The poetry of numbers

 

Art and music

In the early 1970s, Paul Ouwerkerk traveled with his parents to southeastern Nigeria as a boy. His parents worked to rebuild a university that had been destroyed during the Civil War. During this time he became acquainted with the regional polyrhythmic drum music that was played during shamanic rituals. Their complex rhythms had the same effect on the young Ouwerkerk as they are also used in rituals: they put him into a trance. Years later, while studying Western minimal music, Paul Ouwerkerk noticed that some of its structures drew from the same source. Steve Reich, an American composer, drummer and pianist, traveled to Accra in the summer of 1970 because of a book about African drum music, where he took percussion lessons at the University of Ghana and thereby became familiar with polyrhythms.

Even though Paul Ouwerkerk mentions Steve Reich’s influence on his painting, it is not the case that the painter tried to translate sounds into colors. But formal aspects of music are important to the way he constructs his images. In his painterly experiments he is interested in the same patterns and constructions as those used in minimal music, only he approaches them from the visual side. It is fascinating how easily features of polyrhythmic pieces of music can be identified in his pictures. Individual lines or rows of similar figures can be viewed as different voices. Musical polyrhythmics means that these voices have overlapping rhythms or that the rhythmic patterns are combined in a staggered manner. This makes it possible to create a slowly changing but coherent whole. Phases of recognizable repetitions are cleverly shifted by a voice varying the tempo slightly. Sometimes a single tone is enough to trigger a process in which several voices shift against each other and come together again. The more voices, the more complex the grids become, which arise from the diverse rhythmic structures.

If you compare this with Paul Ouwerkerk’s paintings, for example with the painting String Theory, you can also find complicated constellations of different voices. In this case, individual voices among many would be the continuous, cascading bands and the grid of polygonal figures strung together. All of these basic geometric shapes prove to be extremely variable. So much so that ornamental metamorphoses develop in them, small transformations that continue throughout the picture, which lead to the figures or the entire picture surface appearing curved and moving. Although they are neither curved nor moving, the small changes in the shapes, in their dimensions and their proportions are enough to give such an impression. The apparent kinetic quality of the images results from repetition and change. Both parameters form, in music as well as in painting, motifs that are not only fundamental but can also be read metaphorically.

Paul Ouwerkerk also transfers the expanded concept of time of minimal music, as shown in the works of the Dutch composer Simeon ten Holt, into his pictures. Ten Holt’s piece Canto Ostinato, which he worked on from 1976 to 1979, became popular. The duration of the piece is variable. In general, the duration is 80 minutes or more. The temporal variance already announced follows the freedom that the composer gives to those who interpret his pieces. You can repeat individual passages as you wish and thereby make the piece last.

In music, the playing time of a piece determines the perceivable process. You can expand it and change it in other ways. It’s not like that in painting. Once the picture is painted, it remains there. The process of its creation and its perceptibility are separate. When Paul Ouwerkerk introduces temporality as a parameter, he must do so in a different way than in music. Time, he says, is “suspended in the images like air in a balloon.” The first thing he thinks about is the time he spends painting. Since he designs the complex geometric structures largely by hand and then paints them on canvas, he not only uses a classic medium, but also a time-consuming technique. For the painting process, this means a passionate, obsessive, precise, patient dedication on the part of the painter to his work. This experience of time is passed on through the interlocking structures of the images, that is, the formal continuum becomes a temporal one that unfolds as you view it. Time is therefore connected to the space of the image, which must first be structured in order to then orient oneself, perceive the space and measure it.

Like minimal music, Paul Ouwerkerk’s paintings are characterized by repetitive structures. The smallest motivic cells or patterns – these can be geometrically formed, rhythmically placed or color-differentiated units – are strung together and constantly repeated. The progressive change works parallel to the persistent, meditative repetition. These minimal means produce the maximum effect, like a musical ostinato. Nik Bärtsch, a contemporary Swiss composer and musician who is also considered to be a part of minimal music, speaks of modules, i.e. combinable units, when he describes a compositional principle of his music. Modules also form a construction principle of Paul Ouwerker’s pictures. It is clear that in his paintings one geometric figure is associated with the next. Each exists with and because of another. They resemble phrased musical modules that, once found, can always be recombined.

Art and mathematics

Transforming numbers into shapes and, conversely, reducing the shapes to rules that can be described mathematically opens up a connection between two areas: mathematics and poetry, because the transformation and its reversal creates something that goes beyond what was originally given. Paul Ouwerkerk, who worked with Platonic solids in earlier works, refers to these as well as their relatives, the irregular polyhedra, in his pictures. Except that he now deconstructs these bodies for the two-dimensional representation on the screen, so to speak makes them appear as unfolded models.

The gapless and overlap-free coverage of the Euclidean plane by geometric partial surfaces, specifically by several very simple polygons, can lie in the second dimension and lead to the third. The diagonals play an important role here. Visually, they create the appearance of small, unfolded pyramids, and many of these exist next to and among each other. They have form and depth. And they appear as if they were sitting on a curved surface, because the connected, similar elements appear as if they were viewed from different angles. So that the individual surfaces together express the curvature of an entire system.

Representing a three-dimensional space on a two-dimensional image medium is a contradiction. But it can be solved illusionistically. Even if that means making space flat and flatness multidimensional. However, Paul Ouwerkerk’s geometric representations exist somewhere between dimensions 1, 2 and 3. At least. Individual lines usually represent the first dimension, but the way they appear in the pictures they cross other dimensions: two if they are laid out as simple grids of verticals and horizontals and at least three if they span a picture as curved grids.

