FREE ESSAY ON M.C. ESCHER

M.C. ESCHER

The Science of Escher
Though M.C. Escher contended that he knew virtually nothing about mathematics, even
having gone as far as to declare that he was "absolutely innocent of training or
knowledge in the exact sciences," (Schattschneider 67), his art work commonly
incorporates the use of many recognized elements of science and mathematics. It has been
argued that Escher's natural accessibility and his popularity with young art patrons is
due to the Escher's use of symmetry, his use of metamorphosis, and his focus on
representational elements of science in his work (Donato 31). 
Though Escher appeared unwilling to address it during his lifetime, it was evident that
his work was supported by elements of science, including the use of mathematic
formulations and specific geometrical patterns. If he did not study science, he at least
studied visual constructions, and determined his artistic perspective after evaluating
the distinct nature and geometry and color configurations of ancient arts. The link
between Escher's creations and tile patterns of the Alhambra in Grenada as well Islamic
art demonstrates the imbedded nature of his developments and the focus on science and
math (Schattschneider 67; Watson-Newlin 43). 
II. Escher's Perspective
Even as a child, art historians suggest that M.C. Escher had a visual focus that directed
him towards the study of patterns and symmetry (Schattschneider 67). In his younger
years, Escher had an affinity for creating patterned drawings that led him to the study
of patterns in the tiles of the Alhambra in Grenada, as well as to study the geometric
drawings in mathematical papers and in the need, to pursue his own perspective and unique
ideas for the tiling of a plane (Schattschneider 67). 
It was Escher's focus on the coloring in his drawings of interlocked tiles that later
interested mathematicians and crystallographers when evaluating his color symmetry
(Schattschneider 67). As a result of his focus on these elements, Escher's work has
actually been utilized since the late 1950s to illustrate some of these mathematical and
scientific concepts (Schattschneider 67). In 1954, at the International Congress of
Mathematicians in Amsterdam, Escher's works were prominently displayed as representations
of particular mathematical concepts, and the publication of his first book The Graphic
Work of M.C. Escher in 1959 marked his further insurgence into the world of math and
science (Schattschneider 67). 
Though Escher contended that his focus on these elements came not from a knowledge of
science, but from a keen understanding of the geometric laws demonstrated in nature, the
preciseness of his work and the way that many pieces express specific scientific premises
has been a major element of evaluation and speculation in terms of Escher's work
(Schattschneider 67). Escher was fascinated by what he considered to be the "regular
division of the plane" which provided the scientific basis for his conceptualization of
symmetry in art (Schattschneider 68). During his lifetime, Escher created over 150 color
drawings that demonstrated hi scarcity to draw nature, especially animal forms, into
symmetrical and non-representational works of art. His drawing Triangle System 1B3, Type
2 (1948), for example, is a colorful and systematrical drawing of butterflies that links
the abstract and nature inextricably through Escher's perspectives on the symmetry in
nature (Schattschneider 68). His artistic creations often provide a sense of dichotomy or
paradox both in nature and in the world of man (Duran 239). The resulting art works
demonstrated the link between the progression of his design of symmetry and his
representational process. Some have argued that the direct nature of Escher's designs are
linked to the way Escher perceived nature, more than as demonstrations of a knowledge of
math or science. 
III. The Use of Symmetry
Symmetry is the structural concept that shapes many mathematical and scientific processes
(Schattschneider 68). Though Escher liked to make his drawings appear to have a random
construction, a closer look at the particulars of his design orientation demonstrate a
clear sense of symmetry (Schattschneider 68). In the example of Triangle System 1B3, Type
2 (1948), Escher's butterfly design is based on six alternating colored butterflies that
move around the flow of the drawing in a circle. Though the symmetry is not immediately
perceivable, it is directed through circular symmetry, and provides a unique visual
perspective and continuity in the drawing. 
