45 leslie Journal of Architectural Education, pp. 45–54 Q 2003 ACSA, Inc. THOMAS LESLIE Iowa State University Form as Diagram of Forces The Equiangular Spiral in the Work of Pier Luigi Nervi The relationships between form, performance, and construction are uniquely demonstrated in the long-span works of Pier Luigi Nervi. The balance of these forces led in Nervi’s case to a series of works that take the form of the equiangular spiral, a bizarre geometrical phenomenon that appears regularly in the natural world. The afnities between Nervi’s work and the spiral’s natural occurrences can be explained via D’Arcy Thompson’s On Growth and Form, suggesting that this familiar book on biological morphology be seen by architects in a new and more thorough light. The form, then, of any portion of matter, whether it be living or dead, and the changes of form that are apparent in its growth, may in all cases alike be described as due to the action of force. In short, the form of an object is a “diagram of forces.” 1 —D’Arcy Wentworth Thompson, On Growth and Form, Introductory D’Arcy Thompson’s On Growth and Form contains within its literate prose the profound suggestion of a morphology based on empiricism and mathemat- ics—a powerful challenge to our established archi- tectural traditions of style and composition. Thomp- son, of course, had no such motivations in writing, and, despite his occasional use of architectural (or more commonly structural) metaphors, it seems unlikely that his work’s translation into the eld of architecture would have held more than a passing interest for him. Yet his masterwork has an unavoid- able relationship to the work of the human designer. His examinations of the formation and performance of matter in biology contain lessons and examples with inevitable consequences for architecture, in which form is also at least in part determined by both assembly and function. In architecture, the conscious intelligence of the designer takes the place of the latent intelligence accumulated by natural selection; perhaps more importantly, the operations of organic and construc- tive processes are likewise related but distinctly con- ceived. The organism grows by gradual accumula- tion over its life, the architectural structure by relatively instantaneous assembly at its inception. Relationships between organic morphology and architectural form, therefore, can be expected to show dialogical afnities, rather than determinant linkages. This article explores the action of such afni- ties in the work of Italian architect, engineer and constructeur Pier Luigi Nervi (1892–1979). In Nervi’s case, these afnities emerged with striking clarity in a set of long-span works, demonstrating the potential richness of an empirical design process and hinting at a limited though important corre- spondence between the world of the organic and that of the constructed. In these works, the equian- gular spiral emerged as a result of Nervi’s ability to balance forces of construction and performance. Nervi’s roof forms suggest that the strongest link between the organic and the constructed exists not at the level of visual or formal representation, but rather in the deeper structures of geometry and mathematical patterning. Although metaphor and the imitation of striking natural forms may be archi- tecturally tempting, Nervi’s work suggests an “organic” that lies in the relationships among con- structive and structural processes and the deploy- ment of material to enable these. This theme, which also permeates Thompson’s work, connects human- kind’s constructions to the natural world through the notion of design as an arrangement of resources for benet, not design as the construction of spatial or graphic experience. The resulting forms, whether they are natural or human made, display patterns and formations that we recognize as beautiful or engaging not simply because of their visual propor- tions but rather because of our innate recognition of their mathematical efciency, their logic, and their patterning. A comparison between these two realms reveals the mechanisms of this organic beauty in algorithmic geometry and suggests both the poten- tial for and the limits of the conceptual link between organic and structural morphogenesis. In other words, rather than formal or visual connota- tions, a Thompsonian organic will involve parallels between the natural and the man made that lie in the processes of growth, construction, and function. More particularly, these afnities will lie in the per- sistence of simple geometries and patterns that are, in Steven Jay Gould’s words, “optimal representa- tions” of the physical forces at work on a given object, be it architectural or natural. 2 Mechanism and Teleology— Thompson’s View on Growth and Performance Sir D’Arcy Wentworth Thompson’s On Growth and Form has achieved a cultlike following among theo- rists and practitioners of architecture. It is an extraordinarily compelling work of biological expla- nation, written by a scholar whose background effectively bridged quite neatly the two cultures of science and the humanities. 3 Its fundamental prem-