The pioneering architect and geometrical theorist Anne Tyng (1920–2011) knew well the latent power of triangles. In 1953, she drafted the first design of a high rise, space frame tower, using the triangle as a basic structural unit.
As a material structure, the triangle is the most stable shape, distributing force uniformly among its sides. But as the mathematical symbol for change, the triangle denotes imminent flux—a structure on the verge of self-destruction. The pioneering architect and geometrical theorist Anne Tyng (1920–2011) knew well the latent power of triangles. In 1953, she drafted the first design of a high-rise, space frame tower, using the triangle as a basic structural unit.
Tyng began drafting the City Tower as an unpaid side project while employed at the architectural practice of Louis Kahn. The dominant approach to tower design at the time prioritized the appearance of uniformity over genuine structural discipline. The skin-exterior of the common tower played no role in the structural concept of the building, functioning rather to conceal components deemed ugly but necessary, such as joints and mechanical and electrical systems. The traditional tower engaged in an aesthetic of accumulation; to Tyng, this meant that architecture was in hiding, obscuring its inherent rigor under the self-conscious banner of style.
Speculating on alternative workplace architectures, Tyng drew inspiration from the geodesic, or space frame, dome designed by Buckminster Fuller, whom she had met in 1949. A space frame dome is a lightweight but robust structure resulting from a balance of tension versus compression forces that creates a fully triangulated network. An expansion of Alexander Graham Bell’s tetrahedral kite design patented in 1904, Fuller’s space frame dome would inspire both a redesign of the basic military shelter and a counterculture of environmentalist communes in coming years. Reimagining Fuller’s single-layer space frame design for an urban landscape, Tyng set out to create the first multi-layered space frame structure: a triangulated skyscraper that would grow out of its own internal geometry in a consistent and continuous flow.
Modern computers allow us to use geometry in our daily lives without comprehending it, but Tyng had no such luxury when designing the City Tower. She worked analog, careful hands constructing the patterns of an incisive intellect for hours on end. Tyng defined architecture as “giving form to number and number to form,” recalling the Pythagorean axiom: “Everything is arranged by number.” Like the Pythagoreans, Tyng envisioned the universe as a harmoniously ordered whole, and architecture as an expression of the reciprocal relationship between the human mind and the material world, as encoded by geometry. She was fascinated by the principles of geometry described by the ancient Greeks, who realized in the 5th century B.C. that although they could not see “ideal” shapes in nature, they could envision them, describe them, and build them, approximately. In the Timaeus, Plato reduced the intellectual grid of spatial concepts—the interior plane of “ideal” forms conceivable by the human mind—to five basic shapes, each corresponding to an element of the universe: fire the tetrahedron, earth the cube, air the octahedron, water the icosahedron, and, as the symbol of the cosmos, the dodecahedron. The five Platonic Solids, which form the basis of Euclidean mathematics, are the only regular forms possible to conceive and build in three-dimensional space with uniform faces and uniform angles at which those faces meet. The irreducible building block, or atom, of these “ideal” shapes is the triangle.
It is only fitting, then, that Tyng would draft her “ideal” tower within a system of triangular coordinates. The triangulated grid functioned in her mind as a computational universe into which any architectural structure could be plugged, divided, and aggregated, ever-approaching “ideal” geometry. From the discipline of this matrix would emerge the form of the double helix, twisting like a nearly living thing. Tyng envisioned the City Tower as a raw, structural reaction against the forces of nature, allowing the free circulation of air, light, and heat within.
But, of course, no architectural structure simply emerges from an abstract matrix; there are workers, costs, and conflicting interests to consider. When Kahn included the City Tower plan in his proposal for a redesign of Midtown Philadelphia, citing himself as architect and Tyng as associate architect, Philadelphia’s chief urban planner Ed Bacon deemed the proposal too expensive and impractical to be materialized. Although the tower was never built, we know that it would have been a pre-cast, pre-stressed, concrete, triangulated strut frame; that it would have risen 612 feet high and contained three million square feet for city departments and public areas; and that a methodology rooted in “genetics” was a key aspect of its design:
We found a genetic source in the natural order of the geometry for the triangular tilting of interconnected vertical forces and for imagery of an undulating helix braced against the horizontal forces of the wind. —“A City Tower,” Advanced Structures Around the World, 74.I.E.51. Anne Griswold Tyng Collection
Incidentally, a few months before Tyng had begun designing the City Tower, James Watson and Francis Crick had been credited with Rosalind Franklin’s discovery of the double helix form of DNA. The structural unit of the gene was accepted as a foundational concept capable of unifying all biology, as irreducible as the atom and the triangle, just as the discourse of cybernetics was gaining traction in avant-garde circles. In 1948, Norbert Wiener had defined cybernetics, from Greek kybernetike meaning “governance,” as “the scientific study of control and communication in the animal and the machine.” The subsequent revelation that genetic material is, in fact, a code—an information system—was one of a number of intellectual developments that propelled the fundamental concepts of cybernetics, including information, feedback, and systems, into the dominant ontological forces they are today. Through the form of the triangulated double helix, Tyng gave geometrical expression to a moment when new spatial principles of organization, such as networks and flows, were beginning to be applied to intellectual content, or information. If the traditional high-rise tower could be described as a constrictive space housing a bureaucratic culture that workers were critiquing as alienating and authoritarian, Tyng’s concept of a high-rise, space frame typology embodied the relatively expansive principles of autonomy and flexibility promised by the cybernetics revolution.
