M. C. Escher, or Maurits Cornelis Escher, was a Dutch graphic artist and a printmaker whose art was not celebrated for most of his life, and the first time it was ever exhibited was in the year 1968, when he was 70 years of age. Apart from printmaking, Escher also dabbled in making illustrations for books, designing tapestries and painting murals. This century, however, has seen his work being exhibited the world over. His work mixes art with impossible math and geometry to create pieces that boggle the mind. Scientists and mathematicians have pondered over his work: it has been used in some mathematical papers as well as discussed at length in the 1979 Pulitzer Prize winning book – Godel, Escher, Bach – written by Douglas Hofstadter.
M. C. Escher was born in the city of Leeuwarden in the Netherlands, on June 17, 1898. His father, George Arnold Escher, was a civil engineer, and his mother, Sara Gleichman, was his second wife. In 1908, they moved to the city of Arnhem, and that is where M. C. Escher received his primary and secondary education. In 1919, Escher moved to Haarlem to learn drawing and woodcut printing at the Haarlem School of Architecture and Decorative Arts. Escher had suffered from ill health since he was a child and it hindered his studies here too: after a brief initial stunt with trying to learn architecture, he shifted into the decorative arts.
Escher travelled to many cities in Italy and Spain, where he studied the countryside and architecture. While in Italy, he met Jetta Umiker, who too had been travelling in Italy and had fallen in love with the place. The two got married in 1924, and would go on to have three sons. As the Second World War approached, they moved from Italy to Switzerland to Brussels and then finally settled down in the Netherlands. During the latter part of his life, Escher would travel less and while away in his studio, working on his many designs and the math behind them, more. He died at the age of 73 on March 27, 1972.
Math in his Art
The architecture of the Alhambra palace in Granada, Spain left a deep impression on Escher’s creative curiosity. The intricate designs made out of colorful tiles juxtaposing one another to form beautiful geometric patterns at the Alhambra piqued Escher’s interest in the math in art. Especially interesting to him were tessellations. Tessellations are decorative tiling which can either be “periodic”, where a pattern is repeated on all sides, or “aperiodic”, where the patterns are non-repeating. Tessellations are also found in nature, such as in the hexagonal patterns repeating in a honeycomb. Escher also studied nature: landscapes in Italy, insects such as bees, grasshoppers, ants, and mantises, and lichens – all of which feature in the details in his drawings.
Other mathematical concepts such as symmetry, patterns that would interlock, and infinity would also come to grab Escher’s attention. In Snakes from 1969, which also happens to be his last work, Escher experimented with rotational symmetry where three snakes are interlocked with one another, as well as the many rings in the pattern. He created via the wood cut printing method, i.e. carved up a wooden block which, when dabbed in ink and pressed on paper three repetitive times and at three repetitive angels, would create the rotationally symmetric drawing. The snakes sink into an infinity at the center as well as at the perimeter of the circle.
He also experimented with perspectives and outlines, multiple simultaneous vantage points, shaping and reshaping them such that the objects seem to jump out of the 2 dimensional paper and dance and merge into one another. His drawing, Mobius Strip II, consists of a drawing of the mobius strip – a mathematical surface which is a loop but instead of having two surfaces, it has only one surface – and ants crawling on it. The “inside” and “outside” are deflated onto one another in this drawing. Escher’s fascination with loops can also be seen in his print, Drawing Hands, where two 3 dimensional-looking hands seem to be rising out of a 2 dimensional-looking paper and are drawing one another.
His Art Pieces
This piece by M. C. Escher is called “Relativity”, and it showcases an illusionistic structure of a building from the inside: it depicts multiple staircases going every which way, defying gravity and the laws of physics as we know them. They say Escher drew inspiration for this piece from the secondary school in Arnhem that he attended, and that the stairs herein especially, look exactly like the ones he would trudge up and down countless times while at that school. Escher recounted that time as one of the unhappiest ones in his life. That mood in this piece perhaps reflects that too – an endless loop of morose. Each of the arches at the top of staircases depicts an idylllic world outside – a person having bread and wine in the sun, another standing in the archway with a tree in the background (a tree of life perhaps?), and yet another with two people walking side by side, sharing love and affection for one another.
At first glance, the illusionistic structure seems believable, i.e. if you only look more closely, it will start to make sense. However, on closer inspection of the details, the staircases all meet one another at all the rather impossible angles and seem to defy all rules governing our physical reality – the structure is impossible! The three staircases form what we call an “impossible shape”; this impossible shape being a “Penrose Triangle”. A Penrose Triangle, created by Oscar Reutersvard, a Swedish artist, in the year 1934, is a triangular object which can exist on a 2 dimensional drawing but cannot exist as a 3 dimensional solid object in actuality.
