Preston Scott Cohen’s ‘Recilinear Spiriculate’ (1998; in Cohen 2001: 99) is a pencil drawing showing a sequence of perspectival transformations of a blocky object. It comes from a series of formal experiments Cohen entitles ‘Sterotomic Permutations’, in which a hybrid projective / perspectival drawing technique is used to generate a group of house concepts. The drawing is an open-ended trace of a process. It doesn’t simply represent a three-dimensional object in two dimensions: there is no original object, nor a final one (although, of course, one was drawn first and one last). The drawing produces rather than represents. We witness the operation of a drawing machine. In this sense, the drawing is a *calculation* rather than a representation. Cohen sees architecture as the resolution of predicaments, to the extent that he argues predicaments should be actively sought out by the designer, and even introduced if necessary:

An architecture that is compelled to distort, and that ultimately highlights and questions norms, requires the invention of surrogate problems… Architecture could create problems, vigorously attempt to solve them, and never be able to. Architecture would thus keep itself alive by remaining an unfulfilled promise. (Cohen, 2001: 13)

Architecture should be a form of calculation, writes Cohen—but this doesn’t mean simply optimising, discovering a minimum or maximum condition. Rather, he intends that problems engender an open-ended instability, an oscillation or circulation.

‘Rectilinear Spiriculate’ oscillates between perspectival and stereotomic projection. There are two operations going on here. The Taylorian perspective apparatus employed includes a potential ambiguity about whether any anamorphosis is an effect of perspective or a property of the object itself; and Cohen exploits this further by using a procedure derived from Desargues for calculating the three-dimensional angles common in stone-cutting given only the standard figures of plan and elevation. The result of combining these two operations is that each projected figure is simultaneously the three-dimensional result of a calculation and a plane figure that can be re-inflated into three dimensions.

Symmetry is invariance under a transformation. The degree of symmetery is measured by the degree of invariance, or more precisely, the number of different transformations under which the object remains invariant. A cube, for example, remains unchanged by X, Y, and Z rotations of 90º, 180º, 270º, 360º, but is changed by other rotations; while a sphere can be rotated any number of degrees without varying. The sphere has a greater degree of symmetry. The transformations of ‘Rectilinear Spiriculate’ are symmetry-breaking. Lengths, angles, parallels, and ratios between lines are not preserved, although co-linearity is. In mathematical terms, this drawing is something between a projective and a differential space. De Landa writes:

Classifying geometrical objects by their degrees of symmetry represents a sharp departure from the traditional classification of geometrical figures by their essences… even though in this new approach we are still classifying entities by a property (their degree of symmetry), this property is never an intrinsic property of the entity being classified but always a property relative to a specific transformation (or group of transformations) (De Landa, 2002:17).

The object made present in ‘Rectilinear Spiriculate’ is tumbled, stretched and spun. It doesn’t rest or settle into any stable configuration. It oscillates between two and three dimensions, cast back and forth across the picture plane. But through this circulation a degree of invariance is preserved, albeit a small one. This minimal definition describes not a single object, but a *multiplicitous *one that is always being recalculated.