Since one cannot create 'depth' by carving a hole in the picture, and since one should not attempt to create the illusion of depth by tonal gradation, depth as a plastic reality must be two dimensions in a formal sense as well in the sense of color. 'Depth' is not created on a flat surface as an illusion, but as a plastic reality. The nature of the picture plane makes it possible to achieve depth without destroying the two-dimensional essence of the picture plane.. A plane is a fragment in the architecture of space. When a number of planes are opposed one to another, a spatial effect results. A plane functions in the same manner as the walls of a building... Planes organized within a picture create the pictorial space of its composition... The old masters were plane-consciousness. This makes their pictures restful as well as vital...
Hans HofmannRelated topics
architecture attempt building color composition depth formal fragment gradation hole nature number pictorial picture plane plastic possible sense should space surface vital well tonal mastersRelated quotes
...the stereographic projection of the spherical surface. From the north pole P we draw radial lines to project every point of the surface of the sphere upon the horizontal plane [below, perpendicular to a line joining it to P and the sphere's center]. In general this transformation is unique and continuous, although the metrical relations are distorted; for the point P, however, it shows a singularity. Point P is mapped upon the infinite; i.e., no finitely located point of the plane corresponds to it. It can be shown that every transformation possesses a singularity in at least one point. The surface of the sphere is therefore called topologically different from the plane. Only a "sphere without a north pole" [point] would be topologically equivalent to a plane. ...such a sphere has a point-shaped hole without a boundary and is no longer a closed surface.
Hans Reichenbach
It must be emphasized that in seeing a work of art that has been composed by precise means, the viewer does not perceive dominant details. His impression is one of perfect balance to which all the parts contribute, an impression which not only applies to the parts as such, but is transmitted also to the relation existing between the work of art and the viewer. Although it is very difficult to express in words the effect of a work of art, it may be said that the viewer's deepest impression can best be defined as the achievement of a balance between objective meaning and subjective meaning, both directly penetrated by awareness. He has a sensation of height and of depth which are no longer in any way bound to natural conditions or to spatial dimensions, a sensation which places the viewer in a state of consciousness harmony.
Theo van Doesburg
Once helium burning has occurred... the next possible reaction-carbon burning-is not necessarily slow... This reaction involves ...a strong as opposed to a weak interaction. ...Carbon burning results in magnesium. ...Taking a cross section of a highly evolved star would reveal a system of many layers. The inner layers have been subjected to the largest pressures, thereby forced to the highest temperatures, and burned the furthest; the outermost layers, by contrast, have not burned at all. Thus, as we proceed from outside in, there will be an outermost layer with the initial mix of hydrogen and helium, a layer of mostly helium, a layer of carbon, a layer of magnesium, and so on. ...So we arrive at the picture of a star, in the latest stages of its evolution... now composed of mostly carbon nuclei and other explosive material.
Frank Wilczek
In that Renaissance (Cellini, Tintoretto, Titian..) there was an explosion of unique truthfulness, a love of painting and form... Then come the Jesuits and everything is formal; everything has to be taught and learned. It required a revolution for nature to be rediscovered; for Delacroix to paint his beach at Etratat, Corot his roman rubble, Gustave Courbet his forest scenes and his waves. And how miserable slow that revolution was, how many stages it had to go through!... These artists had not yet discovered that nature has more to do with depth than with surfaces. I can tell you, you can do things to the surface.... but by going deep you automatically go to the truth. You feel a healthy need to be truthful. You'd rather strip your canvas right down than invent or imagine a detail. You want to know.
Paul Cézanne
I do not mean to say that formal economic analysis is worthless, and that anybody's opinion on economic matters is as good as anyone else's. On the contrary! I am a strong believer in the importance of models, which are to our minds what spear-throwers were to stone age arms: they greatly extend the power and range of our insight. In particular, I have no sympathy for those people who criticize the unrealistic simplifications of model-builders, and imagine that they achieve greater sophistication by avoiding stating their assumptions clearly. The point is to realize that economic models are metaphors, not truth. By all means express your thoughts in models, as pretty as possible (more on that below). But always remember that you may have gotten the metaphor wrong, and that someone else with a different metaphor may be seeing something that you are missing.
Paul Krugman