Rathgeber-Nets

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					                           Erwin Panofsky, the Quadrate Net and the Grid



For the composition of the (reality of the) image, quadrate nets and grids perform a constitutional

role. Quadrate nets and grids are methods of representation, perception and standardization which

position the figure and specify rooms of action. They are also indispensable tools for techniques of

visualization such as photography and film, computer graphics and animation. Both are composed

of a system of parallel and interlaced lines, the horizontal and vertical, and as such they can develop

different structures. The aim of this essay is not to sketch a history of the (quadrate) nets nor the

grids, but looking systematically at the concept of each with regard to images. The discussion of the

term net is based on the wrongly forgotten essay “The History of the Theory of Proportions as a

Reflection of the History of Styles” by the art historian Erwin Panofsky and contrasted with

thoughts on modernist grid paintings as presented in the essay “Grids“ by Rosalind Krauss. The

interesting point of the Panofsky investigation is that it reveals also the instruments of proportion

and kinetics theory while reflecting on the history. My approach demonstrates moreover that one

can take the Egyptians‟ quadrate net as a starting point in order to explore the history of the ways

that networks of lines have been used to draw the human figure and transfer it in motion. The

rediscovery of the Egyptian net will be juxtaposed with examples of art works with which the

changing relation of net to grid as well as to the figure are explored.



       Panofsky‟s essay on the theory of proportions originated in his early lectures in Hamburg

(Panofsky 1921, English trans. 1957), which he later revised and translated into English in the

collection Meaning in the Visual Arts. (Panofsky 1957, 6 and Michels and Warnke 1998, 12)

Systems of proportions, for Panofsky, are not to be examined in the light of their appearance but of

their meaning. He understood the theory of proportions to mean “a system of establishing the

mathematical relations between the various members of a living creature, in particular of human

beings, in so far as these beings are thought of as subjects of an artistic representation.” (56) He


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posited two systems of proportions, one achieved by breaking down the whole and the other by

multiplying basic units. In this context, portions can be of relevance for the object of the depiction

or the depiction of the object: “The first is a question of „objective‟ proportions – a question whose

answer precedes the artistic activity. The second is a question of „technical‟ proportions – a

question whose answer lies in the artistic process itself; and it is a question that can be posed and

resolved only where the theory of proportions coincides with (or is even subservient to) a theory of

construction.” (56)



       For Panofsky, “objective” and “technical” proportions, i.e. anthropometry, and theories of

construction, only coincide in Egyptian art: “For to determine the „objective‟ proportions of a

subject, i.e., to reduce its height, width and depth to measurable magnitudes, means nothing else but

ascertaining its dimensions in frontal elevation, side elevation and ground plan. And since an

Egyptian representation was limited to these three plans (except that the sculptor juxtaposed while

the master of a two-dimensional art fused them), the „technical‟ proportions could not but be

identical with the „objective.‟ The relative dimensions of the natural object, as contained in the front

elevation, the side elevation and the ground plan, could not but coincide with the relative

dimensions of the artifact.“ (59)



       In the light of this, the regular quadrate net as an instrument on which the Egyptians based

their sculptures, comes into question. “We know,” Panofsky writes,

       that the Egyptians effected this subdivision of the stone or wall surface by means of a finely

       meshed network of equal squares; this they employed not only for the representation of

       human beings but also for that of the animals which play so prominent a role in their art.

       The purpose of this network will be best understood if we compare it with the deceptively

       similar system of squares used by the modern artist to transfer his composition from a

       smaller to a larger surface (mise au carreau). While this procedure presupposes a


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       preparatory drawing – in itself bound to no quadrature – on which horizontal and vertical

       lines are subsequently superimposed in arbitrarily selected places, the network used by the

       Egyptian artist precedes the design and predetermines the final product. With its more

       significant lines permanently fixed on specific points of the human body, the Egyptian

       network immediately indicates to the painter or sculptor how to organize his figure: he will

       know from the outset that he must place the ankle on the first horizontal line, the knee on

       the sixth, the shoulders on the sixteenth, and so on. In short, the Egyptian network does not

       have a transferential significance, but a constructional one, and its usefulness extended from

       the establishment of dimensions to the definition of movement. [60-61]



       Panofsky employs the term „Quadratnetz‟ with its difference to „Quadrierung‟ within his

