regular – Fountain Magazine

The Influence of Islamic Art on M.C. Escher

Louima Cunningham — Thu, 01 Jul 2010 00:00:00 +0000

Although most of us do not remember or have not ever heard the name M.C. Escher, we are probably familiar with the world-famous illustration shown below:

Figure 1: Drawing hands, 1948

Maurits Cornelis Escher (1898–1972) is one of the world’s most famous graphic artists of impossible structures (e.g. “Ascending and Descending”) and transformation prints (e.g. “Metamorphosis I-II-III”). Currently, one can see his work on posters, book covers, calendars, wall hangings, and many web sites enjoyed by millions of people all over the world (1).

His exquisite and mind boggling pictures are drawn from the mathematical world of symmetry, topology, transformational geometry, and regular divisions of the plane. At the same time, they exhibit a rich and artistic talent unrivaled by most. Furthermore, respected scientists have realized that his works are simple illustrations of sophisticated theories (2). For instance, mathematician D.J. Lewis indicates that Escher’s prints entail a systematic approach combined with an ingenious argument similar to the most beautiful results in algebra. In 1952, Herman Weyl, a Princeton mathematician, used Escher’s famous work “Symmetry” for his book cover. Escher’s rendering of “Horseman” was used by Chen Ning Yang, a physicist and Nobel Prize winner, to illustrate his new hypothesis involving symmetry and its application to quantum physics (3). Escher has also inspired scientists in their academic studies. For example, some of his sketches helped his half-brother B.G. Escher, a professor of geology, in solving crystallography problems (4).

Tessellation of a plane, also called tiling, is the mosaic formed by filling the plane with no gaps and no overlaps. A person who is familiar with Islamic art immediately notices the deep connection between Escher’s transformational geometry and tessellations, and that of Islamic patterns. One can even use Islamic art and tessellation techniques to generate Escher-like drawings. In fact, Escher’s 1922 visit to the Alhambra Palace in Spain was the turning point in his life. He was fascinated and inspired by the spiritual significance of the tile work at the palace, and Islamic patterns played a key role in transforming his art (5). This article will explore the intimate relationship between Islamic art and Escher’s work, in particular the significance of themes with “flat surfaces” and “flat surfaces with respect to pictorial representations.”

Brief summary of Escher’s art

Escher produced 448 lithographs, woodcuts, and wood engravings and over 2000 drawings and sketches during his lifetime (1). His understanding of mathematics was largely visual and intuitive, and his works display a strong mathematical component (6). More than 150 of colorful works testify to his ingenuity in regular division of plane. He was very successful at depicting the real world in 2-dimensional plane as well as at translating the principles of regular division onto a number of 3-dimensional objects such as spheres, columns, and cubes. Some of his prints combine both 2 and 3-dimensional images with a startling effect as demonstrated in “Reptiles” (7).

Figure 2: Reptiles, 1943
Upon further examination, one finds three dominating themes in Escher’s works (2):

• Spatial structures: His work before 1937 aims solely to depict realistic structures or scenes composed of mostly landscapes and portraits, and reveals no analytical interest. In contrast, after 1937, he combines these themes with the others described below.

Figure 3: Atrani, Coast of Amalfi, 1931

• Flat surfaces: The subject matter of later works encompasses his major area of expertise: “regular division of plane” including regular tessellations; symmetry and order; identical, congruent figures; or those with graduated surface dimensions. Upon his visit to the Alhambra in 1922, Escher was deeply influenced by the art works of the Moors and worked out a system for periodic drawings. These periodic drawings portray surfaces filled with similar shapes and often illustrate approaches to the infinite. Escher mastered his skills on geometric grids and used them as the basis for his sketches, later improving them with additional designs, mainly animals such as birds, lions, and reptiles.

Figure 4: Day and Night, 1938
• Flat surfaces with respect to pictorial representation: Escher’s final and most famous type of work is his portrayal of “impossible structures.” He was very skilled at illustrating three-dimensional conflicting situations in two-dimensional spatial representations (8).

