The diagram as a tool has historically played a major role within architectural production and discourse as a way of organising and advancing ideas. Yet the omnipresent parametric design methodologies utilised today by architects suggests that we have moved into the post-diagramming era. Through an evolutionary analysis of the diagram’s implementation, it is argued that within this post-diagramming era a new ‘abstract machine’ has emerged, one which is represented mathematically rather than visually. Based on Deleuze and Guattari’s notion of the ‘abstract machine’, this paper aims to address the role of the architectural diagram in the age of parametric design in order to recognise the paradigm shift in its representation.
Figure 1 (Cover): Biothing, Seroussi diagram (Biothing, 2007)
Figure 2 (Above): Biothing, Seroussi diagram (Biothing, 2007)
The Meaning of the Diagram
Looking into diagrammatic procedures is one way to …dislocate the protective and constrictive barriers that architecture has raised to hide its vulnerable centre.
(Bos & van Berkle, 1998, p. 20)
The point of departure of this paper is based on the assertion that the diagram as a tool plays a major role within architectural production and discourse. The primary utility of the diagram, as Allen (1998, p. 16) remarks, ‘is often as an abstract means of thinking about organisation’. The diagram does not represent existing relationships but rather anticipates yet-to-be realised relationships.
With the rise of computational design methodologies which can be generally categorised under the umbrella of ‘parametric’ design, more complex relationships are emerging that require a new notion of the diagram. Parametric design, as Bos and van Berkle (2006, p. 13) describe, refers to the new practice of ‘describing various elements of architectural design as sets of parameters which are themselves expressed as numeric and geometric relationships’. These numeric relationships or algorithms are often calculus-based resulting in non-linear outcomes. These relationships which historically have been expressed visually through diagrams can now be expressed mathematically. Hence it will be argued that the diagram has evolved from the visual diagram to the number or code.
The Abstract Machine
In its most basic and historical definition, the diagram is understood as a visual tool designed to convey ‘as much information in five minutes as would require whole days to imprint on the memory’ (Playfair in Bos & van Berkle, 1998, p. 20). Thus, the diagram can be seen to compress and organise information. For architecture, however, this conventional definition is often appropriated so that it also functions as a proliferating machine; it becomes both an explanatory or analytical device and a generative device (Eisenman, 1998, p. 27). In this regard, the writing of the French philosophers Gilles Deleuze and Félix Guattari becomes highly pertinent to architectural discourse; in particular, their notion of an ‘abstract machine’:
An abstract machine in itself is not physical or corporeal, any more than it is semiotic; it is diagrammatic (it knows nothing of the distinction between the artificial and the natural either). It operates by matter, not by substance; by function, not by form.
(Deleuze & Guattari, 1987, p. 141)
Deleuze and Guattari define an abstract machine as ‘the aspect or moment at which nothing but functions and matters remain’ (Deleuze & Guattari, 1987, p. 141). For them, the abstract machine plays a piloting role as it ‘does not function to represent, even something real, but rather constructs a real that is yet to come, a new type of reality’ (Deleuze & Guattari, 1987, p. 142). The diagram therefore is a performative rather than a representational device, or in other words, a tool of the virtual rather than the real. It is this performative quality which is of primary concern to architecture as it allows the diagram to be seen as an instrument of investigation or research (Benjamin, 2000). For this reason, it is important to note that ‘not all uses of the diagram are equally diagrammatic’ (Somol, 1998, p. 8).
Architecture as built-line diagram
The diagram’s initial emergence, according to Eisenman (1998, p. 27), can be seen in Rudolf Wittkower’s use of the nine-square grid in 1949. Wittkower’s analysis of twelve Palladian villas uncovered a consistent ‘hidden’ typological order. As a tool, it analysed the Euclidean geometry of Palladio’s architecture in pure spatial coordinates. For two decades after its introduction, it served as the discipline’s formal introduction of itself by establishing the discourse on space and structure (Somol, 1999, p. 22). However, while it proved useful in explaining the organisational strategy behind Palladio’s villas, it was unable to show how Palladio worked in the sense that the nine-square grid was a post-analytical tool (Eisenman, 1998, p. 27).
The fixed analytical epistemology of space, characterised by the nine-square grid, was soon to be replaced by a pragmatics of force (Somol, 1999, p. 22). This shift was inspired by Deleuze and Foucault’s discussion of the Panopticon. According to Foucault, the Panopticon is ‘the diagram of a mechanism of power reduced to its ideal form…a figure of political technology’ (Foucault, 1979, p. 205). Architects began to imagine that the Cartesian grid could move from an analytical tool of description to an element which could be manipulated itself (Somol, 1999, p. 10). This set the scene for a new wave of architecture based on process-driven explorations of form.
