Tooling the NaturalOn the Diagram and Abstraction

TRAVIS K. BOSTProf. Irénée Scalbert3473: Concepts of Nature

Fall 2011Harvard Graduate School of Design

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As a powerfully communicative and directive strategy for de-sign, the diagram has enjoyed a series of waves of applica-tion in recent decades of work to manage the interrelation of form and environment in design projects. The popular present conception of the diagram is built largely on the varied inter-pretations of the descriptions of Deleuze that examined it in relationship to the abstract.

However in so doing, much of the layered nuances of ‘ab-straction’ have been eschewed by designers, instead sim-plifying the diagram as a visual or formal abstraction. “It is a representation of something in that it is not the thing itself,” Eisenman flatly declares without enthusiasm.[1] But as they are representations of space—pre-existing, proposed, or only potential—they are conceptions of territory in abstraction that are intended for production. And in this process, “there is a noticeable tendency to reduce the ground itself to commodi-ty…” whereby nature is subdued to a transmutable property in architecture and in aggregation, “urban space … became ab-straction in action – active abstraction – vis-à-vis the space of nature, generality as opposed to singularities.”[2][3] Thus this is a process where perceived wildness of nature is domesti-cated or removed as untenable for human (urban) occupation.

Expanding on Hegel, Lefebvre describes the ancient Greeks as “able to take natural materials, first wood and then stone, and endow them with meanings which rendered concrete and practical such social abstraction as assembly, shelter, and protection.”[4] Where physical space and material arti-facts of nature were here transformed as reflections of social constructs, it is also done in the abstract (or the virtual of De-leuze). Gregotti therefore finds “the origin of architecture is not the primitive hut,”—constructed of natural materials in physi-cal and spiritual connection with nature—“but the marking of ground, to establish a cosmic order around the surrounding chaos of nature.”[5] The diagram is that marking that estab-lishes relationships and divisions of space and their operation in abstraction.

While some of this character is acknowledge is contemporary understanding of the diagram, as Stan Allen states that, “a diagrammatic practice … locates itself between the actual and

the virtual, and foreground architecture’s transactional charac-ter,” there is a note of celebration this character lends to de-sign as communicative rather than consumptive.[6] However this essay endeavors to reveal the expanded role the diagram has played throughout Modernism as a tool of the abstraction of nature, space, and territory; the latest form of which has es-sayed to assert a yet wider influence on both space and time of nature.

The earliest discussions of the forms and uses of the diagram, having major impact, as a part of modernity were featured in the work of D’Arcy Thompson, a natural scientist of the turn of the twentieth century who found truth in and celebrated the seemingly inherent genius of nature in design and form-making of the organic. The genesis of the diagram device in the field of science is important, though perhaps unsurprising, to note as rationalism was the foundational mode of reasoning in early modernization and part of the obsessive collection and clas-sification enjoyed in this period. There was a clarity, simplicity, and transparency of nature in its formation of plant and animal structures that was much admired by rational moderns. By exploring and meticulously documenting the morphology of a wide-range of organisms, the perfect forms of nature were evidently the only true and legitimate forms; this would impli-cate structures built, found, or formed. There was an inherent purity and synthesis of static structure and dynamic process, given that “the form of an object is ‘a diagram of forces’ … which have been impressed upon it when its conformation was produced, together with those which enable it to retain its conformation.”[7] The validity of this statement is contingent, however, on the supremacy of natural structures which are in turn a product of nature for its own, highly specific conditions.

But this was no real impediment for the early rational mod-erns for whom, “no organic forms exist save such as are in conformity with physical and mathematics,” and therefore if humanity is to be master of the natural domain its structures must make use of the same perfection of mathematics which are easily appropriated from nature itself.[7] In discovering and meticulously examining, and reproducing the forms of natural objects, Thompson sought to master the teleology inherent and translate it as a replicable ‘process of mechanism’ or as

Tooling the NaturalOn the Diagram and Abstraction

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might be called today, after the popularization of cybernet-ics in design, an ‘algorithm.’ However the clean perfection of nature’s process—“’adaptation without ‘design’”—in these studies proved inapplicable to the human settlement that was so disorganized and subject to its own structure of synthetic patterns of organization, that is the social, political, economic, etc. But this is a facet of the diagram that has returned in contemporary work which will be discussed later.

