INFLeXions No. 6 – Arakawa + Gins special issue of Inflexions
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Relations must come first. – Piet Mondrian, Letter to László Moholy-Nagy (June 6, 1939)
Grids and Matrices
Grids can appear to present space and time statically. For some people the sight of grids can immediately conjure up notions of fixity, timelessness, and imposed order. According to Lutz Koepnick, grids are "not a product of the unpredictable temporality of the viewers' physical movement and sensory perception but a prearranged logic of compilation and construction, a mechanism seemingly engineering uniformity, universality and unwavering stability" (2006: 53-54). Images such as algebraic graphs, geographic maps and architectural blueprints come to mind. Through their use of Cartesian x/y coordinates, these images produce gridded spaces that establish a methodical, inanimate, and invariant order upon all that is contained within them.  Koepnick and Sabine Eckmann suggest that the grids found in the modernist paintings of the early twentieth century particularly display this inclination towards immutability and predictability. For them, "the grid enabled art's capacity to distance itself from language, figuration, and representation and provided visual experiences favouring simultaneity over the sequential, the spatial over the temporal, the abstract over the representational, and the universal over the particular" (Eckmann and Koepnick 2006: 8). One clear example they give is the paintings of Piet Mondrian. 
When looking at Mondrian's Composition No. 12 with Blue (1936-42), viewers will see that it is an almost square painting (62 x 60.3 cm) comprising a complex black and white grid with a snippet of blue near the bottom. The canvas is filled with a series of black horizontal and vertical lines that cross one another perpendicularly, forming the grid structure. There are several intersections resulting from the six horizontal and the seven vertical lines. These crisscrossing black lines give the appearance of slicing the white background into quadrilateral sections. Near the bottom right corner, caught between two of the black vertical lines and enclosed by black lines along the top and the bottom, is the only coloured section, a square of blue. The black lines along the blue square's top and bottom edges extend to the right. The bottom line stops after intersecting with the next vertical line. Like the line at the bottom, the top line intersects the next vertical line but instead of stopping, it leaps to the next vertical line to continue to the edge of the canvas.
Eckmann and Koepnick contend that modernist works consisting of grids, like Mondrian's Composition No. 12 with Blue, are not only static, but also constitute the image viewers see. For them the painted grid and the seen image appear to be one and the same, approaching viewers "as immediately recognizable and hence devoid of unwanted surprises" (Eckmann and Koepnick 2006: 8). Following the assertion that modernist grids are static, if the images viewers see when looking at Mondrian's painting consists only of the grid composed on the canvas, then the seen images are as immutable as the grids that generate it. As viewers look at Composition No. 12 with Blue with its black perpendicular lines dividing the white background into quadrilaterals of varying sizes and shapes, the generated image is the static grid.
Eckmann and Koepnick believe that modernist grids, like Mondrian's Composition No. 12 with Blue, were freed from their methodical immutability and were reworked into what they call "matrices" with the rise of digital imaging in the late twentieth century. According to Eckmann:
The digital matrix, consisting of pixilated visual bits created by a binary code of numbers, transforms the static modernist grid into a moving configuration, one that is nevertheless still informed by the basic structure of the grid. Yet, in contrast to the modernist grid, the digital matrix may remain invisible and is capable of forming images independent from its own structure. (Eckmann 2006: 16) 
Matrices are bodies generated on the plane of reference. They transform grids from static configurations into bodies that are capable of change. They enable difference to occur across the invariant structure of grids. Because matrices open grids to change, for Eckmann and Koepnick, they "emancipate the grid from its confinement to two dimensions; they displace the grid's tendency towards the static and unchangeable" (2006: 9). Matrices enable grids to extend beyond their own invariance through the displacement of "pixilated visual bits" that change within the grid itself.
Although grids form the underlying invariant structure for matrices, matrices are not grids. The grids that constitute matrices are backgrounded from the viewers' attention. By taking the viewers' focus away from the grids as such, matrices bring the elements that change within grids to the forefront of the viewers' perceptual awareness. A good example of this can be seen in John F. Simon Jr.'s internet artwork Every Icon (1997).  As Eckmann explains, the grid in this work cannot generate the images viewers see as such; rather, it "remains one and the same while the matrix, independent from a fixed form, is shown as the tool that creates these new images" (2006: 17). When looking at Every Icon, the viewers' attention is not on the grid that structures the unfathomable number of images that are generated in this work. Instead, their attention is focused on the frantic oscillation of black and white squares that generated movement across the grid. Viewers do not perceive an invariant grid that happens to contain elements that change; rather, they see black and white moving images that primarily flicker in the upper left corner of the work.
The invisibility of the grids that structure matrices, according to Eckmann, gives the images that are generated the ability to independently produce themselves. "The capability of the matrix to generate images different than itself allows artists to use digital imaging technologies and their underlying grids of mathematical codes without being confined to an abstract and rigid structure" (2006: 17). When compared to the gridded images of modernist painting, like Mondrian's, the ability for matrices to produce images that are different from their underlying gridded structure can easily be understood. This is because movement generated within matrices results from the displacement of the compositional elements across the underlying and imperceptible gridded structure. When viewers look at Mondrian's Composition No. 12 with Blue, the compositional elements – the perpendicular lines, the white background, and the blue square – appear to not physically move or change. For Eckmann and Koepnick, this work can only be seen as a static gridded image. In the absence of any visible displacement, the grid is thrust to the forefront of the viewers' attention and is statically seen as both the image as such and that which generates this image.
Excesses in the Seeing
When Eckmann and Koepnick distinguish those features that comprise gridded images, like Mondrian's Composition No. 12 with Blue, from those images generated by matrices, like Simon's Every Icon, they produce a series of dichotomies.  Upon closer inspection, the opposition between the visibly stable images of modernist grids and the imperceptible moving matrices of digital images begins to unravel. The line that demarcates gridded images from those images generated by matrices is not solid at all. Despite Eckmann and Koepnick's conceptualization of grids stated above, Koepnick reveals that, "whatever appears to be a product of the grid's unyielding structure surreptitiously speaks of that which may exceed the grid's rational order and control" (2006: 55). This means that the gridded images of modernist painting, like Composition No. 12 with Blue, have the potential to reach beyond the structures that compose and contain them.  These works generate a movement that viewers experience through the activity of seeing, which is in excess of their compositional structure. There are excesses in the seeing that go beyond the limits of what is actually painted on the canvas.