Led by Peter Eisenman and Rem Koolhaas, this new wave of architecture moved away from the diagram serving as an analytical device to the diagram acting as a generative device. For Eisenman, the diagram is much more pliable compared to the nine-square grid and conceived ‘as a series of surfaces or layers which are both constantly regenerated and at the same time capable of retaining multiple series of traces’ (Eisenman, 1998, p. 29). These traces of invisible lines suggest potential relationships that can only become visible through various means. Even though much of Eisenman’s diagramming is not immediately visible, the built object is unmistakably a diagram of the process.
Figure 5 (Left): Eisenman, ‘Transformation’, House I, (Eisenman, 1999, p. 62)
Figure 6 (Right): Eisenman, Rotation, House IV, (Eisenman, 1999, p. 64)
Figure 7 (Left): Eisenman, ‘Shifting’, Romeo and Juliet (Eisenman, 1999, p. 54)
Figure 8 (Right): Eisenman, ‘Repetition’, Aronoff Centre (Eisenman, 1999, p. 55)
Importantly, whereas Eisenman’s work talks of ‘traces’ and ‘invisible lines’, the work of Koolhaas’s office, The Office for Metropolitan Architecture (OMA), is quite explicit in its literal implementation of the diagram as a generative device in their built work. Their work which could be classified as ‘Programism’ (Silvetti, 2007) is an investigation into the notion of program as a generator of architectural form. By accumulating and manipulating data, the graphic representation, with very little transformations, becomes the very form of the architectural proposal (Silvetti, 2007, p. 178). This is epitomised in their design for the Seattle Public Library which is a direct outcome of the graphic mimesis of five or six diagrams. The first two diagrams establish two core positions: Firstly, books are technology; and, secondly that the library has a social role. From these core positions, other architectural and programmatic diagrams are developed. The end result is architecture as a built-line diagram which can be seen to have its origins in the ‘Panopticism’ discussions as the diagrams impose a particular human conduct.
Whilst the work of both Eisenman and Koolhaas can be seen as a high modern diagram of the nine-square grid (Somol, 1999, p. 22), Eisenman’s diagramming methodology results in ‘recessive readings of continuous non-linear systems of connections’ (Lynn, 1993, p. 26). These multiple interpretations can be seen juxtaposed to Koolhaas’s work, which is much more literal in its deployment of the diagram. Although both employ linear geometry in their architecture, Eisenman’s avant-garde transformational diagramming techniques to create in essence non-linear geometry, anticipated the need for 3D modelling and animation software which were soon to emerge and proliferate (Somol, 1999, p. 10).
Figure 9 (Left): OMA, Seattle Public Library, Books are technology (OMA, 2000, p. 89)
Figure 10 (Right): OMA, Seattle Public Library, Library’s social role (OMA, 2000, p. 89)
Figure 11: OMA, Seattle Public Library, Uniform flexibility versus Compartmentalized flexibility (Kubo, 2005, pp. 14-15)
Figure 12 (Left): OMA, Seattle Public Library, Program study (OMA, 2000, p. 90)
Figure 13 (Center): OMA, Seattle Public Library (Kubo, 2005, p. 22)
Figure 14 (Right): OMA, Seattle Public Library (Kubo, 2005, p. 26)
The advancement of new computer techniques which came to rise in the late 1990s saw the emergence of a new way of representing the diagram. Based partly on Deleuze and Guattari’s interpretation of Foucault’s recasting of the diagram as a ‘series of machinic forces’, the theory saw the diagram as matter, flows and forces (Eisenman, 1998, p. 27). This fundamental shift in the way architectural form is conceived rejected a passive space of static coordinates in favour for an active space of interactions. An object was no longer defined by a Cartesian fixed-point coordinate in space but rather ‘as a vector whose trajectory is relative to other objects, forces, fields and flows’ (Lynn, 1999, p. 11). Through the various deformations and transformations, topological geometries emerged which were capable of ‘incorporating time and motion into their shapes as inflections’ (Lynn, 1999, p. 23).
This introduction of time-based parameters can be seen in the work of Caroline Bos and Ben van Berkle (UN Studio), Lars Spuybroek (NOX) and the earlier work of Greg Lynn (FORM). For these architects, their architecture is promoted as offering an entirely new horizon of possibilities based not on fixed lengths but rather on topological deformations. As a result of this fluidity, the diagram transforms into a much more pliant tool defined in terms of its ‘intensive quantity’, that is, quantities which cannot be spatially subdivided such as temperature, pressure or speed (DeLanda, 2002, p. 10). If such systems are defined by their intensive quantity and not the extensive quantity systems seen in the work of Eisenman and Koolhaas, what effect does this have on the diagram?
