The Thirteenth Villa


The Thirteenth Villa

Published in the Journal for Architectural Education, 70:1, March 2016.

In a 1994 essay titled “New Variations on the Rowe Complex,” Greg Lynn reflects on the architectural issues of formal and spatial difference, variation, and, more generally, the ideal. Lynn presents what he identifies as a blind spot in Colin Rowe’s comparative analysis of villas designed by Andrea Palladio and Le Corbusier – “the capacity for formal and spatial order to differentiate and become innovative.”[1] Lynn points to the limitations of Rowe’s declaration that the ideal in architecture is inextricably linked to the exact. While constructing this position in his 1947 essay, “Mathematics of the Ideal Villa,” Rowe argues that exact geometries and ideal values are dependent upon the use of proportional harmonics, the single feature that can produce a transcendent language for architecture.[2] Here, the influence of Rudolf Wittkower on Colin Rowe is evident . [3] Wittkower’s analysis of Palladian villas yields the theory that Palladio was working with a set of rules from which he never departed – a single geometric formula that can be found in a variety of villas designed by Palladio over a fifteen-year period.[4] The nature of this analysis, one that disregards the subject matter of the work in favor of its inherent and observable compositional qualities, is one that can be traced to Heinrich Wölfflin, Wittkower’s teacher in Munich. Adopting Wöfflin’s techniques of formal analysis,[5] Rowe generalizes Wittkower’s theory and uses works from both Palladio and Le Corbusier to demonstrate the transhistorical nature of systems of proportion and the triumph of mathematics over humanist ideals tied to contextual, historical, or cultural particularities. Before calling attention to the similar organizational structures employed by these architects, Rowe identifies the different architectural strategies that Palladio and Le Corbusier devise to depart from an unwavering affinity for, and physical manifestation of, the proportional system. These differences – spatial symmetry and centralization against free plan, and punched versus ribbon windows, to name a few – culminate in two drastically different architectural personalities – one rigid, the other far less dogmatic.[6] Despite these differences, the underlying geometric formula remains, and mathematics is revered and acts as a protagonist in the search for the timeless, architectural ideal.

Lynn claims that it was faulty for Rowe to assume that mathematics can only be used to describe an ideal and proposes that an alternative mathematics is necessary to produce a theory, not of the ideal, but of diversity and difference that maintains an affinity for the exact.[7] Dissatisfied with the notion that mathematics only unites the exact with the singular ideal, Lynn turns to Edmund Husserl – and his invention of a new category of geometry, anexact yet rigorous – in order to expand the capabilities of mathematics in the production of innovative architectural forms. Husserl’s research entangles mathematics and the “progressive cancellation of variation” to account for the origin of exact geometries and eidetic forms.[8]  Tending to his dissatisfaction with the limitations of the efficacy of mathematics as an architectural device, Lynn adopts Husserl’s provocation of geometry as a mediating device and develops a strategy for the process of progressive cancellation to produce a collection of unique forms from which original, eidetic forms may have been derived. In rethinking formal and spatial difference, Greg Lynn prioritizes the complex over the reducible, and redirects the understanding of exact geometries away from the ideal and toward the pliant and anexact.[9]  It is here that Lynn’s construction of free differentiation produces an alternative to essential, invariant, and fixed types, and opens up new territory for rigorous formal exploration – perfectly timed to coincide with the arrival of new digital techniques for architectural design.