Figure 5: Waterfall, 1961

Patterns in Islamic art
In Islamic art, the spiritual world is regarded as being reflected in nature through geometry and rhythm. Hence, Islamic artists used geometry as an aid to raise their spiritual understanding as well as the viewer’s:
“Muslim intellectuals recognized in geometry the unifying intermediary between the material and the spiritual world. These patterns may be seen as symbolizing the Islamic principles of ‘Tawhid’ (the unity of all things) and ‘Mizan’ (order and balance), which are the laws of creation in Islam.”(9)
Tessellations are one of the major components of Islamic art. Islamic artists mastered regular division of plane using, in particular, circles on triangular or square grids, because the circle – which has no beginning and no end and thus symbolizes infinity – was considered to be the most perfect geometric form. In mosques, where a wealth of these geometric patterns could be found, one could contemplate the infinite nature of God simply by looking at the walls or ceiling. In short, these geometric forms expressed Islamic artists’ fascination with mathematics as a metaphor for divine order and presence (10). Figure 6, Figure 7, Figure 8, and Figure 9 are examples of triangle and square grids and produced patterns adopted from (11):

Figure 6: Triangular grid (a) and examples of patterns: (b) 6-pointed star-hexagon (c) Ceramic wall panel – Iran – 13-14th centuries.
Figure 6 demonstrates the 6-pointed star-hexagon pattern that can be obtained by coloring a triangular grid whereas Figure 7 integrates circles to produce more complicated patterns and an increase in variety. The examples shown in the figures are real tiles mounted in mosques around the world.

Figure 7: Triangular grid and examples of patterns.
Figure 8 and Figure 9 illustrate the usage of circles on a square grid in two different ways. The square-hexagon pattern in Figure 8(c) is commonly used on the ceilings of mosques whereas variations of the star-cross pattern in Figure 8(c) have mostly been used on walls.

Figure 8: Square grid and examples of patterns: (a), (b) and (c) square-octagon pattern, (d), (e) and (f) star-cross pattern.

Figure 9(c) shows a scallop pattern, often used for fences. The I-Bar pattern in Figure 9(e) is sometimes used in tiling walls, but is more commonly used for floors, pavements, and paths.

Figure 9: Square grid (a) and examples of patterns: (b) and (c) scallop pattern, (d) and (e) I-bar pattern.

The Alhambra’s influence on Escher

Figure 10: (a) A view of the Alhambra, (b) the Lion’s Court in the Alhambra, which inspired Escher’s drawing.

Escher became fascinated by the regular division of the plane in 1922 when he first visited the Alhambra, a fourteenth-century Moorish castle in Granada, Spain. (1). He then studied Polya’s seventeen plane symmetry groups, (thirteen of which are displayed in the Alhambra), and Haag’s mathematical definition of the division of the regular plane (12). But the real metamorphosis in his art began in 1936, with his second visit to Alhambra, which he described as “the richest source of inspiration” in his writings (5). Like many Islamic artists, Escher believed that repetitive patterns indicated a higher source of knowledge that existed before mankind. He considered order, regularity, cyclical repetitions, and renewals to be the “laws of the phenomena” around us; accordingly, the structure of his designs was a simple reflection of these laws from his own perspective (9).

Escher studied, took detailed notes, and made sketches of the tile patterns at the Alhambra. In his writings, he described his fascination with the double use of contours and divisions of the plane as follows:

“The Moors were masters in the filling of surface with congruent figures and left no gaps. In the Alhambra, in Spain, especially, they decorated the walls by placing congruent multicolored pieces of majolica together without interstices.”(8)

Figure 11: Examples of patterns in the Alhambra (adapted from http://www2.spsu.edu/math/tile/grammar/moor.htm)

In his later work, Escher used genuine techniques devised from triangular and square grids, applying reflections, translations, and rotations to obtain great variety of patterns in his tessellations. The simple trick of modifying the grids utilized in Islamic art to ensure the perfect fit of patterns, which Escher used in his tessellations, is demonstrated below:

Figure 12: An example of an Escher-like pattern obtained from the rectangle (adopted from (11).

The idea is to start with a pattern such as a rectangle in Figure 12(a). The tessellation pattern is created by cutting portions of the pattern as in Figure 12 (b) and (d), and mounting them to the correct locations of the pattern considering the rotations and reflections as in Figure 12 (c) and (e). Finally, the pattern is rendered in tile as illustrated in Figure 12(f). One can imagine how easy this novel technique was to apply, yet how complicated it was to discover.

Figure 13: Escher’s symmetry drawings produced from (a) diamond, (b) rectangular, and (c) I-bar patterns. The grids are placed on the original images to reveal the relationships.

