Maurits Cornelis Escher, or: It's all a matter of perspective

Do men really have better spatial reasoning skills than women?

Do men have better spatial reasoning skills than women? Well, that may indeed be the case, but depending on how exactly one defines spatial reasoning and how its existence is tested, the results will likely vary considerably.

But even if this assumption proves true, it doesn't mean that women with a lack of spatial reasoning skills have to accept it without a fight. The ability to perceive the third dimension can be trained , even by those who are completely untalented, whose brains first need to build the necessary connections from scratch.

This spatial reasoning ability can, of course, be excellently trained through art, specifically three-dimensional art, or at least art with a limited degree of three-dimensionality. Simply studying three-dimensional art would be too easy; a cube in space is simply there, and it is always three-dimensional, and our brain always perceives it as such without any special training.

In contrast, a representation that only appears three-dimensional on paper offers completely different possibilities for stimulating the corresponding brain areas.

Art for training spatial reasoning skills

There are many works of art that stimulate our spatial perception; essentially, the works of all artists who have discovered and applied the laws of perspective. This certainly includes the works of most artists who have created paintings since the beginning of the Renaissance, the first Art Movement of the modern era.

For in the Renaissance central perspective was discovered, and with this discovery “painter-architects” such as Giotto or Filippo Brunelleschi (who is even named as the inventor of perspective) began to create works that depicted the traditional motifs of Christian iconography all at once in a spatially correct architectural setting.

Albrecht Dürer also famous for his perspective drawings; in 1525 he even published a book with the first summary of the mathematical-geometric methods of central perspective, the “Underweysung der messung mit dem zirckel un richtscheyt” , and the majority of subsequent artists followed these findings.

However, there are artists whose work is particularly suitable if you wish to explore space, its representation, and the perception of that representation. Among them is Maurits Cornelis Escher , who created extraordinary spatial drawings and graphics that are often witty and sometimes playfully ironic, seemingly depicting space accurately while occasionally turning it on its head.

Maurits Cornelis Escher is better known to us as MC Escher , and many people are familiar with his twisted drawings, which show impossible staircases and equally unthinkable body parts, or dubious worlds above and below water surfaces, or even houses where the outside is inside and the inside is outside.

What's special about it is that it's all depicted spatially, and in such a way that what seems impossible looks as if it could really happen: The hand can draw itself, the intertwined knots never end, and the staircase can be walked around endlessly without going up or down.

With M.C. Escher, there's always something more going on than one can actually imagine, something more than is realistically possible, but purely from a drawing perspective, it all looks wonderfully logical. In any case, looking at his drawings is quite enjoyable, and it strongly encourages reflection on how the artist achieved this depiction; anyone who looks for too long quickly enters a state of meditation.

Escher's pictures fascinate engineers, mathematicians, and scientists, and beyond, anyone who dislikes kitschy flourishes but appreciates precisely drawn images. Escher's pictures also suit any interior design style, lending each room a unique character . And anyone who hangs an Escher picture on their wall demonstrates that they reflect on the world and can maintain a healthy dose of irony.

How and where optical illusions occur and what they are used for is explained in the two following videos by Prof. Bernd Lingelbach from Aalen University of Applied Sciences (TV report by the broadcaster ZDFinfo):

MC Escher – an artist with a hesitant start

M.C. Escher himself only arrived at his elaborate and astonishing body of work, which deeply touched the hearts of intellectuals in the art world, by a circuitous route: He was born in 1898 in Leeuwarden, the Dutch city and administrative center of the province of Friesland. The youngest of five sons of a hydraulic engineer, he proved to be an exceptionally poor student, repeating two grades and even receiving dismal marks in art.

His talent had apparently not yet been recognized, and Escher also ended his architecture studies, which he had begun in 1919, after only a short week. Fortunately, during that week, his lecturer, Samuel Jessurun de Mesquita, had already recognized his extraordinary talent, and the fact that de Mesquita subsequently taught him privately in graphic drawing and techniques had a decisive influence on Escher's development; de Mesquita was already a staunch advocate of a good dose of irony in visual composition.

The Alhambra and Arabic ornamentation

Other elements from Escher's pictures, known to connoisseurs, stem from his study of Arabic ornamentation , which he encountered on his travels from 1921 onwards, for example in the Alhambra.

The Alhambra in Granada exerted an unparalleled fascination on him. The Moorish architecture, characterized by subtle, geometric patterns that multiply endlessly, enchanted him. He was particularly interested in the uniqueness of Islamic art.

Since Islam permits only limited figurative representation, artisans express their talent through organic and geometric patterns. These patterns are often influenced by astronomy and mathematics , fields highly valued by 14th-century Arab architects. It is evident that this influence was significant for M.C. Escher.

During his travels, Escher also got to know Italy, which he liked so much that he and his wife settled near Rome after their wedding in 1924; their first son was born in 1926 and their second in 1928.

During this time, Escher also gained some recognition; by 1929 he had exhibited five times, in Switzerland and the Netherlands. This was despite the fact that he had not yet developed his characteristic graphic art style until well into the 1930s, when he primarily painted Mediterranean landscapes.

Escher discovers perspective and its reversal

With the rise of Italian fascism, the Eschers moved to Switzerland, and a trip including a revisit to the Alhambra in 1936 is said to have been responsible for the change in Escher's subject matter: he began his period of metamorphoses , ornamental representations with the first signs and drawings of fantastic figures .

