06 Statistics and Symmetry

Karl Friedrich Schinkel, Altes Museum. Berlin, Germany, 1830

Whether created for the empirical analysis of an existing urban area or for the proposal of a radically new city, a surprising number of urban diagrams and designs from the first half of the 20th century share a symmetrical organization. Despite their differences in political and physical form, they each use symmetry to structure the distribution of their elements. A closer look at a number of canonical projects reveals symmetry’s presence in their street, buildings, and units plans.1 A plan has many definitions. It is a strategy for controlling behavior, a drawing showing the separation and connection of spaces, and an indication of social relationships and priorities.2 As with symmetry, a plan functions to create a predictable relationship between the present and the future.3

In addition to their geometric similarities, a large number of modernist proposals rely on statistics to guide their decision-making. Statistics are employed to predict future behaviors based on past actions.4 In the language of (group) symmetry, both plans and statistics are deployed to create automorphic conditions, that is, to secure invariance in the face of transformations. The combination of symmetrical plans and statistical analysis is most obvious in the architectural discourse around the existenzminimum dwelling in Europe in the 1920s, and in the search for efficient unit and site plans in America in the 1930s.5 Long before big data, symmetry and statistics were the most efficient tools for addressing issues associated with the creation of radical new cities and of various forms of housing.

Rotation

Only a dozen or so of the one hundred and fifty pages in Ebenezer Howard’s Garden Cities of Tomorrow (1902) are dedicated to its physical design. These include a few diagrams that illustrate its organizational details. The bulk of the book focuses on its political and economic organization. There is much numerical data outlining its revenues and expenses, as well as the analysis for how its infrastructural needs will be met. Howard proposed a cooperative scheme where land would be held in common to keep it free from the forces of financial speculation. In the book’s first edition he included a drawing titled Slumless and Smokeless Cities. It depicts a constellation of six circular, 32,000 person settlements orbiting a 58,000 person “Central City.” Although each of the cities has a slightly different internal configuration, each is also rotationally and reflectively symmetrical. Howard makes it clear that these are diagrams and not the plan for his new city, but the emphasis on the circle, and the resultant rotational and reflective symmetry of the drawing are not random. The early build-outs of Howard’s vision at Letchworth and Welwyn did not take this exact shape. Their overall outline, and the profile of individual blocks and buildings are irregular. There is, however, much symmetry to be found in Parker and Unwin’s street plans and buildings in Letchworth, reinforcing the collective nature of the scheme. As with all symmetry groups, there are no a priori hierarchies between each entity or any orientation. All are equivalent. Symmetry is not a neutral actor but is an ideological entity. It is presented as a clear icon of the egalitarian society that the design is meant to produce.

Reflection

Through his decorative arts training Le Corbusier had an intimate relationship with symmetrical ornament and traditional ornamental techniques. Later he would indicate his commitment to a mathematical basis for architectural composition.6 These dual influences are best on display, not in his buildings, but in his radical urban proposals from the decades of the1920s and 1930s.7 Both the Ville Contemporaine (1922) and the Ville Radieuse (1933) are marked by a strict adherence to reflective symmetry. Moreover, unlike Howard’s diagrams, they were intended to be built that way.

While there is a tension between symmetry and asymmetry in many of his buildings from this era, his urban schemes and the buildings represented in them are dominated by mirror reflections. The redent or “setback” apartment blocks are bilaterally symmetric, while the immeuble villas and the cruciform towers are biaxially symmetric. Within the overall plan of the city these three building types are isolated from one another via the symmetrical subdivision of the scheme by orthogonal and diagonal roadways. It is only at the level of the individual dwelling unit where the strict symmetry begins to break down.

Le Corbusier was also dedicated to industrial methods of building and thinking.8 This included a strong interest in statistics. He devoted an entire chapter in his Urbanisme (1925) praising them for their honesty and for the empirical limits that they established. These facts were to be used as the “jumping off point for poetry:”9 poetry with a decidedly symmetric structure.