Figure 13 presents examples of Escher’s symmetry drawings. Figure 13(a) utilizes a diamond pattern by converting it to a man applying a rotation of 120. whereas Figure 13(b) was created from a rectangle with a rotation of 180. In Figure 13(c), Escher was able to take the I-Bar pattern and adapt it to the totally dissimilar motifs of angels and devils.

In many of Escher’s tessellations, not only the patterns, but also the entire scene is inspired by the circle and eternity as in Islamic art. The “Circle Limit” series is a good example of works that use cyclical tiling with shrinking patterns from the center to the border in a circle. Although a circle is depicted, the patterns theoretically reach an infinitive number of repetitions on the border. In his “Metamorphosis II,” it is also interesting to see that a closed cycle is formed when the two vertical ends of the picture are joined together. Similarly, in his famous woodcut ‘Day and Night,’ which shows black and white birds flying in opposite directions, not only do the birds and landscape complete cycles, but also the print is symmetric with respect to a vertical line (4).

Figure 14: Convex and Concave, 1955
Another famous work by Escher, “Convex and Concave,” exemplifies his “impossible reality” works. The essential idea that governs the entire lithograph is the Islamic tumbling baby block pattern, which appears in the flag on the upper right side. Although the picture, as a whole, seems to portray a normal scene, it actually consists of multi-purpose planar surfaces. Depending on the location upon which the eye focuses, the same planes may serve as ceilings, walls, or floors. Escher’s “Waterfall,” “Ascending and Descending,” “Relativity,” and “House of Stairs” all present similar mind-boggling characteristics (2).

In conclusion, Escher is a world-famous graphic artist, well-known for his impossible structures and transformation prints. He is one of the unique figures appreciated for his ability to apply his mathematical talent in artistic creation. He was strongly influenced by the Islamic patterns in the Alhambra – a fourteenth century palace in Spain. He developed his extraordinary style and mastered his skills after exploring the tessellation techniques Islamic artists used to create the figures in the Alhambra.

Fatih Gelgi has a PhD in computer science. He is currently the computer coordinator of Accord AMSP team in Los Angeles.

Bibliography

1. M.C. Escher, the Official Website. [Online] [Cited: January 10, 2009.] http://www.mcescher.com/.
2. Desoe, Carol D. Marthematics: The Blending of Mathematics and the Art of M.C. Escher. [Online] [Cited: December 10, 2008.] http://caroldesoe.com/IslamicArt/mARThematics.pdf.
3. Broos, C.H.A. Escher: Science and Fiction. In: J.L. Locher. The World of M.C. Escher. New York : Abradale Press, 1988.
4. Locher, G.W. The Work of M.C. Escher. In: J.L. Locher. The World of M.C. Escher. New York : Abradale Press, 1988.
5. Abbas, Jan S. Islamic Patterns: The Spark in Escher’s Genius. In: Doris Schattschneider, Maurits Cornelis Escher and Michele Emmer. M.C. Escher’s Legacy. New York : Springer, 2005.
6. M.C. Escher. Wikipedia. [Online] [Cited: January 10, 2009.] http://en.wikipedia.org/wiki/M.C._Escher.
7. O’Connor, J.J. and Robertson, E.F. Maurits Cornelius Escher. School of Mathematics and Statistics. [Online] May 2000. [Cited: December 21, 2008.] http://www-history.mcs.st-andrews.ac.uk/Biographies/Escher.html.
8. Ernst, Bruno. The Magic Mirror of M.C. Escher. New York : Barns & Noble Inc., 1994.
9. Islamic Patterns and M.C. Escher’s Tessellations. North Texas Institute for Educators on the Visual Arts. [Online] [Cited: December 6, 2008.] http://www.art.unt.edu/ntieva/pages/about/newsletters/vol_14/no_1/.
10. Melikian-Chirvani, A. S. Treasure of Islam. New Jersey : Wellfleet Press, 1985.
11. Islamic Art through the Eyes of M. C. Escher. Desoe, Carol D. Salt Lake City : NCTM Annual Meeting, 2008.
12. Schattschneider, Doris. Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M.C. Escher. New York : W.H. Freeman and Company, 1990.
13. Graber, Oleg. Arts of Islamic Peoples. Encyclopedia Britannica. 1974, Vol. 9.