When viewers look at Composition No. 12 with Blue, the grid that they see is capable of motion but not in the same manner as matrices. Unlike the black and white colours that move across the squares found within the matrix of Simon's Every Icon, the compositional elements in Mondrian's painting – such as black perpendicular black lines and planes of solid colour – do not change. The lines do not change places or angles. The solidly coloured quadrilateral planes of white and blue do not change colour, increase or diminish in size, or move across the black lines of the grid. None of the compositional elements in Composition No. 12 with Blue generate any spatial displacement. This does not mean that movement does not occur in this painting. According to Mondrian:
The vitality of living organisms as well as their physical characteristics is manifested not only through their appearance but through their movement. Vitality is more difficult to discern in inorganic things. Nevertheless we feel the vitality of reality in everything that exists. In plastic art this feeling of vitality is created through the dynamic rhythm of forms and colours. (Mondrian 1986/1993: 387)
Many viewers will experience a motion that is not actually painted on the canvas, but one that is felt through the activity of seeing. Susanne K. Langer believes: "What we call 'motion' in art is not necessarily change of place, but is change made perceivable" (1953: 66, original emphasis). This movement in Mondrian's work generates a dynamism that is beyond vision itself. It exceeds both the compositional elements that comprise the painting and the viewers' ability to see. "To exceed vision is to displace the disciplinary contours of thought to engage with the ephemeral" (Manning 2003: 11). Viewers can sense that there is something at work in Mondrian's painting, yet at the same time there is nothing tangible to verify that anything has actually occurred. As viewers look at Composition No. 12 with Blue, they will see a grid but feel a movement that leaves absolutely no indication that it occurred. According to Henri Bergson: "There are changes, but there are underneath the changes no things which change: change has no need of a support. There are movements, but there is no inert or invariable object which moves: Movement does not imply a mobile" (2007: 122). This felt dynamic movement leaves no trace because there is nothing that actually supports it. Dynamism needs no foundation to activate changes felt in the seeing.
Before viewers experience this dynamism, they will tend to notice two things when initially looking at Composition No. 12 with Blue: it presents a grid and it appears to be static. The painting's black perpendicular lines seem to place a geometric order onto the white background, removing the potential for any movement to occur. The web of intersecting black lines grabs the viewers' attention and stops them in their tracks. Yet, in that brief moment as Mondrian's web holds the viewers' attention, movement begins to emerge. It is not a free-flowing continuous movement but rather one that feels jittery, provoking the viewers' gaze to jump all over the canvas. This is because flashes of whitish-grey begin to appear at the intersections of the black lines. The more the viewers' gaze jump from one intersection to another, the more the flickering appears. This in turn incites the viewers' vision to continue jumping. If viewers try to hold their gaze on one intersection, the fluttering of whitish-grey appears to diminish momentarily. However, within a couple of seconds the flickering resumes in the other surrounding intersections, which eventually provokes the viewers' gaze to move again. What viewers discover is that there is a restless rhythm generated in Mondrian's painting, which can be felt emerging from the flickering intersections. "Thus rhythm runs through a painting just as it runs through a piece of music" (Deleuze 2003: 37).
Composition No. 12 with Blue holds the viewers' attention just long enough to generate visually resonant images: images that emerge from the jittery rhythm of the flickering intersections. The painting does not produce a singular static image but rather generates what Erin Manning would describe as "a felt rhythm that invents itself in the watching" (2009: 188). The images viewers see emerging from Composition No. 12 with Blue, as a frenetically felt rhythm, only occur in the encounter with the painting. This experienced rhythm is a dynamic movement felt in the seeing. Neither the viewers nor the painting produce these rhythmic images alone. This is because, as Mondrian states: "Everything is expressed through relationships" (1986/1993: 86, original emphasis). Understanding images in this light means that no one thing can produce them. It is neither the painting nor the viewers that generate the seen images. Rather, images emerge in the relations occurring between Mondrian's painting and viewers as a shared experience.
When viewers and Composition No. 12 with Blue enter into relations, both the viewers and the painting actively participate in generating the images that are seen through the experience that they mutually share. Images are only visible when viewers experience the painting and, as odd as it may seem, when the painting experiences viewers. This means that the ability to have an experience is not something that is exclusively human. Viewers are not the only entities that have experiences. Mondrian's painting experiences something too, even if it is on some rudimentary level. Even a rock experiences something. "A falling rock 'feels,' or 'perceives,' the gravitational field of the earth. The rock isn't conscious, of course; but it is affected by the earth, and this being affected is its experience" (Shaviro 2009: 12-13).  A falling rock experiences the gravitational field of the earth because the earth has an impact on it by way of physical attraction. Conversely, as a rock falls, the earth also experiences the gravitational field. This is because the gravitational field emerges from the relations that occur between the falling rock and the earth. The gravitational field is the shared experience that arises from these relations, similar to the images that emerge from the shared experience between viewers and Mondrian's painting. So, like a falling rock, Composition No. 12 with Blue "experiences": it is constantly being affected somehow, whether it is the nails holding it to the wall, the contact it has with the wall, the moisture floating in the room, or the attention the viewers visually give it.
The Relational Complex
The felt relations between Composition No. 12 with Blue and viewers, as a shared experience, does not only include the set of relations from which images emerge. According to Mondrian, this is because the painting "must be viewed as a duality or multiplicity – as a complex" (1986/1993: 86, original emphasis). This "complex" involves the relations among the plastic, or compositional, elements of the painting – such as lines, colours, and the planes they compose. For Mondrian: "If purely plastic expression is created by 'the relationships' of line, planes surface, and colour in their purely plastic values, then these means exist only through their relationships. Therefore, relationships are just as important as the plastic means" (1986/1993: 246). The relations that occur between the compositional elements are just as vital to the emergence of images for Mondrian as the compositional elements themselves.
