Regarding the works of M. C. Escher

At some point over the past week (I oddly cannot remember any specifics), I encountered two of M. C. Escher’s drawings, and it struck me that he is truly doing nothing more than combining well-formed units into not-well-formed wholes,1 a process that should be very familiar to us in a different context.

In the English language (and, mutatis mutandis, any using a phonography or syllabary, although not a logography), the fundamental unit of writing is a letter. Letters are composited into words; words are composited into sentences (this three-level hierarchy is somewhat arbitrary; in an inflected language, one could say that letters are composited into roots and endings and these into words, while in most languages one could say that words are composited into subjects and predicates and these into sentences. However, three levels are all we need here). One could print letters at random, but the result would make no sense. Thus, we may distinguish a written word (a sequence of letters) as well-formed if it corresponds to a conceptual word and ill-formed otherwise. Any sentence (a sequence of words) that involves one or more ill-formed word is inherently meaningless; among sentences of well-formed words, we may distinguish between well-formed sentences where the sequence of words corresponds to a thought and ill-formed sentences where it does not. Hence:
“Adw” is an ill-formed word
“Adw oin wfe.” is a sequence of ill-formed words
“Cat” is a well-formed word
“The cat sat on the rug.” is a well-formed sentence
“The cat rug sat the.” is an ill-formed sentence

What does this have to do with Escher? Escher is not, strictly speaking, an abstract painter: no aspects of their paintings are well-formed, and thus the lack of proper formation does not seem incongruous (whatever its artistic merits, or lack thereof). Escher, on the other hand, clearly does use well-formed elements; most sufficiently small sections of his paintings correspond very well to what we see in reality. The painting as a whole, however, is not well-formed; while each flight of stairs corresponds to something that might exist in reality, the staircase as a whole could not.2

What causes our reactions to Escher’s paintings to differ from our reactions to ill-formed sentences? I cannot say for certain. But I cannot escape noting that while language deals primarily with the constructed, sight deals primarily with the natural. All writing is directed by the mind with no structural barrier to the production of ill-formed sentences; only the fact that ill-formed sentences do not serve the purposes for which we use language cause their rarity (at least among the mature). Sight, on the other hand, primarily looks upon what actually exists. Only through some hindrance or through some artificial object of sight (artificial here meaning not man-made, but a means of presenting the eye with an image intended to be taken as something other than the physical object beheld) can sight yield an ill-formed image. When the sight is hindered, as by water or a deficiency in the eye, one tends to recognize it quickly (and, moreover, typically all levels of objects perceived are equally ill-formed, e.g. as out of focus for a near-sighted man. Thus, hindrance of the sight tends to produce ill-formed images, not ill-formed composites of well-formed images). In other instances, such as the infamous case of the oar in the water, while the hindrance causes the image as actually received to be false (here thinking of the image before the mind compensates for hindrances), it does not cause an ill-formed image. Only in the case of drawings such as those of Escher does the eye behold without deficiency an ill-formed composition of well-formed objects. Thus, what seems the product simple lack of skill when it occurs in language, a medium to which ill-formed figures are natural, may seem quite tantalizing when met in a medium to which ill-formed figures are foreign.

1 Well-formed: a composition of symbols that possesses meaning, without regard to whether the meaning is true or false (true meaning “corresponding to reality”; a well-formed image corresponds to what could exist in reality, a true to what does exist).

2 Note that here I distinguish between images and diagrams. A well-formed image produces an image in the eye that corresponds to the image formed by a potential reality; a diagram is meant to communicate a concept without such correspondence. Escher’s diagrams must be classified with images because they move the mind to attempt to imagine the object that would produce the corresponding image, even though the attempt cannot succeed.