‘Turn’, ‘bend’, ‘distort’, ‘pervert’ — these terms are only some definitions of the word twist found in the Oxford and Merriam-Webster dictionaries. “The French translations are: tordre, torquere, torquere; (similar to the English torque/torsion) which means to turn, to turn around, to torture. The association with the notion of torture is particularly interesting: tying up and strangling with a powerful and unavoidable turn enlivens the image of twisting.”^{1 Karel Vollers, Twist & Build: Creating Non-Orthogonal Architecture (Rotterdam: 010 Publishers, 2001).} ’Turn’ and ‘bend’ describe a benign mechanical action. ‘Distort’ and ‘pervert’ suggest something more adverse. In contemporary architectural parlance, both senses of the word are considered to be favorable as they belong to a lineage of motion^{2 Some examples of this are the Baroque favoring of the ellipse over the Renaissance circle, the Futurists’ fascination with speed associated with the automobile, and the more recent forays into animate form.} on one hand and dislocation^{3 This directly refers to Peter Eisenman's notion of “the dislocation of an ever-reconstituting metaphysic of architecture.” See Peter Eisenman, “Misreading Peter Eisenman,” in Houses of Cards (New York: Oxford University Press, 1987).} on the other. Twisting is a specific kind of bending or distortion that has all but been exhausted in the past two decades of architectural production. Examples of twisting abound worldwide and at various scales, not for unwarranted reasons. A simple twist to a material, form, or body can yield powerful effects. The dance craze “the twist” became an overnight sensation throughout the U.S. and Europe when Chubby Checker performed it on Dick Clark’s “American Bandstand” in the late 1950’s.^{4 Christine Keeble, "The Twist and 60's Fad Dances," How to Jive (DVD ,2008)} The main part of its appeal to teens and young adults is that it perverted what was considered socially acceptable movement between male and female: the gyrating and twisting action of the body on the dance floor suggested sexual activity and desire, which dislocated the metaphysic of dancing. In architecture, a specific kind of dislocation occurs in relation to twisting and a qualitative distinction must be made between an actual or literal and an apparent or phenomenal twist.

As it pertains to architecture, literal twisting is the deformation of a generic substance/material through opposing rotation at its ends along an axis perpendicular to those ends, whereas phenomenal twisting is the appearance of such achieved by other means of formation. The distinguishing terms are deformation in the former and formation in the latter, foregoing any implication as to one being real and the other being a mere appearance.^{5 The title of this text is a variation on Colin Rowe and Robert Slutzky’s essay, “Transparency: Literal and Phenomenal.” Rowe and Slutzky allude to the notion that literalness is associated with the real while the phenomenal merely seems to be.} They are both considered equally real. Grounding his discourse in perceptions, Merleau-Ponty discusses the interplay of things, experiences, and ideas in terms of the visible and invisible, emphasizing the way these two interact with and change each other, calling attention to what he calls the ‘profound carnality of their doubling’.”^{6 Jeffrey Kipnis, “...And Then, Something Magical,” in A Question of Qualities: Essays in Architecture (Cambridge, Mass: MIT Press, 2013).} In terms of effects, this is precisely what twisting does: it produces an oscillation between the visible and invisible parts of a surface/form. Along with these performative effects of twisting, the ushering in of the digital era of the early 1990’s and an aggressive interest in topology contributed to its popularity. A catalog of the various scales at which the twisting effect occurs reveals the qualitative and quantitative differences between them.

