Planes, Projections and Transformations
Painting provides us with opportunities to see the historical development of human perspectives regarding the concept of space symbolically and scientifically. Throughout time, the use of devices to render complex figural arrangements have contributed to the communication of ideologies concerning our relationships to the world. Armbrogio Lorenzetti’s use of the vanishing point in his Annunciation of the Pinacotheque of Sienna from 1344 illustrates an infinite distant point at which all orthogonal lines of the floor meet. Later on, Jan van Eyck used a systematic arrangement of coordinates to represent space reaching forward to the surface plane of the painted canvas. As for projective geometry, the first correct use of one-point perspective is attributed to a painting by Mansolino de Panicale’s, St. Peter Healing a Cripple and the Raising of Tabitha, 1426-27. This technique was introduced in the Renaissance by architect Fillipo Bruneschelli. The projective diagram demonstrates a geometrical method of perspective, presenting a linear mathematics in planar projections that artists could use to depict distance and proportions in painting, and solid forms as they would appear in perspective. With one point-perspective, an artist could organize a universe around a vanishing point located arbitrarily in a distance. Before projective space enters the picture, artists of the late Middle Ages, such as Giotto di Bondonne, implied spatial relations by overlapping figures upon a two-dimensional plane. According to art historian Erwin Panofsky, the aggregate space of Giotto and other artists would, by the Renaissance, come to be superseded by a true central perspective extending infinitely into space. This, he says, demonstrates an abandonment of the idea of a cosmos “with the middle of the earth as its absolute center and with the outermost celestial sphere as its absolute limit.”[2] As a result, the idea that actual infinity exists beyond and outside the physical world became conceivable.
The first shadow tracing was probably not intended to be a study in geometry. Nevertheless, this gesture did represent a mathematical projection. A casted shadow is an example of a type of parallel projection (orthography). It is a transformation geometry, concerned not with elastic transformations, but with straight lines and length. With it, an artist may use converging lines to make enlargements and reductions in the scale of an image by changing the relationships between the distance of an object, a source of light, and the surface onto which the object’s shadow will be traced. In representational work, shadows help a viewer enter an environment. They can direct the eye towards a light source, such as the sun in a landscape, or even light felt to exist somewhere outside the depicted scene. These mappings of light sources are useful in one-point perspective paintings. In Caravaggio, for example, Cartesian space, composed of linear elements that intersect only at right angles, merges the painting’s space with the viewer’s. This illusion of reality made possible the exploration of theatricality by intensifying the contrasts of light and dark (called chiaroscuro) and carefully exaggerating the perspective of the viewer. Depicting the light source in the painting as if it were coming from the space of the viewer, Caravaggio was able to bring viewers into the space, inviting them to become more intimately engaged with the depicted events to which they become an immediate witness.
I paint in a space somewhere between shadow projection and Cartesian perspective, or at least I think that’s a good way to characterize it. This mapping was first introduced in my practice in 2009, after I had come across the word affine[1] in Felix Guattari and Gilles Deleuze’s text Anti-Oedipus: Capitalism and Schizophrenia. They wrote that, in barbaric societies, a woman, mother, could become an affine to her offspring. As “affine,” she was a place wherein a child could position him or herself in the matrix of the cosmos.[1] Locating this geometric space within the body was, as I saw it, a way to place the universe, infinity, back into the world. It is positioned as the meeting of the earth with that which is beyond. Mathematically speaking, I was imagining this to be a site—a structure set in a topological space which makes those categories in it act as open sets of that space. In this site, conditions are loose and flexible, defined by properties of connectedness or continuity. Through intensive visual studies of this geometry I came to see how this matrix would serve as a network structure through which I could explore abstracted figures interacting with elements of their environment—in painting, the environment is mostly represented as color, geometric objects, and light. Abstracting a body into these movements was, I thought, a way for me to immerse a figure in its environment and free it from a singular projective perspective through subversive action.
[1] Rosenbloom, Robert, “The Origin of Painting; A Problem in the Iconography of Romantic Classicism,” The Art Bulletin, Volume 39, Number 4 (Dec., 1957), 271.
[2] Panofsky, Erwin, “Perspective as Symbolic Form,” trans. Christopher S. Wood (New York: Urzone, 1991), 65.
[3] Gilles Delueze and Felix Guattari, “…Levi Strauss’s kinship atom—with its four relationships; brother-sister, husband-wife, father-son, maternal uncle-sister’s son—presents itself as a readymade whole from which the mother as such is strangely excluded, although, depending on the circumstances, she can be more or less a kinswoman or more or less an affine in relation to her children. Now this is indeed where the myth takes root, the myth that does not express but conditions. As Griaule relates it, the Yourougou, breaking into the piece of placenta he has stolen, is like the brother of his mother, with whom he is united by the fact: “This individual went away into the distance carrying with him a part of the nourishing placenta, which is to say a part of his own mother. He saw this organ as his own and as forming a part of his own person, in such a way that he identified himself with the one who gave birth to him. She was the matrix of the world, and he considered himself to be placed on the same plane as she from the viewpoint of the generations…” Anti-Oedipus: Capitalism and Schizophrenia, trans. Robert Hurley, Mark Seem, Helen R. Lane, (Minneapolis: University of Minnesota Press, 1983), 157.
[3] Gilles Delueze and Felix Guattari, “…Levi Strauss’s kinship atom—with its four relationships; brother-sister, husband-wife, father-son, maternal uncle-sister’s son—presents itself as a readymade whole from which the mother as such is strangely excluded, although, depending on the circumstances, she can be more or less a kinswoman or more or less an affine in relation to her children. Now this is indeed where the myth takes root, the myth that does not express but conditions. As Griaule relates it, the Yourougou, breaking into the piece of placenta he has stolen, is like the brother of his mother, with whom he is united by the fact: “This individual went away into the distance carrying with him a part of the nourishing placenta, which is to say a part of his own mother. He saw this organ as his own and as forming a part of his own person, in such a way that he identified himself with the one who gave birth to him. She was the matrix of the world, and he considered himself to be placed on the same plane as she from the viewpoint of the generations…” Anti-Oedipus: Capitalism and Schizophrenia, trans. Robert Hurley, Mark Seem, Helen R. Lane, (Minneapolis: University of Minnesota Press, 1983), 157.