Architectural form is always paradoxical.  It remains estranged and autonomous because it escapes the cultural categories by which it is assimilated and situated.  The programs that necessitate and the materials that give body to form are also protagonists in the struggle against its self-determinacy and autonomy.  With regard to the demand for it to be categorized, form is instigative and reactive; autonomy thrives on contestation.  Accordingly, the formally autonomous project of architecture continually reasserts and transgresses its authoritative paradigms of argumentation and reconfiguration.

What are some of the remaining legible paradigmatic operations to be transgressed?  One could begin with the distortion of symmetry, serially, linearity, progression, scale, elasticity, intersection, folding–operations that can attempt, but never fully succeed, to separate and rationalize themselves.  It could be argued, however, that the exponents of paradox in architecture are not configurative but rather inscriptive.  One such instigator can be found among the conflicts and synonymies of perspectival and stereotomic techniques of projection.  This is where the project Stereotomic Permutations begins.

Perspective and orthography are instrumental to a discipline that produces artifacts that are not self-identical with their medium.  Is it possible for the disparity between drawings and buildings to correlate with the discrepancy between paradigms and their distortions?  In Stereotomic Permutations, opposing systems of projection are peculiarly combined in order to become techniques of formal transgression.  The Distance Point method of perspective projection introduces a distortion of symmetrical and serial operations and configurations; stereotomy is deployed to refute the categorical distinctions between perspective and orthography.

The Distance Point method constructs a volatile symmetry by requiring that the perspective be reversed in relation to its object across a measuring line.  The result is a set of similar configurations (an orthographic object and a perspectival object) that differ proportionally and dimensionally.  Conventionally, the measuring line defines and holds apart the opposing methods of representation: the convergence and illusionism of perspective vs. the parallelism and actual dimensions of orthographics.  In this project, the implicit symmetrical order is repeatedly brought to bear on its objects and perspectives by forcing them to intersect, join and fold back on themselves to form a series.

When the lineaments of a perspective are brought into coincidence with those of stereotomic projection, fixity of point of view and the infinity of orthography become mired in a logical contradiction.  On the one hand, points of convergence (the eye and distance point) constellate a perspective and an object.  On the other hand, these same points, extended as fold lines, are shared by the surfaces of three-dimensional objects formed by both the original object and its perspective; since they are stereotomic, these combinatory objects contradict perspective by positioning the viewer at an immeasurable distance from the entire object.  The result is an apparent anamorphosis with the points from where one could gain an undistorted view in positions that can never be occupied.

From three dimensions to two and back to three again–reversals exaggerate the combined methods and in so doing eliminate the boundary between description and perception.  The matrix that once separated things by distinctly defining them has become the process by which things are rendered indivisible.

Corollary to this reversal is the fact that the Distance Point method functions by allowing its objects and perspectives to be reversed in their roles relative to one another.  Hence, any possibility of linear temporal progression is confounded in advance.  As realized in three dimensions in this project, planes of coincidence provide other non-directional links between permutations.  All of the surfaces of the building, their true shapes, intersections, joining details, lines of convergence, coplanar and other affiliations, collapse the categories of inside and outside, back and front, beginning and end, plane, volume and mass.  Differing scenarios compete to define the procedures by which any particular iteration was determined.

Each arbitrarily introduced iteration is converted into a necessity by the projective matrices; once instantiated, each constituent is systematically linked by configurative, dimensional, and proportional data to aggregations previous as well as forthcoming.  As if modeled on Leibniz’s monadology, the axis of each verifiable distortion redefines the whole with respect to its parts.  Furthermore, the axes are diffused or partially hidden by the uninterrupted surfaces and consequential intersections of their three-dimensionality. Inextricably linked and always potentially determinative, the axes register different portions of objects and perspectives with reference to different orientations, degrees of concealment and interference between them; the axes become the intervals of a variegated series.

Preston Scott Cohen is an architect in Boston and teaches at Harvard University Graduate School of Design.

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