In 1937, another move took place near Brussels, and experiments with surface fillings followed. From Brussels, in 1940, shortly before the invasion of the National Socialists, he moved to Baarn in the Netherlands, where Escher survived the war and saved a large part of the work of his teacher de Mesquita, who had been deported to the Auschwitz concentration camp and murdered there.

After the war, Escher increasingly turned to perspective representation and received more and more commissions, selling many of his prints for good money and becoming a sought-after artist in the USA by 1950.

His diverse graphic works were created during this time; Escher was a master of woodcut, wood engraving and lithography, and mastered a wide range of graphic styles.

Impossible possibilities – Optical illusions as a perceptual phenomenon

His works increasingly displayed impossibilities of perspective; optical illusion as a perceptual phenomenon became his trademark and earned him a status similar to that of a pop star. Escher also enjoyed exploring phenomena such as Möbius strips or fractals, optical distortions and reflections ; for example, there is a self-portrait of him as a reflection in a glass sphere.

Escher began experimenting with optical illusions in the 1940s by designing figures that could only exist on paper. This was because up and down, foreground and background, and inside and outside were not clearly distinguishable. The key was that the depicted objects appeared normal at first glance, the composition logical, and the perspective natural.

Escher's tidy and clear drawing style reinforced this impression. The realistic surroundings, such as mountains, palm trees, rows of houses, and backyards, as well as the people he placed within them, contributed to this effect. Only upon closer inspection did it become clear that the depiction couldn't possibly work. It involved paradoxes of perspective .

While these could easily be designed on paper, they were impossible to create as three-dimensional figures in physical reality. They merely simulated reality. Ultimately, it was a game with the way the human brain interpreted the visual information from the eyes.

Perceptual psychology recognized numerous such "errors." The principle was that the human brain learns over the course of a lifetime how lines on paper must be arranged to convey the impression of three-dimensionality—distances, spatial depth, and proportions. Therefore, it also attempted to construct three-dimensional objects from Escher's drawings, but reliably failed. Yet, this very fact constituted the appeal of the game.

Although Escher wasn't the first to use these techniques, he perfected them. He initially created his "impossible pictures" for his own amusement. The buildings were often based on the Moorish architecture of the Mediterranean countries he had visited as a young man, as were the landscapes in the background.

Escher becomes a star, despite all the art criticism

Although Maurits Cornelis Escher was practically worshipped by his followers for his optical illusions, he always remained a problem for theorists of art history, because optical illusions and perspectival impossibilities are simply not classic themes of art, they do not fit into any traditional category, and many art critics therefore still deny Escher the status of an artist .

“It doesn’t matter ,” Escher would probably say, and might have found it much more interesting to be admired by generations of mathematicians and scientists for his exact work and his sensual and joyful approach to mathematical topics and scientific problems.

MC Escher and Mathematics

Euclidean geometry, Riemann surfaces, cylindrical perspective, and hyperbolic maps may sound obscure to some, but for M.C. Escher, they were the tools of his artistic work. As a passionate follower of mathematical theories, he considered them his vocabulary.

Escher's encounter and friendship with the mathematicians Roger Penrose and Harold Coxeter significantly contributed to the development of his knowledge. This enabled him to create visionary works that represented imagined mathematical image projections.

Among the artist's fascinating works are the "impossible objects." By multiplying viewpoints or using other optical tricks, he created forms that cannot exist in the real world. The Möbius strip, an endless band without an inside or outside, and the Necker cube, an ambiguous drawing of the edges of a cube, are just two examples.

The Penrose triangle , named after Escher's friend Roger Penrose, is an object that can only exist in two dimensions. The illusion in the third dimension is maintained by an optical barrier.

Escher's work is a unique interplay of mathematics and art that continues to fascinate and inspire.

Escher, surprisingly to many, claimed to have no knowledge of mathematics himself. Nevertheless, he was frequently invited to give mathematical lectures; whether he accepted these invitations is unknown. It is known, however, that he gave numerous lectures throughout Europe on his own work, which were exceptionally well-attended, not only by scientists but also by esotericists and pop culture enthusiasts.

Death and legacy

The artist died in 1972 in Hilversum, Netherlands. In 2002, the Escher Museum opened in The Hague, showcasing his graphic work, as well as many private photographs and, most importantly (for the curious), studies of his work, which aim to convey an impression of how Escher created his seemingly impossible geometries.

If you are not yet very familiar with MC Escher, it is definitely worth taking a closer look at his work, and not only to train your spatial reasoning skills, but for a much more obvious reason: Maurits Cornelis Escher is simply fun!

Famous works by MC Escher

Over the course of his career, M.C. Escher created 448 prints and over 2,000 drawings and sketches. Within this extensive collection, several works significantly contributed to his reputation.

Of particular note is “The House of Stairs” – a house that makes the viewer dizzy due to its various perspectives and angles. The architecture of this house is completely impossible and thus represents a unique work of art.

Escher's illustrations are not only inspired by mathematical theories but also influenced by the art of trompe-l'oeil . This type of imagery creates an illusion that arises in the eye of the beholder.

Escher's works transcend boundaries through perspective effects and the use of light and shadow. In Hands, the illusion is primarily created by the hands protruding from the frame, which previously appeared to define the artwork's limits.

Artwork collection by Maurits Cornelis Escher on Pinterest

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Further information

• mcescher.com/ (Official homepage of the artist MC Escher)
• die-scheune.info/ (Official homepage of Prof. Bernd Lingelbach)