Twisting in architecture can be categorized into three scales: the material component (small), massing moments (medium), and the whole mass (large). At the material component scale we typically find strips or slats of sheet material (metals, wood, plastics, etc.) and usually in large numbers. This scale requires small parts and many of them (hundreds and thousands) and begins with the literal twisting of a basic strip of material. The phenomenal effects achieved are delivered at a larger scale when a critical mass of twisted strips yields field effects such as a moiré pattern. In the better cases, a dematerialization of a larger surface occurs where the accumulated twisting of the strips reveals something akin to an apparition of the thing it is enveloping, producing atmospheric effects. A prime example of this is Herzog & De Meuron’s Signal Box in Basel, Switzerland, which is wrapped in horizontal strips of copper at 17.50 cm. wide that twist from zero degrees (flat and closed) to sixty degrees from negative z.^{7 There is a sister Signal Box in Basel that was completed in 1999. They are almost identical except for a massing change whereby the sister version is a trapezoid at ground and a rectangle at the roof, producing a large-scale twisting of one of the facades, as well as ribbon window cutouts of the copper strips.}  While the conventions of frontality and facade are maintained, continuity occurs in both the surgical handling of assembly and a small fillet rounding off the corners. The limitation of the twisting from zero to sixty degrees is one imposed by material and methodological constraints. The twisting occurs gradually over a long enough span not requiring mechanical means of deformation. It is simply a byproduct of connecting the strips to gussets at evenly spaced and variably angled intervals. But the limitation also contributes to the apparition-like qualities: by not twisting to a full ninety degrees the conventional interior is never fully revealed when viewed frontally. This also privileges viewing it from the ground at a specified distance in order to receive maximum (but never full) exposure of what lies beyond. Twisting a planar and rectilinear strip of material beyond a certain angle threshold would result in the distortion of the material into a new figure and requires advanced means of formation vis-a-vis computation. Arguably, the Signal Box project serves as a contemporary canon for twisted effects found in digitally generated architecture. Ironically, the project was achieved through analog means, right at the cusp of the digital era.

At the middle scale we find a shift in effects and material logic. Massing moments of twisting are found when a project employs the twisted surface at a scale larger than the material component but not as one large move of a single mass. It is a means to simultaneously break down a building’s massing yet maintain coherence through surface and spatial continuity. While twisting at the scale of the material component focuses all of its energy on surface (perceptual) effects, this middle scale of twisting enters into organizational territory: the scale of the twisting action moves space around. At the small scale, the twisting effect is directed at the eye. At the middle scale it is directed towards the body. It exchanges deformation of material with deformation of massing geometry and can be constructed out of an undistorted planar sheet logic, a modular unit (brick), or molded (cast-in-place concrete).

A clear example of the latter is Miguel Fisac’s Jorba Pharmaceuticals Laboratory near Madrid, Spain (fig.1). A seven-story tower of repetitively stacked floor plates is distorted by rotating the alternate slabs forty five degrees in plan. The rotation is interpolated by twisted surfaces made of cast-in-place concrete. The overall mass is broken down into constituent parts (as floor volumes) yet made continuous through the twisted surfaces. The eye is invited to wander in rhythmic undulation, from any stationary vantage point, from base to top. But more importantly, the body is invited to move around the building to receive alternating compositions of the stacking as it snaps into alignment every forty five degrees: a double sense of frontality where “whole units of space are put into motion.”^{8 Quoted from Preston Scott Cohen during a lecture given at SCI-Arc in 2009.} In this case the twisted element is revealed as an index of the form-work and one can identify the panel seams located at ¼ intervals along each edge of a face. The literal twisted unit of construction appears to be modular and repeated, with each half being composed of two inversions of the ¼ unit. This legibility gives way to an understanding of the analogical sequence, thus the lack of need for computational intervention.

At the large-scale, that of the single twisted object, again we find a shift in effects from the previous two scales, but often a shared tectonic logic of the middle scale. This scale is best exemplified in the typology of the tower and is probably the most global, due to its ability and ease in achieving iconic status. The problem with the examples at this scale is that they tend to be either large caricatures of the small scale in singular form, or simply metaphors of bodies in motion. A case in point is the Turning Torso (an explicit adherence to the body metaphor) by Santiago Calatrava, in Malmo, Sweden. Inspired by a sculpture of a twisting human spine by the architect, the residential tower twists a full ninety degrees from base to top and is comprised of nine pentagonally-shaped stacked volumes. The building confounds frontality and simultaneously turns away from, and towards, a viewing subject. At this scale, these effects aren’t strong enough. The added feature of an exoskeleton, where the structure is exposed on two of the five faces, incurs an inflection in the envelope (where the other sides slightly bulge outward), and adds a bit more drama to the story. In this example there is the phenomenal twisting at the large scale but also a literal twisting at the component scale. The aluminum skin panels are actually twisted which contributes to the smoothness of the overall twist, save for the two-meter deep gaps every sixth floor.