There are apparently multiple centres (or rather, axes?) of gravity within this building, which help make sense of why each staircase is oriented the way it is. Rotating the image around reveals there are multiple relative worlds or realities where each staircase makes sense in a way. Depending upon your vantage point, your reality can change completely!
Hand with a Reflecting Sphere
Escher experimented with reflections and spherical geometry in his works as well. The Hand with a Reflecting Sphere, also known as Self Portrait in a Spherical Mirror, was completed by Escher in the year 1935. In it, Escher holding a spherical reflective surface with most of the room behind him is shown, as Escher gazes into the sphere. The hand in the reflection looks as real as the one holding it, and it confounds the reality – which one is real? Escher loved to play with the theme of switching up vantage points and thereby flipping reality.
Metamorphosis II, a woodcut print, was made between November 1939 and March 1940. It is 7.5 inches by almost 12 feet. An elongated strip, it shows patterns and insects and architecture metamorphosising into one another. One image morphs into the other through merging its tessellated pattern into the other’s. A checkered pattern turns into reptiles that morph into a honeycomb out of which bees are born and transform into butterflies which turn into fish and then birds. The birds then merge into three dimensional red-topped blocks, which morph into a cityscape (that of the coastal town of Atrani in Italy) which tessellates into a chess board, and all then loops back into the checkered pattern we started with.
The Waterfall was completed by Escher in October 1961. It depicts a perpetually in motion waterfall, where water from the waterfall goes into an aqueduct which apparently flows downstream until the onlooker realizes it was going upstream and that it then connects and flows into the waterfall itself. The aqueduct turns three times abruptly before it flows back into the waterfall again. These turns in the aqueduct make use of the Penrose Triangle. Escher also creates optical illusions in his work not by playing with depth, which a lot of the other illusion artists have done and do, but by playing with the proportions in his drawings. For example, in this one, the proportions of the pillars, the changing depth of the trough of the aqueduct as it moves “upstream”, and the ridged brick edges of the aqueduct giving it an impression as if it is moving “downhill”, all work together to help create this illusion. The building structure has two towers with geometric shapes atop each of them, which again points towards Escher’s love for math in art. The plants at the foot of this structure seem to be magnified lichen and moss which Escher had extensively drawn as part of his study in 1942.
Belvedere was completed in May 1958, and shows a belvedere structure. A belvedere structure is an architectural building or part of a building, built to enjoy the beautiful vista around it. The one in Escher’s print, at first glance, looks plausible, but at closer inspection, the objects are all out of sync with their three dimensions! Escher modelled it after his “impossible cube” – a 2 dimensional cube that gives the perspective of a 3 dimensional cube but all its lines and corners are drawn inconsistently from an actual 3 dimensional cube.
The boy sitting at the foot of the Belvedere building, is shown holding an impossible cube. The building shares the same features as this cube. The two floors are open to the sides and the roof is supported by pillars. The pillars on the middle floor all seem to be of the same length. However, the ones at the back are positioned at a greater height than the ones at the front. The floor above is supported by pillars below. However, the whole top storey is oriented at a different angle from the one the middle floor is. This means the pillars below should be all at the same height and not on an angled floor, but a flat horizontal floor. Also, the front of the top floor seems to be supported by the pillars at the back of the middle floor, and the back of the top floor seems to be supported by the pillars at the front of the middle floor. The background is that of the Morrone Mountains in Abruzzo in southern Italy, where Escher had travelled to several times while living in Italy.
Escher was a graphic artist who incorporated math into his artwork. His art was not acknowledged as “art” for a long time, because the artists at the time deemed his artwork to be too mathematical and “intellectual” – and not “lyrical” enough – to warrant being called “art”. However, going into the twenty-first century, his art gained global recognition, in addition to many mathematicians and scientists employing his art into their conceptual understanding of math, science, and computer science. Escher drew inspiration from his travels to Italy and Spain, where he would draw out the landscapes, architecture, and the plants and insects found in nature. The tessellated decorative designs at the Alhambra palace in Spain caught Escher’s eye particularly, which he then incorporated into his art too. Apart from tessellations, Escher was very fond of symmetry (including rotational symmetry), geometric shapes, “impossible objects” such as the Penrose Triangle and the “impossible cube”, as well as loops and the concept of infinity. His work creates masterful optical illusions using paradoxical proportions that he lends to the objects in his drawings and prints. Looking at his art, the mind is left tumbling over itself!
Featured Image Credit: M.C. Escher’s Day and Night (1938). (c) The M.C. Escher Company B.V. All rights reserved. www.mcescher.com