Reality can be thought of in one of two terms: the discrete or the continuous. Attempts to bridge the two invariably result in all kinds of conundrums filled with paradoxes and undecidability. As Badiou has argued convincingly, it is necessary to subtract the idea of God from the concept of the infinite since only then is it possible to render effective Nietzsche's pronouncement of the death of God. The modern secularization of the infinite as a mathematical concept has profound implications in dealing with the nature of thought and the world including architecture.
The gap between the finite and the infinite has come to symbolize what Lacan once suggested in a different context as a hole in knowledge that resists absolute penetration by thought. These concepts may seem too abstract and far removed from normal day to day existence since the history of architecture is essentially defined by the deployment of discrete forms and shapes. Only with the development of topology in the early 20th century have architects, such as Frederick Keisler, began to think in terms of topology in the design of architectural form.
The project for the studio was to design a formal building structure that incorporates elements of the discrete and the continuous as part of its morphology. Emphasis was on the generative development of architectural form as opposed to interactive sculpting of three dimensional shapes be they biomorphic or otherwise. Although no programmatic function is given, each project has to manifest itself as a proposition of architecture and the question of formal relations have to be solved in relation to this proposition.