Mondrian takes a radically empirical approach to his painting practice, in which "the relations that connect experiences must themselves be experienced relations, and any kind of relation experienced must be accounted as 'real' as anything else in the system" (James 2003: 22-23). Because the "complex" Mondrian composes for his painting cannot be experienced without the relations that gather among the compositional elements, these relations must be considered as much a part of the experience viewers encounter with the work as the lines, colours, and planes seen on the canvas. Since relations are key to the generation of Mondrian's "complex," it can thus be called a relational complex.  It is important to note that these relations occurring among the compositional elements are not just vital to the shared experience viewers and Mondrian's work generate. The relational complex that emerges from the compositional elements and their relations is in fact crucial to the experience viewers have with any artwork.
It is from this relational complex that images begin to incipiently form as a rhythm felt in the seeing. Mondrian testifies to this, stating that: "Rhythm arises through the relationship of plastic means" (1986/1993: 313). As the relational complex comes together, the rhythm that viewers feel when looking at the painting does not generate fully formed images. Rather, the relational complex, along with the shared experience occurring between viewers and the painting, initiates a process out of which images emerge. This process is felt as the incipiency of images. It is the compositional elements in Composition No. 12 with Blue – the black perpendicular lines, the planes of white, and the blue square – that gather and begin forming a relational complex, making it possible for images to begin emerging.
The emergent images that arise from the shared experience between the relational complex of Composition No. 12 with Blue and the viewers are more dynamic than Eckmann and Koepnick's notion of either grids or matrices. Recall that Eckmann and Koepnick's understanding of gridded images assumes that the relationship between viewers and artworks is based on a notion of stability. For them, viewers see immutable images when looking at gridded images. Brian Massumi points out that if artworks are assumed to be static, this affects how vision is understood.
The idea that there is such a thing as fixed form is actually as much an assumption about perception as it is an assumption about art. It assumes that vision is not dynamic – that it is a passive, transparent registering of something that is just there, simply and inertly. If vision is stable, then to make art dynamic you have to add movement. (Massumi 2011: 40-41)
In this light, grids are immutable because both the seen artwork and the viewers' ability to see are believed to be stable, whereas matrices are full of motion because movement is added to compositional elements that are contained within its underlying static gridded structure. This means that Composition No. 12 with Blue cannot be considered a grid, as defined by Eckmann and Koepnick, because viewers actually see movement occurring in the form of the jittery rhythm that emerges from the flickering intersections of the black perpendicular lines.
Viewers experience a seeing that exceeds what is painted on Mondrian's canvas. Alternately, this also means that grids are not stable as such. They are never as immutable as they seem. The fluctuation of grayish-white in the intersections of the grid provokes viewers to constantly shift their focus from one section of the painting to another. Their gaze is not fixed upon the painting as a whole but instead is endlessly darting about the canvas. For Mondrian, "vision does not start from a single given point, but takes its viewpoint everywhere, from no fixed place" (1986/1993: 197). The instability of the viewers' vision is instrumental to the dynamism that is generated with the work.
Composition No. 12 with Blue cannot be classified as a matrix either. This is because, first, the movement that takes place in the painting does not result from the addition of motion to the compositional elements; second, the black lines make the grid visible; and third, it is not a digital artwork. The moving images viewers see in Mondrian's painting are not caused by changes that are exclusively generated from the work itself. There is no underlying binary code that was programmed to move or change the compositional elements within the visible grid, unlike Simon's Every Icon. Rather, when viewers look at Composition No. 12 with Blue, the moving images they see are co-generated through dynamic relationship between the relational complex of compositional elements and the shared experience that the viewers and the painting mutually encounter together. It is the excesses in the seeing that generate the dynamism that is felt as the incipiency of images of Mondrian's work.
Composition No. 12 with Blue shows that the line that demarcates grids from matrices is not solid because the dynamic movement generated from the jittery rhythm felt in the seeing blurs this boundary. In Mondrian's last completed painting, Broadway Boogie Woogie (1942-43), the criteria that separate grids from matrices become even more tenuous. This is because Broadway Boogie Woogie generates a dynamism felt in the seeing without any black perpendicular lines. There is no grid that is immediately visible, unlike Composition No. 12 with Blue. Rather than composing this painting with black perpendicular lines, Mondrian fills Broadway Boogie Woogie with an array of rectangular and square planes of varying sizes. The larger planes are primarily white and are surrounded by smaller, mostly square, planes that are composed of four different colours: red, yellow, blue, and grey. What is striking about this square painting (127 x 127 cm) is that as viewers look at it, they begin to notice that the smaller planes that border the larger white planes actually form a series of perpendicular lines. These colourfully composed lines, in turn, generate a gridded pattern that echoes Mondrian's previous work, such as Composition No. 12 with Blue. 
In Broadway Boogie Woogie, the perpendicular lines and the grid can actually be difficult for viewers to see as a cohesive whole because these compositional elements are not a uniform colour. This is because the lines and the grid are generated in the seeing. Discussing Broadway Boogie Woogie, Mondrian explains that the perpendicular lines composed of the small planes are not the only things that are produced through the activity of seeing, but that the planes themselves are as well. He states that, "the lines are absorbed by the colour planes; but the limitation of the planes shows themselves as lines and conserve their great value" (Mondrian 1986/1993: 356). The perpendicular lines viewers see, which form the grid, are composed of the small coloured planes. The coloured planes themselves are composed of contour lines that surround their edges. These contour lines, which delineate the planes' shape, emerge in the relations between the coloured planes. The contour lines and coloured planes mutually compose each other and together generate the painting's relational complex. It is the mutual composition of and relations between the coloured planes and the contour lines that enable the emergence of the perpendicular lines and the grid.
