Grids and Beauty

Grids and Beauty Ryan Lawber ARCH 503 5/14/08

Abstract The grid is purely a creation of man’s intent of an organizational structure. Square, triangular, hexagonal, and other grid forms have been utilized in the overall design of cities to the design of the most minute of objects, including the complex circuitry of modern technology. However, from their unnatural, restrictive regularity, grids have developed into an aesthetic tool. This paper will analyze these grids in relation the question of “what is beauty?” More specifically, what defines beauty in nature and what aspects of this are seen in the artificial gridded forms?

Grids Rosalind Krauss writes of two types of functions that emerge from grids: spatial and temporal.

Spatially, grids extract an identity within the grid itself and anything it might overlay, creating a flat, “geometricized,” field. Krauss states of a general grid: “…it is antinatural, antimimetic, antireal. It is what art looks like when it turns its back to nature. In the flatness that results from its coordinates, the grid is the means of crowding out the dimensions of the real and replacing them with the lateral result not of imitation, but of aesthetic decree. Insofar as its order is that of pure relationship, the grid is a way of abrogating the claims of natural objects to have an order particular to themselves; the relationships in the aesthetic field are shown by the grid to be in a world apart and, with respect to natural objects, to be both prior and final."

The spatial character of grids is a complete exclusion of natural systems. Temporally, grids have become a symbol of the antimimetic modernity, and have become “emblematic” of modern art and architecture, with the power that these grids are capable of creating. Grids have the potential to “mask and to reveal [shame] at the same time. (Krauss 12)” Spatially, the grid tells no story, but temporally, it may unintentionally reveal a structure. Even if the grid is not architectural, vertical lines can be perceived as posts, horizontal lines as lintels. As Krauss indicates, there is an underlying (inadvertent) symbol that can sometimes be found within these grids, and is subject to the screen of the human eye. As Krauss shows, with a nine square grid, filling in the center column and center row will display a Greek cross, and suffer/benefit from the unintentional meaning related to this (Krauss, 10). Similarly, filling in alternating squares on an 8 by 8 grid illustrates a chess board and will, in our minds, expand from the meanings derived from this contextually.

Mentioned above, the artificial grids, encompassing the typical Cartesian, triangular and radial grids, are purely a realization of man. These grids have no relation to nature (perhaps opposing nature), and have the sole purpose of being functional, being that they are prescribed only as a form of restrictive organization. If a grid is abstracted in any way before applying information, the grid is not a grid, but rather an application of overlaid lines intersecting, but applying or delineating no usable information. However, if the grid is manipulated after information has been

applied, then the grid is one that has been warped and still usable for determining information and data. The difference between these two instances, before and after manipulation, is that the latter can always be returned to a quantifiable unit, giving the grid purpose. Instances of this can be seen in D’Arcy Thompson’s On Growth and Form (figure 1)

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Figure 1. Thompson’s Grid Transfomations

As inferred by the name, the form of these artificial grids cannot be found naturally. By analyzing many natural objects, including sunflowers, magnetic fields, sound waves, etc., the nearest a material or ethereal natural object relates to the artificial grid is through fractals. These fractals create a structure from a set of rules. These forms often take on the rules of common fractal geometries, such as the Mandelbrot set and the forms created from the Fibonacci series.

Thompson writes of similar types of systems: “We are apt to think of mathematical definitions as too strict and rigid for common use, but their rigor is combined with all but endless freedom. The precise definition of an ellipse introduces us to all the ellipses in the world” (Thompson, ch. 9).

The natural system developments, according to phases like this, are based on mathematical definitions. With a mathematical formula integrated into natural systems, growth develops into specific fractals accordingly. Though, it would be impractical to infer that mathematic formulas are the reason that both nature and grids have aspects of beauty.

Nevertheless, when an artificial grid is placed within a natural system, such as certain instances in a city grid, this develops into a hybrid system. In these examples, a grid is not just overlaid onto the site, but integrated into the landscape. Portions of the grid become landscape and sections of the site become grid. The same occurrence can be seen with architecture. Grids in the facades and plans of structures delineate spaces and become livable, while intentioned habitable spaces can become lost within the grid.

Modern Thought Modern aesthetic has embraced the grid as the most simplistic, pure form. It can easily be found in modern architecture and design. According to Krauss, “no form… has sustained itself so relentlessly while at the same time being so impervious to change.” Through time, the grid has developed into a new modern aesthetic. Yet, if we consider purity as beauty, and nature as pure, why are these grids considered pure? The grids have no relation to nature, and could be viewed as a direct antithesis of these natural systems.

When applied as a structure, the grid expresses the pure function. Within architecture, specifically on facades, grids become a transition between interior and exterior spaces. From Colin Rowe and Robert Slutzky, we can determine the transparency of these grids and develop them into either literal or phenomenal transparencies. By their definitions, literal transparencies correspond with typical glass and steel Bauhaus-esque structures and phenomenal transparencies define a more refined layering of material and spaces.

Considering the Bauhaus building in Dessau, Germany (figure 2) as a candidate for literal transparency, we can see the glass façade revealing the structure and function of spaces behind. This building does create an additional layer of transparency by reflecting the adjoining building into the façade, giving an additional depth to the elevation. This building can also be viewed as a form of what Kant defines as accessory beauty because of its unambiguous façade.

