Horizontal Lines and Vertical Lines in Science and Art

Leonardo, Vol. 16, No. 4, p. 310, 1983. Printed in Great Britain. 0024-094X/83 $3.00 + 0.00 Pergamon Press Ltd. HORIZONTAL LINES AND VERTICAL LINES IN SCIENCE AND ART Giorgio Careri* In the scientific context, horizontal and vertical lines form a grid; they create Cartesian space, an effective way to organize an area. Confined within this rigid lattice of three rectangular dimensions, such space is homogeneous and isotropic; its dimensions interchangeable. Within this space, science endeavors to identify the general laws that govern the movement of stars as well as atoms. Within this grid marked by co-ordinate signposts, every point is the same as any other point. Every object is held in precise numerical relationships with every other object; the space itself becomes an object, independent of the observer's eye. Depth is no more than the third dimension, and on the plane, a line is called horizontal or vertical only by definition. There is no reason to wonder what is horizontal and what is vertical when one is looking through a microscope or a telescope. Even in science, horizontals and verticals have meaning only within the limited space surrounding the observer. However, as Merleau-Ponty rightly says, "Descartes was wrong to liberate this space. He erred in constructing it as a positive being, not subject to any point ofview, stripped of any latency or profundity, with no true depth of its own" [1]. And indeed, we are aware that the schematic nature ofthe perspectiva artificialis, which is implicit in Cartesian space, differs from the authenticity of the perspectiva natura/is, which gives an intrinsic sense of depth to our world. Similarly for the plane, it seems to us that the horizontal line is substantially different from the vertical line. Of course we can find a simple reason for all ofthis in our learning process having a sensorial basis. The development of our brain depends on our visual environment, and the visual cortex adapts to the visual experience as the individual matures. In the visual world that surrounds us vertical and horizontal lines gradually become associated with very different sensations, such as the fatigue of climbing the vertical, and free movement along the horizontal surface of the earth. This difference in visual order is a good example of the old conflict that still exists between science and common sense based on everyday perception: as I am going to show, when taken to its extreme, it becomes the conflict between science and the visual arts. In Cartesian space, we can take measurements, and using the numbers which express these measurements, we can communicate simply and objectively; we can even verify this operation by repeating it at different times with different observers. In sensory space this is not always possible; every man is alone in his space, which he sees as quite rich but also as complex and changing. Most experiences are unique and unrepeatable. Thus on the one hand a scientific fact is selfcontained in its schematic simplicity, while on the other hand the whole uncorrelated series of individual experiences accumulates, and its meaning is often ambiguous. Stated in these terms, science and art seem to have such divergent attitudes towards the surrounding world that we find difficulty integrating them within the human personality. *Physicist, Dipartimento di Fisica, Universita di Roma, Rome00185, Italy. 310 In order to overcome this conflict, we can ask ourselves whether it is possible to identify a middle ground between the homogeneity of the Cartesian space and the complexity of sensory space, an intermediate zone characterized by the reproducibility and objectivity of the sensations, so that these can become the raw material for further mental operations. We know this is certainly possible, because our mind is able to give conceptual order not only to numerical data but also to signs with symbolic value, which are communicated and thus transmitted even among generations. At this point, let us consider again the case of horizontal and vertical lines when conceived as symbols. The simplest sign is the line, and one ofthe first distinctions of the line on a plane is between being horizontal or being vertical. Each of these orientations is associated with a symbolic meaning...