Viewers initially encounter the emergence of the relational complex in Broadway Boogie Woogie through the dazzling display of colours found in the planes. It is the array of coloured planes that grab the viewers' attention, as opposed to the perpendicular lines they generate. This is because, according to painter Bridget Riley, Mondrian "paints the sensation that his own work generates: the little tiny squares in Broadway Boogie Woogie originate in the afterimages of the linear intersections that were the beginning to crop up in his paintings" (2009: 318). Instead of the perpendicular lines generating a jittery rhythm of whitish-grey flickers, like in Composition No. 12 with Blue, Mondrian reverses the roles of the flickers and the perpendicular lines in Broadway Boogie Woogie. It is the flashes of colour, now made corporeal and embodied as the coloured planes painted on the canvas, which generate the dynamism that is felt in the seeing. As the colours of the planes take hold of the viewers' attention, a dynamic movement begins to appear that follows the sequences of the small coloured planes. This dynamic movement is discontinuous, but not like the jittery flickers of Composition No. 12 with Blue. It flows through the sequences of reds, yellows, blues, and greys around the larger white planes as an irregular rhythm. From this flowing irregular rhythm, the perpendicular lines and the grid are made visible as the images that viewers see.
The array of coloured and white planes that compose Broadway Boogie Woogie, as well as the perpendicular lines, the grid, and the irregular rhythm that viewers experience in the seeing, might be considered as what Madeline Gins and Arakawa call landing sites. According to Gins and Arakawa, landing sites designate "the 'coming alive'… of anything whatsoever, including even the most fleeting sensations" (2002: 6). As new encounters are experienced between Broadway Boogie Woogie's compositional elements, the gathering relations among the elements and viewers, more landing sites are felt in the seeing. These felt landing sites cannot be specifically located. They are not stable places that can be mapped with any sort of precision. They do not occur in or on Mondrian's painting. Rather, landing sites are what constitute the composition of the experienced encounter, as they are being experienced. Landing sites generate a space for experience to be felt, enabling viewers to "feel the vitality of reality in everything that exists" (Mondrian 1986/1993: 387).
As landing sites, the array of coloured and white planes tease out an intensity that is experientially felt between viewers and the relational complex of Mondrian's painting. While these planes are being experienced, they become "the landings of sites for future cueing and aligning" (Manning 2010: 6-7). They are what mobilize potential into the felt dynamism that flows throughout Mondrian's painting, generating the irregular rhythm and enabling the incipiency of images. This means that what is generated in the midst of the viewer-artwork experience is composed of landing sites, including all the relations that occur between landing sites and the experiences themselves. This is because, according to Gins and Arakawa, what is actualized into perception is composed of configurations of landing sites. As well, each landing site that is experienced is always composed of more landing sites. "Anything perceived can count as both a landing site in and of itself and as a larger landing site" (Gins and Arakawa 2002: 9). Because there are landing sites within landing sites that constitute even bigger landing sites, Gins and Arakawa further refine the conception of landing sites and specify that there are three distinct types: perceptual landing sites, imaging landing sites and dimensional landing sites. The composition of anything that emerges into experience involves all three of these types of landing sites simultaneously. This is because, as Gins and Arakawa state, "[l]anding sites dissolve into each other, or abut, or overlap, or nest within each other" (2002: 8). It is through the overlapping of the three types of landing sites that experience emerges, changes, and is made perceptible. As the three types of landing sites constantly shift their configurations, the experience that they compose and recompose is always in the making.
The first of these landing sites that compose experience are called perceptual landing sites. They can be understood as the "building blocks" of all landing sites. This is because these sites, as Gins and Arakawa state, "serve up the initiating sites of all sites" (2002: 11). Perceptual landing sites consist of what is actually perceived as it is being perceived. "All points or areas of focus, that is, all designated areas of specified activity, count as perceptual landing sites (visual, aural, tactile, olfactory, proprioceptive, kinesthetic, somaesthetic [pain])" (Gins and Arakawa 2002: 10). Perceptual landing sites are the compositional elements that are actually seen in Mondrian's paintings, such as the colours and shapes of the planes in Broadway Boogie Woogie. They are also the assemblages of these compositional elements, like the grouping of colored planes that generate a particular horizontal line or a set of these perpendicular lines, which then forms the grid that viewers eventually come to see. Perceptual landing sites, according to Manning, "are singular and multiple at once" (2009: 211). Each individual perceptual landing site is a singular site onto itself, like the coloured planes, but they also make up other perceptual landing sites that are experienced through their multiplicity, such as the perpendicular lines and grid that are composed of many coloured planes.
Imaging landing sites are the second type of landing sites. These landing sites extend beyond the experiential limits of the perceptual landing sites. As Gins and Arakawa explain: "Taking off from perceptual landing sites (actual points of focus), imaging landing sites (generalizing factors) extend and diffuse surfaces and volumes. Imaging landing sites enlarge the areas over which qualities hold sway" (2002: 12). Imaging landing sites are the incipient actions that generate the about to become perceptible of experiences.  They constitute the dynamism that is felt gathering throughout any composition that is experienced. They are the excesses in the seeing that are felt when viewers look at Broadway Boogie Woogie. The dynamic movement that viewers feel as the irregular rhythm that compose the perpendicular lines and the grid visible are the imagining landing sites, which flow throughout Mondrian's painting.
Finally, dimensional landing sites are the sites that occur between perceptual landing sites and imaging landing sites. Gins and Arakawa state that dimensional landing sites combine "the qualities of a perceptual landing site with those of an imaging landing one, coupling and coordinating direct responses with indirect ones, the formed with the formless" (2002: 8). Dimensional landing sites are the sites of relation that arrange the spacing and the placing of all landing sites. They generate the depth and emphasis necessary to any experience. In Broadway Boogie Woogie, dimensional landing sites simultaneously enable viewers to take in the composition of planes on the canvas, feel the emergence of the dynamic irregular rhythm, and see the perpendicular lines and the grid that this rhythm generates. Dimensional landing sites connect the composition of planes to the irregular rhythm they generate in the seeing and bring them both to the forefront of the viewers' experience in order to make the perpendicular lines and the grid visible. Without these dimensional landing sites to coordinate the felt excesses of imaging landing sites and the perceived compositional elements of perceptual landing sites, the act of experiencing the world would be made completely chaotic.