The modernist goal of a society perfected in reason, however, was undeterred. If there was (filthy) disorder in the urban en-vironment as a result of social processes, the diagrammatic perfection of nature’s forms could be abstracted and graft-ed onto the city in those structures that would rectify those shortcomings. Before, and in contrast to, the machinic work of super-modernists—Archigram, Archizoom, Superstudio—who left the ground plane (a term of greatest abstraction for the natural) entirely by virtue of the artificial, the work of Buck-minster Fuller and Frei Otto used highly scientific means to ab-stract the structural logic of nature to generate environments for humanity that were, like Thompson, somehow in tune with nature.

By claiming to ‘do the least with the most’, Fuller experiment-ed endlessly with geometric patterns that he found in innumer-able natural forms and processes, on minute and enormous scales. This implied to him a scalelessness of perfect geom-etry as he generated proposals at the scale of the home in his patented geodesic dome houses to proposals for entire enclosed urban environments as in the Montreal ‘67 Expo or his project for the enclosure of midtown Manhattan. So suc-cessful were his abstracted natural structures that in a bizarre reversal he himself has been abstracted onto articles of such extremes of scale as The Fuller Projection in global-scale car-tography and the microscopic buckminsterfullerenes. Though his structures could indeed be found in nature, their recon-struction for habitation made clear the process of abstraction as a conventional door was ineloquently grafted to its side and traditional furnishings filled its interior (not to mention the pro-posals for their being dropped in place by helicopter). Frei Otto had a more rigorous and less grandiose method in work-ing with the patterns of nature that “focuses on physical rather

than biological autonomous formation processes,” which is di-rectly in line with those aspirations of Thompson.[9] For both, despite the inherent active processes of growth, the fascina-tion was with the physical product as resulted from the active processes of selection: “the mere expression or resultant of a sifting out of the good from the bad, or of the better from the worse.”[10] A departure from the work of Fuller, Otto’s method preferred, though only in a controlled way, the process of natu-ral form generation :

“Human beings can use these natural processes for their own purposes by triggering them in order to create their own technical constructions. When such processes take place spontaneously or are systematically exploited during the production and planning of technical constructions, Frei Otto calls these constructions ‘natural’ ones.”[11]

Thus the diagram of nature was in its ‘preferences’ with which Otto worked to manipulate in his incredibly rigorous docu-mentation and experimentation (not unlike that of Thompson) to ‘find’—rather than to generate—those ideal forms for the given purpose.

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The aviary at the Hellabrunn Zoo in Munich designed with Frei Otto is an odd juxtaposition of Otto’s exploitation of nature’s logic in its structure and the extraction of nature itself for its preservation, ironically, from the nature outside. In addition to the desire for lightweight structures as minimal use of material, the structure is to disappear, in its appear-ance as well as its openness to environmental conditions of precipitation and sunlight. However it is only minimally successful in any of these respects. Far from mimicking the natural canopy condition, it has reversed the notion of canopy to appear to be exerting force downward on the aviary’s garden to hold it within. The project is a microcosm of the process of abstraction whereby nature is appropri-ates for directing nature to humanity’s control.

The diagram as an agent of analysis for space, rather than form, arose in abundance in the era of mid-century mature modernism with the ubiquitous ‘nine -square grid.’ Despite its incessant usage as a generator of projects, its early us-age by Rudolf Wittkower was in analyzing the villas of Palladio. A useful tool for this purpose, the diagram was “a mediation between a palpable object, a real building, and what can be called architecture’s interiority,” that is between the accumu-lated history of the discipline as well as the differentiation in the typology of, in this case, the villa.[12] The nine-square grid was quickly adapted, however, to a generative device and as Robert Somol has observed, “[t]he diagram (or concrete machine) of the nine-square was necessary before the essen-tial definition of modernism as the independent articulation of space and structure was conceivable.”[13] Thus while a Pal-ladian villa can be understood in relationship to another, the diagram of the nine-square grid served as an abstraction of a type of space to concretize the modern movement. This is demonstratively evident in the series of houses of John Hejduk which most popularized the diagram and has been repeatedly referenced and added to in defining modernism as a discipline but also, of course as subjects of critique later in the work of Peter Eisenman and on into that of Rem Koolhaas.

