marcel duchamp

over duchamp en t schilderij hier afgebeeld: (bron: david shambroom)

Paintings are flat surfaces. Spatial illusions in paintings are derived from monocular, not binocular, vision. Leonardo was fascinated by the transformation from physiological optics to the artifice of painting, so he studied the behavior of a pair of human eyes. When an object to be looked at is placed close to the face, the paths of vision of the two eyes cross. Duchamp took Leonardo’s X-shaped diagram of cross-eyed vision, along with the wording of his title, directly from this passage in the Treatise. In a posthumously-published sketch for To Be Looked At... he even used Leonardo’s letters "A" and "B" to identify the eyes, or viewing points, represented by circles at the extremities of the cross. But he then placed the configuration on a receding plane, in perspective, and turned it into a pair of giant scissors, a device soon to appear in The Large Glass. Now the cross-eyed observer, it would seem, could cut his way through the visual field by flexing his eyeballs together and apart to make the scissors work. In the small glass To Be Looked At... most of this peculiar tool lies outside the rectangle of the picture, so only its tips can be seen.

The squat, transparent pyramid hovering above the scissors would appear to transport the setting of this one-act farce for eyeballs to ancient Egypt. But it does not. Instead we are right back in the arena of the optics of Leonardo, who wrote frequently and vehemently about the "pyramid of vision." According to Leonardo:

The body of the atmosphere is full of infinite pyramids composed of radiating straight lines (or rays of light), which are produced from the bodies of light and shade, existing in the air; and the further they are from the object which produces them the more acute they become, and although in their distribution they intersect and cross they never mingle together, but pass through all the surrounding air, independently diverging, spreading, and diffused.(2)

If you look into a mirror and close one eye, you will have formed a visual pyramid pointing at your open eye, whose base is the shape of your face. Leonardo displays remarkable insight into the mechanism of light as it reflects off our surroundings. The receiving human eye always forms the apex of a complex geometric solid, whose base is delineated by the outline of an object in view, and whose sides are formed by the rays of light racing towards the viewpoint from its edges. Leonardo’s use of the word "pyramid," however, is confusing, because in common usage a pyramid sits on the earth, on a perfectly square base, its axis pointing up to the sky. Duchamp’s Egyptian pyramid in To Be Looked At... is a deliberate and mocking distortion of Leonardo’s idea as it occurs, in the Treatise on Painting, at the center of his theory of optics.
In 1918, from the isolation of Buenos Aires, where he made To Be Looked At..., Duchamp had good reason to poke fun at the visual pyramid. He was probably sick to death of it. His brother, the painter Jacques Villon, was, in contrast, obsessed. Villon believed that Leonardo’s pyramid could provide the unifying theory in his enterprise to make Cubism more than just a passing fad, to transform it into an enduring, classical art form. In 1915, the last time the two were able to meet until after the Great War, Villon would talk of nothing else. All this had started in 1911, when the brothers and their Cubist friends became fascinated by Leonardo’s optical formulations: "Every body in light and shade fills the surrounding air with infinite images of itself; and these, by infinite pyramids diffused in the air, represent the body throughout space and on every side."(3)

Was Leonardo da Vinci a Cubist himself? He was, it is true, presenting a vision of the space around objects filled with latent images. The eye at any given location could only perceive one image at a time. Visual pyramids "intersect and cross [but] they never mingle together..." But could a painter, a Cubist painter, overcome the laws of light and vision? Could his imagination and intuition capture these half-formed, transparent images, as evoked by Leonardo, before they are condensed into a point, as they overlap, interpenetrate, and jostle for predominance? Jacques Villon struggled to embed this concept of latent visual pyramids into his paintings for the rest of his life.

Marcel Duchamp discussed these ideas with his brother in the early days of Cubism. Then he chose a different path, a directly-perceptual method of creating transparency and overlapping planes in the visual field. He preferred the method that children use. He crossed his eyes.