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 “rather than locally unambiguous, but globally impossible, they are everywhere locally ambiguous, yet globally impossible” (Quoted from Coxeter, 154).
Two of the most extensively analyzed works of art are Diego Velasquez's Las Meninas and Jan Van Eyck's Arnolfini Double Portrait. Both of these artist's talent won them recognition not only during their lifetime but after as well. Both Velasquez and Van Eyck have a justly earned title as the most talented artists of their respective times. A detailed examination of the details and intricacies of these artist's respective masterpieces, their similarities, and what sets them apart not just from each other but from other paintings from their time period and style, will lead the viewer to a better understanding of the mentalities of these gifted artists and how they transcend their respective genres and contemporaries to create their own artistic identities.
In the science-fiction short story “And He Built a Crooked House” by Robert A. Heinlein, a mathematically inclined architect named Quintus Teal constructs a house based on the unfolded net of a tesseract in order to save on real estate costs. However, to Teal’s dismay, an earthquake occurs the night before he shows a friend the house, and the house had fallen through a section of space and seemingly had been shaken into an actual tesseract. Despite its mathematical basis, “And He Built a Crooked House” is a quality example of science-fiction.
According to Roland Shearer (1992) the release of non-Euclidean geometries at the end of the 19th Century copied the announcement of art movements occurring at that time, which included Cubism, Constructivism, Orphism, De Stijl, Futurism, Suprematism and Kinetic art. Most of the artists who were involved in these beginnings of Modern art were directly working with the new ideas from non-Euclidean geometry or were at least exposed to it – artists such as Picasso, Braque, Malevich, Mondrian and Duchamp. To explain human-created geometries (Euclidean, non-Euclidean), it is a representation of human-made objects and technology (Shearer
Gombrich, Ernst Hans Josef. Art, perception, and reality. London: The Johns Hopkins University Press, 1972. Print.
... upon solution to water access disagreements, social and political powers must be willing to compromise since the risks associated with disagreements regarding water allocation may be too great. As stated by Shiyyab (2004), “If sustained over a period of time, these problems will directly affect social harmony, domestic stability and eventually, regional peace.” (p. 30). Investments must be made by industry as well as local and national governments for purification of wastewater so that clean water, when needed, will be available. The necessity of obtaining water is a fundamental human right and,
...e after all, he is the most sinister. The irony of this situation is compelling once we are told that Satan is in fact the “…soul that suffers the most.” (Canto XXXIV. Line 61).
He uses extreme methods to attract attention to his artwork and in doing so, challenged the social norms. In his early life, Sagmeister had been keeping a running list of life-learnings in a diary titled ‘Things I Have Learned In My Life So Far’. Eventually, he translated these private thoughts into a series of typographic artworks and public installations that shocked society, exploring everything from obsession, confidence and love; the list of quotes was influenced by the personal experiences he gained throughout his life. However, the hidden message behind these works was left open for
Maynes, Charles. "The Middle East in the Twenty-First Century." Middle East Journal 52.1 (1998): 9-16. JSTOR. Web. 6 June 2011.
Non-euclidean geometry not only **, but also suggests that the characteristics of “necessity” and “university” could be questioned, as “universality” and “necessity” seems to suggests, once the proposition of
... of Israel, 2d ed.: A Theological Survey of the Old Testament. Garden City: Baker Academic, 2002.
For example, when placing composite materials or sealants an etchant has to be placed before the actual restorative material. An etchant is used to partially demineralize enamel rods. This is critical for micromechanical retention of material to adhere to the tooth surface. If these microscopic cavities were to be filled by saliva and debris from contact with the tongue, the material bonding process would fail. The oral cavity is a very hostile environment. In order to achieve maximum function of dental materials, the environment has to be stabilized. In some cases stabilization of the oral cavity involves temporary elimination of those conditions by tooth
“Every student in the nation should have an education in the arts.” This is the opening statement of “The Value and Quality of Arts Education: A Statement of Principles,” a document from the nation’s ten most important educational organizations. The basic message is that music and art programs in the schools help our kids and communities in real and substantial ways. There is an abundant amount of facts and information that supports this statement. The benefits of arts education can be narrowed down into 4 basic categories: success in developing intelligence, success in ...
Palmer, C. (2013, September 16). American Dental Association. Retrieved January 28, 2014, from ADA: http://www.ada.org/news/8898.aspx
The following paper examines a close reading of the figure of Moses in Exodus, Numbers, and Deuteronomy with respect to the issue of why he is barred from entering the Promised Land of Canaan as well as in the Quran. Moreover, after considering the stories and character of Moses in these respective texts, I will then analyze the two accounts in order to examine their similarities and differences.
The Greeks are credited with inventing philosophy and it was believed that whoever pursued a deeper understanding in a subject was a philosopher. Since then, the subject of philosophy has grown and has helped us analyze complicated questions such as what is real and what is beauty. The questions encountered in philosophy can fall under four areas, but in this essay we will focus on one of them, Metaphysics. Metaphysics is the branch of philosophy that deals with questions relating to the physical world. Further, in life we encounter many physical objects in which we can touch and feel. However, what makes these objects real? Plato introduced his metaphysics idea of Theory of Forms, which presents a view of what makes an object real. In this paper, I will touch upon the Theory of Forms and explain that a world of forms does exist separately from concrete/permanent things.