Figure 15: Intensive and Extensive (Reiser, 2006, p. 73)
Relatively few diagrams were produced by UN Studio, FORM and NOX, yet those which were produced all possessed topological qualities. These topological diagrams can be considered to define spatial qualities rather than the procedural qualities promoted by Deleuze and Guattari: ‘The diagram is the possibility of fact – it’s not the fact itself.’ (Deleuze in Somol, 1999, p.23). For example, UN Studio’s self-defined ‘mathematical model’ (Bos & van Berkle, 2006) clearly shows three variations of a topological diagram: The Möbius strip; the Klein bottle; and, the Trefoil. These topological diagrams become design models which they argue offers fully informed design concepts (Bos & van Berkle, 2006, p. 17). Although these diagrams posses organisational qualities, they function more as a concrete assemblage than an abstract machine as the prescriptive nature of the diagram precludes any further investigation. This lack of abstractness could be inadvertently attributed to the suddenly acquired freedom bestowed to these architects as a result of technological developments. Seen by some (Silvetti, 2007, p. 185) as a misguided pursuit, the architectural ‘blobs’ produced forms with no precedents or referents. This freedom combined with the introduction of non-linear design methodologies, could explain the relatively limited role of the diagram in this approach to form.
Figure 18 (Left): UN Studio, Klein Bottle (Bos & van Berkle, 2006, p. 137)
Figure 19 (Right): UN Studio, Living Tomorrow, 2003 (Bos & van Berkle, 2006, p. 168)
Morphogenetics and Limitations
More recently within architectural discourse, the morphodynamical systems characterised by the topological ‘blobs’ of the 1990’s have been replaced by morphogenetic systems as the theoretical motivation to the design and construction of buildings. These systems are complex, self-organisation systems in which materials are active agents that seek nothing but agency, thereby creating an order that emerges from the bottom up. Chu (2006, p. 42) argues that although the morphogenetic systems are still in its embryonic stages, they are far more fundamental and necessary compared to morphodynamic systems as they deal directly with the construction of the object itself.
Morphogenetic systems utilise calculus as a means of proliferating an infinite set of possibilities to emerge from a single set of relationship between parts and whole. This approach allows endless variations to emerge whilst still maintaining the same numeric and/or geometric relationships. This approach can be seen in the work of Lynn, a protégé of Eisenman.
Lynn attempts to situate his work ‘outside of the 1980s theoretical model of justifying spaces by processes of analytic transformation’ (Rocker, 2006, p. 89). Yet unlike UN Studio, Lynn has departed from his force-informed topological ‘blobs’ of the 1990s to embrace designs that explore parts-to-whole relationships. This can be seen in his design for the Embryological House. Here Lynn designed a whole collection of houses to create an infinitesimal variation among parts. This shift from a morphodynamical system to a morphogenetic systems rejects the Modernist mechanical kit-of-parts design, to a design that explores parts-to-whole relationships where the whole is more than the sum of the parts (Rocker, 2006, p. 90).
Figure 22: FORM, Embryological House, 1999 (Rocker, 2006, p. 92)
Figure 23: Biothing, Diagram of algorithmic speed-distribution and cellular relationships (Ednie-Brown, 2006, p. 74)
The premise that matter and materials behaviours must be implicated in geometry itself requires Deleuze and Guattari’s notion of the abstract machine to be once again readdressed (Reiser, 2006, p. 72). Delanda elaborates on the problem:
The question of the objective existence of problems (and their defining diagrams) is a crucial issue in Deleuze’s philosophy of matter and form, a philosophy which attempts to replace essentialist views of the genesis of form (which imply a concept of matter as an inert receptacle for forms that come from outside) with one in which matter is already pregnant with morphogenetic capabilities, therefore capable of generating form on its own.
(De Landa, 1998, p. 30)
The problem therefore emerges that the algorithmic ‘code’ inherent in these morphogenetic systems is the ‘abstract machine’. The capacity for these non-linear systems to create their own genesis of form is ‘neither metaphor nor symbol, but a literal employment of the order itself’ (Reiser, 1998, p. 51). Given that representation is unavoidable and that the code is the abstract machine, how then does one convert the abstract machine into graphic form?