Figure 2. Literal Transparency of the Bauhaus

Looking at Rowe and Slutzky’s analysis of Corbusier’s drawings of the Algiers Block (figure 3), they describe a set of temporal perceptions as: 1. The eye may be engaged by the three horizontal bands which divide the structure into four definite areas 2. If these are overlooked or become recessive the eye may become absorbed with the cellular pattern of the brise soleil and this pattern will gradually be felt to extend itself behind the horizontal bands.

3. As the disruption of the brise soleil pattern to the left of the façade becomes apparent, the observer will construct a further figure which, in mediating the two brise soleil grids, appears as a kind of channel cutting open the façade and connecting the pilotis of the lower floors with the incidents upon the roof.

4. When this new figure is discovered to be interwoven with the three central floors of the building, the eye (or the mind) is compelled to provide further explanation and the observer comes to see the composition as a kind of E-shaped overlay imposed upon the “neutral” background provided by the brise soleil. (Rowe, Slutzky, 288)

Figure 3. Phenomenal Transparency of LeCorbusier’s Algiers Block

From this list we can see that the phenomenal transparency regulates an alternating composition based on the certain factors of the grid. Phenomenal transparency describes multiple compositions or patterns visualized at the same time. For example, the time of day will regulate the amount shade and shadow, determining the visual intricacy of the brise soleil, and determine the resulting form visualized. This creates a complex imagery that could be viewed as, in the opposing method of the grid, becoming ornament. Unlike the Bauhaus, the Algiers Block comes closer to ambiguity in its entirety, and therefore approaches what Kant defines as free beauty.

Also, within architectural plans of new and existing cities, the grid has become a predominant design feature. Ludwig Hilberseimer’s Study for Ideal City (figure 4) becomes a layering of transportation and habitation grids with a pedestrian path grid overlaid onto and above a vehicular street layer, overlaid above a subterranean rail transit, infilled by residential and office blocks traversing between the layers. This becomes quite a phenomenal transparency, producing a depth within spaces and alternating, interwoven, layerings. However, it has been noted that in the case of Hilberseimer’s city study, the grid becomes a “useful instrument of organization with disturbing emotive properties” (Watson, 83).

Figure 4. Hilberseimer’s Gridded City Planning

Grids in Art Examining grids in artwork can reveal the same suggestions of literal and phenomenal transparencies. The works of Agnes Martin (figure 5) can be seen as a very literal vision of a grid; nothing is implied (although we could still infer a column and grid story from the temporal aspect of the grid). The lines delineate the square work of art into a minimalist grid. Looking at the paintings of Piet Mondrian, we can see a method that entails a technique of much more visual layering. In Broadway Boogie-Woogie (figure 6), the grid is implied with the layering of colors, so while flat in dimension, creates a phenomenal transparency, and alternates fields of interest temporally.

Figure 5. Agnes Martin, Untitled 2.

Figure 6. Piet Mondrian, Broadway Boogie Woogie.

In a third dimension, we can consider Sol LeWitt’s modules based on the structure of a cube.

These designs play with a literal transparency, while approaching a phenomenal transparency in some works. The LeWitt designs from the Incomplete Cube series imply cubes with a minimal amount of edges. From these partial cubes, the phenomenal transparency has, in a sense,

been extracted from one design, removed chronologically, and displayed side by side in a series. The outcome is seen in figure 7.

Figure 7. Sol LeWitt, Incomplete Cubes.

Kant’s Aesthetics and Relation to the Grid Kant defines beauty as “...what, without a concept, is liked universally” (Kant, 1987). Beauty emerges from material/immaterial that holds no concept as to what the object is intended to be.

To analyze grids, we need to look at purposiveness alongside beauty. According to Kant, beauty with purpose/concept is not as beautiful as purposeless beauty (Kant, 1987). As mentioned previously, grids are only a tool of purpose. So, according to this, grids should be quite low on the scale of beauty. However, as can be seen in the Mondrian works, the result of utilizing a grid for certain applications does not appear solely purposive. Broadway Boogie Woogie (figure 6) could be viewed as free beauty and ornament. .

Conclusion The proposed questions of “what is beauty” and how grids imitate/utilize natural systems haven’t fully been answered in this paper. These questions will most likely take a lifetime to comprehend. But, we can see that grids embody a certain spatial aesthetic exemplified in art and architectural facades and within the literal/phenomenal transparency and accessory/free beauty demarcations.

Bibliography Kant, I. (1987). Critique of Judgement. (W. S. Pluhar, Trans.) Indianapolis/Cambridge: Hackett Publishing Company.

Krauss, R. (1986). Grids. The Originality of the Avant-Garde and Other Modernist Myths, 8-22.

Rowe, C. & Slutzky, R. (1971). Transparency, Literal and Phenomenal, Part II. Perspecta, 13, 287-301 Thompson, D. (1917). On Growth and Form. Dover Publications.

Watson, V. (1999). Abstract Architecture and the Desire to Make Something that is New. The Journal of Architecture, Volume 4, Spring 1999, 81-87.