In an Author’s Mind

Louima Cunningham — Sun, 01 Mar 2009 00:00:00 +0000

Rational, Romantic, and Regular were three roommates. They were all new writers with splendid ambitions. They all dreamt of displaying the best of their talents one day. For this, they had different styles and writing strategies. Rational, who had graduated from the school of science, always sought a sound reason for writing, and did not schedule a time for writing otherwise. Romantic, on the other hand, had not had any formal education. But she had been very well trained by her parents to become a keen observer both materially and spiritually. So, Romantic reserved ample time to wait for inspiration and to dress it in the most beautiful words whenever it came. Regular, a graduate of a military school, split his days into well-defined slots, and had a regular time for writing.

Reductionist, their next-door neighbor, was editor-in-chief of a highly recognized magazine. He was kind of older, and so had rather a fatherly attitude toward them. Not surprisingly, each of the three writers had one thing in mind-to catch the attention of their next-door neighbor, which was a really tough job. Having seen thousands of different articles in his life, and still editing several of them every day, Reductionist had become very good at categorizing ideas and pieces of writing. So, it was really difficult, if not impossible, to come up with something that he would call original. This state of Reductionist caused competition, and sometimes jealous actions, among the three writers.

Reductionist used to invite his neighbors to accompany him whenever he was invited to a program related to writing. Rational especially liked them because he learned new things from different people. Romantic loved staying alone, but doing this in different settings opened ways for new inspiration. Regular, on the other hand, was not very thrilled at the idea of traveling because it disturbed his daily schedule. But he thought it was OK being with friends as part of a bigger schedule that spans a larger time.

At the end of one of those trips, they were traveling back home on a dark and rainy night. As they covered each mile of the road, they talked about various topics. After some random ones, they started talking about a topic that really interested all of them: writing. They discussed different issues surrounding the main idea of writing, such as how to start writing, how to write well, how to make your words carry meanings that would satisfy the mind and the heart, and so on. When it came to the issue of inspiration and new ideas, Romantic told a short story:

“A farmer had two fields. He started cultivating both. After the first season, he saw that one of the lands was yielding produce but the other one didn’t. Several consecutive trials only confirmed the quality of the fertile one. The more trials the farmer made, the faster he received the produce and the more he reaped. Then the farmer decided not to use the barren field anymore.

“The inspirations are gifts from God. He plants seeds in our hearts in that way. People who value and pay due respect to inspiration are like the fertile field in the story. The farmer enjoys the produce and uses that field more. People who ignore inspiration or postpone dealing with it are the barren land. They don’t foster the seed, and the farmer ceases using them.”

After the apt parable, everybody was submerged in silent thought for a while. Then Romantic suggested, “Why don’t we pull over and talk about this all together with peace of mind? I’m really enjoying this.” But Rational did not share her perspective: “You know, I really would love to, but we have a long way to go. It is not wise to stop and forget about our trip. What are you going to do when we are all sleepy and not able to continue on the way? And what is wrong with talking while traveling, anyway?”

At the words of Rational, Romantic started crying: “You never listen to me; you always want me to forget my heart. I feel like I am among friends who are like dead statues.” Irritated by the words of Romantic, Regular took a turn, but talked in a way so as to manage the feelings of everybody: “Hey, umm… I think focusing on the discussion is a good idea, but it is not what we usually do. We are not near a lake or on top of a hill. It is neither sunset nor nighttime in a café. So, it may be better to wait until tomorrow.” Although these words were as neutral as they could be, Romantic still felt neglected: “I don’t think you are going to give yourselves to the matter if we keep going and talking at the same time. Instead, you are going to exploit and consume this lovely talk as a means to keep awake. This is a clear betrayal; it is hypocrisy toward your heart.”

“Wait a minute. I don’t think being wise is the same thing as hypocrisy. Do you have a really good reason to forget about everything else for the sake of this topic? I mean, what makes this topic so important that you want us all to sacrifice everything for it?” rebutted Rational.

Romantic could not answer this question, and turned her face outward into the darkness veiling the fresh green of the trees. She thought, “I am just like those trees and flowers that suffer from not being able to display their beauty because of the darkness.”

Reductionist, who was driving while listening to all the talk, said, “What is it that you are aiming to get from this talk, whether we do it now or later? I don’t want to be discouraging here, but isn’t this another hay-fire that is going to give a burst of heat and light, but will prove ordinary and transient in the end? This is just another emotion-provoking breeze about inspiration. I have experienced several of those, and yet here comes another. What difference is this going to make when we already have thousands of them out there? What is the point in discovering America over and over?”