Beyond the initial generative work of this diagram in the ‘50s and ‘60s, the critical, post-structuralist movement deepened the role, particularly that of abstraction, for the diagram. The nine square grid was paramount as a subject of critique as it had developed as the representative form of the discipline in modern architecture, or in the language of the era, the ‘signi-fier’ of the discipline. Thus to critique the diagram it was to critique the entire discipline by working at what Peter Eisen-man described as:

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“…an intermediary condition, that is, the diagram, between what can be called the anteriority and the interiority of architecture, the summation of its histo-ry as well as the projects that could exist as indexed in the traces and the actual building.”[14]

By using the logic of post-structuralism, the projective became possible in the diagram—an abstraction expanded further—where only the collective discipline of the past and present were addressed before. The led to an incredible focus on the process of the diagram in its contortions and manipula-tions (not unlike those rigorous processes of Frei Otto in pur-suit of form) of the defined space of the nine-square discipline best exemplified in Eisenman’s series of ten houses (in clear reference to Hejduk) that were methodically acrobatic in their deformation. The spaces of this process, projected or other-wise, for the most part reach a concretized existence only as a formation of lines in two dimensions which are only a repre-sentation removed and indifferent to the physical space in the environment that would be produced. By using the diagram to define space—of actually existing, previously existing, or potentially existing spaces, each being treated with equal im-portance—for the purposes of referencing or collectively de-fining a discipline or critique, territory and material have been abstracted to a profound extent.

It is fitting to investigate House IV as representative of Eisen-man’s predilection for the diagrammatic space of laborious iterative process over that of the singular physical space as it, like the majority of the houses in the series was confined to paper in its construction. The process of manipulation of an abstracted space (located at no specific location) pro-ducing in its wake an abundance of fictional spaces that are simultaneously real to the degree that they reference the ‘interiority’ of Architecture’s discipline. Though the process generates dead-ends and unfinished trajectories of devel-opment of the form, it still maintains a linear progression towards an end result which contrasts with the later formal processes of the 90s digital studies. Finally, it is interesting to note that Eisenman’s process actually begins with lines of one dimension to construct diagrams of three, though both are definitive of space.

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The plethora of abstract signifiers in lieu of real space, pro-duction of which the diagram permitted, were dispensed with along with iterative formalism more generally in contempo-rary usage; where now van Berkel and Bos assert that “[a]rchitecture focuses more on the reading and consumption of diagrams than of their labor-intensive production.”[15] The trouble with the diagrammatic iterations of space of the post-structuralists from the point of view of capitalist development is that they were non-consumable as they were iteration along a path to a designed product—in other words ‘waste.’ How-ever, if one recalls that a “a diagram acts like a surface that re-ceives inscriptions from the memory of that which does not yet exists, that is, of the potential architectural object,” then this surface is the location of innumerable transactions of events (inscriptions) involving the project and its site, iterations, dis-cipline, etc. which are instantaneously consumable.[16] In this pursuit Somol has likened the role of the diagram to the Menger sponge where the surface area approaches infinity and its volume nears zero:

“Beyond being a means to activate the gap or void [the waste], this diagram can serve as a contempo-rary disciplinary response to the modern invention of space, which was reified in the nine-square prob-lem, an organization that is all surface and event rather than space and structure.”[17]

The expanded area of the diagram is also in service to the in-corporation of the vast amount of ‘horizontal forces’ that have influence on the urban environment: economic, political, cul-tural; local and global. These are those same messy social processes that Thompson could not force to fit the model of the ‘clean’ and ‘perfect’ formation processes of nature. “It is by means of the diagram that these new matters and ac-tivities, along with their diverse ecologies and multiplicities, can be made visible and related;” which is to say to be made consumable.[18] These horizontal forces are acknowledge, discussed, and interpreted as data, meaning the “diagram is today very usefully understood as information” that is input into the surface mediating the project.[19] Meanwhile the cor-respondent implication is that the “role of the architect in this model is dissipated, as he or she becomes an organizer and

channeler of information,” who responsibility has become a management of events and effect.[20]

