Formulations

An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century.

In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects.
            Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. 
            Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.
 1 Models, Machines, Manuals, and Cabinets 9 
2 A Machine Epistemology: Encapsulated Knowledge and the Instrumentation of Architecture 31
3 Theorems Made Flesh: The Architectonics of Mathematical Maquettes 61
4 Alternate Dimensions: Measuring Space from Building to Hyperbody 101
5 A Virtuality Atlas: Stereoscopic Drawing and Geometric Dream Space 141
6 Illusion Engines: Drawing at the Speed of Light 181
7 Labyrinths, Topology, and Meinong's Jungle: Architecture's Impossible Objects 221
8 All You Need Is Cube: The Political Economy of Grid Space 273
9 Geometry's Mass Media: Broadcasting Technique in Architecture's Hyperbolic Era 307
10 Crystal Collectives: Architecture's Chemical Subcultures 343
11 Of Dabblers and Virtuosos 387
Notes 395
Acknowledgments 419
Index 421“A brilliant and thought-provoking navigation through complex mathematical notions, models and machines, spatial patterns, and construction techniques. A must-read for anyone interested in the relationships between architecture, mathematics, and digital techniques.”
—Antoine Picon, Harvard University Graduate School of Design
 
“Since the rise of modern science, some designers have prized verifiable calculations above intuition. Andrew Witt’s Formulations offers a superb, scholarly, and most enjoyable overview of maths-driven design from its early modern rise to its postmodern fall.”
—Mario Carpo, Bartlett School of Architecture, University College London/University of Applied Arts, Vienna
 
“Witt’s keen exploration of architecture’s intertwining with mathematics is outstanding and timely, a long-ranging history from graphs and grids to crystals and lattices—and far beyond. ” 
—Molly Wright Steenson, Vice Provost for Faculty, Carnegie Mellon University; author of Architectural Intelligence: How Designers and Architects Created the Digital Landscape and co-editor of Bauhaus FuturesAndrew Witt is Associate Professor in Practice of Architecture at Harvard University Graduate School of Design and cofounder of Certain Measures, a design and technology studio based in Berlin and Boston.