Hearing all these arguments, Romantic, Rational and Regular all shut their mouths. Although the three roommates wanted to talk about the new perspective that Romantic had presented, their dispute about how to do it had weakened them in the face of Reductionist’s arguments. Nobody could say a word after Reductionist had spoken, and silence covered the quartet like the night.

Although she had been upset by the rest of the group, Romantic was still awake and happy in her mind. She decided to daydream about previous inspirations she had received. That way, she lived again the exhilaration and joy that came along with them. Triggered by that energy, Romantic gave a giggle that disrupted the increasing weight of the dark and silence. Rational, who was sorry to have upset Romantic, used this as an opportunity: “I have an idea. By going slower, we can sincerely concentrate on each other and on Romantic’s inspirations. That way, we can convert our trip into a journey toward the making of an article.” This suggestion triggered Regular to say: “Yeah, depressed nights, too, are part of our custom for in-depth talks.” Now everybody was waiting for Reductionist to approve the idea. Reductionist first slowed down. The reduction of the noise from the engine strengthened the silence. In the tense atmosphere, Reductionist laughed like a thunderclap, and said, “I am going to tell you guys a little story. A writer had three pens. He picked the first one and wrote an article with it. After finishing it, the pen said, ‘I wrote this article for you. Do you like it?’ The writer smiled back and said, ‘Yes, thank you.’ Then the writer put that pen in his office so that it could do things for him. Another day, the writer used the second pen to write a piece. After he finished it, the pen turned to him and said, ‘I wrote what you told me. Do you like it?’ The writer smiled back and said, ‘Yes, thank you.’ Then the writer put that pen in his bag so that it would write things as he wanted. And finally the writer used his third pen to write another article. After finishing it, the pen turned to him with a smile and said, ‘Thank you for using me.’ The writer smiled back at the third pen and put it in his pocket right next to his heart. He carried it everywhere he went, and whenever he had an original idea, he welcomed it with the help of his third pen.”

By that time, the rain outside had turned into a rain of smiles inside the car. Motivated by the unexpected story Reductionist had told, everybody engaged in an effort to welcome the inspiration that came through the one next to the heart. Romantic was not late taking her turn: “You know, for everything there is a season. You have to sow your seeds in the fall and wait until summer to reap. If you sow any time else, you not only waste your time but also lose your seeds. So, I guess the best time to work on an idea is when it first descends from the heavens to your heart.”

Both Regular and Rational looked at Romantic with wide open eyes. Regular said, “You have an important point there.”

“That is absolutely right,” concluded Rational.

Seth Mette has a PhD in Aerospace Engineering and is currently working as a postdoctoral fellow at West Virginia University. He has a special interest in psychological fiction.

Symmetry and Beauty

Louima Cunningham — Fri, 01 Oct 2004 00:00:00 +0000

When visiting Moscow University, Paul Adrien Maurice Dirac, the famous physicist and the founder of Quantum Mechanics, as well as being the fifteenth Lucasian Professor of Mathematics at Cambridge University, was asked about his philosophy in physics and he wrote on a blackboard “physical laws should have mathematical beauty.” This phrase remains preserved on the same blackboard today. As Sir Michael Berry said at the opening of Dirac House in 1997, “he showed that the simplest wave satisfying the requirements was not a simple number but consisted of four components. This seemed like to complicate matters, especially for those minds that were still reeling from the unfamiliarity of “ordinary” quantum mechanics. Four components! Why should anybody take Dirac’s theory seriously? Foremost and above all for Dirac was the fact that the logic leading to the theory was, although deeply sophisticated, in a sense beautifully simple. Much later, when someone asked him “what do you think of the equation?” he is said to have replied: “I think that it is beautiful.” In fact, Professor Dirac knew that very significant mathematical equations occur in all created things. Even though these consist of deeply sophisticated matters, at the same time they occur with a beautiful simplicity and are a clear description of the action of creation of the Eternally Besought of All. When we examine his quotation in this light, we are better able to understand what he meant.

Be they physical or chemical, many attributes of beings are dependent on mathematical laws and their appearances are also shaped along mathematical principles. When we observe creation from this standpoint, we can perceive the perfection as well as the spectacular beauty that is inherent in every being. As reflections of the Attributes of the Names of God Almighty, Jamil (The Owner of Beauty), Bari (The One Who Creates from nothing), Sani (The Maker of All) and Musawwir (The Designer), this beauty found in the external appearance of beings is dependent on more than one factor coinciding. The most important factor here is “symmetry,” which is described as “an exact correspondence and beautiful balance among the parts of an object.” Beings are created with various symmetrical attributes and with great artistic beauty.

