The Ambiguities of the Present

Architects need mathematics to embrace the contradictory longing for power and for restraint, for standardisation and for invention. To put it in the historical perspective adopted here, mathematics appear neither as foundational nor as tools. In computer-aided design, one no longer deals with objects but with theoretically unlimited series of objects. Simulation goes with the new importance given to scenarios and events. Another path worth exploring is simulation. First, the mathematical principles are very often hidden behind their effects on the screen. It can be argued that architecture’s contemporary embrace of the geometries of modern mathematics has occurred derivative of, but largely removed from, the corresponding evolution in the foundational basis of space and shape that these advances propose. This might result from the fact that the polarities evoked earlier have not been reconstituted. As algorithmic design has emerged through application of a collection of discrete geometric techniques, the contemporary language of form has become a disparate archipelago of geometries with unique topological signatures, collectively instantiated into space but otherwise disconnected from any unifying framework. One has to do with parametricism, but parametricism understood as restraint and not only as power, and also parametricism as having to do with the quest for standards and not only of invention. For the first time, architects can really play as much with time as with space. Dennis R Shelden and Andrew J Witt
of Gehry Technologies here seek to address this by reconnecting theory and practice with developments in modern mathematics. Restraint and control through the establishment of standards have been lost so far. 1
There is currently a disjoint between the enthusiasm that is expressed for geometry in architecture and the disparate manner in which it is applied spatially. This is what parametric design is about: considering relations that can be far more abstract than what the design of objects usually entails. Second, one has the disturbing nature of the underlying mathematical principles mobilised by design. First, it seeks to reconnect the theory and discourse of contemporary architectural form to its origins in the development of modern mathematics, and in doing so bring to light the radical implications these theoretical developments offer to the epistemology of form. In many cases the computer veils the presence of mathematics. In architecture, today’s mathematics is about power and invention. Various reasons may account for this situation. This is a real issue that should be overcome in the perspective of truly mastering what is at stake in computer-aided design. As a central example, the framework is applied to the oppositions of continuous and discrete topologies, and demonstrates that these apparently contrary signatures can be seen as duals, co-emerging from a common origin. From the basis of this emergent theoretical foundation, a framework for the examination of form is proposed that reveals the distinct topologies of contemporary architectural form as aspects of a synthetic and unifying problematic.

Updated: 28.10.2014 — 10:57