To grasp how the vectorization of space triggers such a phenomenological and architectural revolution, let us turn to Eisenman's project for the Virtual House competition (1997). According to Luca Galafaro, one of Eisenman's assistants, this was the first of Eisenman's projects to use vectors in the place of hand-drawn models.¹7 In mathematics, vectors are quantities "having direction as well as magnitude, denoted by a line drawn from its original to its final position" (OED). Because they have direction and density, vectors express forces or potentialities, rather than simply representing something already known. When they are used as the basis for architectural modeling, vectors liberate the architect from the need to convert a mental conception of space into a hand-rendered, axial drawing or modelization. Accordingly, vector modelization frees architecture from its rootedness in static spatial conditions: by injecting time into space, vectors unfold space as a field of intensity, a spatial field coequivalent to the matrix of potential connections it affords.
Virtual House was based on the memory of the spatial concept from Eisenman's House IV (1971), for which he wrote a text entitled "The Virtual House" (1987). Effectively, Virtual House deploys vector modelization to actualize the potential of the project that Eisenman considers his "first purely diagrammatic project"xiii and that Kurt Foster, in the Jury discussion to the Virtual House competition, describes as the summation of Eisenman's early House projects, where the "cube itself does not become the site of operations but a cube separated from itself."18 In Virtual House, the potential field of interactions among the nine cubes of House IV is actualized via the expression of each potential connection as a vector.xiv Each vector unfolds a field of influence in which its virtual movement through time is actualized; this actualization is, in turn, visualized through the effect of each vector on the lines within its sphere of influence. In this way, the lines, with their constitutive geometric properties, become forces, and, because they emerge through a set of arbitrarily assigned constraints operating on one another as local forces, the traces left by these lines record the condition of each vector within the space (see Figure 4.6).
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