A similar project, but of a more modest scale and expression, is the Gehry Tower in Hanover, Germany by Frank Gehry. Rather than being an isolated object, this nine story building is situated at the corner of an urban block. The rotation from base to top is limited to approximately twenty degrees. This subtlety of twisting is less about confounding facade orientations and more about the mass gently turning to find its comfort zone. The effect created is more a suggestion of turning away rather than a full-fledged turn. Similar to the Turning Torso (on the non-exoskeleton sides), the exposed faces of the Gehry Tower have a slight bulge to them and the skin panels are comprised of curved stainless steel. The site constraint, paired with the subtle handling of the mass, seems to be productive with regard to the twisted object-building: it replaces the ambitions of iconicity with one of posture and character, producing more of an “awe, shucks” presence rather than one announcing “here I am”.

Early examples of literal twisting in architecture and related practices can be found in medieval metalsmithing. From cutlery to weapons to ornamental grilles, twisted iron has a long tradition of accessorizing our environment. During the Middle Ages, iron manufacture and the three inter-related practices of mining, smelting, and smithing made significant advances. The blast furnace and the application of waterpower are two important technological advances made in this period. “The blast furnace used waterpower to increase draft and, therefore, temperature, allowing iron to be smelted much faster, cheaper and with the option of creating cast or wrought iron.”^{9 Brigitte Weinsteiger, The Medieval Roots of Colonial Iron Manufacturing Technology (Penn State University Center for Medieval Studies). URL: http://www.engr.psu.edu/mtah/articles/roots_colonial_iron_technology.htm} Steel is the combination of both cast and wrought iron with small amounts (1% or so) of carbon. The wrought variety (wrought, from “wreak”; to bend or twist) is a soft and ductile version and is closest to pure iron. It can be easily worked and bent into various forms but loses its sharpness easily and is only moderately strong. The cast variety comes out of the smelter in liquid form and is poured into molds not unlike bronze. It makes up for the former’s lack of strength but is very brittle and will crack if worked over, even at high temperatures. So the twisting of iron is limited to its wrought form.

An array of implements was used to twist wrought iron, from small hand-held tools to larger machines. One device was used to produce numerous and continuous rotations, from end to end of flat stock material or bars (fig. 2). Another tool was used to make half-turns of flat stock where the twisting action occurs within a variable span of material (fig. 3). An account of both tools is written about in A Treatise on Architecture and Construction V3.^{10 The Colliery Engineering Co., A Treatise on Architecture and Construction Vol. 3: Prepared for Students of the International Correspondence School (New York: Eaton & Mains, 1899).} The implement used for twisting generic materials such as strips and bars raises the issue of the mechanics involved in the twisting process. In this case, great force (torture?) is required in order to twist a relatively small flat metal bar at least one full revolution (but often times several) of 360 degrees. In contemporary architecture we rarely see this degree and type of twisting. Moreover, given the role of computation, the literal twisting of flat stock material has given way to a literal twisting of geometric surfaces, which are sometimes also referred to as ruled, scroll, or developable, which are then unrolled into flat shapes for fabrication to produce phenomenal effects. The primary difference between a ruled and developable surface is that developable surfaces can be unrolled without deformation (stretching) while the same is not always true of the former. Most developable surfaces are ruled with the exception of those embedded within four dimensions.^{11 David Hilbert and Stephan Cohn-Vossen, Geometry and the Imagination, 2nd ed. (New York: Chelsea, 1952).}

A series of diagrams (fig.’s 4, 5, & 6) attempts to geometrically simulate the variable twisting (torturing) of a surface strip to visualize the relationship between a ruled surface in three dimensions, its unrolled (flattened) projection in two dimensions, and the degree of deformation between the two. Each set of diagrams corresponds to three different numbers of revolutions occurring from base to top: one (360 deg), two (720 deg), and four (1440 deg). Each diagram is organized vertically according to speeds of twisting (slow on the top, fast on the bottom). These speeds refer to the vertical distribution of rotation angles per strip. Horizontally, the variable is the location of the rotation axis: justified to one edge, 25% along the edge, and the midpoint. The strip is shown in axonometric with the colored region indicating the back face. Projected in XY is the unrolled version of each showing the flat shape required to produce the twisted strip in question. The faint erratic set of lines is the curvature graph of the unrolled strips, which graphically indicates the degree of deformation occurring. To the left of the axon strip are the front and side views, respectively, orthographically projected to the picture plane. The “Length Ratio” number indicates the ratio of the longest unfolded edge length to the length of the strip.