All three landing sites are necessary in order for any visual experience to occur. The images that viewers see when looking at Broadway Boogie Woogie all arise from the ever-changing configurations of these three types of landing sites. The perpendicular lines and the grid are made visible not only from the configuration of perceptual landing sites that are immediately seen as the composition of planes, but also from the imaging landing sites that generate the dynamism felt in the seeing and the dimensional landing sites that constitute the relations that occur between all landing sites. As these landing sites compose and recompose what viewers experience, they also coordinate the emergence of the relational complex and the shared experience between Mondrian's painting and viewers. The relations among landing sites bring forth the notion that the viewers' experience is in constant negotiation between the overlapping of landing sites, forever composing, in which there is no distinct division between the viewers' body, Mondrian's painting, or the experiences that both share. It is from the constantly changing configurations of landing sites that the incipiency of images is made possible.
Landing sites are not only constantly configuring what viewers visually experience when looking at Broadway Boogie Woogie, they also are perpetually composing all the visual experiences viewers have of anything they see, whether they are gridded images, like Mondrian's paintings, or images generated by matrices found in digital imaging, like Simon's Every Icon. The encounter viewers have with a single white square in Every Icon generates a landing site that is experienced in and of itself. This same encountered white square is also a part of a larger composition of squares that generates different landing sites for the experiencing. All of these landing sites that are felt in Every Icon, like those in Mondrian's paintings, continually shift about configuring an experience for viewers, as that experience is itself emerging into existence. Whether images emerge from digital means or with paint, everything that viewers see is constituted in the shared experience generated through the encounter with landing sites that are felt as "a depositing of sited awareness everywhere" (Gins and Arakawa 2002: 7). Images actively emerge in midst of a shared encounter with the world that is infinitely populated with landing sites.
Tentatively Constructing Images
Because landing sites are active within every shared experience with and within the world, rather than attempting to classify the images as either being gridded or generated by matrices, all images – digital, modernist or otherwise – should be considered to be what Gins and Arakawa call "a tentative constructing towards a holding into place" (2002: 23ff., original emphasis). The images emerging from the shared experience between an artwork and its viewers arise from the constantly shifting configurations of landing sites. Because everything that is experienced changes as the landing sites rearrange themselves, any images that are made visible never last as such for very long. As Gins and Arakawa explain: "Everything is tentative" (2002: 49). It is important to be mindful of the nuanced manner in which Gins and Arakawa use the term "tentative," which is defined by them in both its provisional and hesitant sense (2002: 82). Specifically, tentativeness should be understood provisionally as an arrangement that lacks fixity and hesitantly as a momentary pause. This means that the images that viewers see when looking at Mondrian's Composition No. 12 with Blue or Broadway Boogie Woogie emerge as "a tentative constructing towards a holding into place" that is provisionally "constructed" but that is also hesitantly "held."
The experiences that are shared between Mondrian's paintings and the viewers are provisionally tentative because at any moment these particular experiences can change or even vanish. When Gins and Arakawa discuss the tentativeness of the biosphere, or what they call the "bioscleave," they assert that if any single element fails to hold, then this could potentially create disastrous effects for the entire planet.  Although the consequences are not as cataclysmic when a shared viewer-artwork experience does not take hold, emergent images and shared experiences are nonetheless tentative in this provisional way. For example, when viewers walk away from Composition No. 12 with Blue or Broadway Boogie Woogie, the shared experience between the viewers and the painting ceases, while the developing relational complex and the incipiency of images continue to persist by taking new and different forms. This is what makes the "constructing" of images so provisionally tentative. Even minor changes to the experience shared between Mondrian's paintings and its viewers can affect the incipiency of images. A blink of the eye, a stomach gurgling with hunger, a gentle breeze flowing through the gallery space, a cough made by another viewer, or even an appearance of crack in the paint that is just beyond perceptibility can all tentatively impact the shared experience.
The key is that these provisionally tentative, shared experiences need to be held long enough to enable the coming together of relations and allow for the incipiency of images to occur. In order for this holding to happen a hesitation must occur. Neither Mondrian's paintings nor the viewers are capable of provoking this hesitation. Rather, according to Gins and Arakawa, critical holders enable this hesitation. Critical holders emerge to help the viewers detect and piece together incipient images while they are "activated and held and holding and activating" (Gins and Arakawa 2002: 82). Recall that when viewers first encounter Composition No. 12 with Blue, the web of perpendicular black lines holds their attention for a brief moment just before the whitish-grey flickers begin to emerge from the intersections. The moment viewers encounter the painting, the black perpendicular lines initiate a composing of an about-to-become image. This causes a hesitation to occur in the seeing. It is important to understand that the composing black lines are not yet an image as such. This composing or incipient action should be viewed as the initial coming together of the relational complex. When viewers look at Composition No. 12 with Blue, as the black lines begin composing, a hesitation is generated in the seeing. When looking at Broadway Boogie Woogie, the critical holder is the array of colours that dazzle the viewer into hesitation. As the viewers begin looking at the colours found in the painting, compositions of coloured planes begin to emerge, which then generate the irregular rhythm that takes the viewers on a journey around the various white planes throughout the canvas.
It is the critical holder that enables this hesitant moment to take place so that the relational complex can continue coming together enabling the incipiency of images to occur. This is because the critical holder exists in a relationally emergent field that includes Mondrian's paintings, but also extends beyond them. It invites viewers to engage with these paintings through its ability to attract and hold the viewers' gaze. The initial configuration that begins to become visible in Mondrian's paintings is the critical holder, which takes form as the composing black lines in Composition No. 12 with Blue or the coloured planes in Broadway Boogie Woogie. In that hesitant moment when the critical holder emerges, several actions occur almost simultaneously, enabling the incipiency of images. To begin with, the viewers' attention is held. Then the shared experience is activated between Mondrian's paintings and the viewers. Finally, the relational complex continues to come together after viewers see the initial configuration of the black lines, in the case of Composition No. 12 with Blue or the composition of coloured planes in Broadway Boogie Woogie. From these three nearly simultaneous occurring actions a rhythm becomes active in the seeing. Images then emerge from the jittery and irregular rhythms of these paintings, holding the viewers' attention even longer.
