Tuesday, June 16, 2009

Maurits Cornelis Escher

(17 June 1898 – 27 March 1972), usually referred to as M.C. Escher, was a Dutch-Frisian graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations.

Early Life

Maurits Cornelis, or "Mauk" as he came to be nicknamed, was born in Leeuwarden, The Netherlands. He was the youngest son of civil engineer George Arnold Escher and his second wife, Sara Gleichman. He was a sickly child, and was placed in a special school at the age of seven and failed the second grade. In 1903, the family moved to Arnhem where he took carpentry and piano lessons until he was thirteen years old.

From 1903 until 1918 he attended primary school and secondary school. Though he excelled at drawing, his grades were generally poor. In 1919, Escher attended the Haarlem School of Architecture and Decorative Arts. He briefly studied architecture, but he failed a number of subjects (partly due to a persistent skin infection) and switched to decorative arts. Here he studied under Samuel Jessurun de Mesquita, with whom he would remain friends for years. In 1922 Escher left the school, having gained experience in drawing and making woodcuts.

Later Life

In 1922, an important year of his life, Escher traveled through Italy (Florence, San Gimignano, Volterra, Siena) and Spain (Madrid, Toledo, Granada). He was impressed by the Italian countryside and by the Alhambra, a fourteenth-century Moorish castle in Granada, Spain. He came back to Italy regularly in the following years. In Italy he met Jetta Umiker, whom he married in 1924. The young couple settled down in Rome and stayed there until 1935, when the political climate under Mussolini became unbearable. Their son, Giorgio Arnaldo Escher, named after his grandfather, was born in Rome. The family next moved to Château-d'Œx, Switzerland where they remained for two years.

Escher, who had been very fond of and inspired by the landscapes in Italy, was decidedly unhappy in Switzerland, so in 1937, the family moved again, to Ukkel, a small town near Brussels, Belgium. World War II forced them to move in January 1941, this time to Baarn, the Netherlands, where Escher lived until 1970. Most of Escher's better-known pictures date from this period. The sometimes cloudy, cold, wet weather of the Netherlands allowed him to focus intently on his works, and only during 1962, when he underwent surgery, was there a time when no new images were created. Escher moved to the Rosa-Spier house in Laren in 1970, a retirement home for artists where he had his own studio. He died at the home on 27 March 1972, at 73 years of age.


Escher's first print of an impossible reality was Still Life and Street, 1937. His artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. Well known examples of his work also include Drawing Hands, a work in which two hands are shown, each drawing the other; Sky and Water, in which light plays on shadow to morph the water background behind fish figures into bird figures on a sky background; and Ascending and Descending, in which lines of people ascend and descend stairs in an infinite loop, on a construction which is impossible to build and possible to draw only by taking advantage of quirks of perception and perspective.

He worked primarily in the media of lithographs and woodcuts, though the few mezzotints he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures and space. Additionally, he explored interlocking figures using black and white to enhance different dimensions. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals.

In addition to sketching landscape and nature in his early years, he also sketched insects, which frequently appeared in his later work. His first artistic work, completed in 1922, featured eight human heads divided in different planes. Later around 1924, he lost interest in "regular division" of planes, and turned to sketching landscapes in Italy with irregular perspectives that are impossible in natural form.

Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—Escher's work had a strong mathematical component, and more than a few of the worlds which he drew are built around impossible objects such as the Necker cube and the Penrose triangle. Many of Escher's works employed repeated tilings called tessellations. Escher's artwork is especially well-liked by mathematicians and scientists, who enjoy his use of polyhedra and geometric distortions. For example, in Gravity, multi-colored turtles poke their heads out of a stellated dodecahedron.

The mathematical influence in his work emerged around 1936, when he was journeying the Mediterranean with the Adria Shipping Company. Specifically, he became interested in order and symmetry. Escher described his journey through the Mediterranean as "the richest source of inspiration I have ever tapped."After his journey to the Alhambra, Escher tried to improve upon the art works of the Moors using geometric grids as the basis for his sketches, which he then overlaid with additional designs, mainly animals such as birds and lions.