The work of Deleuze serves as the basis for the bulk of con-temporary design’s formation of the diagram as operating in ephemerality and through the flow of information. This grounding is not a complete departure nor denial of that of the post-structuralists such as Derrida, as Deleuze confirms that the “diagram is a possibility of fact—it is not the fact itself…,” as earlier conceived; however, “[n]ot all figurative data should disappear, and especially, a new figuration, that of figure, should emerge from the diagram and carry sensation to the clear and the precise.”[21] This clarity of sensation in the land-scape is now the goal of the designer as channeler of informa-tion. But the question of manifestation of sensation is unclear. Given that the formal products of the post-structuralists have been dispensed with in this latest formation of the diagram, it is the case that “for Deleuze, diagrams have no intrinsic con-nection with visual representations,” as they did for Wittkower and Eisenman.[22] Therefore those products produced, the events or sensations, are immaterial by way of their inherent ephemerality (which also makes them all the more consum-able) and thus in the products of the diagram there is an aban-donment of space in lieu of time. This process of abstraction on the landscape is known in Deleuze as deterritorialization which is a function of his apparatus, the abstract machine, which wreaks this process on nature with the diagram as its tool: “[a]n abstract machine in itself is not physical or corpo-real, any more than it is semiotic; it is diagrammatic ... The diagrammatic or abstract machine does not function to rep-resent, even something real, but rather constructs a real that is yet to come, a new type of reality.”[23] But what comfort this reality (this produced, synthetic space) may give is short-lived as, again, it is ephemeral which allows that “an abstract machine sees the building [designed space] as a component in a larger assemblage [formerly the landscape] that can be recontextualized according to the progressive rearrangements of the other components [the horizontal forces] in this social/technical/urbanistic machine,” according to Stan Allen.[24] This endurance of the produced space by virtue of its adapt-ability (ephemerality) is precisely the process by which the dia-gram allows, conquering of physical space by time – the latest

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dimension of the diagram’s domain.

In order to work in and on the dimension of time, Kwinter has identified three methods of engagement that have developed in the use of the diagram: integration, organization, coordina-tion. These are each ways of managing things in time as well as time itself. The fundamental difference in each is the direc-tion of approach for the diagram on time, functioning varying degrees of embeddedness or remoteness of time. The inter-ests of Thompson are again evident in these methods, as in the formal progressions of time in the early work of Greg Lynn or Lars Spuybroek or the taxonomy of form and landscape in the work of FOA (as best exhibited in their Phylogenesis). This revisiting of subjects is possible and interesting for the newly enable focus on the subject through time rather than because of time that is enabled by the three methods. While integration was perhaps the earliest and most readily pursued, organization has certainly been the most popularly acknowl-edge, for example Stan Allen has claimed, “the primary utility of the diagram is as an abstract means of thinking about orga-nization,” which again is made interesting by the integration of ‘horizontal forces’ that “include both formal and programmatic configurations: space and event, force and resistance, density, distribution, and direction,” all of which are functions of the newly abstracted time.[25] But gaining the most traction at present is that of coordination that operates across time and space; Keller Easterling notes in observing spaces of global commerce, “[l]andscape is a diagram or repertoire—a set of events and behaviors unfolding over time,” and gives the ab-surdist example: “elaborate time-shire diagrams of Cancun developers, for instance, chart visitor rotations in a way that makes palpable mining of time as property.”[26] While these examples originate in globalized industrial spaces, strategies of coordination can also be observed in the work of Stan Allen and James Corner/Field Operations to diagram (and abstract) the developing natural-artificial ecologies in their projects over enormous territories and time scales. Thus while those sub-jects of interest in design may shift (or not), their origination in the natural environment and their subsequent abstraction for purposes of control and exchange, the spatio-temporal scale of their control expands with the diagram in practice.

Bernard Tschumi’s project for the Parc de la Villette (not unlike OMA’s second place proposal) addressed time and the unforeseen. As in the multiple layers of the exploded axonometric, there were multiple layers in the design that addressed the organizing of program, space, and time. The difficulty of the scale on the site led to the laying of the immediately orienting grid of follies whose points allowed the accommodation of a great many programs in the park, many of whom were unknown or subject to change at the beginning of the design process. As a recently vacated site, formerly a large district of industrial slaughterhouses, the site was viewed as having no history unto itself. Thus the landscape does little to reflect anything of the condition of the landscape’s historical, cultural, or topological aspects. As an extension of the logic of abstraction by time, compre-hension of the site for the user is designed to be achievable only in parambulating through the site, as ordered by the follies that are continuously differentiating.

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FOA’s Yokohama Port Terminal stands as both the apotheo-sis of the 90s dialogue of the diagram as formulated by De-leuze as well as the project popularizing the notion of build-ing as artificial landscape. The foundation of both these achievements if the use of the diagram in the formalizing of movement patterns. The description of the diagram as intermediating surface, by both Peter Eisenman and Stan Allen, is significant in this project as it is nearly entire the product of surface manipulation. In this way it could be viewed as approaching the Menger’s cube as described by Sanford Kwinter. There is confusion however in the actual rendering of the surface finish beyond its form. The artifi-ciality of the rolling landscape is brought out by the use of wood and asphalt, however the somewhat late introduction of the patches of turf on the roof are confused. However their grafting onto the surface is an ironic turn that is in a way a reversed strategy of the grafting of Fuller and Otto.