The most common symmetry type is the bilateral symmetry; this creates a mirror effect which is an exact correspondence between the right and left sides. An object forms an exact symmetry with its reflection in the mirror. A perfect symmetry that is very similar to the mirror effect can be found in the human body. The left and right sides of our body are symmetrically corresponding. Imagine a dividing line that passes from the middle of the forehead, through nose, chin and down the chest, we can see a perfect symmetry on both sides of the body. Our arms, legs, eyes, ears, nose and lips are designed with a bilateral symmetry. The same symmetrical structures can also be seen in most other creatures. All mammals, reptiles and birds are symmetrically created.

Another type of symmetry is rotational (radial) symmetry. Imagine a metal object that is in the shape of an equilateral triangular placed on the sand. If we will rotate this object 120o around an axis that passes through its center, the new position of the object will fit exactly into its original mark left on the sand. The reason for this is that the radial symmetry for equilateral triangles is 120 degrees. In the same way, a square has a radial symmetry of 90^o and a regular polygon with n number of sides has a radial symmetry of 360/n degrees.

The beautiful symmetry of snow flakes, with their regular hexagonal shape are a beautiful natural phenomenon. In addition to these there are shapes in nature that have a three-dimensional radial symmetry. The most significant of these shapes are regular polyhedrons. An example of such polyhedrons is the salt crystalline elements that have cubical structures. Until recently, the fact that there is a creature in nature that has a regular polyhedral shape, consisting of twenty sides, was unknown. However, when a type of adenovirus that causes infections and hepatitis in dogs was discovered, it was found that there is a creature with twenty regular sides in nature.

One of the most beautiful samples of radial symmetry in nature is the daisy. Symmetrical structures do not only exist in the normal world and in the micro worlds, but also can be found in the macro world, like all the huge celestial objects, the Sun, the Moon, galaxies, star clusters in the sky . . . . All planets move around the Sun in a symmetrical manner, whereas galaxies have a spiral symmetry. It is interesting that the symmetrical structure of living beings is overwhelmingly apparent externally, rather than internally. For example, the internal organs in the human body, like the lungs, liver, stomach and intestines are not symmetrical and we have only one heart in one side of our chest cavity. Moreover, the lobes of the brain are not symmetrical either. However, all the metabolic processes in human body function properly. Does this mean that the mathematical beauty found in our external appearance is merely for aesthetical reasons? God does not create things for only one reason or purpose, on the contrary, He creates them to serve many motives and in relation with many functions. For example, if we did not have two eyes and if they were not symmetrically placed on our faces, we would not be able to see objects three-dimensionally. In the same way, if our ears were not symmetrically placed on our heads, then we would have great difficulty in determining the direction and source of sounds. If we did not have symmetrical feet and legs, we would not be able to walk well, and if our arms were not symmetrical, we would not be able to balance our body’s center of gravity while walking. If birds did not have symmetrical wings, they would not be able to fly, and if the fins of fishes were not symmetrical, they would not be able to swim smoothly.

Symmetry is also closely related to physical and mental robustness. According to one study, women who suffer from an infectious disease during pregnancy are more likely to have babies with asymmetrical features. The same study claims that asymmetrical babies are more susceptible to heart disease than symmetrical babies.

Another study shows that people with asymmetrical teeth are more likely to have more harmful microorganisms in their mouth than those who have symmetrical teeth. It is interesting that there tends to be a greater difference between the fingerprints on the left and right hands of schizophrenic people than on those of normal people.

Symmetry is a phenomenon that is used by animals and insects. For example, an experiment showed that bees prefer flowers that are symmetrical. Actually, flowers with perfectly symmetrical shapes produce more nectar than those that are asymmetrical. In one investigation, a symmetrical flower was made asymmetrical with a pair of scissors. The flower had been attractive to bees before its shape was changed; after made asymmetrical, the flower became unattractive to bees, even though it had just the same amount of nectar as before.

All these facts reveal that there is much wisdom and beauty hidden within the symmetry that the Almighty Designer uses to shape all beings. We take symmetry for granted. To have two eyes placed equidistance and two ears on each side of the head is the norm. Anything else strikes us as strange. But if we just take a few moments to think about why our eyes are where they are, and why our ears are placed on the sides of our heads, the answer is obvious. God’s mercy is infinite; in even the simplest example of symmetry there is a reason. We should not take this world for granted, but rather use every opportunity to dwell upon and be thankful for the wonderful world that has been created for us.