The omnipresent parametric design methodologies utilised today by architects and the lack of diagrams being produced suggests that we have moved into the post-diagramming era. This proclamation assumes that the ‘abstract machine’ is not interpreted literally as to necessitate a visual diagram but rather that the code itself is seen as the abstract machine.
As presented earlier, according to Deleuze and Guattari, diagrams have no intrinsic connection with visual representation. Yet, on the other hand, representation is unavoidable as Allen argues:
A diagram is a graphic assemblage that specifies relationships between activity and form, organizing the structure and distribution of functions. As such, diagrams are architecture’s best means to engage the complexity of the real…But since nothing can enter architecture without having been first converted into graphic form, the actual mechanism of graphic conversion is fundamental.
(Allen, 1998, p. 17)
In light of this, it is proposed that the abstract machine in Deleuze and Guattari’s terms is more relevant than ever, yet these abstract machines which emerge are now being represented mathematically rather than visually. In a sense ‘algorithmic processes become a vehicle for exploration that extends beyond the limit of perception’ (Terzidis, 2003, p. 71).
Significant precursors working in the post-diagramming field can be identified in the work of Aranda/Lasch, Philippe Morel (EZCT), Alisa Andrasek (Biothing) and Kokkugia. For these architects, the majority of their design is actually in the undertaking of designing the abstract machine. It is the generative diagram which does not dictate explicit geometrical outcomes but describes a generative process of becoming, which, when executed may take on many formal or spatial outcomes. The diagram therefore contains that which would endure over many design outcomes using the same process. Yet this abstract machine takes its form as code, not graphically, which sets it aside from previous incarnations of the diagram.
Figure 24 (Left): Biothing, Pavilion diagram (Scripted by Purpose, 2007)
Figure 25 (Right): Biothing, Pavilion diagram (Scripted by Purpose, 2007)
Given the visual connotations associated with the term ‘diagram’, many authors have coined an alternative to address the diagram’s graphic ambiguity in the parametric era. Reiser (1998, p. 51) for instance, advocates the ‘dynamic diagram’ to describe non-linear systems such as weather systems. Similarly, Ednie-Brown on reviewing the work of Biothing proposes an ‘affective diagram’ which she describes as ‘a configuration wherein affective and abstract relationality explicitly coalesce’ (2006, p. 75). Whichever term is used, it seems apparent that evolved architectural structures must begin with an adequate diagram. This seems prudent as one of the main criticisms of morphogenetic design is that the evolutionary process seems to run out of possibilities. Delanda (2002, p. 11) argues that ‘new forms do continue to emerge but they seem too close to the original ones, as if the space of possible designs which the process explores had been exhausted’. Thus architects working in parametric design must somehow find a way to incorporate the diagram as a means of going beyond mere breeding.
Figure 26: Biothing, Seroussi diagram (Biothing, 2007)
The impetus of this paper was to address the role of the architectural diagram in the age of parametric design in order to recognise the paradigm shift in its representation. It opened by claiming that the diagram as a tool plays a major role within architectural production and discourse. Through the discourse of Deleuze and Guattari, it was argued that the diagram is a performative rather than a representational device, or in other words, a tool of the virtual rather than the real. Beginning with Wittkower’s nine-square grid of 1949, it was shown that the diagram has evolved to respond to the various attitudes of form. Wittkower’s use of the diagram was analytical in nature as it attempted to post-rationalise the organisational typology of Palladio’s villas. Some thirty years later, architects such as Eisenman and Koolhaas saw potential that the diagram could function both analytically and generatively. Through their manipulations and transformations, process-driven explorations of form emerged which saw architecture as a built-line diagram.
With the arrival of new computational techniques, non-linear geometry emerged categorised by flows and forces. As a result of this new fluidity, the diagram transformed into a much more pliant tool defined in terms of its intensive quantity. This resulted in topological diagrams that defined spatial rather than the procedural machines promoted by Deleuze and Guattari. It was then argued that with the emergence of morphogenetic design methodologies, the abstract machine has once again returned to Deleuze and Guattari’s notion of the abstract machine, making the diagram more relevant than ever.
Despite their radically divergent aesthetic, the diagrammatic methodologies of the architects presented have been shown to be central to their work. What separates each approach from another is the way the diagram has been represented. This can be primarily attributed to the shift from linear based geometry to non-linear based geometry. As a result, parametrics has prompted a renewed understanding of the diagram in terms of an abstract machine. The organisation relationships which define the abstract machine have been shown to evolve from the visual diagram to the number or code. No longer are these relationships expressed visually, for it appears that mathematics has replaced the drawing.
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