In that brief pause between experiencing a composition of visual elements and a dynamic rhythm that incites the viewers' gaze to move about the canvas, the critical holder, to paraphrase Gins and Arakawa, enables viewers to hold the images that hold them.  "Everything stops dead for a moment, everything freezes in place – and then the whole process will begin all over again" (Deleuze and Guattari 1983: 7). The perpendicular lines in Composition No. 12 with Blue or the coloured planes in Broadway Boogie Woogie emerge as the critical holder that hesitantly facilitates the "construction" or incipiency of images, while simultaneously holding the shared experience between the painting and viewers in place. The critical holder enables viewers to feel the emergence of a dynamism that can only be felt in the seeing during the shared experience.
Forces Felt in the Seeing
As the jittery flickers of whitish-grey in Composition No. 12 with Blue or the flowing irregular rhythms that emerge from the coloured planes in Broadway Boogie Woogie are encountered in the shared experience between Mondrian's paintings and viewers, these ephemeral occurrences could be easily dismissed as having no bearing on the viewers' actual perception. For Evan Thompson, these ephemeral occurrences do not have a place in his understanding of visual perception because they are not stable and distinct entities. This is because, for him, the jittery flickers and irregular rhythms viewers experience when looking at Mondrian's paintings are not solidly grounded in something like the paint on a canvas or something rational like the structure of grids. Thompson believes that: "In perception, one is aware of things as stable and distinct entities in relation to an indeterminate background" (1995: 247). This would mean that in order for viewers to encounter the images generated in the shared experience with Mondrian's paintings, they would have to background the dynamic movement that is actually experienced as the flickers and the irregular rhythms felt in the seeing. Viewers would have to encounter the compositional elements in these works, and the paintings themselves, as a set of stable entities that constitute the images they see. They would have to concentrate solely on the perceptual landing sites, paying absolutely no attention to either the imaging and dimensional landing sites that occur in the seeing, which enable the activation of the dynamism that is felt in the midst of the shared experience.
If perception unfolds how Thompson believes, then, according to Bergson, it would "be inextensible; it would consist of the assembling of certain specific materials, in a given quantity, and we should never find anything more in it than what had been put there in the first place" (2007: 113). Mondrian's paintings would be no more than the paint on the canvas and the grid pattern it presents. Viewers would not experience any movement when they encounter either Composition No. 12 with Blue or Broadway Boogie Woogie. Yet the excesses in the seeing present in the experience shared with Mondrian's paintings in the form of the jittery and irregular rhythms extend beyond Thompson's stable understanding of perception. This is because there is always more that is experienced than is directly perceived. As painter Bridget Riley notes: "We feel with our eyes more that we see" (2009: 69, emphasis added). When viewers gaze upon Mondrian's paintings they are experiencing a seeing that exceeds what is actually visible.
The dynamism felt in the encounter between viewers and Mondrian's paintings enables both to surpass the rational and stable order that grids tend to impose. Neither viewers nor Mondrian's paintings can generate the dynamism that is experienced on their own. It is the felt intensity of dynamic movement generated through the activity of seeing that draws viewers into a shared experience, rather than the depictions of grids or the sense of stability the grid may offer. This means the dynamism that is experienced exceeds both what Mondrian's paintings offer to be seen, as the emergent relational complex, and the viewers' actual vision. What is experienced is co-generated through the relations that occur between the viewers and Mondrian's paintings through the activity of seeing. The jittery flickers of Composition No. 12 with Blue and irregular rhythms of Broadway Boogie Woogie felt in the seeing are compositional forces that compose the images that come to be seen. These compositional forces are co-generated though the relations that occur within the shared experience because, according to Gilles Deleuze, "any force is already a relation" (1988b: 70). These felt compositional forces are the relations viewers encounter with Mondrian's paintings. They are what thrust the incipiency of images into action.
When looking at Composition No. 12 with Blue or Broadway Boogie Woogie, viewers simultaneously experience two conflicting compositional forces that constitute the dynamism felt in the seeing. This is because, according to Mondrian, "the opposition of two forces creates dynamic movement" (1986/1993: 384). One force centrifugally spirals outward, while a second force moves in the opposite direction, centripetally spiraling inward. The centrifugal force both exceeds the confines of the surface of Mondrian's paintings, spilling out beyond the works' relational complex and into the world. It also surpasses the perceptual limits of the viewers' vision, lavishing viewers with more than they can actually perceive. This centrifugal force is the conduit that enables viewers to feel the emergent excesses in the seeing.
The other compositional force felt in the seeing draws viewers towards Mondrian's paintings by luring their attention with the potential of experiencing a novel perception. This centripetal force pulls the viewers' attention to the visual offerings of Composition No. 12 with Blue or Broadway Boogie Woogie by subtracting many of the excess that viewers encounter through the centrifugal force. The centripetal force generates a seeing in which viewers perceive less than what they actually experience. Deleuze asserts that "perception is not the object plus something, but the object minus something, minus everything that does not interest us" (1988a: 24-25, original emphasis). This does not mean that the centripetal force removes these felt excesses from the shared experience viewers have with Mondrian's paintings. Rather, this inwardly turning force enables particular excessive sites of attention felt in the seeing to potentially become something that viewers actually perceive.
When the centrifugal and centripetal forces encounter each other within the shared experience between Mondrian's paintings and viewers, they eventually reach a state of equilibrium. This equilibrium for Mondrian "is not a static state without action, as generally thought but, on the contrary, [it is] a continuous and mutually annihilating opposition of equivalent but unequal elements" (Mondrian 1986/1993: 252). Just because a state of equilibrium is reached between the centrifugal and centripetal forces within the shared viewer-artwork experience, it does not mean that these forces stop being active. The centrifugal force continues to generate the more-than of experience, while at the same time the centripetal force persists in producing the less-than of perception. As one force enables more to be actually experienced, the other constantly lures the viewers' attention towards particular occurrences felt in the seeing. Because of the continued activity these opposing compositional forces produce, the equilibrium they co-generate constantly shifts and reconfigures itself, which in turn creates the dynamism that is felt in the seeing. Together these vertiginous compositional forces felt in the shared experience between viewers and Mondrian's paintings generate a dynamism that, according to Koepnick "at once point our attention inward and outward, suspend our perception and stir our appetite for more" (2006: 55).
