and delightful configurations. Not for geometry’s sake alone, the spaces are relevant to the particularities of tropical living—both as naturally ventilated spaces and as enclosed areas that feature air-conditioning.

For Rudolph, having been educated in Alabama, and later, having worked in Florida, designing spaces in tropical climates was part of his architectural upbringing. As a mature architect, The Colonnade along Singapore’s Grange Road, as well as his Wisma Dharmala Sakti office tower in Jakarta, Indonesia employ multiples to produce compelling exterior spaces shaded from the tropical sun, an extension of his work in the American South.

Rudolph employed geometry for compelling and contextual ends, creating verandah spaces, outdoor living spaces and breezeways rather than for operative meaning alone, as we find in Eisenman’s work. Rudolph extended the multiple and the urban into vertical configurations, as evident most spectacularly in the Colonnade Condominium, merging architectural singular complexities with the demands of urban densities unique to tropical Asia.

What is interesting about Rudolph is the combination of singular elements deployed in multiple configurations, creating intensely tropical and urban architecture.

The formal traditions are steeped in a long history. Rowe and Slutzky wrote Transparency: Literal and Phenomenal in the Yale Architecture Journal Perspecta 8 in 1963 some 50 years ago.2 Maki’s Investigations on Collective Form was published in 1965. Eisenman’s prolific career began in 1962. Paul Rudolph’s prolific career fell out of favor in America, after the 1972 publication of Venturi, Scott Brown and Izenour’s now infamous Learning from Las Vegas though he reestablished his career in Asia working on large-scale projects through Southeast Asia until his death in 1999. Remment Koolhaas claimed to have a preference for the formal in his conversations with Maki: “I empathize with your side (implying group form), though I can’t quite participate in it.”6 For Koolhaas, the single—the architectural object— prevails.7

The work presented in this book is rooted in those traditions. The intent is to extend Maki and Rowe’s research on form, merging singular complexity with aggregate form; to reinvigorate the conversation on form, the architectural body, and the urban collective in the contemporary tropics. The examples that we find in Rudolph seem to merge these categories more successfully, combining the formal and the tropical, the singular and the multiple into immensely urban and powerful forms. And yet we have too few examples of Rudolph’s work in tropical Asia to prove that such a mode of working is indeed successful.

The drawings and models in the following pages show two distinct modes of operations. The first chapter provides illustrations of architectural concentration on the single formal body, the second chapter on its multiplicity as an urban condition. The Parametric is held at bay if only to foreground and more thoroughly mine these earlier examples of compelling formal research.

To impact the urban and tropical world around us, starting at elemental ideas of the single and multiple—starting at form itself— remains an important act of architecture. The work in these pages is not fully architectural in its complexity—they are proto architectures composed of formal research in single and multiple operations. Yet in totality, the work suggests a potential for extension into the architectural sphere, a beginning, a suggestive possibility, a trigger for a more thoughtful conversation and extension of architecture’s core—its form.

Erik G. L’Heureux, AIA LEED AP BD+C Assistant Professor Department of Architecture School of Design and Environment, NUS

Endnotes: http://archinect.com/features/article/2875457/5projects-interview-5-alexander-maymind, accessed March 20, 2013 http://ad009cdnb.archdaily.net/wp-content/ uploads/2010/11/1288678052-milamresidence1.png, accessed December 10, 2012. http://2.bp.blogspot.com/_TSJ1g2k6Y4c/ Smegl70xiaI/AAAAAAAABAk/Z4MRy3nzvHk/s320/ wisma01.jpg, accessed December 12, 2012. http://ad009cdnb.archdaily.net/wp-content/ uploads/2010/11/1288892010-oc1-125x125.jpg, accessed December 10, 2012. http://si.wsj.net/public/resources/images/NY-BQ036_ SPACES_G_20120502171528.jpg, accessed November 10, 2012. http://structurehub.com/blog/wp-content/ uploads/2010/02/massachusetts-umass-dartmouthuniversity-library-brutalism-paul-rudolph-from-kelviinon-flickr2.gif, accessed December 10, 2012. http://ad009cdnb.archdaily.net/wp-content/ uploads/2010/11/1290197902-5-125x125.jpg, accessed December 11, 2012. http://farm3.staticflickr.com/2774/4437194998_ f057591b49_z.jpg, accessed December 12, 2012. http://www.loc.gov/pictures/item/2003689352/ accessed February 13, 2012.

1. Eisenman was mentored by Colin Rowe during his time at England’s University of Cambridge.

2. Hoesli, B. (1997). A Note on Poche. In C. Rowe, R. Slutzky & B. Hoesli,Transparency: Literal and Phenomenal (p.118). Basel, Switzerland: Birkhäuser Verlag.

3. See Maki, F. (1964). Investigations in Collective Form. St. Louis: School of Architecture,Washington University.

4. Rowe, C. and Slutzky, R. (1963).Transparency: Literal and Phenomenal.The MIT Press on behalf of Perspecta, 8, 45-54.

5. See Rowe, C. and Koetter, F. (1984). Collage City. Cambridge, MA: MIT Press.

6. Koolhaas, R., Obrist, H.-U., Ota, K., & Westcott, J. (2011). Project Japan: Metabolism Talks. Köln:Taschen.

7. Koolhaas’s greatest architectural trick as a champion of the urban is the introduction of the urban (multiple) into the architectural singular body. In another word, for Koolhaas, urban experience becomes a device with which to intensify the architectural body. Rarely do his architectural bodies intensify the urban conditions in which they sit.

Images courtesy of: http://www.archigraphie.eu/wp-content/ uploads/2010/02/Terragni_Casa_fascio.jpg, accessed December 20, 2012.