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Writing Architecture #23
Formulations: Architecture, Mathematics, Culture
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 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.
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 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.
432 pages, Paperback
Published January 11, 2022
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Displaying 1 of 1 review
August 28, 2023
A brilliant survey of the foundations of maths-based design and architecture, Formulations covers epistemology, taxonomy, machines, maquettes and other representations and models, means of measurement, stereoscopics, rules surfaces and topological approaches to curved design, cube / grid-based design w/ its attendant political philosophy of economy and equality, the democratization of design, and crystallography.
These mathematics and techniques are now largely embedded within computer software, which "dissolves accepted hierarchies of knowledge in favor of a promiscuous and polyglot patchwork of representation and technique, accessible to the uninitiated layman."
New vocabulary:
--Geodesy: "fused cartography and surface geometry into the same discipline." pg. 118
--Parameterization: "the process of describing shapes with mathematical functions." pg. 131
--Eidetic: relating to or denoting mental images having unusual vividness and detail, as if actually visible.
--Armature: a metal framework on which a sculpture is molded with clay or similar material.
--To limn: suffuse or highlight (something) with a bright color or light.
--Benthic: refers to anything associated with or occurring on the bottom of a body of water.
--Zine: Any self-published unique work of minority interest, usually reproduced via photocopier.
--Avuncular: relating to an uncle.
These mathematics and techniques are now largely embedded within computer software, which "dissolves accepted hierarchies of knowledge in favor of a promiscuous and polyglot patchwork of representation and technique, accessible to the uninitiated layman."
New vocabulary:
--Geodesy: "fused cartography and surface geometry into the same discipline." pg. 118
--Parameterization: "the process of describing shapes with mathematical functions." pg. 131
--Eidetic: relating to or denoting mental images having unusual vividness and detail, as if actually visible.
--Armature: a metal framework on which a sculpture is molded with clay or similar material.
--To limn: suffuse or highlight (something) with a bright color or light.
--Benthic: refers to anything associated with or occurring on the bottom of a body of water.
--Zine: Any self-published unique work of minority interest, usually reproduced via photocopier.
--Avuncular: relating to an uncle.
Displaying 1 of 1 review