Mathematical Art of M.C. Escher
A central concept which Escher captured is that of self-reference, which any believe lies near the heart of the enigma of consciousness ï¿½ and the brain’s ability to process information in a way that no computer has yet mimicked successfully.
The lithograph Drawing Hands and the woodcut Fish and Scales each captures this idea in a different way. In the former the self-reference is direct and conceptual; the hands draw themselves much the way that consciousness considers and constructs itself, mysteriously, with both self and self-reference inseparable and coequal. In Fish and Scales, on the other hand, the self-reference is more functional; one might rather call it self-resemblence. In this way the woodcut describes not only fish but all organisms, for although we are not built, at least physically, from small copies of ourselves, in an information-theoretic sense we are indeed built in just such a way, for every cell of our bodies carries the complete information describing the entire creature, in the form of DNA.
On a deeper level, self-reference is found in the way our worlds of perception reflect and intersect one another. We are each like a character in a book who is reading his or her own story, or like a picture of a mirror reflecting its own landscape. Many of Escher’s works exhibit this theme of intersecting worlds, but we will here consider only one of the exemplars. As is common in Escher’s treatment of this idea, the lithograph Three Spheres II makes use of the reflective properties of a spherical mirror. Here, as Hofstatder noted, ï¿½every part of the world seems to contain, and be contained in, every other part . . ..ï¿½ The spheres relfect one another, the artist, the room in which he works, and the paper upon which he draws the spheres.