When Tyng’s model of the City Tower was exhibited at the “Visionary Architecture Exhibition” at the Museum of Modern Art in New York in 1960, it gained attention as a revolutionary expansion of the tetrahedral lattice—a significant feat of structural flexibility, verging on a model of organic growth. The avant-garde group Archigram would further the pursuit of the “liberation of form” by adopting the tetrahedral lattice as the foundation of its 1964 “Plug-In City,” a megastructure designed to accommodate rapid change in response to the desires of its inhabitants. Yet even as the cybernetics-inspired architectural practices of the late 20th century were striving to free inhabitants from the spatial awareness of imposed orders, new patterns of communication and organization, or information architectures, were reifying as a behavioral apparatus within the workspaces of the high-rise tower, tying workers to corporate interests in novel but just as material ways. In his 1996 essay “Immaterial Labor,” Maurizio Lazzarato describes the late-20th-century emergence of a new type of labor involving cybernetics and computer control, resulting in a shift from the traditional production of objects to the production of informational and cultural content, which previously had not been considered “work.” The commodities produced by immaterial labor include audiovisual production, advertising, fashion, software, photography, cultural activities, and the like. Immaterial labor, according to Lazzarato, encompasses abstract activity that demands the worker’s investment of subjectivity, obscuring the asymmetrical power relations of the workplace and resulting in the regulation of the ideological or cultural environment of the consumer through the manipulation of information. The result is an “intellectual proletarian” marked by “precariousness, hyper-exploitation, mobility, and hierarchy.” “It is worth noting that in this kind of working existence it becomes increasingly difficult to distinguish leisure time from work time,” he writes. “In a sense, life becomes inseparable from work.”
The rise of immaterial labor can be linked to breakthroughs in geometry that have allowed us to see beyond the “ideal” forms described by the ancient Greeks. While regular geometry has for centuries enabled the macro-restructuring of the environment through feats of architecture and engineering, the imposed geometry of human constructions differs from the emergent geometry of natural systems in ways that we have only recently begun to comprehend spatially. Although many people throughout history have looked at the form of a leaf and seen veins that resemble branches, and branches that resemble trees, and trees that resemble the human nervous system, descriptions of the self-similar patterns of nature have, for the most part, represented them as expressions of chaos. Only in the 1980s was Benoit Mandelbrot credited with the discovery of what he called “fractal geometry” when he ran simple functions through the computers at IBM, where he worked. The computers produced visual representations of the irregular geometries of natural systems—models of organic growth pursued by architects like Tyng—in a reproducible mode. Mandelbrot famously wrote: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” If technology has enabled our capacity for spatial awareness of irregular geometries, it has also enabled us to reposition our architectural and computational capacities away from the management of human behavior, as described by Lazzarato, and towards the sustainable management of the natural systems that have been disturbed by our imposed constructions.
As smart technologies and intelligent infrastructures grow more embedded in our daily lives as a global network, in no small part through the office spaces of the high-rise tower, it becomes increasingly clear that the “ideal” or virtual can no longer be conceived as a sphere above or separate from physical reality. On the contrary, the information ontology is a mode of interpretation that collapses the distinction between the “ideal” and the material, and with it, our established grounds for moral judgment. Considering the ideologies that have historically overlapped within flexible architectures, such as Buckminster Fuller’s conflicting military and environmental ambitions, we must ask our avant-garde architects, engineers, and computer scientists now: What power do you have to affect a technocratic landscape, and how will you use it?
“A City Tower,” Advanced Structures Around the World, 74.I.E.51. Anne Griswold Tyng Collection, The Architectural Archives, University of Pennsylvania.
Kahn, L.I. 1953. “Towards a Plan for midtown Philadelphia.” Perspecta 2.
Kahn, L.I. and Tyng, A. G. 1957. “A City Tower: a concept of natural growth.” New York, US Steel Corporation Publication.
Kenner, Hugh. 1995. “Fractals.” Mazes: essays. Athens: University of Georgia Press.
Lazzarato, Maurizio. “Immaterial Labor.” Radical Thought in Italy: A Potential Politics. Edited by Paolo Virno and Michael Hardt, vol. 7, University of Minnesota Press, 1996.
Tyng, Anne Griswold. 1969. “Geometric extensions of consciousness”. Zodiac / Association Pour La Diffusion Artistique Et Culturelle, Bruxelles. 130–162.
Tyng, Anne Griswold, Alicia Imperiale, and Ingrid Schaffner. Anne Tyng: Inhabiting Geometry. Philadelphia: Institute of Contemporary Art, 2011.