Diagrams: Tropes, Tools, Abstract Machines. Christoph Lueder

       Fig. 1 : Field, fabric, rupture, interstice (Chicago). Drawing by the author.

      What is a diagram?

      The quotes from Benjamin’s essay fragment and Deleuze and Guattari’s seminal book align diagrams with two diametrically opposed vectors of transposition. The first vector points from objects and processes observed in the world towards their notation and abstraction; the second vector points from abstraction towards actualisation and incorporation in the world. Hence, diagrams are tools of analysis as well as generative devices.

      Diagrams are transparent as well as corporeal. The word diagram originated from two distinct Greek roots, firstly, dia, meaning across, through, and secondly, graphein, meaning to write, draw, mark out with lines. First, diagrams are transparent representations that enable us to look through their visual form, at a subject that they notate, abstract and explain. This is different to paintings or photographs that recreate the appearance of their subject on a flat surface. Second, diagrams are marked out with lines, inscribing the gestures of the diagram-maker into a receptive medium, such as sand or paper. Hence, diagrams are diaphanous abstractions as well as material inscriptions evocative of explanatory gestures and of human corporeality.

      The term diagram entered the English language through the French term diagramme. Its earliest recorded use dates from 1613 and does not refer to architecture; it is used by a physicist in a treatise on magnetic bodies and motions (Ridley 1613, 126). Later in the 17^th century, the term came to denote a list, register or enumeration (Weever 1631,8), a figure aiding in the proof of a mathematical proposition (Stone 1645, 74); and, in the 19^th century, notation of a process (Robinson 1839, 157). In the late 20^th century, the term acquired yet another meaning, as the French philosopher Deleuze argued for a redefinition of the diagram from “visual archive” to “display of the relations between forces which constitute power” and “abstract machine” (Deleuze [1986] 1988, 36). Deleuze inferred this new meaning from Foucault’s analysis of disciplinarian societies, but also from morphogenesis in geology, biology, thermodynamics and beyond (Deleuze and Guattari [1980] 1987). The evolutionary history of meanings and interpretations of the term diagram is one of translations between disciplines; architecture’s participation in those transactions has progressively intensified over the course of the 20^th century.

      The multiplicity of disciplinary and historical tropes and trajectories, the flow of travel from conceptualisation to actualisation and vice versa, interact with further layers to constitute a complex methodological field, an unbounded fabric woven from specialist territories, interstices and overlays. This monograph assembles an array of deep probes into this paradoxical field, taken at key coordinates and intersections of ideas, practices and conven8 tions. Each probe—each monograph chapter— adopts a diagrammatic method as point of departure to retrace transactions between authors and commentators across disciplines, situate discourses and methods within cultural and disciplinary milieus, examine rapport with corporeality and embodied practices, map out analytical and speculative usages unlocking critical and inventive potentials.

      Chapter one, on Poché and Free Section, explores the Beaux Arts notion of poché as a nexus between embodied thought, representational convention and inventive potential. Its literal translation from French is “pocket;” at the Ecole des Beaux Arts in Paris during the 19^th century it denoted thick, sponge-like masonry walls that contained secondary spaces. The sectioned surface of such walls was hatched. At urban scale, poché manifests in the Nolli Map of Rome (1748, Figure 2), and diagrams relationships between public and private space. Since then, poché has been appropriated and reinterpreted in different ways: Rowe conceived of it as the imprint on the ground of heavy walls and principle of tectonic poïesis, Kahn recognised a principle of spatial hierarchy, with servant spaces contained as voids in the poché, Venturi theorised open poché that exposes those voids as volumes; leading up to Koolhaas’ radical reinterpretation, inverting poché from its early 20^th century role as antagonist of the Corbusian free plan to protagonist of a newly theorised free section.

      Chapter two, on Analytical and Choreographic Notations examines the graphical method, developed during the 1920s by the Russian/German/Israeli architect Alexander Klein, intended as a tool for the evaluation of architectural plans according to objective criteria. The long roots of this mathematical conception reach beyond Taylorism and scientifc management, beyond the scientific abstractions of the 17^th century, all the way to Euclidean geometry; they have developed alongside competing notions of diagrams as emplaced and embodied in space and culture. While contemporaneous architects and theorists questioned the merits and methods of achieving objectivity, Klein’s visually arresting and productively evocative diagrams concurrently elicited surprising alternative readings as choreographic notation (Löwitsch 1930a, 31). Abstract and corporeal readings of Klein’s diagrams competed and co-evolved over a long arc of interpretations and transactions between disciplines that encompassed critiques of determinism (Evans 1978) alongside appropriations to new ideas and ideologies (Gloor 1970; Warhaftig 1985).

      Chapter three, Cardinal Transposition, examines exchanges of ideas between artists, performers, composers, filmmakers and architects that strategically exploit the spatiality of canvas and screen, of upright figure and diagrammatic trace on the ground, of building section and landscape, of drafting table and framed view. Walter Benjamin’s juxtaposition of two sections through the world’s substance reminds us that space is not isotrophic; we perceive a picture held vertically before us differently from a drawing laid out horizontally on a desk or a mosaic at our feet. Acts of cardinal transposition produce new meaning in exchanges between working and viewing surfaces and in transactions between disciplines and practices.

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