Many of the grids have a regular structure. This is part of their function as organizing, i.e. systematic, structures. The regular is a statement. The irregular too. The regular is a form of structure. The search for it serves to abstract oneself from the world. This in turn describes the world together with the ordering of the world. The ornament, as a repeating pattern, appears as a rule and the rule as something underlying and the underlying as the premise of connections. But there are also deviating, irregular passages. The deviation is even revealed by the rule. It is a reaction to secondary steps. To the unexpected. Something that cannot be classified. Shows the curvature of space. The vibration of the straight. Creates oscillating manifolds, multistable perceptual phenomena and multidimensional geometric landscapes.

The canvas itself is already a grid of threads and this woven painting surface remains visible.

To design a system of geometric structures, the painter first selects a canvas, looking for ideal formats. For him that would be 80 x 80 cm or 60 x 60 cm, for example. Size ratios in which two different grids can easily be inserted are favorable. This can be seen in a short calculation. From the 60 x 60 cm format, if you subtract a little margin on all sides, a ratio of 56 x 56 cm can be derived. This is so advantageous because 56 is divisible by 7 and 8. That’s why grids of 7 x 7 and 8 x 8 lines are possible on an image of this size. Both, when applied simultaneously and overlapping, result in a phase shift, very similar to that in polyrhythmic music. This means that rhythms that shift relative to one another can also be perceived visually. Namely two grids that are different yet similar, so that the grid structures alternately move away from each other, come closer and even meet in individual parallel lines. This creates effects such as superimposed dimensions, that is, several spatial orders existing at the same time. Because they work with and against each other, they give the impression of a kind of visible acceleration when you look at the images. This is what the matrix of images consists of. It is an arrangement and form of organization on which everything else is based. Sometimes it remains visible, sometimes it is hidden, but can still be seen in a different way, which will be explained shortly.

Space and play

First of all, the intersection points of the grids create opportunities to connect them linearly. New connections result in new, separated areas that Paul Ouwerkerk fills with color. He fills them with intuitively mixed shades. Through equally intuitively chosen levels of transparency, he isolates superimposed, progressive patterns. But some of the areas initially outlined are left out. Which helps to emphasize the constructedness of the composition. Paul Ouwerkerk calls it “leaving a hole through which you can see inside the machine”. Once you have looked inside, you may not fully understand the principle on which the machine works, but you know that there is a process going on inside. Even if some parts of the picture are painted over with white, thick enough that the white paint appears as a covering material, this feeling remains.

Recurring colors include yellow and brown, orange and blue. Paul Ouwerkerk paints from dark to light, from coarse to fine, from thick to thin brushes. He uses acrylic ink for thin lines and acrylic paint for the areas. Several layers of acrylic paint applied one on top of the other create the impression of opaque depth. This impression is very strong when, for example, there are four layers of transparent white, painted with a thin brush in four directions, that is: each layer was painted in a different direction. The individual areas are developed from layered components that determine their character and their relationship to the surrounding colored areas. Its edges are both: a connection point and a clear border. In addition to brushes, the painter also uses tapes that he sticks along pre-drawn lines in order to precisely separate the individual colors. Once the tape is removed, the colored surface has an edge as clear as a cut. But between the sharply defined edges you can see the signs of hand-painting. Semantically opposite, yet formally harmonious, the precisely taped-off and the painterly action that remains visible coexist. So something is combined that, on the one hand, negates the individual form through the machine-supported straightness and, on the other hand, emphasizes the human, direction-giving hand of the painter. He says: “It’s like playing polyrhythmic music with classical instruments and yet sometimes it sounds like electronic music.”

Paul Ouwerkerk often uses a square format. To him, more than other formats, it seems to give the impression that an image could go beyond the limited canvas, even continue indefinitely. It would then take up a large part of the perceived reality, which, conversely, creates the idea that reality, or at least part of it, consists of patterns and structures as seen in the image. Combined from simple building blocks, the respective arrangement results in an incredible number of variations. On a semantic level, the image, created from individual geometric parts, refers to freedom and found similarities and views of the world. This opens it up to other, larger concepts such as scientific understandings of nature, physics, the structure of crystals or particle movements.

In addition to the format, the image size is an important factor. Paul Ouwerkerk started with relatively small formats between 40 x 40cm and 80 x 80cm. The images now reach sizes of almost 2 x 2m and larger ones are planned. The large image physically evokes a different experience than a small one. But the immersive experience does not only depend on the size relationship between the image and the viewer. It also depends on the distance from which you look at the images. The painter conceptualizes the different perceptibility analogous to the film language with its different shot sizes. From a distance the image appears as a multi-colored object and outline. From a medium distance it appears as a complex structure. And the paint application can be seen close up.

The painter shapes the variations of his theme as possibilities within narrow rules of the game. The format and size of the canvas create a closed space for which number-based rules, limited shapes, few colors are selected. This coolly distant opening becomes increasingly charged with emotion as it expands to include random connections, intuitively chosen colors and surprising contradictions between spatial and color perspectives. The reality of the finished picture consists of a sum of eventualities that are tried out in a playful way.

The rules set at the beginning result in an almost chaotic spread of structures. The title Modular Mess takes up this phenomenon because it is a play on words about the contradiction between order and chaos. The painter confides in this. He starts with a strict concept and then lets the image take over, so to speak. One could almost say that the picture paints itself within the parameters set by the painter.

Paul Ouwerkerk plays with the image and the image with him. They react to each other. Quitting eventually becomes an important decision. Essentially it is the only or final control the painter has. Paul Ouwerkerk is not an artist who tells other people what to think. When he questions the perception of reality and the shape of the material world, it is to open doors to other perspectives, to keep transitions open and to enable a kind of trance like the one he experienced as a child.

Heike Endter