Thomas Goldstein
Dawn of Modern Science
In explaining various types of projection, Ptolemy had touched on the problem of foreshortening and suggested a method for its cartographic representation. Alberti realized the underlying problem for artists was basically the same. He took a clue from Ptolemy and applied his mathematical concept to the type of foreshortening involved in the simple visual perception that is represented in a painting. Generations of Renaissance painters and basrelief sculptors from then on could indulge in the accurate depicting of depth, the problem with which artists had wrestled since the time of Giotto, introducing a major dimension of realism and drama—all thanks to a cartographic concept.
Map projection and perspective painting, in other words, were developing plong parallel lines in a mutually fruitful relationship for some hundred and fifty years, or across most of the Renaissance. In fact, the method for projecting the curved surface of the earth on a map while keeping actual distances in their proper proportion, and the painter's technique in capturing perspective images on a canvas in the exact geometrical order in which they appear to the eye are two ways of dealing with the same problem. Whether one wishes to represent a large portion of the earth, or merely the tiny sector the eye comprehends at a glance, the mind is, in principle, faced with the identical challenge. In both cases a window is opened, so to speak, on a segment of earthly space, whether small or large—just as Giotto had 'opened a window' on the world when he broke through those bland backgrounds of the traditional Medieval paintings—and the threedimensional image presenting itself to us is then reduced to flat shapes on a twodimensional surface, in a way that suggests the true distances and proportions. (Alberti in his book on perspective actually suggests that the problem facing the painter may be reduced to the appearance of threedimensional objects on a windowpane.)
