AndYou are walking on a ladder that leads to the top of a tall square tower. It climbs one way, then the next, then the next – and then all of a sudden you’re right back where you started. It’s the kind of problem that people stuck in the geometrically impossible, yet oddly plausible, world of MC Escher have to deal with all the time. Dimensions collide in his mind-boggling compositions and mediocrity merges. Looking at her pictures is like standing on the very edge of a cliff – and being at the bottom at the same time.
The Dutchman’s illusion has been famous and beloved since the 1950s, when fans far and wide first began claiming to see hidden cannabis plants in his art. And now we have Kaleidocycles, a Taschen book about an artist with paper puzzle kits that allow you to actually build your own contrasting structures at home in a way that seems unlikely. The tome has been re-released just in time for Christmas and the 50th anniversary of his death next year. His work seems perfect for the festive season, it is all fun and games. Or at least it seems so initially.
A Nobel Prize winner used his work to explain the non-Euclidean ‘hyperbolic’ geometry behind a new theory of the universe
Escher’s visionary nature was not limited to the arts: he also entered the world of science. His profound yet implausible approach seems to predict virtual reality’s biggest trick. Yet Maurits Cornelis Escher – born in 1898 in Leeuwarden, a town north of Amsterdam – showed absolutely no aptitude for any academic subject in school. His father was a hydraulic engineer – an important job in a country where so much land was obtained from the sea. Although he was disappointed with his son, he supported the young Maurits in his studies at the art college in Haarlem and in his travels around Southern Europe, where he spent years developing his style.
In the 1920s, the Piet Mondrian and De Stijl movements were moving Dutch art into pure abstraction. Meanwhile, Escher was in Italy – using traditional printmaking skills to depict timeless cities on picturesque hills. These designs would become the building blocks of his deceitful universe. a thick ink St. Peter’s Carving The vast interior of the Vatican Basilica, which he built in 1935, is seen from inside the dome with a spectacular, godlike view from above. We see little people on the floor below, as the pillars fall towards them in running, terrifying perspective.
In this powerful engraving, you can clearly see the roots of Escher’s art. The work reveals his love of perspective, a method of depicting deep space and distance invented in Renaissance Italy. For the likes of Leonardo da Vinci, perspective was not merely an art but a science. Fascinated by this mathematical technique, he filled his notebooks with sketches of buildings and landscapes.
Earlier this year, a film titled Escher: Journey into Infinity saw the artist anew, examining how he achieved cult status in the US counterculture, with bootleg versions of his work on T-shirts. appeared. As well as exploring his influences, which range from densely packed Italian hill towns to the music of Bach, we learned that Mick Jagger once asked Escher to create an album cover. Not only did the artist collapse, he asked Rolling Stone to address him by his first name.
A flat surface is just a flat surface. As soon as you paint something on it that seems to have depth and solidity, you are creating an illusion. In Escher’s most mature and disturbing works, he takes this to the extreme, orchestrating the multi-dimensional accidents of alternate realities. In his 1953 picture Relativity, everything is drawn into strict perspective. The only trouble is that there are three points of view to the three vanishing points (the point where the lines will actually be parallel that meet on the page). The artist calls these “different worlds” and in one of them, a waiter walks down an inverted staircase to serve an al fresco dinner, whose table is vertical. In another, lovers stroll through a garden in defiance of gravity. Only a flight of stairs leading up from the bottom of the picture is the “right way up”. Still turn the square image on its side and everything changes. A different world now becomes real.
Escher’s dive into the beauty of mathematics and science began when his eyes were opened to an art older than the art of the Renaissance. When he visited the medieval Islamic palace Alhambra, which stretches along a cliff overlooking Granada in southern Spain, he was taken in a magic carpet of inspiration. Its rooms were lined with brightly colored tiles arranged in intricate patterns that were strung together in a lattice of adorable symmetry, all inspired by Arab science. Mathematics calls this tessellation: the complete covering of a surface by joining figures together without gaps. This is the glory of Andalusian Islamic art.
Escher was transfixed. They also felt challenged – as if they were watching the work of rivals. He began making his own tessellated surfaces, but with a difference. While the Alhambra is filled with abstract figures, Escher set out to tease out figurative images. Bird, fish, lizard, angel, devil – he fits these repeated forms together in a hallucinatory flow that shifts from one thing to another. The fish swim to the bottom of the sea with their mouth open while the birds glide up: then you see that the gaps between the birds are fish-shaped, and vice versa. They meet in a dazzling metamorphosis on the surface of the ocean.
As soon as Escher saw the artistic light, Europe was moving into the shadows. Frightened by the idea of his sons being brought under fascist ideology, he moved his family from Italy to Switzerland. He then moved to Belgium but, after his mother died and the country was seized by the Nazis, he returned to the Netherlands to be closer to the family and settle his legacy. Escher despised the Nazis and refused to ever go to Germany.
So it’s certainly no coincidence that the moment the world was being sucked into a black hole, it began to reveal gaps in reality. In his 1938 print Day and Night, two flights of swans, black and white, tessellate as they fly in opposite directions across the border between day and night. Look long enough and you realize that night and daylight landscapes are mirror images of the same European vistas. Escher depicts a terrifying symmetry between light and dark in the year of the Munich Agreement, in which the continent is on a knife-edge between war and peace.
In 1944, back home in what is now the Nazi-occupied Netherlands, it would fall to Escher to move into the home of his beloved Jewish art teacher, Samuel Jesurun de Mesquita – to save as much of the art as he could. “The Mesquita family,” he would later write, “were thrown out of bed and taken away. It must now be considered practically certain that S. Jesurun de Mesquita, his wife and their son Jaap were all in a German camp. were killed.
Escher’s brilliant tessellation brought the mathematics of the Alhambra face-to-face with modern physics. Roger Penrose, who won the 2020 Nobel Prize for his pioneering work on black holes, confronts Escher’s art during a conference in Amsterdam in the 1950s. He went home and tried to figure out Escher-like puzzles, publishing a paper that unveiled two “impossible” objects: a ladder that loops itself without going up, and a solid triangular structure that resembles a real Looks completely absurdly connected, with all three of its vertices actually being pushed outwards on the same plane.
When Escher saw these Escheresque objects, he responded with his brilliant interpretations of infinite ladders and the Penrose triangle. His 1960 print Ascending and Descending shows figures of Cowle marching up and down a staircase above a palace that takes him back to where he started. In 1961’s Waterfall, he gives the same enticing depth and detail to the sight of a mill working waterfall. After hitting the wheel of the mill, the water flows along a flat, zig-zagging channel—improbably—it falls again. Escher explained that it was based on the Penrose triangle. So, in the 1960s, this Dutch graphic artist, who had failed in school, was conversing with the most advanced mathematics around.
Another print depicts angels and devils intertwining on a circular surface, getting smaller as they get closer to the edges of the world. When striking, it looks almost straight Escheresque – yet in his book Cycle of Time, Penrose uses this work to explain the non-Euclidean “hyperbolic” geometry behind a new theory of the universe. In the world of art-and-science crossovers, this is an extraordinary feat.
Art is just another way of thinking about the universe. It can describe mathematical phenomena that some may follow in some other way. Escher took two artistic traditions, Islamic abstraction and the Renaissance perspective, and stitched them together. The result is a diversity of delights with no right path up or down. Escher proved that watching can be a magical kind of thinking.