Emergent symmetries: a group theoretic analysis of an exemplar of late modernism: the smith house by Richard Meier
Din, Edouard Denis
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Formal systems in architectural design aim at the systematic description, interpretation, and evaluation of existing works of architecture as well the systematic creation of new works of architecture. Currently all formal analysis using group theoretical tools focus on repetitive designs that show immediately their recursive structure. It is suggested here that highly complex designs can still be described and analyzed with group theoretical manner. The broader question that is opened up here is whether a complex architecture object or part depending on the interest of the researcher, can be interpreted as a layered object whose parts are all related symmetrically; in other words whether an asymmetric shape or configuration can be understood in terms of nested arrangements of some order of symmetry. The object of analysis has been polemically selected here to be the NY5 architecture, a set of designs that are all clearly exemplifying formal qualities of abstraction, layering, complexity, depth and so on, all appearing impenetrable to a systematic and rigorous analysis using the existing group theoretical formal methods. For example, Richard Meier s work has been presented here as a hyper-refinement of the modernist imagery. The computation is entirely visual. A reassembly of the layered symmetries explains the structure of the symmetry of the house and provides an illustration of the basic thesis of this research on the foundation of a theory of emergence based on symmetry considerations. All plans of the house are represented in three different levels of abstraction moving successively away from the architectural representation to a purely diagrammatic one that foregrounds divisions of space. All representations are fed into an analysis algorithm to pick up all symmetry relationships and the parts are constructed as instances of a binary composition of a family of rectangular grids. Finally the process is reversed to fully account for the construction of the space of the house as a three dimensional layered composition. Lastly, this research points to two categories of extension; a) on the improvement of the system itself; and b) on the interpretative capabilities it affords for the construction and evaluation of critical languages of design.