Lynn’s ultimate critique of Colin Rowe’s analytical approach is that the result yields a system that is closed and incapable of discovering new paths for the development of architectural form and organizational logic. For both Rowe and Wittkower, processes of repetition are deployed for iterative reduction – in search of the fixed ideal. Wittkower uses Palladio’s repetition to cancel difference and Rowe proposes transhistorical repetition to identify a formal structure for architectural that is both timeless and ideal. In the years following the publication of his essay, Lynn makes good on his promise to invent an alternative mathematics, and in the process of doing so, transforms the use of repetition from an analytical tool to an instrument for more projective architectural design. Lynn’s particular transformation of repetition and difference is one that can be traced to his teacher and mentor, Peter Eisenman, a student of Colin Rowe. In “Dummy Text, or The Diagrammatic Basis for Contemporary Architecture,” R.E. Somol defines Eisenman’s alternative version of repetition as one that prioritizes the production of difference over the construction of identity.[10] Somol writes that Eisenman’s transformational diagramming techniques, following a critique of the static diagrams produced by Rowe, anticipate the use of (and necessitate the need for) animation software, positioning time as an active element within the design process and allowing difference to be manifested through heterogeneous repetition.[11] In a project such as the Embryological House, Lynn demonstrates a further development of these alternative systems of repetition. Enabled by advanced animation techniques, Greg Lynn extends Eisenman’s diagramming project, calling on variation over time to produce innovative formal and spatial results. This transformation of repetition from analytical to projective produces a critical restructuring of the ideal through optimization routines that proliferate, rather than reduce variation. The Embryological House project demonstrates this systematized proliferation of difference and exemplifies the potential of a more speculative process of differentiation that does not pursue the single ideal type, but instead embraces an architecture that is both irreducible and intensive. Ultimately, Lynn’s construction of a new relationship between architecture and mathematics expands the ways in which architects can actively pursue variation while maintaining an affinity for the exact .

The Thirteenth Villa is a conceptual project inspired by Lynn’s provocations and instantiates the tradition of formal analysis to generate a new villa, one comprised solely of the non-ideal characteristics and traits of each of Palladio’s eleven villas studied by Rudolf Wittkower. Where Wittkower identifies discriminate characteristics and cancels out variation during his conception of a twelfth ideal villa, the Thirteenth Villa cancels the ideal from the original eleven to yield a composite variant. And where Lynn serializes difference in the Embryological House, the Thirteenth Villa overlays the anomalies and aberrations found in the comparisons between Wittkower’s twelfth and Palladio’s eleven. In effect, the Thirteenth Villa is a composite of errors and a conflation of sequential difference.

The Thirteenth Villa demonstrates the ways in which the discipline of architecture is constantly revitalized by the recurrent collusion between history and design and how every generation has the opportunity to alter one with the other. Evidence for this process of continual interrogation and evolution of architecture’s most salient issues can be found in the lineage from Wittkower to Rowe to Eisenman to Lynn, where one extends and, in many cases, breathes new life into the theoretical research conducted by the other. To extend this narrative sequence, the Thirteenth Villa acknowledges the current shift away from speculative work in hot pursuit of gradient logics, seamlessness, tectonic intricacy, and formal elegance, and proposes an alternative solution to the problems of difference and variation .

[1]  Greg Lynn, “New Variations on the Rowe Complex,” Folds, Blobs, and Bodies, (Brussels: La Lettre volée, 1998), 218.

[2]  Colin Rowe, “Mathematics of the Ideal Villa,” in Mathematics of the Ideal Villa, (Boston: MIT Press, 1982)

[3]  From 1945 to 1946, Colin Rowe was instructed by Rudolf Wittkower at the Warburg Institute. (Source: Herbert Muschamp, “Colin Rowe, Architecture Professor, Dies at 79,” New York Times, November 8, 1999, Accessed November 13, 2015,

[4]  Rudolf Wittkower, Architectural Principles in the Age of Humanism, (New York: WW Norton & Company, 1971), 71.

[5]  In his book Principles of Art History: The Problem of the Development of Style in Later Art, Heinrich Wölfflin presents formal analysis of Renaissance and Baroque art to attain a set of classifying principles that characterize the differences between the styles of these two periods. His technique to remove the subject matter of the art to focus, more objectively, on the compositional strategies employed by the artists is one that influences both Wittkower’s and Rowe’s analysis of the works of Palladio.

[6]  Lynn, “New Variations,” 206.

[7]  Ibid., 201.

[8]  Edmund Husserl, “The Origin of Geometry,” Edmund Husserl’s Origin of Geometry: An Introduction, (Lincoln: University of Nebraska Press, 1989), 157-180.

[9]  Lynn, “New Variations,” 213.

[10]  R. E. Somol, “Dummy Text, or The Diagrammatic Basis for Contemporary Architecture,” Diagram Diaries, (London: Thames & Hudson, 1999), 8.

[11]  Somol, “Dummy Text” 10.