The difference between what viewers encounter when looking at Mondrian's work and what is visibly painted on these canvases creates a disparity that Gins and Arakawa believe is "between the world as it happens… and the world, reduced and distorted, made to appear as other than what it happens as" (2002: 51). If viewers truly believe that the images they see are exclusively the grids painted on the canvas, then they will not visually encounter images as "a tentative constructing towards a holding into place." Viewers who see Mondrian's paintings as merely static grids potentially miss the dynamism that the activity of seeing has to offer. "Instead of visualizing a complete triumph of modern rationality over any remaining trace of uncertainty, Mondrian's grids simultaneously invite centrifugal and centripetal readings" (Koepnick 2006: 54-55). Works such as Composition No. 12 with Blue and Broadway Boogie Woogie enable a seeing in which dynamic movement is felt in the seeing experience. Disregarding the jittery flickers and the irregular rhythms felt in the seeing goes against one of Mondrian's most important beliefs, "that reality is in constant movement" (1986/1993: 351, original emphasis). Mondrian held movement in such high regard because, as he states, "it evokes the sensation of life" (1986/1993: 351).
 For a more detailed analysis on Cartesian space in relation to static form in art see Lynn 1999 and Manning 2009: 163-168.
 In the exhibition catalogue for the art exhibition entitled [Grid< >Matrix], which they also curated, Eckmann and Koepnick specifically discuss Mondrian's painting Composition of Red and White (1938-42).
 Several other authors have drawn a connection between the digital and the concept of the matrix. Tim Lenoir, like Eckmann, understands the digital image to be "a matrix of numbers, a table of integers, a grid of cells capable of being stored in computer memory, transmitted electronically and interpreted into an image by a display device (such as a video screen) or printer" (2004: xiii). However, one of the most notable and earliest conceptual examples of the digital matrix can be found in William Gibson's science-fiction novel Neuromancer (1984). In the novel the matrix is the equivalent of an immersive version of the internet in which users, such as the protagonist Case, experience "bright lattices of logic unfolding across [a] colourless void" (1984: 4-5). Media critic Lev Manovich in his book The Language of New Media applies Gibson's conception of the digital matrix as a void in order to differentiate digital, or computer, space from human space. He states:
In contrast to human space, in which the verticality of the body and the direction of the horizon are two dominant directions, computer space does not privilege any particular axis. In this way it is similar to the space of El Lissitsky's Prouns and Kazimer Melevich's suprematists compositions – an abstract cosmos, unencumbered by the earth's gravity or the weight of a human body […] William Gibson's term "matrix," which he used in his novels to refer to cyberspace, captures this isotropic quality. (Manovich 2001: 262)
Manovich understands digital space of the matrix as having no particular grounding; unlike human space, which emerges from the horizontality of the actual ground and verticality of the body.
 I discuss John F. Simon Jr.'s Every Icon in more detail in Rhoades (2011).
 In their introduction to the catalogue for the art exhibition [Grid< >Matrix], Eckmann and Koepnick clearly state that the distinction between grids and matrices "form[s] a central dialectic of modernism and postmodernism" (2006: 8). Although it would be interesting to challenge this claim, it steps outside the scope of the present discussion.
 Beyond Mondrian, Koepnick also claims that the grids depicted in paintings of Theo van Doesburg have the ability to exceed their structure (2006: 55). As well, Rosalind Krauss mentions several other artists who use grids in their work that similarly exceed their compositional structures, such as Josef Albers, Ellsworth Kelly, and Sol LeWitt (1985: 22).
 In his address at the Fourth Annual Conference of the Whitehead Research Project titled "Consequences of Panpsychism," Shaviro suggests that rocks and other non-organic entities not only feel but that they also have minds and the ability to think. This concept that all entities are able to think is called panpsychism. Shaviro summarizes this concept stating:
We cannot restrict mentality just to human beings; nor can we restrict it to mammals, or to organisms that have nervous systems, or even to the entire animal kingdom. Rather, we must say that plants, fungi, and unicellular organisms think; and what is more, that nonliving entities, like stars and lumps of granite, think as well. (Shaviro 2010: 1)
So not only does Mondrian's painting have experiences, it also has the ability to think on a very rudimentary level.
 The notion of the relational complex is a reference to the notion of the "diagram" in the writings of Deleuze and Guattari and "significant form" in the writings of Susanne K. Langer. See Deleuze and Guattari 1987, Deleuze 2003, and Langer 1953 and 1957.
 When Mondrian moved to New York in 1940, he began to experiment with the compositional elements in his paintings. This can be seen in his New York series of paintings, produced between 1941 and 1942, in which the perpendicular lines were no longer coloured black. Instead, he used a variety of red, yellow, and blue lines. This use of coloured lines foreshadows the fragmented coloured lines seen in Broadway Boogie Woogie and the painting left on his easel upon his death, the uncompleted Victory Boogie Woogie (1942-1944).
 For a more detailed analysis on incipient action see Manning 2009 and Massumi 2002.
 In replacing the term biosphere with bioscleave, Gins and Arakawa want to emphasize the dynamism and tentativeness they believed was missing in most standard descriptions of the natural environment. In the following they define what they mean by this new term. They state:
All species belonging to bioscleave exist only tentatively (which remains true whatever turns out to be the truth about natural selection, whether it happens randomly or with directionality), with some species, all things being unequal, existing on a far more tentative basis than others. Additionally, bioscleave stays breathable and in the picture only so long as elements take hold of each other in particular ways, only so long as there can be a cleaving of a this to a that and a cleaving of a this off of a that. So that there might be new and different link-ups, fresh points of departure, ever renewed tentative constructing towards a holding in place, a firm and definite taking hold, which gives one sense of the term to cleave, must also readily entail cutting apart, cut-off, relinquishment, the other sense of the term. (Gins and Arakawa 2002: 48)
 The phrase originally stated: "She holds the architecture that holds her" (Gins and Arakawa 2002: 82).