Bruno Taut’s work is similarly paradoxical. Although celebrated for his expressionist use of form, color, and material, his work—such as the Glass Pavilion and Alpine Architecture—is almost always symmetrical. His design (with planner Martin Wagner) for the Britz or Horseshoe Siedlung (1927-33) is organized via a series of local and global symmetries and near symmetries. Reflective and translational symmetries can also be found in the individual buildings. The project’s cooperative financial structure, its size, its location on the outskirts of the city, and the diversity of its building types were all grounded on the statistical analysis of economic and infrastructural data done in Berlin’s city planning office, headed by Wagner.10

The combination of rigorous numerical analysis and symmetrical plans would soon make its way to the United States. By the 1930s, the US government was publishing pamphlets showing ideal housing unit plans based on statistical analysis.11 It also produced guidelines for site plans for low-cost housing that were almost exclusively arranged symmetrically. Subsequently, most limited profit, non-profit, and even some public housing projects built from the 1930s through the 1960s followed their lead.12 Examples such as Radburn in New Jersey, Stuyvesant Town and the Red Hook Houses in New York City, and Baldwin Hills Village and Park La Brea in Los Angeles share both alternative financing structures and a symmetrical shape.

Translation

Reflection was not the only variety of symmetry used by modernist planners. Translational symmetry was also prevalent, especially in German Zeilenbau schemes composed of parallel and equally spaced buildings. A translation is a movement of an entity in a specific direction and distance without a rotation or a reflection. In other words, it is the simple repetition of an element at a consistent interval. Translational patterns are often referred to as frieze patterns and are commonly used in the horizontal band of ornament found in the entablatures of classical architecture. They also describe the modular repetition of standardized elements found in much industrial era architecture.

Many of Walter Gropius’s designs for housing estates from the decade of 1920 are defined by translational symmetry. His deployment of parallel rows of townhouses and apartment blocks were arranged to maximize the amount of light, air and views for each unit.13 Based on geometric analyses, it was concluded that the higher the building the better access one had to these environmental amenities, as well as allowing for increased density on the site. In short, the symmetry was informed by data. However, these were not the only considerations. Gropius also relied on sociological statistics to argue that different demographic groups could best be respectively served by low, mid, or highrise building types.14 These qualities are on display in the plan for the Dammerstock Complex in Karlsruhe. The repetition of the linear buildings gives the project a prototypical modern sensibility. However, a closer look reveals that in addition to translations, there are multiple reflections and even rotations in the overall plan and in the plans of the buildings themselves.

Ludwig Hilberseimer also studied the formal and spatial effect that maximizing sunlight and ventilation had on building and block types. He was committed to symmetry. His perspectives and plans in Großstadt Architektur (1927) show a series of urban blocks distributed in a relentless application of translations across the city. The blocks are made up of buildings that accept rotations and reflections. His proposals for the American landscape are similarly symmetrical.15 The basic “settlement unit” he proposed for this context is distributed on the land via translations. The unit is internally organized around a reflection, and the individual

houses on each street are translations of one another. A relatively small version of this regional vision was built at the Lafayette Park development in Detroit, designed in conjunction with Ludwig Mies van der Rohe and Alfred Caldwell.16

Equivalence

Does the presence of symmetry in these canonical and often-radical modernist projects undermine their modernity? Or, was symmetry also updated, as it was in physics and math? Certainly, there is no attempt, neither discursively nor formally, to adhere to the classical definition of symmetry as the harmonizing of unlike parts (via the use of proportion) to create objectively beautiful objects. Rather, in these urban schemes one finds an emphasis on consistency and predictability. What is emphasized is the equivalency of the parts. Things are not proportional to one another, they are identical with one another. This shift from harmony to uniformity is precisely the change symmetry made in math and science. Harmony is the integration of multiple elements—sounds, people, or colors—into a complex whole. In contrast, equivalence is the repetition of identical elements to make a simple one. This is the logic of mass production. This is a significant change. To live uniformly is very different from living harmoniously. If traditionally symmetry was a guarantor of beauty, it is now a guarantor of uniformity. Symmetry is still symbolic, but instead of representing an aesthetic hierarchy it expresses a set of social and statistical equivalences.

