Conceptos para la construcción de un modelo dinámico

The representations of space in Byzantine and Medieval art as a reversed variant of perspective had several different sources; the terms “inverted” or “reversed perspective” were used by two art historians at the turn of the nineteenth century as expressions to name these deviances from perspective as based on central projection through a plane. Byzantine iconographic scholar Dimitry V. Ainalov (1900) used “reversed perspective” as a name for a stylistic trait con- necting Russian Orthodox icon painting with the Early Christian tradition, and understood it as resulting from mistakes caused by the artists’ inability to make correct foreshortening.26

14.6

Summary of Different Perspectival or Oblique Views

A German art historian, Oskar Konstantin Wulff, suggested that, in the inverted perspective (der umgekehrte perspective), the image is oriented toward the viewer who is in essence inside the picture itself.27 _{For the inner viewer the}

representation then follows the laws of normal perspective. For Wulff, a psy- chological cause is the reason for the occurrence of reversed perspective. As cause, he argued for the notion of “empathy”, as described by Theodor Lipps in 1903.28 _{Empathy is not a result of reflection, but an aesthetic primitive reac-}

tion before the understanding of unspecified presence as a thing.

In a remarkable essay, dedicated specifically to the inverse perspective, and in his lectures at the VKhUTEMAS (Russian acronym for Higher Art and Technical Studios) was the Russian state art and technical school founded in 1920, Florensky points out that through the inverse perspective we are look- ing within the imaginal sphere of human cognition.29 _{In the essay, Florensky is}

attempting a demonstration of the existence of the inverse perspective through mistakes that can be seen in many of the perspectives before the affirmation of the so called costruzione legittima and in a few others done after the legitimiza- tion of the monocular view that took place during the Italian Renaissance.

Florensky, to demonstrate how the perspective of the costruzione legit- tima fails to recognize interior light as a necessary component of representation, analyzes the sequence of four famous incisions from Albrecht Dürer’s Painter’s Manual showing the few mechanical aids to be used for drawing a costruzione legittima.30 _{The first illustration of the sequence shows a bedroom where an}

artist is making a perspective portrait—probably a legitimate likeness—using a portable perspective machine. A table on which is vertically set a frame contain- ing a glass plane or a sheet of almost transparent oily paper constitutes the core

14.7

162 Cosmopoiesis and World-Making

of this portable machine. In front of it, an adjustable contrivance holds the drafts- man by the nose in the required position for a fix point of view. This machine is an emblematic rendition of the rules governing the costruzione legittima.

The second illustration has often been misread and misapplied by ver- bose-gazers in love with a contraption called the “lucinda”—a square frame within which a grid of strings divides the space in 36 squares. The illustration in question shows a working table upon which lays a female model, while the draftsman is viewing her through a lucinda and he is getting ready to draw her

14.8

on a piece of paper already traced with the same grid of the lucinda. The eye of the draftsman is trained on the wanted spot with the help of a miniature obelisk. In this apparatus there is already a quadratura an indication in nuce of a coordinate system that will eliminate sight from the site of perspective drawing.

The third illustration shows a bedroom—quite a dim space—where an artist is reproducing an urn on a transparent oily sheet held in a frame that stands between the artist and the urn. He looks at the urn through the oiled paper using an optical pipe attached to a ring on the wall behind him. The art- ist’s eye is still part of the process, and moves deliberately following the tracing of lines by looking inside the narrow pipe, but the eye is not the hub of the construction lines anymore. The real center of this perspective is located in the ring secured on the wall to which the optical pipe is attached.

The fourth illustration, the most specific of the series, shows a very nar- row room with a pair of artists and a pair of windows. One window is open and the other is closed; one artist is standing and the other is sitting. At the center is a huge working table holding a lute and a special kind of perspectival apparatus made by combining a lucinda with movable orthogonal arms and with a turning frame holding a drafting sheet. The perspective delineating string is connected with a ring in the wall and it is kept in tension by a counterweight, meanwhile a wand, held and maneuvered by the standing artist to delineate the contours of the lute, is connected to the other end of the string. Using the coordinated device of the lucinda, the sitting artist records one by one the “digital points” necessary for the construction of the image. The points are then pricked on a sheet of heavy paper stretched on a movable panel. No human or divine vision is needed in this perspectival construction. The two fellows could be as well two visually impaired artists making a Braille rendition of the lute. Synthetic geometry has been replaced with analytic geometry. With their machine they can reproduce any three-dimensional object in a jiffy and probably with fewer distractions than visually able artists executing the same task.

