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Other "perspectives"

Although every human being (of whatever ethnicity) experiences the natural visual illusion of parallel edges—like Figure 7. Drawing by five-year-old Anna Filipczak. Pen and crayon. COURTESY OF ANNA FILIPCZAK, WILLIAMSTOWN, MASS. roadsides or railroad tracks—appearing to converge toward a point as they approach the horizon, it is not natural to reproduce this illusion in pictures. In other words, while everybody sees the same phenomenon in reality, no one, no matter how artistically talented, is innately predisposed to picture it (except, remarkably, certain autistic prodigies). Perspective is a technique that generally must be learned. Therefore there is no reason to believe that nature rather than nurture had anything to do with why artists in other ages and cultures did not pursue the "realism" preferred in the West.

Young children do instinctively make pictures from a number of viewpoints simultaneously, as in Fig. 7, a drawing by Anna, a five-year-old Ukrainian girl. Notice how she shows the trees and hammock in schematic side view but, because she wants to indicate her mother lying inside the hammock, depicts her posed as teetering on the edge; it is as if her mother is now imagined as being viewed from above. Until the infusion of Euclidean geometry and optics in the arts of western Europe during the early Renaissance, no artists anywhere had cultural need to have their pictures replicate the optics of single-viewpoint vision, and almost all the conventions they employed for signifying solid form and distant space—even in the most sophisticated art of the pre-Renaissance West and all other non-Western cultures—evolved from similar expressions found in the instinctive art of children.

This does not mean that non-perspectival pictures should be labeled "childlike" in the sense of being primitive (or inferior) to the Western style. Quite the contrary. Multiple viewpoints and other innate pictorial signifiers, such as placing nearby figures and objects at the bottom of the picture surface and those more distant at the top, have been refined into some of the most aesthetically beautiful and stylish painting in all art history. Manuscript illumination in medieval Persia is a fine example (Fig. 8). Interestingly, while medieval Islam possessed Greek optics, including Euclidean geometry, long before the West—with Muslim philosophers even adding their own commentary—Muslim painters never applied optics to art, and only used geometry for the creation of elaborate abstract designs in their magnificent architecture.

Artists in China and Japan, on the other hand, refined two perspective conventions that had naught to do with optical geometry. (Euclid was unknown in the Far East until the seventeenth century.) One method was a kind of axonometric projection whereby rectilinear objects were drawn as if their perpendicular sides were set at an angle, just as in Western perspective, but with their parallel edges remaining parallel and never converging (Fig. 9). The other convention, called aerial or atmospheric perspective, provided an effective illusion of distant landscape simply through the tonality of color. Far-off mountains, for instance, were painted in hazy gray or blue in contrast to the brighter colors of nearer foreground objects, thus creating an ideal complement to the Chinese predilection for philosophic contemplation. During the Renaissance, atmospheric perspective was also explored by Western artists, notably Leonardo da Vinci.

Another perspective convention, foreshortening, does not necessarily involve optical geometry and was also independently realized in other cultures. This is the pictorial illusion of an object appearing to extend forward or backward in space even though only one end of it can be observed, such as a body limb depicted as if thrust directly at the viewer. (Think of James Montgomery Flagg's famous "I Want You" World War I recruiting poster.) Ancient Mayan artists in Central America, for ideological reasons peculiar to their culture, applied a similar foreshortening convention when representing their rulers seated with one leg bent sharply sideways (Fig. 10): note the twisted right foot of the seated male. This pose had special meaning because it signified the auto-sacrificial ritual in which Maya

Let me tell you what I do when I am painting. First of all, on the surface of which I am going to paint, I draw a rectangle of whatever size I want, which I regard as an open window through which the subject to be painted is seen; and I decide how large I wish the human figures in the painting to be. I divide the height of a man into three parts, which will be proportional to the measure commonly called a braccio [.5836 meters]; for, as may be seen from the relationship of his limbs, three braccia is just about the average height of a man's body. With this measure I divide the bottom line of my rectangle into as many parts as it will hold; and this bottom line of the rectangle is for me proportional to the next transverse equidistant quantity seen on the pavement [Illus. A]. Then I establish a point in the rectangle wherever I wish; and as it occupies the place where the centric ray [from the painter's eye] strikes, I shall call this the centric [vanishing] point [Illus. B]. The suitable position for this centric point is no higher from the base line than the height of the man to be represented in the painting, for in this way both the viewers and objects in the painting will seem to be on the same plane. Having placed the centric point, I draw straight lines from it to each of the divisions on the base line. These lines show me how successive transverse quantities visually change to an almost infinite distance [Illus. C].…

I have [another] drawing surface on which I inscribe a straight line, and this I divide into parts Illustration a. ILLUSTRATIONS A–G COURTESY OF THE AUTHOR Illustration b. Illustration c. like those into which the base line of the rectangle is divided. Then I place a point above this line, directly over one end of it, at the same height as the centric point is from the base line of the rectangle, and from this point I draw lines to each of the divisions of the line [Illus. D]. Then I determine the distance I want between the eye of the spectator and the painting, and, having established the position of the intersection at this distance, I effect the intersection with what mathematicians call a perpendicular.… This perpendicular will give me, at the places it cuts the other lines, the measure of what the distance Illustration d. Illustration e. should be in each case between the transverse equidistant lines of the pavement. In this way I have all the parallels of the pavement drawn [Illus. E].… A proof of whether they are correctly drawn will be if a single straight line forms a diameter of connected quadrangles in the pavement [Illus. F]. When I have carefully done these things, I draw a line across, equidistant from the other lines below, which cuts the two upright sides of the large rectangle and passes through the centric point [Illus. G]. This line is for me a limit or boundary, which no quantity exceeds that is not higher than the eye of the spectator. As it passes through the centric point, this line may be called the centric [horizon] line. This is why men depicted standing in the parallel furthest away are a great deal smaller than those in nearer ones, a phenomenon which is clearly demonstrated by nature herself, for in churches we see the heads of men walking about, moving at more or less the same height, while the feet of those further away may correspond to the knee-level of those in front.

Illustration f.

Illustration g.
SOURCE: Leon Battista Alberti, On Painting and On Sculpture. Translated by Cecil Grayson, 55–57. London: Phaidon, 1972.

kings spread their legs apart in order to draw blood from the penis and offer it to the gods.


Damisch, Hubert. The Origin of Perspective. Cambridge, Mass.: MIT Press, 1994.

Edgerton, Samuel Y. The Renaissance Rediscovery of Linear Perspective. New York: BasicBooks, 1975.

Kemp, Martin. The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat. New Haven: Yale University Press, 1990.

Summers, David. Real Spaces. New York, Phaidon, 2003.

White, John. The Birth and Rebirth of Pictorial Space. Cambridge, Mass.: Belknap, 1987.

Samuel Y. Edgerton

Additional topics

Science EncyclopediaScience & Philosophy: Pebi- to History of Philosophy - IndifferentismPerspective - Renaissance-style Linear Perspective, Other "perspectives", Bibliography