Escher is also famous for using symmetry as a means of demonstrating the infinite, and
his drawing Circle Limit IV (1960) uses negative space and the picture of a gargoyle
incorporated into circular symmetry in such a away that it appears that the circular
construction continues with out end (Schattschneider 68). Escher also considered this
element of negative space as a representation of duality, which corresponds with the
mathematical concept of negation, that each statement has a counterpart or negative
correlate (Schattschneider 68). In math and in the drawings of Escher, this concept of
duality suggests that each element has a complement, and that the link between both
provides a complete definition (Schattschneider 68).
This concept of duality is also the fundamental element in what has been described as
Escher's technique of tessellation, which features patterns that have equivalent weight
given to both the positive and the negative images (Walczak 29). Tessellations have been
defined as "repetitive designs in which positive and negative shapes are of equal
importance and consume the entire surface" (Walczak 29). 
As an extension of his perspective on symmetry, Escher also pursued the use of
self-similarity, based on the mathematical concept of the recursive algorithm
(Schattschneider 68). Escher's illustration entitled Square Limit (1964) is constructed
using a recursive scheme, or a set of directions that is applied to each new object on
and on so that the representations and the transformations appear without end
(Schattschneider 68). The final product is a picture that is self-similar, but that has a
clearly differentiated final objects when compared to the first image transformed
(Schattschneider 68). 
Escher addressed many other scientific principles in the design of his work, including
dimension, relativity, reflection, and infinity, and underscored the way in which art can
demonstrated more complex scientific principles (Schattschneider 69). But it was also
Escher's contention that this was not his intent, and instead, that this link was simply
the culmination of his individualized perspectives on the particulars of nature and
focused on the way that other cultures recognized these same scientific and mathematical
elelemts within their artistry. 
IV. The Geometric Shapes, Escher's Perspective and Islamic Art
The geometry of nature and of art were primary concerns for Escher, who demonstrated
these elements through the use of metamorphosis, geometric progression and visual plane
distortion techniques to demonstrate these elements (Doornek 25). Escher demonstrated and
understanding of differential special perceptions that were designed by considering the
spatial circumstances within which elements of nature come into correlation and
underscoring an artistic depiction based on these elements (Doornek 25). 
Two of Escher's more popular works, Day and Night and Three Spheres II are both artistic
creations the underscore this defining focus on form over substance (Doornek 25). They
also demonstrate the process by which Escher extends mathematics and scientific concepts
into his artistry, and underscore the emergence as a reflection of his understanding of
nature and of other cultures. Perhaps the most notable element of both of these works is
the process of applying different spatial perceptions to the specific elements of his
artistry, based on the desire to demonstrate a particular visual effect (Doorneck 25). 
But one of the most notable elements of Escher's work, especially in its earlier
development, came as a relationship between his evaluations of systematic and patterned
tilings created in ethnic and religious communities, that utilized geometric shapes. The
study of the 
repeated geometric shapes in a number of his works based on Islamic influenced
mathematical variations as well as the influence of the Alhambra of Grenada and the Le
Mesquita of Cordoba underscored the prevalence of this kind of artistic design
(Watson-Newlin 43; Schattschneider 17).
Escher began his study of the complex weavings of cultural artistry when he traveled to
the Alhambra in Spain and discovered the centuries of Islamic artistry developed through
the use of geometrical shapes, often in configurations that were both repetitive and
symmetrical. But the standard notion of symmetry was also challenged within these
constructs, and it was evident that there were elements that supported a more complex
element to the nature of symmetry, perhaps rooted in an understanding of complex
mathematics and their implications for art (Watson-Newlin 43).
