Protogeometry in Architecture
Protogeometry is the third of three concepts underlying my theory of material practices along with techne and bricolage. My next post will attempt to weave these concepts together into a tentative aesthetic theory.
Protogeometry is a concept explored in philosopher Edmund Husserl’s 1936 essay “The Origins of Geometry.” 60 years later it was later introduced into the theory of architecture by philosopher David Farrell Krell, in his essay “A Malady of Chains.”
Protogeometry refers to early – inexact – geometry, before the creation of pure – exact – geometry. As Husserl wrote, early geometry emerged from ancient humans’ observations about the preferred formal properties of objects which make them useful:
“First to be singled out from the thing-shapes are surfaces— more or less “smooth,” more or less perfect surfaces; edges, more or less rough or fairly “even”; in other words, more or less pure lines, angles, more or less perfect points; then, again, among the lines, for example, straight lines are especially preferred, and among the surfaces the even surfaces . . . .”
Krell used this notion of the protogeometric as a point of departure to sketch an approach to architectural form which decenters its foundations in pure (as opposed to proto-) geometry by creating:
“rough surfaces, unclean edges, muted corners, hazy lines, and all of it with not point at all. . . . an ecstatic as opposed to a foundationalist sense of space, time and the human body . . .”
Husserl, and to a greater degree, Krell, criticize how modern thought, because of its foundations in geometry, “mathematizes” nature – and, by extension, human imagination. It reduces the rich complexity of the world and human existence to the mechanized simplicity of a machine (physicist Fritjof Capra has also written elegantly about this outmoded mechanized view of the universe).
Philosophers Gilles Deleuze and Felix Guattari, in A Thousand Plateaus, note the similarity between Husserl’s protogeometry and their concept of smooth space:
“Husserl speaks of a protogeometry that addresses vague . . . morphological essences. Protogeometry is . . . anexact yet rigorous (“essentially and not accidentally inexact”). . . . [for example] roundness is a vague and fluent essence, distinct both from the circle and things that are round . . .”
Deleuze and Guattari describe smooth space as the “haptic space of close vision,” in opposition to “striated space,” geometrical space.
Protogeometry may be applied to in the arts:
- Architecture: Roughhewn, weathered, or highly tactile materials
- Visual Arts: Use of found objects with the above properties, deliberately unpracticed use of media
- Music: Dissonant, distorted, noisy, arrhythmic, or rough sounds
- Literature: rough language and imagery
- Film: low-tech camera action – shakiness, skipped frames, unfocused images, or “insufficient” lighting
In architecture and the visual arts creative works are made of materials, many of which will be visible in the final work. These materials have formal properties – shape, texture, color – which may be more or less pure or impure. Protogeometric materials have impure – heterogeneous – qualities.
A material may have protogeometric properties when it’s made – a roughhewn handmade building material for example.
Or, a material may have exacting geometric properties, but become protogeometric over time, due to weathering and use – a metal roof in which it’s immaculate smooth grey surface weathers into a mottled patina, for example.
(Im)purification as Aesthetic Strategy
The concept of protogeometry, like techne, and bricolage, offers a useful tool for theorizing material practices.
It legitimizes the aesthetic values of marginalized phenomena such as indigenous culture, vernacular/folk culture and popular/mass culture. The traditional aesthetics of these cultures privilege qualities that are “rough” (“pre-, or protogeometric”), qualities used historically by the dominant culture to subordinate them to “high” culture.
It provides a framework for understanding the deep structures of these and applying that understanding to the creation of new creative works.
It provides a concept which, like techne and bricolage, integrates aesthetics with socio-political meaning and offers strategies of resistance.
© Donald E. Armstrong and Material Practices, 2013