The Crisis in Geometry

The Crisis in Geometry

Peter Halley, Arts Magazine, New York Vol. 58,  No. 10, June 1984

Where once geometry provided a sign of stability, order, and proportion, today it offers an array of shifting signifiers and images of confinement and deterrence.

The formalist project in geometry is discredited. It no longer seems possible to explore form as form (in the shape of geometry), as it did to the Constructivists and Neo-Plasticists, nor to empty geometric form of its signifying function, as the Minimalists proposed. To some extent, the viability of these formalist ideas has simply atrophied with time. They have also been distorted and bent to conform to the bourgeois idealism of generations of academically-minded geometric classicists. But the crisis besetting geometric art for the last two decades can also be viewed as characteristic of the crises that have beset formalisms of all kinds in the postwar era : those that precipitated the transition from literary formalism to structuralism and from structuralism to the post-structuralist re-examinations that have taken place in the work of such figures as Barthes 1 and Foucault2. 

For, like these crises, the crisis of geometry is a crisis of the signified. It no longer seems possible to accept geometric form as either transcendental order, detached signifier, or as the basic gestalt of visual perception (as did Arnheim). We are launched instead into a structuralist search for the veiled signifieds that the geometric sign may yield. These questions arise : to what purpose is geometric form put in our culture ? Why is modern society so obsessed with geometric form that, for at least the last two centuries, we have striven to build and live in geometric environments of increasing complexity and exclusivity ? Why has geometric art been so widely accepted in our century, and why has geometric imagery gained an unprecedented importance in our public iconography? 

To answer these questions, we turn to an examination of the sociology of geometry in the modern era, to literally a sociology of formalism. Geometry will here be examined in relation to its changing role in cultural history rather than as an a priori ideal of the mental process. This essay will focus on two texts relevant to these questions, texts which have both influenced the production of geometric art and can be used to decode the geometric work produced during these years of "crisis". They are Discipline and Punish by Michel Foucault3 and Jean Baudrillard's Simulations 4. Foucault's work is most relevant to the geometric art produced during the 70s, while Baudrillard's text, which in many ways draws upon Foucault's, is crucial to an understanding of the geometric art that has appeared in the present decade. 

In Discipline and Punish, we find deconstructed the great geometric orderings of industrial society. The omnipresent unfolding of geometric structures in cities, factories, and schools, in housing, transportation, and hospitals, is revealed as a novel mechanism by which action and movement (and all behavior) could be channeled, measured, and normalized, and a means by which the unprecedented population of the emerging industrial era could be controlled and its productivity maximized. 

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