This reveals that even in the least torturous version (360, slow, 0.5 axis) there is some deformation, consistent with that of material behavior. It also shows the impossibility of some of these to be materialized as a single uninterrupted piece of material. The unrolled projections that fold (intersect) onto themselves would have to be rationalized into parts, thereby foregoing deformation (literal) techniques and requiring other means of formation to produce phenomenal twisting (like most in the tower genre). The ones that don’t intersect themselves could be considered absolute twists, where a literal twisting of material produces phenomenal twisting effects.

The Mobius strip makes a clear case for the role of topology in contemporary twisted surfaces and is an oft-referenced topological model in architecture. There is a distinction between topology as a branch of mathematics and how it is used/understood in architecture. For hardcore mathematicians topology should not be visualized in images because it reduces the equations they represent to caricatures. Because topology deals with certain kinds of shapes and spaces, architecture has relied on precisely those images that mathematicians try to avoid. In a general sense topology is the study of continuity. More specifically, “A topologist is interested in those properties of a thing that, while they are in a sense geometrical, are the most permanent-the ones that will survive stretching and distortion.”^{12 Stephen Barr, Experiments in Topology (New York: Thomas Y. Crowell Company, 1964).} This provides the reason why a torus (donut) can become a coffee cup and why a square is no different than a circle, as long as the sequence of points defining the curve is maintained.

The desire for continuity was part of a broader agenda for moving past the conflict-and-contradiction values of deconstructivism, articulated in the canonical Folding in Architecture edited by Greg Lynn in 1993. In Greg Lynn’s essay, “Architectural Curvilinearity: The Folded, the Pliant and the Supple,” he states, “Deconstructivism theorized the world as a site of differences in order that architecture could represent these contradictions in form. This contradictory logic is beginning to soften in order to exploit more fully the particularities of urban and cultural contexts. This is a reasonable transition, as the Deconstructivists originated their projects with the internal discontinuities they uncovered within buildings and sites. These same architects are beginning to employ urban strategies which exploit discontinuities, not by representing them in formal collisions, but by affiliating them with one another through continuous flexible systems.”^{13 Greg Lynn, “Architectural Curvilinearity: The folded, the Pliant and the Supple,” Architectural Design 102 (March/April 1993).} This theoretical position paved the way for topology as a diagrammatic and morphological instigator in the smoothing of architectural form. A set of terms and operations derived from this discourse on continuity (bending, twisting, pleating, braiding, knotting, weaving, etc.) set the stage for advancing techniques for both practitioners and design pedagogy. As a diagram, the Moebius strip clearly illustrates the power of this brand of continuity. As a surface object, it confounds the notion of sidedness. It is a single-sided surface where inward and outward facing moments are within a continuous system of exchange. As a spatial object it confounds the notion of interiority/exteriority: space moves continuously and seamlessly between the two.

Figure 7 illustrates the latter example and reveals the contradiction of continuity/discontinuity when seen as a generative sequence. If we disregard the color and notational codification then we have a single-sided continuous surface. But if we account for the operational sequence then its two-sidedness is revealed in the color coding of each side as well as the orientation in the lettering sequence. In its Moebius form, one end is upside down in relation to the other. Maybe this is less a contradiction and more an ambivalence, simultaneously having it both ways. Or, more precisely, perhaps it is the difference between a literal and phenomenal Mobius, with architecture heavily privileging the latter. Since a literal Mobius has already been rejected as a possibility by mathematicians of the highest ranks then architecture could only contend with either the appearance of one, or, more productively, treating it as a primitive that undergoes further transformation as it absorbs increasing amounts of information (i.e. site constraints, structure, program, circulation, ornament, etc.)

