In my prints I try to show that we live in a beautiful and orderly world and not in a chaos without norms, as we sometimes seem to. My subjects are also often playful. I cannot help mocking all our unwavering certainties. It is, for example, great fun deliberately to confuse two and three dimensions, the plane and space, or to poke fun at gravity. Are you sure that a floor cannot also be a ceiling? Are you absolutely certain that you go up when you walk up a staircase? Can you be definite that it is impossible to eat your cake and have it?
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Variant translations: Are you really sure that a floor can't also be a ceiling? I can't keep from fooling around with our irrefutable certainties. It is, for example, a pleasure knowingly to mix up two and three dimensionalities, flat and spatial, and to make fun of gravity.M. C. Escher
I try in my prints to testify that we live in a beautiful and orderly world, not in a chaos without norms, even though that is how it sometimes appears. My subjects are also often playful: I cannot refrain from demonstrating the nonsensicalness of some of what we take to be irrefutable certainties. It is, for example, a pleasure to deliberately mix together objects of two and three dimensions, surface and spatial relationships, and to make fun of gravity.
M. C. Escher
As you may have known, I got myself into a bit of trouble lately. [audience cheers] And I'll tell you what happened. I was heading down to Florida to do a show, and I flew in on a private jet that you guys bought me. Thank you. It's niiice. We landed in Vero Beach, Florida, and there were cops waiting for me, and cops love me, so do firemen. Sometimes they will escort me from the airport to the venue, and this...wasn't one of those times. The cop came to me and said, "Mr. White, we have been told there are drugs on this plane by an anonymous tip." I said, "There are absolutely no drugs on the plane." I did have a bit of weed in my bag, but it's not on the plane, so technically I'm not lying. And the cop says, "Well, may we search the plane?" I said, "You may absolutely not search this plane unless you have probable cause," because I still have civil liberties, you know what I mean? [Audience cheers] I do.
Ron White
Since one cannot create "real 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 Hofmann
Some forms of Kantianism put great weight on “what we can imagine” holding that this can be a source of insight into necessary connections. Thus various of Kant’s arguments about space and time depend on the purported fact that it is impossible for us to imagine certain things: we can know, Kant claims, a priori that space has only three dimensions because we cannot imagine it as having more than three dimensions. History in the form of non-Euclidean geometry and modern physics has put paid to that particular line of argument, but in general we should beware of depending too much on “What we can imagine?,” especially in politics. As Nietzsche puts it somewhere, sometimes the fact that you can’t imagine a situation in which things are very different from the way they are now is not an especially good argument for the claim that they must be as they now are, but, rather, represents a failure of your powers about which you should feel mildly apologetic.
Raymond Geuss
Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. ...Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue... Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. ...the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.
Hans Reichenbach
Escher, M. C.
Espenson, Jane
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