ONE COULD SPEND A LIFETIME studying “perspective.” Dating back to the ancients and the geometer Euclid, perspective has meant simply “to see.” For visual artists, the interest has been how to replicate what we see in terms of distance: how to make buildings on a street look like they are getting farther from us, or how to make mountains look close or far off.
In short, it's a matter of how the biological eye works in combination with the reality of geometry, or how lines make shapes. At bottom is the nature of light, which allows us to see. Light travels in straight lines. Accordingly, when light reflects off objects, it comes to our eyes in straight lines.
Now it becomes a little complicated. As the light hits the eye, its angle is changed by the lens of the eye. All the points of light hitting the eye are bent, so to speak, to strike a single point at the back of the eye. This change in angle determines the “field of vision” of the human eye. As the human eyes look out upon the world, the field of vision widens (in other words, has a widening angle, like a fan opening up).
Things that are closer are caught in a narrower field of vision, while things farther away are taken in by a widening field of vision. This change with distance explains what we call visual “perspective.” Things close up look larger, while things grow smaller in the distance as the field of vision widens. It is relational, and not an easy concept to grasp.
Nevertheless, that is why a ten-foot-tall tree looks large close up, but the same ten-foot tree looks small in our wider distant field of vision. The same goes for that famous example of railroad tracks: They are apart close up, but over distance they merge into a single point, what is called the “vanishing point” in visual perspective drawing.
The mechanics are limitlessly complex, and you'll have to talk to your local physicist or geometer to learn all the ins and outs. For the visual artist, however, by the time of the Italian Renaissance, it came down this question: How can I draw and paint a scene so that its perspective is accurate, matching what we really see?
As to this technique, the breakthrough came with experiments by the Italian architect Brunelleschi (who drew from a mirror) and, after him, the humanist author-painter Alberti (who used floor tiles to illustrate) to codify how true perspective may be drawn. Later, Leonardo da Vinci simplified its practical application by saying, “Perspective is nothing else than the seeing a place behind a sheet of glass . . . on the surface of which all things may be marked that are behind the glass.”
A painting, thereafter, was considered simply as if looking through a window to see something beautiful. Again, this was practical application (as was that of Brunelleschi and Alberti) because the science of the biological eye and geometry were still in their infancy.
For painters today, four practical rules of thumb apply. The first is that lines converge on the distant horizon—a horizon determined by the position of the viewer. Thus, depending viewer, you have one-point, two-point, and three-point perspective. The second rule of thumb is that objects grow smaller in the distance, and the same object grows smaller on a geometric line, not randomly. Third, objects closer will overlap objects farther away, not the opposite. And finally, because water vapor fills the air, distant objects can become softer, dimmer, or bluer to human vision.
It took a few centuries for this knowledge to sink in. Eventually, it became part of the standard tool box of the painter. A horizon was chosen. Perspective lines were drawn, or conceived. Objects took their correct size along these lines. And, what is closer is sharper, what is distant becomes softer.
Attempts at achieving this “concept” of distance were made at different times and in different cultures. Medieval art put the large and small into practice, but the angular perspective and horizon line was left out. African art also used size to represent space or importance. The same in Asian art, even up to the present, as a culturally preferred way to represent scenes with distance. Japanese art introduced the aesthetic of flattening objects, adding an evocative design elements to scenes that, in the real world, include spatial relations.
In our time, art historians and postmodern philosophers have rejected the Euclidian mandates about geometry and vision and instead argued that “seeing” is a “cultural” phenomenon, not a scientific one. Linear perspective, at worst, is a “Western bias” forced on other cultures.
I once met a graduate painting student of this persuasion who, pointing into a large room, contended that its lines did not work according to perspective (presumably because the mind, culturally conditioned, can see anything it wants). Our conversation was a bit impossible.
I could not find a rejoinder, and it was a friendly exchange anyway. What I should have done is cited the quote from the art historian Ernst Gombrich, who noted that every culture uses the same kind of eyeglass to improve vision. “Can it not be argued,” Gombrich concluded, “that perspective is precisely what it claims to be, a method of representing a building or any scene as it would be seen from a particular vantage point?” In short, biology, not culture, determines visual perspective.
Even so, artists and painters are absolutely free to represent visual reality anyway they want, and all to the good. But if one is pursuing, say, a “realist” painting, there's no getting around what Euclid and the science of biological vision and light have told us.
Meanwhile, for the more theoretically inclined, there is much beyond the Euclidian-biological space in the basic tool box of drawing and painting. There’s relativity, Minkowski space, probability space, topographical space and, on top of all this, neuro-aesthetics, with all its mysteries of how brain cells and modules interpret what we see.