Graphing theory : new mathematics, design, and the participatory turn

Abstract

In the 1960s mathematically inclined architects involved with academic research advocated for a shift from the points and lines of geometric shapes to points and lines of another kind - ones representing abstract objects and their relationships. A story of propinquities between architecture and mathematics, this dissertation investigates this shift through the lens of the mathematical concept that catalyzed it: the graph. I take the graph as an entity with fluctuating symbolic and operational properties and "follow" it across institutional and disciplinary boundaries to reveal historical connections hitherto unseen. I begin by locating the graph's entry into architectural theory at transitions and transactions of mathematical and architectural modernism. Mathematical modernism promoted a structural model of disciplinary knowledge free of empirical intuitions, while boosting new mathematical varieties that represented structures and relations. Architects turned to structural abstraction in efforts to purify their inheritance of interwar Modern architecture from stylistic doctrines and empirical conventions. The graph's amenability both to visual depiction and to mathematical analysis furnished it with a strategic position among modern mathematical varieties: graphs made structural abstraction visible and workable. By virtue of this property, graphs proliferated in architectural theory as harbingers of a veritably modern discipline founded on rationality and geared toward ensuring functional efficiency. The end of the 1960s found advocates of functionalism and rationality turning to ideals of intuition and espousing the "unpredictabilities" of participatory design. By delving into four contexts of architectural theory production in the United Kingdom, the United States, and France, I expose technical and conceptual continuities among propositions sitting on opposite sides of this "participatory turn." I argue that the "turn" was undergirded and motivated by a new regime of seeing and subjectivity, for which the graph was an instigator, symbol, and facilitator. "Intellectual vision," as I call this regime, assumes an abstract invariant structure that underlies concrete appearance and delimits the extents of subjective choice in a combinatorial manner. I identify forces that legitimized intellectual vision in 1960s and 1970s architectural theory and critically analyze the ways in which it was used to conceptualize creativity and open-endedness both in architectural design and in theories of participation. I close with an evocation of alternative engagements between architecture and mathematics as pathways to reclaiming shape and recouping perceptual seeing.