On order
Order surrounds us as part of our everyday experience of the world. We see this in the games we play, the tables that we eat at and even the books that we read. On a football field, a line defines sides, a perimeter defines borders and a frame defines the goal. A place setting structures a meal and defines it as either casual or formal. Text presents itself as words, sentences, paragraphs, sections and chapters. As you read this page, you rely on its organization, its division of space. A large vertical portion holds the text while off to the side is a smaller portion holds illustrations and notes. This is the architecture of this book – its order.
Our book uses a common organizational strategy for its pages: big piece, small piece – primary and subordinate. As we add other typographic furniture – headers, footers, notes, etc. – this also conforms to that basic architecture to
keep things clear. We experience such strategies as relationships of parts to whole. Ordering those relationships is what composition means as a practice.
One of the ongoing debates for architects and designers concerns whether compositional form is part of the content, or only a means. We find that debate irrelevant to learning composition. After all, good writing reflects its composition, whether that writing is a poem, an essay or a set of instructions.
Similarly, composing music requires a sense of, if not a theory for, harmonic principles. It is fair to admit that we, the authors, find form intrinsic to archi-tecture and not merely a means to an end.
It is improbable that we would make a building without placing a stake in the ground, literally or figuratively. We start from somewhere and proceed to define a figure. Even the architecture of the space station defines a particular place relative to the universe and its boundaries describe its perimeter. This focal reality, ‘centeredness’, derives from both our expectations and our visual perception.
Gestalt psychology informs us that when we see a square, we perceive its center at nearly the same moment (). As we observe the figure of the square, we measure it and apportion it. We recognize its center, its corners and its middle (). We do much the same with other shapes. Such perceptions lead us to organize the world in terms of the components of visual composition:
edges, axes, centers, and subdivisions. The clarity of these perceptions depend on a perceptual capacity that we term –.
Figure 2: Line drawing of the classic figure-ground ambigu-ity towards reading either face or vase as the figure.
Figure 4: Tonal shapes of the same figure-ground example.
The emphasis of this version lends some figure dominance to the faces.
Figure 3: A third, volumetric version demonstrates a surpris-ingly strong figure-ground ambiguity.
Roughly speaking, figure-ground identifies our perception of edge. It is how we establish order amidst visual ambiguity. It is the visual framework that helps us locate an object in space with our eyes. We mention this psychologi-cal term because it affects the practice of drawing. Ordering visual ambiguity is how a drawing becomes a coherent image. In order to comprehend a draw-ing, we must respond correctly to its formal qualities. Ultimately, comprehen-sion also involves us in a cultural framework of convention and expectation, but all of that follows from perceived visual order (–).
The history of drawing embodies a long tradition of recording what we observe, and projecting what we imagine, a tradition shared with the history of architecture. Therefore, to understand architecture – whether to sustain it or challenge it – requires an understanding of how drawing, composition and architecture intertwine and conflate.
Drawings exist on a page, a surface real or virtual. They can either float in a near-infinity, or exist within a visible boundary. They show things in a two-dimensional format utilizing contrast to either illustrate two-two-dimensional
Figure 5: Another classic figure-ground ambiguity, the young and old woman.
Figure 6: A related modern variation of figure-ground ambiguity, the young woman and the saxophone player.
Figure 7: Perspective figure-ground ambiguity, in which the spatial/volumetric character of the form resists clear resolution.
Figure 8: This perspective shows the two possible resolu-tions of the ambiguity – a truncated pyramid or frustum and its hollow inverse.
Figure 9: We use common references to speak of measure-ment. Here the two hands indicate a distance between them.
Figure 10: Leonardo DaVinci, the great Renaissance master, left us this classic interpretation of the Vitruvian Man – shown above redrawn after the original.
Figure 11: The architect, Le Corbusier, also had a great interest in the rela-tionship of human proportion to design. His famous Modular Man set about measuring the golden section in relationship to the body.
shape and area or suggest three-dimensional form and space. Comprehending an illustration requires interpretation, and provokes questions. Does a draw-ing reference somethdraw-ing besides its own example? How big is the thdraw-ing that it references? What is its size and scale? Such questions lead us readily to ideas of measurement.
On measure
Rulers and their units of measurement are so nearly ubiquitous that we can scarcely imagine them as not pre-existing. If someone asks ‘How big was the fish?’ you might find yourself illustrating the answer as a space between two hands (). You might also add, ‘It was twelve inches across,’ never seeing the gesture and description as conflicting or distinct. This brings us to an impor-tant if subtle point. The gestural measurement is relational: it uses something that is actually there – the space between your hands – to refer to something absent – the fish. The verbal description makes use of yet another absentee, the unit of measurement.
The inch (from the Latin uncia) signifies one twelfth, a relation without a necessary parent or source. We make sense of the fish’s size if we know that an inch in this instance is the twelfth part of a foot and by also knowing – from prior experience – how large a foot is, however approximately. Someone with a background in the metric system might not be able to sort it out at all.
The verbal description – twelve inches across – leads us back to ideas of drawing. How do you find a twelfth, one might ask. It turns out that the basic action, finding a center, helps us find halves and fourths and eighths, thirds, sixths, and twelfths as well. This sort of practice resides at the heart of our earliest understanding of geometry.
Geometry – the art of measuring ground – begins with the simple tools of the straightedge and the compass. It is an elementary practice that founds itself in the perception and measure of the world. To understand architecture requires that we also understand how we go about measuring things. Sub-dividing a square works from the outside inward. In contrast, the Cartesian grid starts from an origin – the zero point – and works outward. This is an important distinction. The world of the infinite grid and the ruler, by exten-sion, is an unbounded world. Infinity is a scary proposition for human beings.
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Figure 12: A simple method for deriving geometric quarters and linear thirds using straight line geometries. Further divisions show the extension into eighths and sixteenths as well as sixths and twelfths. The resulting compound grid is often referred to as a tartan grid due to its resemblance to traditional Scottish fabric weaving.
Note that dividing the form down the horizontal and vertical centers yields linear halves and quarter areas (13·1). Similarly, linear thirds yield ninths as areas (13·2).
Diagram 13·1: Finding the cen-ter and quarcen-tering the square.
Diagram 13·3: Further subdivi-sions into fourths.
Diagram 13·5: Continued subdivisions into eighths.
Diagram 13·7: The resulting tartan grid.
Diagram 13·2: Finding the thirds within the square.
Diagram 13·4: Halving thirds to find sixths.
Diagram 13·6: Half again to determine twelfths.
Diagram 13·8: The grid and its geometry.
The familiar, by contrast, anchors us to reality. Distinguishing relationships between the familiar and the alien occupies much of the history of humanity and architecture. One of the first tasks in architecture is making a safe place, a familiar place, a defined place. Geometry arises from this need, and shapes its practice.