References

Stewart, I. & M. Golubitsky, Fearful Symmetry, Blackwell, 1992.
Rosen, J., Symmetry Discovered, Cambridge University Press, 1975.
Tarasov, L., This Amazingly Symmetrical World, Mir Publishers, Moscow: 1986.

Advocating for Gifted and Talented Student Programs

Louima Cunningham — Mon, 01 Jul 2002 00:00:00 +0000

Our school systems need to advocate for curricula differentiation and for grouping gifted and talented students. Advocates of gifted and talented student programs relentlessly seek to convince teachers and administrators that setting up an honors class is not enough to meet the needs of our gifted student population.

Americas gifted population

America has approximately 3 million gifted students, a number that represents 6 percent of its entire student population. The Council for Exceptional Children for the U.S. Office of Education reported that 39 states have legislation on gifted and talented education. These states generally define giftedness in terms of intellectual ability, creativity, leadership, and artistic talent (Zettel 1980).

Mitchell (1984) has reported that most states select gifted and talented students through multiple criteria. However, many school districts still use intelligence tests as the key identifier. Intelligence is measured through established IQ tests, and identifying the gifted is based on those scores. The population of gifted individuals is referred to as moderately gifted (IQ range 130-144), highly gifted (IQ range 145-159), and exceptionally gifted (IQ >160) (Clark 2002). However, using test scores alone is not sufficient to identify the great potential of highly creative students, for other factors need to be considered.

Giftedness traits

If a child displays outstanding traits, it is likely that he or she is gifted. In a study by Rogers (1986), the following characteristics distinguished the 38 gifted from the 42 average third and fourth graders: a brisk learning ability, an excellent memory, a long attention span, perfectionism, a fondness for older buddies, a broad vocabulary, a sense of humor, an interest in books, a knack in puzzles and mazes, maturity, inquisitiveness, perseverance, and intense observation.

Other factors that set gifted students apart from their peers are a rich memory, curiosity, reflectivity, and an openness to experiences. Resnick (1997) identifies six types of gifted students. The challenging student is creative and rebellious. The successful gifted student achieves most of the time and prefers to conform to the environment. The underground type is shy and lacks self-confidence. The gifted dropout student is angry and explosive. The autonomous student is intrinsically motivated and passionate. The sixth type consist of the double-labeled students who are both gifted and disabled and sometimes labeled as having ADD (Attention Deficit Disorder) due to their lack of focus.

Modified programs

Gifted students learn faster, understand more complex issues, and have distinctive emotional needs. So, regular school programs must be modified to accommodate their needs. Gifted students should be provided with acceleration options and various forms of enrichment that broaden the conventional school curriculum.

Organizing a comprehensive program to satisfy gifted and talented students is a complex task. Schools should create such opportunities as acceleration, enrichment, self-paced classes, or advanced classes. Staff members should be educated to identify and provide an appropriate curriculum for gifted students. Differentiated Educational Plans (DEPs), which briefly describe the modified content, activities, and assessment planned for such students and his or her group should be filed for each student.

Once the DEPs have been implemented, students should be encouraged to move through content areas at their own pace. If they master a particular unit, they need to be provided with more advanced learning activities, as opposed to more of the same activity. In other words, burdening gifted students with more trigonometry homework or drills, just because they can do it and need to be kept engaged, is not considered to be part of acceleration or enrichment.

Two very helpful strategies in running optional activities toward enrichment and acceleration are compacting and contracts.

Compacting. Students are provided with enrichment and spend less time working on skills they have already mastered in the regular curriculum. For example, a seventh grade student who has a grade equivalence of above 8 in math is usually uninterested in math classes. The teacher can provide him or her with challenging puzzles, competition questions (such as Math Counts or International Math Olympiads), math project samples, and help the students develop advanced and versatile skills separately from their peers.

Contracts. Students and teachers agree on what students will learn, how they will learn it, how long it will take them to learn it, and how they will be evaluated. A science teacher and a student might agree on a cycle of 6-week periods when the student will complete and present a science project or a portfolio. Contracts should include a calendar, written student and teacher roles, a scoring guide (a rubric), and a product format. Students and parents must join the teacher in the decision-making process while outlining this contract (Parke 1989).