A project that my office^{14 The project was done in collaboration with Matthew Au.} is currently fabricating at Oregon State University in Corvallis serves as an example of a minor lateral advancement (as opposed to a major vertical advancement) of phenomenal twisting at the material component scale. The project is titled Afterglow^{15 Afterglows are the optical phenomena associated with the scattering of light particles during sunset that produces a range of rosy hues in the sky. This effect gets amplified by the occurrence of volcanic ash in the atmosphere, which deepens the color range with reddish hues. While the last major eruption of Mount Hood was over a century ago (1866), it has contributed to the atmospheric effects all across Oregon, and beyond, to this day. This can be experienced during the hour of twilight in certain climatic circumstances (clear to partially cloudy skies) and is one of the elements that makes Oregon’s atmosphere unique.} (fig 8) and belongs to the aesthetic sub-genre of atmosphere.^{16 I consider atmosphere to be a sub-genre of field effects in architecture, in the perceptual rather than organizational sense.}  It is a permanent installation for a new Student Union building, which is a four story structure with a three story atrium terminating at the ceiling of the third floor. The exterior of the building is required to mimic the neoclassicism that pervades the campus, whereas the interior contrasts stylistically. The atrium is comprised of overlapping elliptical figures that stack and contain a public staircase and provided an opportunity to intersect two diagrams, one planimetric (fig 9) and one sectional (fig 10), that suggest competing formal narratives of the building.

The plan diagram is empathetic to the eccentric architecture of the atrium, which has multiple centers, and seeks to amplify that condition, moving toward an ecstatic space by multiplying and extending the radial curves. The sectional diagram is sympathetic and understands the atrium as a dome and rotunda that is cut short at the last level. Our proposal conceptually forces a dome and rotunda into the existing space which then undergoes transformation due to the mis-fit. The final result is a two-part intervention (fig 11). One continuous shredded surface adheres to portions of the stair, fascia, guardrail, ceilings, and walls. A separate ceiling piece is bounded by an undulating and variable shredded surface with mirrored and flat tiles on the interior. The pattern of the mirrored tiles is the flattened projection of two intersecting, hexagonally subdivided hemispheres based on the outer radii of the ceiling figure. The mirror is intended to bring back the vertical effect of the absent dome. The project also focuses on local qualities, the geometry, materiality and fabrication of the fascia strips (fig 12).

The atrium fascia is composed of the floor edge and the open guardrail with balusters spaced at 4” intervals. Their current relationship is discrete, in that there is no continuity between them. Our proposal supplements this condition with a continuous shredded surface that mediates baluster, fascia, and ceiling in the form of (or what appear to be) twisted strips. The problematic of the fascia is that there is an almost six inch offset between the strips at the floor’s edge and the baluster (fig 13A). This means that the twisting of a straight flat strip of material would not resolve the discrepancy without having to add extraneous support. But even then any sense of continuity would be lost since the guardrail and baluster would remain dis-integrated. The solution employed is a conic patch that interpolates between the outer edges of generic vertical strips with those of the balusters (fig 13B). This produces phenomenal twisting (fig 13C) achieved through the rolling of a formed (figured) flat shape. Fig 14 illustrates the geometry and mechanics involved in conic rolling, which is a developable surface since there is no deformation when unrolled. This solution can be situated between the techniques of bending and twisting (fig 15) in that it is the only one that employs a different operation from the effect it produces (fig. 16).

Twisted surfaces in architecture are a contemporary phenomenon due in large part to the computer and advanced geometry. They also have a lineage in related disciplines and other cultural modes of production. At the large scale the twisting effect seems to have been all but exhausted. It may be that the small scale has also reached its limit (if it hasn’t already) in terms of field effects such as atmosphere. The middle scale appears to have the most room left to engender a broader range of effects, such as posture and character. This is due to its ability to address the body and the eye in a sophisticated choreography of space. It can also absorb the effective qualities of the other two scales producing a possible matrix of twist on twist action, both in the literal/phenomenal and geometric/tectonic sense.

The literal/phenomenal template, set up by Colin Rowe nearly sixty years ago, still proves useful across a range of architectural qualities and effects. What is different, and hopefully implicit in this paper, is the attitude towards such a binary framework. The modernist ideal was to sustain distinctions, to maintain categorical boundaries, keep the labels in their place. A contemporary attitude allows for the relaxing of initial dichotomies towards strange mixtures, requiring a more complicated form of judgment. As Bruno Latour argues, “Whatever label we use, we are always attempting to retie the Gordian knot by crisscrossing, as often as we have to, the divide that separates exact knowledge and the exercise of power - let us say nature and culture.”^{17 Bruno Latour, We Have Never Been Modern (Cambridge, Mass: Harvard University Press, 1993).}