From September of 1936 until the following March, Escher evaluated the Islamic sketches
of as well as Moorish designs that he has attained from designs in majolica tiles in
order to determine the importance of these elements in creating a specific artistic
design (Schattschneider 17). The design for his first attempt at creating a complex,
symmetrical and geometrically complex and repetitive design was based on the tile images
recovered from the Alhambra (Schattschneider 17). An explanation of his symmetry of this
initial drawing entitled "weightlifters" provides some insight into the process for
Escher: "It was not the geometric shape of a single majolica tile that led to Escher's
human shape, but rather the relationship of a single tile to ever other copy surrounding
it. Each single weightlifter in Escher's drawing can be transformed into one of the five
weightlifters which ajoin it by making either a quarter turn (where elbows touch) or an
180 degree turn (where two heads meet)" (Schattschneider 18).
At the Alhambra, Escher determined that the Islamic artists had used repetitive geometric
patterns and shapes in colorful mathematical variations and that the general base for
their representations was deeply imbedded in a cultural and religious affinity for nature
(Watson-Newlin 43). The Islamic art that became a foundation for the work of Escher
presented no humans or animals, and instead focused solely on natural elements and shape
representations in the art (Watson-Newlin 43). The Islam's believed that the presentation
of geometric shapes, flora and even calligraphy provided a reverence for God and a
demonstration of the preservation of God's ideals (Watson-Newlin 43). 
Though Escher did not necessarily embrace the ideological focus of the representations at
Alhambra, he did focus on the artistry and based many of his subsequent drawings on the
complex and challenging designs that he experienced. He learned that the basic elements
of their designs were not so difficult to understand if they could be evaluated in terms
of the repetition rather than simply on the basis of the primary element. He also copied
patterns from the Alhambra and utilized them to create some of his most significant
works, including metamorphosis (I) in 1937, a woodcut print that was based on the
geometric tilings of the Alhambra (Schattschneider 19). 
V. Conclusion
The essential nature and complexity of the developed drawings and artistic creations of
Escher were linked not only to his study of the Islam at Alhambra and the Moors, but also
through the demonstration of what has been described as the metaphor of Escher. Though
the artist contended that his work was not the product of a complex study of the
mathematics and scientific principles surrounding the symmetric and recursive nature of
the artistry, it became evident that Escher's drawings systematically underscored basic
principles of math and created a dichotomous view between Escher the artist and Escher
the mathematician. 
The progression of examples like Escher Metamorphosis, for example allow for the
demonstration of the principles of symmetry, dimension, relativity, and the use of
negative space to provide a distinct visual experience that leads the viewer through the
progression of the piece of art. Escher was famous for bringing art lovers into his
pictures and enhancing their experience by requiring them to evaluate and re-evacuate
what they have seen. The imbedded nature of his developments in the knowledge and
application of mathematical and scientific principles is an imperative element in
understanding Escher's creation. 
In the years that have passed since Escher's death, a number of artists have not only
turned to his work for inspiration, but also have utilized his work as starting point for
the development of complex and mathematically based artistic developments (Nickell 2).
Escher focused on many different and complex systems of design for his artwork, which
ranged from drawings and block prints to origami (Nickell 2), and the differentiation in
his artistic pursuits were almost as complex as the designs he created.
Bibliography
Works Cited
Donato, Beverly Brand. "The Escher Experience." School Arts, (1994): March, pp. 31-32.
Doornek, Richard. "M.C. Escher: beyond the craft." School Arts, (1994): March, pp.
25-28.
Duran, Jane. "Escher and Parmigianino: a study in paradox." The British Journal of
Aesthetics, (1993): July, pp. 239-245.
Nickell, Joe. "Gardnerfest: Admirers 'Gather for Gardner' to fete the modest genius."
Skeptical Inquirer, (1996): May-June, pp. 2-3.
Schattschneider, Doris. "Escher's Metaphors." Scientific American, (1994): November, pp.
66-71.
Schattschneider, Doris. Visions of Symmetry: Notebooks, Periodic Drawings and Related
Works of M.C. Escher. (New York, NY: W.H. Freeman and Company, 1990).
Watson-Newlin, Karen. "Stairways to Integrated Learning." School Arts, (1995): October,
pp. 43-44.
Walczak, Jan. "Escher tesselations." School Arts, (1994): March, pp. 29-30.