Compacting and contracts do not stop students from attending regular classes. Depending on the student’s characteristics, availability on campus, reports from teachers, and the curricula, a student, for example, might stay in regular science and social studies classes, spend half of his or her time working independently in language arts, and not attend regular math classes at all so that he or she can work with the school Math Olympiad team.

Before each campus decides which format will best serve their students’ needs, they should decide what is applicable and feasible. Special magnet schools, pull-out programs, a gifted school within a school, resource rooms, flexible grouping provision based on definite needs, and mainstreaming are some of the available alternatives (Daniel and Cox 1988).

When gifted students are taught in a traditional slow-paced classroom and subjected to an inadequate curriculum, they do not apply themselves, have low stimuli, and even drop out. If schools do not allow gifted and talented students to flourish, their achievement and motivation will fade in a relatively short period of time. Parents of gifted students may choose to enroll their children in alternative programs, such as home schooling or other gifted and talented schools.

Grouping

Rogers (1991) believes that gifted and talented students should spend the greater part of their school day with others of corresponding abilities and interests. Gifted students benefit from learning together and need to be placed with similar students in their areas of strength so that they can understand their learning differences in gifted classes.

Grouping gifted students cannot be considered elitism or a violation of equity in education. It is an erroneous belief that all students are best assisted in heterogeneous learning environments. There are many grouping methods in which average and below-average students may benefit as well as the gifted do. Rogers (1991) suggests many strategies and grouping options. He recommends a cluster grouping of students if schools cannot maintain a full-time gifted program.

In enrichment clusters, advanced learning experiences and higher-level thinking skills are combined in groups of various graded members. Students and teachers learn authentically, work on real problems, and act as practicing professionals to produce a product or effect a change for a real audience. The clusters work according to an extended and flexible schedule (Renzulli 1997).

Accountability

Prosperous people are accountable to the state and are obliged to pay taxes on what they possess. In return, the state has the duty and responsibility to provide services for these people. Gifted and talented people should feel accountable to God, state, and their nation for how they use their potential (for good or bad) and the extent to which they use it (efficiently or wastefully). They should not enjoy the relaxation of saying: This is the best I can do, for their potential is dynamic and subject to improvement. Pure talent must be accompanied by industriousness, perseverance, and conscientiousness. As Thomas Edison stated: Genius is one percent inspiration and ninety-nine percent perspiration. As a result, a genius is often a talented person who has simply done all of his or her homework.

On the other hand, the state, society, and educational components are responsible for buttressing gifted and talented programs and for using these students’ special abilities instead of wasting them. Gifted and talented people should be identified and helped so that they can assist others.

Another critical component of educating the gifted generation is preventing the developing a corrupt, threatening mob of talented people obsessed with selfishness, evil, or lawlessness and deprived of moral values, ethics, and good intentions. Such an outcome is even worse than wasting the gifted generation’s talents. Notorious dictators, criminals, and militants are all known to be geniuses. We are held accountable for developing a fruitful, qualified, and fully activated gifted generation, one that is decent, just, and ethical and can lead and help the world.

References

Clark, B. Growing up Gifted. Upper Saddle River, NJ: Pearson Education, Inc., 2002.
Daniel, N. and Cox, J. Flexible Pacing for Able Learners. Reston, VA: The Council for Exceptional Children, 1988.
Mitchell, B. An Update on Gifted and Talented Education. U.S. Roper Review 6 (1984): 161-63.
Parke, B. N. Gifted Students in Regular Classrooms. Needham Heights, MA: Allyn & Bacon, 1989.
Renzulli, J. S. A Bird’s Eye View of the Schoolwide Enrichment Model: A Practical Plan for Total School Improvement (1997). Retrieved 25 April 2002, from www.sp.uconn.edu/~nrcgt/sem/semart07.html.
Resnick, D. and Goodman, M. Research Review. NW Education Magazine (1997).
Rogers, M. T. A Comparative Study of Developmental Traits of Gifted and Average Children. Ph.D. diss., University of Denver, 1986.
Rogers, K. The Relationship of Grouping Practices to the Education of the Gifted and Talented Learner: An Executive Summary. Storrs, CT: The National Research Center on the Gifted and Talented, 1991.
Rogers, K. Grouping the Gifted and Talented. Roper Review 16, no. 1 (1993): 8-12.
Zettel, J. Gifted and Talented Education from a Nationwide Perspective. Reston, VA: Council for Exceptional Children, 1980.