In my last post I promised to upload my paper on Piet Mondrian’s paintings that I gave at the first Conference on the Image. You will find it below.
I also presented this paper at the AG3: The Third International Arakawa and Gins: Architecture and Philosophy Conference in February 2010. All the conference proceedings were published online and my paper can be found as a PDF here.
Tentatively Constructing and Holding Images: Mondrian, Relations, and Critical Holders
Relations must come first.
– Piet Mondrian, Letter to László Moholy-Nagy (June 6, 1939)
Grids and Matrices
Piet Mondrian’s Composition No. 12 with Blue (1936-42)  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 a grid-like 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 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.
For some people the sight of grids can immediately conjure up notions of fixity,
timelessness, and imposed order. Grids can evoke images that present space, time, and
movement statically. According to Lutz Koepnick, girds are “not a product of the
unpredictable temporality of the viewer’s physical movement and sensory perception but
a prearranged logic of compilation and construction, a mechanism seemingly engineering
uniformity, universality and unwavering stability” (Koepnick, L., 2006, p. 53-4). 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 order upon all that is contained within it.ii Koepnick,
along with Sabine Eckmann, suggest that the grids found in the modernist painting of the
early twentieth century, like in Mondrian’s work, particularly display this inclination
towards immutability (Eckmann, S. and Koepnick, L., 2006, p. 9).
With the rise of digital imaging in the late twentieth century, Eckmann and
Koepnick state that the modernist grids were freed from their methodical immutability
and were reworked into what they call “matrices”. 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” (Eckmann, S., 2006, p. 16). In other words,
although grids form the underlying structure for matrices, matrices are not grids because
the elements held by these grids change, instigating movement in images. Grids can be
found both in modernist painting and in digital images. However, the grids found in
digital images are transformed into matrices because the changes that occur among
particular compositional elements, such as the pixels and the binary code, create moving
images. Consequently, if we understand Eckmann, Composition No. 12 with Blue can
only be a gridded image, as opposed to an image containing matrices, because the
elements in this painting – the black lines, the white background, and the blue square – do not move or change.
Another important difference between grids and matrices is that grids are visible
while matrices are not. The invisibility of matrices, according to Eckmann, gives images
the ability to produce themselves independently from the grid structure: “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” (Eckmann, S., 2006, p. 17). When compared to gridded
images, the ability for matrices to produce images that are different from their underlying grid structure can easily be seen. Eckmann contends that in modernist works, like Mondrian’s painting, grids visibly constitute the image, whereas in digital video, matrices invisibly generate the image (Eckmann, S., 2006, p. 16). Thus, on the one hand, when we, the viewers, look at Mondrian’s painting with its black perpendicular lines dividing the white background into quadrilaterals of varying sizes and shapes, the image is the grid. On the other hand, it is rare that we see the gridded structure of matrices. For example, when watching digital video we seldom see the pixels (except when the image is heavily compressed) and we never see the underlying binary code.
Shared Relational Experiences
When looking at Composition No. 12 with Blue more closely, it appears to be a static grid, with the perpendicular lines placing a geometric order onto the white background, thus removing the potential for any movement to occur. The web of intersecting black lines grabs our attention and stops us in our tracks. As Mondrian’s web holds us, movement begins to emerge. It is not a free-flowing continuous movement but rather one that feels jittery, causing our eyes to jump all over the canvas. Flashes of whitish-grey begin to appear at the intersections of the black lines. The more our eyes jump from one intersection to another, the more the flickering appears, inciting our eyes to continue jumping. If we try to hold our gaze on one intersection, the fluttering of whitish-grey appears to diminish momentarily but then the flickering resumes in the other surrounding intersections, inciting our eyes to move again. What we find is that there is a restless rhythm in Mondrian’s painting that can be felt emerging from the flickering intersections.
What is important here is that Composition No. 12 with Blue momentarily holds
our visual attention long enough to generate a visually resonant image: an image that
emerges from the jittery rhythm of the flickering intersections. The painting does not
produce a static image but rather one that generates what Erin Manning would describe as “a felt rhythm that invents itself in the watching” (Manning, E., 2009, p. 188). The image that emerges from Composition No. 12 with Blue, as a frenetically felt rhythm, only happens in the moment that it is looked at. Neither we as its viewers, nor the painting, produces this image alone. This is because, as Mondrian states: “Everything is expressed through relationships” (Mondrian, P., 1986/1993a, p. 86; original emphasis).
