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Author: Norman Crowe
Bases for the Geometry of Building

Bases for the Geometry of Building


Nature and the Idea of a Man-Made World, (Cambridge: MIT Press, 1995), p. 46 – 69.

An alternative idea of wild nature as a source of human existence is gaining a public hearing.  This idea questions the long-entrenched, civilized-primitive dichotomy, a bifurcation grounded in an assumption that the human story lies in our triumph over a hostile nature.  The idea of nature as the source of human existence, rather than a mere re-source to fuel the economy, is the outcome of the second scientific revolution, initiated in the nineteenth century by Charles Darwin and Rudolf Clausis.
    —Max Oelschlaeger, The Idea of Wilderness (Yale University Press, 1991), p. 1

The Geometry of Dwelling  

Most ancient dwellings and settlements were laid out on an orthogonal matrix.

  • Why is this?  Nature doesn’t organize things along orthogonal lines, and it would seem that nature must have been ancient man’s primary paradigm (a natural default program).  So why foursquare geometry? (Nature..., p. 50)


 Images by Norman Crowe in Nature and the Idea of a Man-Made World, courtesy of MIT Press. Used with permission. All rights reserved.



We perceive space through the physiology of our bodies.  Because we have two sides and a back and front, foursquare geometry becomes our reference to the world.  (Nature..., p. 50, 125)

The obvious answer has to do with how we perceive space.  We have a front, back, and two sides and we perceive the world around us relative to that.  Further, we stand upright and so are aware of a vertical axis perpendicular to the normative surface of the earth.  Gravity.

Many, if not most, early cities were laid out in a foursquare pattern. The Roman castrum is an often cited example, with its cardo and decumanus. (Nature..., p. 52)


City Symbols



Four representations of the town or city:  Clockwise, from upper left,

  • Early Chinese ideogram for “village,” 1300-612 BC;
  • Assyrian bas-relief showing scenes of city life, c. 1600 BC;
  • Egyptian hieroglyph for “city,” 3110-2884 BC;
  • Icelandic drawing of the “heavenly city of Jerusalem,” 13th century AD.

Images by Norman Crowe in Nature and the Idea of a Man-Made World, courtesy of MIT Press.
Used with permission. All rights reserved.


The bi-lateral symmetry of the human body is responsible in large part for how we perceive the world around us.


Left, a dolmen provides shelter that is related to the body; a nomad’s canopy provides a dignified presence in a featureless landscape; standing on the axis of a great temple lends stature to the moment.

Above Right, a campfire’s light fills a dome of space in the darkness. —Nature …, p. 53.


Images by Norman Crowe in Nature and the Idea of a Man-Made World, courtesy of MIT Press. Used with permission. All rights reserved.



Perception of our position in the landscape is innate.  It arises from a physiological awareness that evolved to ensure our survival in nature.  Thus, the way we build, how we configure architecture, is in response to these natural, evolved proclivities.

We may choose a position within a complex architectural enclosure that suits our spatial needs in relation to intentions.  Here, a young woman (from a TV advertisement for tissues) has a cold, feels vulnerable, and has positioned herself where she is neither inside nor out, but can observe both; and most importantly, has chosen a space suited to her body-related perception, her own niche.

The Geometry of Building 

Materials of construction either come from nature directly, as in the case of stone and wood, or indirectly, as in the case of brick or steel which require heat and other industrial processes to create.  Stages of processing that take a material farther and farther from its natural origin may be seen particularly well in timber construction: a building may be built of sticks and logs, or of refined, sawn lumber.  The level of processing of materials, or lack of it, affects our awareness of the origin of the materials in nature. 

Tectonics refers to the geometry of architectural structure—not just the structure that holds up a building such as columns and beams, but the order of a building’s elements as well (windows and other openings, roof, walls, surfaces and so forth, as well as a poetic expression of the structure latent within).

 Techniques of putting materials together to form walls, roofs, and the like are most easily accomplished by means of a geometric order.  There are two primary systems of building, trabeation and bearing wall construction.  Trabeation arose from timber construction and bearing wall construction from stone.  In East Asia trabeation evolved using timber to the fullest most refined extent, while in the West, masonry construction evolved.  The two systems produce buildings of two very different characters, and therefore participate in two very different dialectical relationships with the civilizations with which each evolved.


Below: Evolution of Masonry Construction

Images by Norman Crowe in Nature and the Idea of a Man-Made World, courtesy of MIT Press. Used with permission. All rights reserved.

 Below: A Roman bearing-wall masonry building, left, compared with a Japanese trabeated timber building, right.

 A Roman bearing-wall masonry building compared with a Japanese trabeated timber building

 Images by Norman Crowe in Nature and the Idea of a Man-Made World, courtesy of MIT Press. Used with permission. All rights reserved.


Behavioral patterns and deeply rooted customs of a culture are attuned to the environment in which that culture evolved.  For instance, Japanese customs of ritualized privacy and more formalized personal interactions between individuals contrasts with comparatively casual counterparts in the West.  One may be seen to have evolved within buildings of essentially open and flowing space, while the other in compartmentalized and easily privatized interiors, both visually and audibly.     (Nature …, p. 64–68)

It is safe to say that new construction that does not respect deeply embedded traditions will yield unpredictable results over the long term with respect to interactions with normative social patterns.  Examples may be found among variations in population densities and building interior configurations that do not respect long-standing custom.  For instance, a city newly overcrowded by refugees, or newly standardized housing for the urban poor that is of a form and type they are unaccustomed to such as “project housing” of mid-rise slabs set back from the street, etc. 


Discussion Session

  1.  If indeed, “new construction that does not respect deeply imbedded traditions may yield unpredictable results in terms of interactions with normative social patterns,” do you know of some examples of this from your own experience?
  2. Assuming the foregoing quotation to be true, how may innovation in architecture and urbanism take place without risking unpredictable results that negate the advantages gained from innovation?
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