A powerful commentary on Dürer’s drawing machines is also a canvas done by a Sicilian architect observing a surrealist practice in the arts of paint- ing and stage design. Entitled “Colloquium (Conversazione)”, Fabrizio Clerici’s oil painting shows all the drawing machines presented by Dürer sublimated in a super-drawing machine located within a perspective box. The surrealistic characters presented together with the super-drawing machine are a mask and an eyeball. The eyeball represents the sublimated eye of the draftsman and the mask is the object to be represented. Beyond the mask is placed a mirror that reveals the inverse side of the mask, demonstrating the condition of the ren- dering of faces with inverted perspective in Byzantine and Eastern Icons, which look at the backs of masks. The presence of the mirror delegitimizes the view of perspective and projects the potentiality of this super-drawing machine as a key to opening the gate of the realm of drawings that are real within a different tangible materiality.

164 Cosmopoiesis and World-Making

e x e r c i s e # 1 0

Icons

In some Byzantine and Russian icons one finds both nearby objects and build- ings in the background depicted in very accentuated inverted perspective. This practice and other ways of providing visual effects are important in these icons, for they have significance in metaphysical terms. However, many art historians in the eighteenth, nineteenth and twentieth centuries maintained that there is no significant rationale beyond these inverted perspectives. For these art histo- rians, painters, especially during the medieval times, were simply unable to rep- resent on picture planes “reasonable” representation of the visually observed objects, because they didn’t yet know or understand how to apply the optical laws of visual perception. These laws are necessary to produce a perfect image that is almost identical to what we could see through the frame of a window. In many pseudo-perspectives—such as herringbone, multifocal and axial—visual irregularity and absurdities were skillfully concealed by the painters. The paint- ers who did inverted perspectives did not even make attempts to avoid or to conceal the evident geometric inconsistencies or absurdities.

Contradictory visual situations often arise, although we are not usually consciously aware that this is happening. The viewing of a three-dimensional rendering of a building is one of the most obvious examples. While admiring a rendering of a building, the pattern of binocular disparities specifies that you are looking at a flat two-dimensional surface. However, the shading, highlights, texture gradients, and perspective variations are more parsimoniously consis- tent with a three-dimensional interpretation.

It is not possible to translate the perceived shapes of a building into a two-dimensional surface of a drawing without distorting some of them. Those

14.9

Plan and Elevation Derived from an Inverted Perspective

who draw, no doubt, understood this insoluble challenge a long time ago; the result was that in different cultures dissimilar rules were adopted for the depic- tion of objects by deciding which distortions should be accepted, avoided or minimized. This may account partially for the fact that many architects exercise the “right to distort” selectively in their drawings and sketches what they see or conceive. Distortion is the alteration of the original shape (or other charac- teristic) of an object and the distortion reverses the flow of architectural space, creating a disorienting, anti-naturalistic sense of space.

The aim of this exercise is to draw the perspective of a building, build- ing element or the interior of a room first using an inverted perspective done as watercolor and with the sky or space around (ceiling in the case of the room) rendered with silver mirror-like-paint and then to draw a plan, section and elevation of it in CAD as if the inverted perspective is a tradition- ally correct representation of the building or the building element.

For instance, if you have drawn a surface as a possible parallelogram in the inverted perspective, the translation in the orthogonal representation should be a skewed trapezoidal surface. Lines that in the inverted perspec- tive should be horizontal or vertical—because of our cognitive understand- ing—but, out of orthogonality in the inverted perspective rendition, must be represented out of perpendicularity and horizontality in their translation in the orthogonal drawing. The second part of this exercise is to take the orthogonal drawing and draw its object in an isometric rendition where the plan and the roof or the base, the top part of the building element or the plan and the ceiling of the room are both present as horizontal planes and connected to the visible vertical planes.

14.10

166 Cosmopoiesis and World-Making