Bergson, Henri. The Creative Mind: An Introduction to Metaphysics. Trans. Mabelle L. Andison. Mineola, NY: Dover Publications, 2007.
Deleuze, Gilles. Bergsonism. Trans. Hugh Tomlinson and Barbara Habberjam. New York: Zone Books, 1988a.
Deleuze, Gilles. Foucault. Trans. Seán Hand. Minneapolis: University of Minnesota Press, 1988b.
Deleuze, Gilles. Francis Bacon: The Logic of Sensation. Trans. Daniel W. Smith. Minneapolis: University of Minnesota Press, 2003.
Deleuze, Gilles and Félix Guattari. Anti-Oedipus: Capitalism and Schizophrenia. Trans. Robert Hurley, Mark Seem, and Helen R. Lane. Minneapolis: University of Minnesota Press, 1983.
Deleuze, Gilles and Félix Guattari. A Thousand Plateaus: Capitalism and Schizophrenia. Trans. Brian Massumi. Minneapolis: University of Minnesota Press, 1987.
Eckmann, Sabine. "[Grid < > Matrix]: Take I." [Grid < > Matrix]. Eds. Sabine Eckmann and Leo Koepnick. St. Louis: Mildred Lane Kemper Art Museum/ Washington University in St. Louis, 2006. 15-39.
Eckmann, Sabine and Leo Koepnick. "Introduction." [Grid < > Matrix]. Eds. Sabine Eckman and Leo Koepnick. St. Louis: Mildred Lane Kemper Art Museum/Washington University in St. Louis, 2006. 8-10.
Gibson, William. Neuromancer. New York: Ace Books, 1984.
Gins, Madeline and Arakawa. Architectural Body. Tuscaloosa, AL: University of Alabama Press, 2002.
James, William. Essays in Radical Empiricism. Mineola, NY: Dover Publications, 2003.
Koepnick, Leo. "[Grid < > Matrix]: Take II." [Grid < > Matrix]. Eds. Sabine Eckman and Leo Koepnick. St. Louis: Mildred Lane Kemper Art Museum; Washington University in St. Louis, 2006. 47-75.
Krauss, Rosalind. The Originality of the Avant-Garde and Other Modernist Myths. Cambridge, MA: MIT Press, 1985.
Langer, Susanne K. Feeling and Form: A Theory of Art Developed from Philosophy in a New Key. New York: Charles Scribner and Sons, 1953.
Langer, Susanne K. Philosophy in a New Key: A Study in the Symbolism of Reason, Rite, and Art. Third Edition. Cambridge, MA: Harvard University Press, 1957.
Lenoir, Timothy. "Haptic Vision: Computation, Media, and Embodiment in Mark Hansen's New Phenomenology." In Mark B. N. Hansen. New Philosophy For New Media. Cambridge, MA: MIT Press, 2004. xiii-xxviii.
Lynn, Greg. Animate Forms. New York: Princeton Architectural Press, 1999.
Manning, Erin. Ephemeral Territories: Representing Nation, Home, and Identity in Canada. Minneapolis: University of Minnesota Press, 2003.
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Rhoades, Troy. "From Representation to Sensation: The Transduction of Images in John
F. Simon Jr.'s Every Icon."
|INFLeXions No. 6
Arakawa + Gins
Edited by Jondi Keane & Trish Glazebrook
Madeline Gins i-viii
Here Where it Lives...Biocleave
Jondi Keane and Trish Glazebrook 1-21
Mapping Reversible Destiny
Trish Glazebrook and Sarah Conrad 22-40
Escaping the Museum
David Kolb 41-71
Jean-Jacques Lecercle 72-79
The Reversible Eschatology of Arakawa and Gins
Russell Hughes 80-102
Chaos, Autopoiesis and/or Leonardo da Vinci/Arakawa
Hideo Kawamoto 103–111
Daddy, Why do Thing have Outlines?: Constructing the Architectural Body
Helene Frichot 112–124
Tentatively Constructing Images: The Dynamism of Piet Mondrian's Paintings
Troy Rhoades 125–153
Evidence: Architectural Body by Accident, Destiny Reversed by Design
Blair Solovy 154-168
Breathing the Walls
James Cunningham 169–188
Technology and the Body Public
Stephen Read 189-213
Bioscleave: Shaping our Biological Niches
Stanley Shostak 214-224
Arakawa and Gins: The Organism-Person-Environment Process
Eugene Gendlin 225-236
An Arakawa and Gins Experimental Teaching Space – A Feasibility Study
Jondi Keane 237–252
KEYNOTES AND CONFERENCE STREAMS:
The Mechanism of Meaning: A Pedagogical Skecthbook
Gordon Bearn 253–269
Wayfinding through Landing Sites and Architectural Bodies: Exploring the Roles of Trajectoriness, Affectivatoriness, and Imaging Along
Reuben Baron 270-285
Trajectory of ARAKAWA Shusaku: from Kan-Oké (Coffin) to the Reversible Destiny Lofts
Fumi Tsukahara 286-297
Tom Conley 298–316
Made/line Gins or Arakawa in
Marie Dominique Garnier 317–339
The Dance of Attention
Erin Manning 340–367
What Counts as Language in a Closely Argued Built-Discourse?
Gregg Lambert 368-380
Constructing Poiesis: Storyboards for an immersive diagramming
Alan Prohm 381–415
Open Wide, Come Inside: Laughter, Composure and Architectural Play
Pia Ednie-Brown 416–427
What Arakawa Did
Don Byrd 428–441
Don Ihde 442-445
For Arakawa, Nine More Lives
Jean-Michel Rabaté 446–448
Approximately Arakawa and Gins
Ken Wark 448-449
A Perspective of the Universe
Erin Manning and Brian Massumi
Axial Lecture on Self-Organisation