His first study of mathematics, which would later lead to its incorporation into his art works, began with George Pólya's academic paper on plane symmetry groups sent to him by his brother Berend. This paper inspired him to learn the concept of the 17 wallpaper groups (plane symmetry groups). Utilizing this mathematical concept, Escher created periodic tilings with 43 colored drawings of different types of symmetry. From this point on he developed a mathematical approach to expressions of symmetry in his art works. Starting in 1937, he created woodcuts using the concept of the 17 plane symmetry groups.

In 1941, Escher wrote his first paper, now publicly recognized, called Regular Division of the Plane with Asymmetric Congruent Polygons, which detailed his mathematical approach to artwork creation. His intention in writing this was to aid himself in integrating mathematics into art. Escher is considered a research mathematician of his time because of his documentation with this paper. In it, he studied color based division, and developed a system of categorizing combinations of shape, color and symmetrical properties. By studying these areas, he explored an area that later mathematicians labeled crystallography.

Around 1956, Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher's interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher's works Circle Limit I–IV demonstrate this concept. In 1995, Coxeter verified that Escher had achieved mathematical perfection in his etchings in a published paper. Coxeter wrote, "Escher got it absolutely right to the millimeter." His works brought him fame: he was awarded the Knighthood of the Order of Orange Nassau in 1955. Subsequently he regularly designed art for dignitaries around the world. An asteroid, 4444 Escher, was named in his honour in 1985.

In 1958, he published a paper called Regular Division of the Plane, in which he described the systematic buildup of mathematical designs in his artworks. He emphasized, "Mathematicians have opened the gate leading to an extensive domain.

"Overall, his early love of Roman and Italian landscapes and of nature led to his interest in the concept of regular division of a plane, which he applied in over 150 colored works. Other mathematical principles evidenced in his works include the superposition of a hyperbolic plane on a fixed 2-dimensional plane, and the incorporation of three-dimensional objects such as spheres, columns and cubes into his works. For example, in a print called "Reptiles," he combined two and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality and described himself as "irritated" by flat shapes: "I make them come out of the plane."

Escher also studied the mathematical concepts of topology. He learned additional concepts in mathematics from the British mathematician Roger Penrose. From this knowledge he created Waterfall and Up and Down, featuring irregular perspectives similar to the concept of the Möbius strip.

Escher printed Metamorphosis I in 1937, which was a beginning part of a series of designs that told a story through the use of pictures. These works demonstrated a culmination of Escher's skills to incorporate mathematics into art. In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif. This effect symbolizes his change of interest from landscape and nature to regular division of a plane.

One of his most notable works is the piece Metamorphosis III, which is wide enough to cover all the walls in a room, and then loop back onto itself. After 1953, Escher became a lecturer at many organizations. A planned series of lectures in North America in 1962 was cancelled due to an illness, but the illustrations and text for the lectures, written out in full by Escher, was later published as part of the book Escher on Escher. In July 1969, he finished his last work before his death, a woodcut called Snakes. It features etchings of patterns that fade to infinity both to the center and the edge of a circle. Snakes transverse the circle and the patterns in it, with their heads sticking out of the circle.

Tuesday, June 9, 2009

Pens of Hope

I am helping my friend in their drive to gave pencils for the less fortunate children of Northern Samar. You can extend your help until the end of June. Please contact numbers on the poster.

My Frustration

Late april of this year, I decided to loan on my Pag-ibig contribution for some not very important reasons. I decided to do so just to check how healthy my contribution records has been. Days and days passes but still I got no feedback on my application. So I did asked the person processing it. Then it was known to me that I need to apply the transfer of my records from the other branch since my previous employer wasn't of my present Pag-ibig branch.

I can't do anything except to comply what was required, so I did sign the transfer application form and have it submitted personally on the requesting branch, Cebu office. Upon submission, I was told to verify my request one and a half month after. For me, the given duration was too long and to clarify the process I did email the public affairs division of Pag-ibig in Manila. There I was informed that it wouldn't take that long.

