Out of Sorts: On Typography and Print Culture

Chapter Seven. The Representation of Representation: Versions of Linear Perspective

c h a p t e r s e v e n • The Representation of Representation: Versions of Linear Perspective The model of linear perspective has been in practical use by drawing manuals for centuries and has been the subject of many recent studies. It is simple in its theory and in its geometry; its construction is equally simple in practice. Yet this simplicity and elegance has not prevented it from being grossly misrepresented , even by those art historians who have studied it closely and by artists who are perfectly competent in using it.1 Problems associated with this model are an extension of the typographical problem I have been dealing with throughout this study: how does one represent something—an idea, a statement, a three-dimensional object—on a two-dimensional plane? And to what extent do conventional ways of seeing or thinking dominate the sometimes contradictory and recalcitrant facts of objects? Here, our misconstruction of what we see and read seems essential to our understanding of what these things represent. The present chapter considers three variations: (1) the model itself and traditional misreadings of it; (2) the classical reception by Piero della Francesca and Leonardo and what is known as the three-column paradox; (3) the use of the model in the construction of seventeenth-century stages and contemporary representations of those stages in printed books. The Classical Model: Alberti and Viator The model of linear perspective is usually associated with Leon Battista Alberti ’s De Pictura of 1434, first printed in 1540 (in Latin) and 1547 (in Italian).2 142 chapter seven Neither the earliest manuscripts nor the earliest printed editions of Alberti contain illustrations, although his descriptions are sufficiently clear for a consensus to have developed both on the technique and the pictorial form of the model, which I reproduce in my own variant in Figure 24. In its simplest form, the model of linear perspective is the solution to the problem of how to draw an angled checkerboard on a two-dimensional picture surface. The problem is more complicated than that simple formulation makes it seem, since ‘‘how to draw’’ is a function of ‘‘how the picture will be viewed,’’ and that will be one of the subjects of the present chapter. Among the basic principles of linear perspective are the following: all straight lines in space will be straight when represented in perspective on a two-dimensional surface; a fixed viewpoint implies a horizon on the picture plane and a series of planes emanating from that horizon; any set of parallel lines imagined on any of these planes will intersect at a vanishing point on that horizon.3 The checkerboard, the basis for Alberti’s discussion, can be constructed purely mechanically, although it is far more cumbersome to describe verbally than to demonstrate in a figure. In Alberti’s construction, the checkerboard pattern is imagined as set with one side parallel to (or simply as) the base of the picture. A series of equidistant points is marked on the this baseline: two points are drawn on the arbitrary horizon (one usually the central point of the frame, the other generally outside the frame); a series of lines are drawn from each of the two points to the points on the baseline. A vertical line is drawn from the rightmost point of the checkerboard base to the horizon. The lines of the second horizon point will intersect with that vertical line, and horizontal lines drawn from those intersecting points will determine the receding horizontals of the checkerboard. The correct viewpoint is determined by an imagined perpendicular line from the intersection of the vertical and the horizon; the viewing distance VD will be the distance between the vertical and the second point on the horizon (see Figure 24). A second, often cited variant of Alberti’s procedure is by Viator (Vignola, or Jean Pelèrin).4 In Viator’s method, a series of equidistant points is placed on the base and two points are placed anywhere on the horizon. Here, however , the intersection of the lines with each other determines the proper foreshortening of the horizontals of the checkerboard; the viewing distance VD is equal to the distance between the two horizon points (Figure 25). The two methods of construction by Alberti and Viator are effectively the same; Al- The Representation of Representation 143 Figure 24. Alberti’s model. berti’s vertical line is...