Understanding images in this light means that no one thing can produce them. Instead,
images emerge in the relations between two or more entities as a shared experience.
It should be noted that humans are not the only entities that have experiences.
Mondrian’s painting has experiences. Even rocks have experiences. According to Steven
Shaviro: “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, S., 2009, p. 12-13). So, like a rock, Mondrian’s painting can
experience us because our presence affects it at some rudimentary level, even if it is some
minor acceleration of its eventual decomposition.
The relations between Composition No. 12 with Blue and the viewers, as a shared
experience, are not the only set of relations from which an image emerges. This is
because the painting, as Mondrian states, “must be viewed as a duality or multiplicity – as a complex” (Mondrian, P., 1986/1993a, p. 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. Out of this relational complex between the compositional elements, images begin forming (Mondrian, P., 1986/1993b, p. 317). As the relational complex comes together, it does not produce a fully formed image, but rather initiates a process out of which images emerge. Specifically regarding
Composition No. 12 with Blue, this means that the compositional elements in the painting – the black perpendicular lines, the planes of white, and the blue square – come together as a relational complex and through the development of this complex images start appearing.
The coming together of the compositional elements as a relational complex is not
a self-initiating process. Rather, this process begins the moment that the viewers start
looking at Composition No. 12 with Blue. The relational complex among the
compositional elements comes together as the experience shared between Mondrian’s
painting and the viewers begins, from which the flickering intersections and the jittery
rhythm emerge. Conversely, the shared experience only starts when the relational
complex comes together. Neither the relational complex nor the shared experience pre-
exists the other; rather, they mutually produce each other the moment the viewer begins
looking at the painting. As the relational complex and the shared experience create each
other, they conjunctively generate the flickers and frenetic rhythm from which the image
in Composition No. 12 with Blue emerges.
The image that emerges in Composition No. 12 with Blue, from a shared
experience and a relational complex that mutually produce each other, is more complex
than Eckmann and Koepnick’s grids and matrices. This is because Eckmann and
Koepnick’s understanding of images assumes that our vision and the artwork have a
passive relationship. According to Brian Massumi: “If vision is stable, then to make art
dynamic you have to add movement” (Massumi, B., 2007, p. 72). In this light, on the one
hand, grids are immutable because both artwork and our vision are believed to be stable;
on the other hand, matrices are full of motion because movement is added to
compositional elements that are contained by its underlying grid structure. Thus,
Mondrian’s painting cannot be considered a grid because movement takes place in the
form of the jittery rhythm emerging from the flickering intersections of the black
perpendicular lines. It also cannot be classified as a matrix because the movement that
takes place in the painting does not result from the addition of motion that may cause
changes to the compositional elements. Rather, the movement in Mondrian’s painting
arises from relations that are co-generated between the compositional elements and the
shared experience that the viewers have with the painting.
Tentatively Constructing and Holding Images
Instead of attempting to classify images as either being produced by grids or by
matrices, we should instead consider images – digital, modernist or otherwise – to be
what Madeline Gins and Arakawa call “a tentative constructing towards a holding into
place” (Gins, M. and Arakawa, 2002, p. 23, 48, 69; original emphasis). This is
particularly the case for those images emerging from Composition No. 12 with Blue
because, according to Gins and Arakawa: “Everything is tentative” (Gins, M. and
Arakawa, 2002, p. 49). However, we should be mindful of the nuanced manner in which
Gins and Arakawa use the term “tentative”, which should be understood in both its
provisional and hesitant sense (Gins, M. and Arakawa, 2002, p. 82). Specifically, it
should be understood provisionally as an arrangement that lacks fixity and hesitantly as a
momentary pause. This means that in Composition No. 12 with Blue, the images that
emerge as “a tentative constructing towards a holding into place” are provisionally
“constructed” but also are hesitantly “held.”
