January 17th, 1971
HOLLAND M.C. Escher has produced numerous works of art; however, the debate continues on if he is considered an artist or a mathematical genius. The answer is, of course, both.
I am fortunate enough to be sitting down with this man of ground-breaking proportions and learning the story behind the art.
SC: To begin, I would like to ask about your childhood. How did you grow up, and what impact did that have on your later life and work?
MCE: I was born in the town of Leeuwarden, Holland in 1898, the youngest child of a Dutch engineer. My parents had expected me to follow in my father's footsteps and become an engineer, but I decided that my true calling was graphic design. I dropped out of the School of Architecture and Ornamental Design in Haarlem in 1922 after accepting this change of heart. My career was much influenced by my direction under a master printmaker, Jessurun de Mesquita. It was here that I received training on a style of art called woodcutting, with which all my early work was done.
SC: How do you view your earlier pieces?
MCE: They are of little or no value now, because they were for the most part merely practice exercises.
SC: You have been called a mathematician as well as an artist. What is your view on the issue?
MCE: Although I am absolutely without training or knowledge, I often seem to have more in common with mathematicians than my fellow artists.
SC: In what ways does your work connect with mathematics?
MCE: I see it as relating both through the geometry of space, and what may be called the logic of space. The geometry of space translates to a reoccurring theme in my creations: the tessellation. A tessellation is an arrangement of closed shapes that completely covers the plane without overlapping and without leaving gaps. The regular division of the plane had been considered solely in theory prior to me, some say. I diverged from traditional approaches, and chose instead to find solutions visually. Where other mathematicians used notebooks, I preferred to use a canvas.
SC: Are tessellations the only geometric element present in your pieces?
MCE: No, not at all. I also employed alterations of basic repeating shapes, such as triangles, to obtain the desired effect. To gain access to a greater number of designs, I used transformational geometry techniques including reflections, glide reflections, translations, and rotations. The result is a mathematical tessellation of artistic proportions, certain critics have said. I feel that one of the best representations is in my "Regular Division of the Plane with Birds" (1949).
SC: One masterpiece in particular has caught my attention: "Möbius Strip II" (1963). It only has one side and one edge, how is this possible?
MCE: The nature of space itself served as the inspiration for many of my creations. In this work, I made use of topology, a new form of mathematics at the time. In geometry, topology is the study of properties of shapes that are independent of size or shape and are not changed by stretching, bending, knotting, or twisting. According to the laws of topology, the ants in the picture are all walking on the same side of the strip.
SC: When you mentioned that your art
utilized and exploited the logic of space, what did
MCE: I attempted to challenge the traditional views of the geometry of space with my many representations of impossible objects. I created optical illusions by violating the necessary laws of spatial relations among physical objects. At the base of many of these works is Penrose's impossible triangle. I feel that it becomes more evident in some of my later works, especially in Belvedere (1958) and Waterfall (1961). Waterfall, 1961
SC: You, M. C. Escher, have shaken the
worlds of mathematics and art by uniting the two, seemingly
contrasting realms. You have said that the things I want to
express are so beautiful and pure, yet your expressions led
to an exploration of the geometrical plane and a new view on the
idea of space itself. In a way previously thought impossible, you
are both an artist and a mathematician. I would like to thank you
for your time.
Cordon Art, B.V. The Official M.C. Escher Website. 21 Feb 2002. www.MCEscher.com
This site provided detailed data about the work of M.C. Escher, especially from an artistic point of view. Its best attribute is the large number of Escher's pieces available.
Fellows, Miranda. The Life and Works of Escher. Great Britain: Parragon Book Service Limited, 1995.
This book provided much of the information on the history of Escher. It went fairly in depth with his past, and gave a summary of each and every picture in the book. This was my main source of data.
"The Mathematical Art of M.C. Escher." Math Academy Online. 21 Feb 2002. http://www.mathacademy.com/pr/minitext/escher/index.asp
Of all the
online sources I reviewed, this one was the most comprehensive
and helpful. It had certain quotes, which I used in the article
(yes, all the quotes were actually said by Escher). Seeing as how
this is the Math Academy, I would expect that they
have this type of valuable information for many different math