Good thing that public affairs division help me facilitate my appeal. They emailed concerned branches and there I was getting a li'l hope on their actions. Ended, my files was successfully transfered to Cebu branch as of the 2nd day of June.

Prior to the verification of my records, it needs to be consolidated first by the recipient branch. It will be now the merging of my previous records with my new employment contribution. Since my records has been forwarded already as of June 2, so I went to Pag-ibig office to verify it. I was so sorry to know that it wasn't done yet, and I was told to go back the following week.

On my obedience, I went back just this afternoon. Sad to say they weren't able to consolidate it yet. On my frustration to their process, I emailed public affairs office again and below is my email:

To whom it may concern;

I would just like to update you guys on my recent appeal to transfer my records from Mandaue to Cebu Branch. Unfortunately it wasn't consolidated yet. I emailed Jennifer Roca c/o
mcd_cebu@yahoo.com verifying the status of transfer but there was no reply. My second option was to call the phone number given by Maricar Cabreros of Mandaue branch but I got no answer like no one was around. What I did next was to went to Pag-ibig office and ask the information about it. I also asked what causes the delay. The teller guy told my that when tranferring, they have to encode my records to their system. To me, the alibi was a big LIE cause files nowadays are electronic.

Just this afternoon around 4:40pm Cebu time, I went to Pag-ibig office to personally do the verification. Upon reaching the records section, I was told by a guy that verification of transfer shall be done only at the information, then I said I was already there but my records wasn't consolidated yet according to the teller. So this guy called the incharged Jennifer Roca. The later told me right away that transfer from Mandaue will only appear to them 7 days after, so I said it must be here now coz I was notified June 2nd that my records has been forwarded already. Then she gets my ID to check.
After a while, I asked the girl regarding the noreply to my email then she said that she's not the only one using the email account, okay granted. Then I ask again why there was nobody taking my call and she replied that their phone wasn't working those days. Ohhh come on....how many alibis should I need to hear?

Now, herecomes my questions with regards to the items in RED BOLD above.
encode my records to their system - is this really true?
appear to them 7 days after - what IT system are we using?
I know these are all big alibis but reasons like these are fooling us citizens of the Philippines. Alibis are not forbidden but please see to it that the reasons you will gave is close to what is reality. These are merely cover-ups of their ineffective and delayed services.

Hope to hear actions for these...!!!

Things like these are very frustrating. When are we Filipinos be awaken? No wonder others have flown to the moon and went back, then we Filipinos are still riding on top of our slow carabaos, the government. How do the government rate the productivity of their employees? There must be a good system for these cause as I can see, there service is very ineffective and most of the time delayed.

There should be a CHANGE in the government system...!!! Wake up my comrades.

Thursday, June 4, 2009

Vincent van Gogh

He is one of my ultimate idol in visual art. Vincent Willem van Gogh, in full name (30 March 1853 – 29 July 1890) was a Dutch Post-Impressionist artist. [1] Some of his paintings are now among the world's best known, most popular and expensive works of art.

Van Gogh spent his early adult life working for a firm of art dealers. After a brief spell as a teacher, he became a missionary worker in a very poor mining region. He did not embark upon a career as an artist until 1880. Initially, Van Gogh worked only with sombre colours, until he encountered Impressionism and Neo-Impressionism in Paris. He incorporated their brighter colours and style of painting into a uniquely recognizable style, which was fully developed during the time he spent at Arles, France. He produced more than 2,000 works, including around 900 paintings and 1,100 drawings and sketches, during the last ten years of his life. Most of his best-known works were produced in the final two years of his life, during which time he suffered recurrent bouts of mental illness, which led to his suicide.

The central figure in Van Gogh's life was his brother Theo, who continually and selflessly provided financial support. Their lifelong friendship is documented in numerous letters they exchanged from August 1872 onwards. Van Gogh is a pioneer of what came to be known as Expressionism. He had an enormous influence on 20th century art, especially on the Fauves and German Expressionists.