OMA’s proposal for the national library of France, ‘Très Grande Bibliothèque, is a clear reference to and critique of the formal and spatial determinism of the nine square grid in it ubiquitous application throughout modern architecture. As a fundamental break with the traditional usage of the diagram, the featured images of the project show no final exterior form of the library in favor of the signature program-matic elements rendered in whimsical geometry so as to speak to their indeterminateness and readiness for adap-tation to specific programs as determined later, similar to the follies of Tschumi. Accessed by the nine square grid of elevator towards, the proposal is clearly understood as infrastructure of the appropriation of space that is not even in connection with the landscape.

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While the expansion of the spatial and temporal realms up to this point has continuously expanding in both scale and scope, the work of Corner and Allen has been representa-tive of a new colonization that is vastly greater. The manipu-lation of ecology is not particularly new in design, especially not in the realm of regional and environmental planning; however, by treating the design with the provision of inde-terminacy, that is integral to their work, the ability to abstract and coordinate nature in space and time is expanded by vir-tue of the mastery of possibility and the unforeseen. Again, this is not unlike the strategies of OMA and Tschumi, but the combination of all previous tactics of abstraction makes for the difference. The diagram here is capable of anticipating the form, actions, and events of ecology and landscape.

1. Eisenman, Peter. “Diagram: An Original Scene of Writing” in Ben van Berkel; Caroline Bos (eds.). “Diagram Work.” ANY: New York, 1998, n. 23. 27-29: 27.

2. Frampton, Kenneth. 1999: Raoul Wallenburg Lecture: Megaform as Urban Landscape. University of Michigan A. Alfred Taubman College of Architecture + Urban Planning: Ann Arbor, 1999: 39.

3. Lefebvre, Henri; Donald Nicholson-Smith (trans.). The Pro-duction of Space. Blackwell: Oxford; Cambridge, 1991 (originally 1974): 269.

4. Lefebvre, 1991: 238.5. Vittorio Gregotti qtd. in Frampton, 1999: 42.6. Allen, Stan. “Diagrams Matter” in Ben van Berkel; Caroline

Bos (eds.). “Diagram Work.” ANY: New York, 1998, n. 23. 27-29: 16.

7. Thompson, D’Arcy Wentworth; John Tyler Bonner (ed.). On Growth and Form. Cambridge University Press: Cam-bridge, 1992 (originally 1917): 11.

8. Thompson, 1992 : 10.9. Barthel, Rainer. “Natural Forms – Architectural Forms” in

Winfried Nerdinger. Frei Otto: Complete Works: Light-weight Construction, Natural Design. Birkhauser: Basel; Boston, 2005: 17.

10. Thompson, 1992: 4.11. Barthel, 2005: 18.12. Eisenman, 1998: 27.13. Somol, Robert E. “The Diagrams of Matter” in Ben van

Berkel; Caroline Bos (eds.). “Diagram Work.” ANY: New York, 1998, n. 23. 23-26 : 24.

14. Eisenman, 1998: 27. 15. van Berkel, Ben; Caroline Bos. “Diagrams – Interactive

Instruments in Operation” in Ben van Berkel; Caroline Bos (eds.). “Diagram Work.” ANY: New York, 1998, n. 23. 19-23: 20.

16. Eisenman, 1998: 28.17. Somol, 1998: 25.18. Somol, 1998: 24.19. Kwinter, Sanford. “The Geneology of Models: The Ham-

mer and the Song” in Ben van Berkel; Caroline Bos (eds.). “Diagram Work.” ANY: New York, 1998, n.23. 57-62: 60.

20. Somol, 1998: 24.21. Deleuze, Gilles; Constantin V. Boundas (ed.). “The Dia-

gram.” The Deleuze Reader. Columbia University Press: New York, 1993. 193-200: 199.

22. de Landa, Manuel. “Deleuze, Diagrams, and the Genesis of Form” in Ben van Berkel; Caroline Bos (eds.). “Diagram Work.” ANY: New York, 1998, n. 23. 23-34: 30.

23. Deleuze, Gilles; Félix Guattari. A Thousand Plateaus. Uni-versity of Minnesota Press: Minneapolis, 1987: 141-142.

24. Allen, 1998: 18.25. Allen, 1998: 16.26. Easterling, Keller. Enduring Innocence: Global Architecture

and Its Political Masquerades. The MIT Press: Cambridge, 2005: 63; 24.