The shared experience between Mondrian’s painting and its viewers is a
provisionally tentative one because at any moment this experience, out of which images
emerge, can change or even vanish. When Gins and Arakawa discuss the tentativeness of
the biosphere, they state that if any single element fails to “hold its own,” then this could
potentially create disastrous effects for the entire biosphere (Gins, M. and Arakawa, 2002 p. 48). Although the consequences are not as cataclysmic when images fail to emerge or when a shared viewer-artwork experience does not take hold, emerging images and shared experiences are nonetheless tentative in this provisional way. For example, if we walk away from Composition No. 12 with Blue, then the shared experience, the developing relations and the incipient images disappear. Another possible situation that would be more severe with respect to the emergence of images is for the viewer to walk by and ignore Mondrian’s painting. This is because there would be no shared experience or development of relations and thus there would not be any emerging images. This is what makes the “constructing” images, relations, and experiences so provisionally tentative. Even a minor change in the experience shared between Composition No. 12 with Blue and its viewers can affect the coming together of relations and alter the incipiency of images.
The key is to hold these provisionally tentative, shared experiences long enough
to enable relations to gather and images to emerge. In order for this holding to happen a
hesitation must occur. 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, M. and Arakawa, 2002, p. 82). Recall that when we, the viewers, first look at Composition No. 12 with Blue the web of perpendicular black lines holds our attention for a brief moment just before the whitish-grey flickers begin emerging from the intersections. The moment we begin looking at the painting, the black perpendicular lines start composing an image, causing us to hesitate. It is important to understand that the composing black lines are not an image. Instead, we should view this composing action as the initial coming together of the relational complex. When we look at Mondrian’s painting, the black lines begin composing, causing us to hesitate. In this hesitant moment, the relational complex continues coming together and the image starts emerging. The initial configuration that we begin to see arising from the composing black lines is the critical holder for Composition No. 12 with Blue.
In that hesitant moment, as the critical holder arises from the composing black
lines, several actions occur simultaneously, enabling an image to emerge. First, the
viewers’ attention is held. Second, the shared experience is activated between
Mondrian’s painting and the viewers. Third, the relational complex continues coming
together after we see the initial configuration of the black lines. From these three
simultaneously occurring actions the intersections begin to flicker and the jittery rhythm
begins activating. From the jittery rhythm, images emerge, holding our attention even longer. In that brief pause between seeing only black lines on a white background and seeing the jittery rhythm that incites our eyes to move about the canvas, the critical
holder, to paraphrase Gins and Arakawa, enables us to hold the images that hold us (Gins, M. and Arakawa, 2002, p. 82). The perpendicular lines in Composition No. 12 with Blue, emerging as the critical holder, enable the viewers, to hesitantly “construct” images,
while holding the shared experience between the painting and us in place and, thus,
enable images to emerge.
Evoking the Sensation of Life
As we look at Composition No. 12 with Blue, the jittery rhythm of the whitish-
grey flickers that we experience could be dismissed as merely an afterimage effect that,
according to Evan Thompson, has no bearing on our perception. He states: “In
perception, one is aware of things as stable and distinct entities in relation to an
indeterminate background” (Thompson, E., 1995, p. 247). Afterimages have no place in
this understanding of perception because they are not “stable and distinct” entities. Thus, in order to look at Mondrian’s painting as an image, we would have to ignore the flickers and the jittery rhythms and view the compositional elements in the work and the painting itself as a set of stable entities. This creates a disparity, Gins and Arakawa believe, “between the world as it happens… and the world, reduced and distorted, made to appear as other than what it happens as” (Gins, M. and Arakawa, 2002, p. 51). If we deny the relations that arise from the shared experience between Composition No. 12 with Blue and we the viewers, rebuff the critical holder’s hesitation that grasps our attention, and disregard the frenetic emergence of the whitish-grey flickers, we will not see images as “a tentative constructing towards a holding into place.” Instead, we will see Mondrian’s painting as a merely a grid. Ignoring the fact that movement does occur in this work, through our shared experience with it, would be going against one of Mondrian’s most important beliefs, “that reality is in constant movement” (Mondrian, P., 1986/1993c, p. 351; original emphasis). Mondrian held movement in such high regard because, as he states, “it evokes the sensation of life” (Mondrian, P., 1986/1993c, p. 351).
 An image of this painting can be found on the National Gallery of Canada’s website: http://cybermuse.gallery.ca/cybermuse/search/artwork_e.jsp?mkey=7924
 For a more detailed analysis on Cartesian space in relation to static form, see (Lynn, G., 1999) and (Manning, E., 2009, p. 163-168).
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