German essay. In his own English translation he uses „network of equal squares‟ or „system of

squares‟. With this terminological distinction as articulated in the citation above he hints at a variety

of conceptional differences and consequences for its use. To deliver an insight there is to add that

throughout the history of representation and observation practices there were different such

techniques and instruments used, for example the three-panelled grid (Dürer), the velo (Alberti), an

equally subtle network of lines (Leonardo), a network of frame or threads (Rodler) or the paviment

for drawing in the figure (Lautensack). Panofsky‟s discussion of the net in its usage as a means of

presentation and construction of a figure has been built on in a number of different ways. However

the interesting point for our discussion is that in the mid-twentieth century, the conservative art

historian Panofsky was interested in nets for construction and proportion, approximately at the same

time as modernist artists began exploring grids. There is no clear connection in the literature

between the two and this is why the coincidence of the establishment of the net itself in different

usages is emphasized here. At the end of the century, Panofsky's inquiry was largely forgotten

(except by historiographers interested in the history of art history), but the grid as a modernist

phenomenon was rethought by a number of scholars. Most prominently, there is the move towards


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the use of the concept grid with the notion of a synthesis of disciplines as Hannah B. Higgins shows

in her seminal volume „The Grid Book“. (Higgins 2009) Earlier, in 1978, the term figures

importantly in Rosalind Krauss discussion of the emblematic structure of modern art in her essay

„Grids“ (Krauss 1978, 8-22).

       Here, the coordinates of a grid are no longer used for positioning the figure within the

picture. Instead, as Krauss puts it, they formulate “the autonomy of the realm of art... flattened,

geometricized, ordered” in a spatial sense and in the temporal dimension. “[T]he grid is an emblem

of modernity by being just that” (9f). The work “Stars“ by Agnes Martin in 1963 illustrates this

point forcefully. It shows a square gridded field on a white background. The hand drawn ink lines

and blue watercolor reveal the gesture of the drawn pattern and the use of a ruler does not

necessarily lead to drawn directness. (Boehm 2009, 43-59, 51) The regular grid here demonstrates

its construction contrary to the use of the constructional Egyptian net.




       Basically, the net and the grid are two different concepts and yet similarities attract our

attention. In contrast to art historical topoi of perspectival representation such as frames or windows

(Alpers 1983, 105f), Panofsky speaks of the Egyptian‟s use of the quadrate net as having a

constructive significance in addition to the specification of measurements and the determination of

movement (Panofsky 1957, 60-61). This constructional feature of the net can be compared to meet

Krauss idea of modernist grids. “The grid“, she states, is “a structure that has remained emblematic

of the modernist ambition within the visual arts ever since“ (Krauss 1978, 8-22, 9). Egyptian nets

were used to measure figures, and modernist grids are simply “the result not of an imitation, but of


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aesthetic decree. Insofar as its order is that of pure relationship, the grid is a way of abrogating the

claims of natural objects to have an order particular to themselves“ (9f).




        Still there is to add, however, that the viewer takes up a significant role in reference to the

grid. The installation by the Austrian artist Peter Kogler in 2000 surrounds the viewer with a net

structure which is projected on all four walls of the exhibition space. As time passes, lines of the

evenly composed net lose their determined coordinates and the projected elements are in permanent

dissolution or transformation of their orthogonal structure. This causes an instability in the viewer

as the projection continues moving side- and upwards on all four walls.

        In the work of Martin, it is even more the viewers themselves who set the visual network of

lines in motion as becomes clear with regard to her grid drawings. This animation of the viewer can

be compared to what Higgins foresees with respect to the evolutionary power of grids as “the

animating feature of living things” as well as her argumentation which follows Henri Focillon to

strengthen the “use that brings each grid to life“. (Higgins 2009, 10f) Moreover, the work of Kogler

creates a shift in the relationship between the figure (viewers themselves) and (back)ground. In the

light of the moving grid structure the unmoved viewers are moved themselves, because they need to

be in accordance to their (static) reference system. These approaches are challenging not only for

image studies because human beings from the very first are incorporated within the horizontal and

the vertical, which open up a network – the space of movement. (Cf. Merleau-Ponty 1945, Bühler

1934)

                                                                                      Pirkko Rathgeber


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