1 Catherine Bauer, Modern Housing (Boston: Houghton Mifflin, 1934). Richard Pommer, “The Architecture of Urban Housing in the United States during the Early 1930s,” Journal of the Society of Architectural Historians vol. 37 no. 4 (December 1978), 235-264. Roger Sherwood, Modern Housing Prototypes (Cambridge: Harvard University Press, 1979). Manfredo Tafuri and Francesco Dal Co, Modern Architecture 1 & 2 (New York: Abrams, 1979). Peter Rowe, Modernity and Housing (Cambridge: MIT Press, 1993). 2 Robin Evans, “Figures, Doors and Passages,” in Translations from Drawing to Building and Other Essays (London: Architectural Association, 1997), 55-91. 3 Manfredo Tafuri, Architecture and Utopia: Design and Capitalist Development (Cambridge: MIT Press, 1979), 125. 4 Ian Hacking, The Taming of Chance (New York: Cambridge University Press, 1990). 5 On existenzminimum see Eric Mumford, “CIAM Urbanism after the Athens Charter,” Planning Perspectives vol. 7 no. 4 (1992) and The CIAM Discourse on Urbanism 1928-60 (Cambridge: MIT Press, 2000). Martin Steinmann (ed.), CIAM: Dokumente 1928–1939 (Stuttgart: Birkhäuser, 1979). On the emphasis on efficiency and statistics in the United States, see Richard Plunz, A History of Housing in New York City (New York: Columbia University Press, 1990), 207-246. US Federal Emergency Administration of Public Works, Unit Plans (Washington D.C., 1935). “Housing Number,” Architectural Record 77 (March, 1935), 148-189. 6 Paul V. Turner, The Education of Le Corbusier, a Study of the Development of Le Corbusier’s Thought 1900 1920 (New York: Garland Publishing, 1977). Reyner Banham, “Conclusion: Functionalism and Technology,” Theory and Design in the First Machine Age (New York, Praegar, 1962), 328. 7 Thomas H. Beeby,“The Grammar of Ornament/Ornament as Grammar,” VIA III (1977), 10-29. 8 Mary McLeod, “Architecture or Revolution: Taylorism, Technocracy, and Social Change,” Art Journal 43 (Summer 1983), 132-147. 9 Le Corbusier, “Statistics,” The City of Tomorrow and Its Planning (New York: Dover, 1987) [1929], 105-126. 10 Esra Akcan, Architecture in Translation: Germany, Turkey, and the Modern House (Durham: Duke University Press, 2012), 152-177. Barbara Miller Lane, Architecture and Politics in Germany 1918-1945 (Cambridge: Harvard University Press, 1985) [1968]. 11 US Federal Emergency Administration of Public Works, Unit Plans (Washington D.C., 1935). “Housing Number,” Architectural Record 77 (March, 1935), 148-189. 12 For their presence in New York City, see Richard Plunz, op. cit. 13 Susan R. Henderson, Rationalization Takes Command: Zeilenbau and the Politics of CIAM in Building Culture: Ernst May and the New Frankfurt Initiative 1926-1931 (Bern, Frankfurt, London, New York: Peter Lang, 2013). 14 Walter Gropius, Sociological Premises for the Minimum Dwelling of Urban Industrial Populations in Scope of Total Architecture (New York: Collier, 1955) [1929], 91-102. 15 Ludwig Hilberseimer. Metropolisarchitecture and Selected Essays, translated by Richard Anderson (New York: Columbia University Press, 2014) [1927]. 16 Caroline Constant, “Hilberseimer and Caldwell: Merging Ideologies in the Lafayette Park Landscape” in Charles Waldheim (ed.) CASE Hilberseimer/Mies van der Rohe, Lafayette Park Detroit (Munich: Prestel, 2004), 95-111.