The Impossible World of M. C. Escher :: Mathematics Science Papers

The Impossible World of M. C. Escher Something about the human mind seeks the impossible. Humans want what they don’t have, and even more what they can’t get. The line between difficult and impossible is often a gray line, which humans test often. However, some constructions fall in a category that is clearly beyond the bounds of physics and geometry. Thus these are some of the most intriguing to the human imagination. This paper will explore that curiosity by looking into the life of Maurits Cornelis Escher, his impossible perspectives and impossible geometries, and then into the mathematics behind creating these objects. The works of Escher demonstrate this fascination. He creates worlds that are alien to our own that, despite their impossibility, contain a certain life to them. Each part of the portrait demands close attention. M. C. Escher was a Dutch graphic artist. He lived from 1902 until 1972. He produced prints in Italy in the 1920’s, but had earned very little. After leaving Italy in 1935 (due to increasing Fascism), he started work in Switzerland. After viewing Moorish art in Spain, he began his symmetry works. Although his work went mostly unappreciated for many years, he started gaining popularity started in about 1951. Several years later, He was producing millions of prints and sending them to many countries across the world. By number of prints, he was more popular than any other artist during their life times. However, especially later in life, he still was unhappy with all he had done with his life and his art—he was trying to live up to the example of his father, but he didn’t see himself as succeeding (Vermeleun, from Escher 139-145). While his works of symmetry are ingenious, this paper investigates mostly those that depict the impossible. M. C. Escher created two types of impossible artwork— impossible geometries and impossible perspectives. Impossible geometries are all possible at any given point, and also have only one meaning at any given point, but are impossible on a higher level. Roger Penrose (the British mathematician) described the second type—impossible perspectives—as being â€Å"rather than locally unambiguous, but globally impossible, they are everywhere locally ambiguous, yet globally impossible† (Quoted from Coxeter, 154).