perspective

=Perspective=

toc Read here about perspective, an art of visual proportion and rendering that has some profound lessons for anyone seeking to comprehend scales.

=Overview=

In the visual arts, the English word perspective refers to the optical illusion whereby a picture on a flat, two-dimensional plane appears to be three-dimensional; as if the represented objects were actually in a deep space receding behind the picture surface (like looking at them through a window or in a mirror), and in some cases seeming even to project forward in front of the picture. The term itself derives from the Latin participle perspectus of the verb perspicere, meaning “to see through.” While artists in nearly every world culture since the beginning of the human race have sought to create some kind of illusion of visual reality in their image-making, none were so preoccupied with perspective mathematics as the painters of the Italian (and then pan-European) Renaissance.

Image: Logarithmic foreshortening and horizon in painting, after Alberti.

The original perspectiva had only to do with explaining the nature of light rays, how they always travel in straight lines, how they are reflected in mirrors, refracted when entering a denser medium, and, especially, how they affect the way the human eye sees.

Perspectiva naturalis was regarded as the special handmaiden of Euclidean geometry, the latter also just revealed in the West in the twelfth century. Since light rays were understood by the ancient Greeks as always radiating from their source in the shape of a pyramid (a three-dimensional triangle), Euclid reasoned that the images framed by them must conform to his fundamental law of similar triangles; for instance, in Fig. 2, if A be the point of light source, and BCD the surface illuminated, then a consistent proportion always exists between the distance of AC from BCD and the relative size of BCD; in other words, AC:BCD as AF:EFG as AI:HIJ, etc. Greek and Arab commentators on Euclid were quick to realize the significance of this in explaining how the images of very large objects can penetrate the tiny pupil of the eye. Let A in Fig. 2 now stand for the human eye, and HIJ the object being observed (Arab commentators liked to use the camel as their example). As the distance AI between these points diminishes to AF and then to AC and so on, the illuminated “camel” will grow ever smaller in proportion until it is finally able to enter the eye and be “seen.” Brunelleschi innovated the horizon principle, realizing that the eye level of the person looking into a mirror sees not only his or her own eye reflected at that same level, but the edges of other reflected objects parallel to the ground on which the viewer stands, all appearing to converge to “vanishing points” on that same eye-level line.

=Perspective And The Western World=

Why was linear perspective so unique to Western civilization? The advent of artificial linear perspective in the West had much to do with an idealized geometry that seemed to reveal the workings of God’s mind, and thus, when applied to the making of holy pictures, should reenergize Christian faith.