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The Mindbending Art of M. C. Escher

Writer's picture: Mishkat BhattacharyaMishkat Bhattacharya

Art and science have had connections since a long time. The Platonic solids played a central role in the thinking of scientists from Euclid to Kepler. Techniques like linear perspective have revolutionized drawing. Geometrical design reached one of its pinnacles in Islamic art. Movements like Pointillism were tied to the particle theory of light emerging around that time. There is in fact The Bridges Organization, which works to connect art to mathematics.


This post is a note about the astonishing marriage of art and science achieved by the profoundly original Dutch graphic artist Maurits Cornelis Escher (1898-1972). Escher is a great favorite of scientists due to the explicit mathematical/physical/sometimes biological nature of his art, especially the crucial role often played by symmetry in his compositions.


Born in the Netherlands in 1898, Escher was trained at the Technical College of Delft and the Haarlem School of Architecture and Decorative Arts. As an artist, he was not an early success. He was appreciated late in life, around the time he turned seventy. He passed away in 1972.


To the scientific community, a substantial introduction to Escher's work was provided by Martin Gardner's column in the Scientific American. On his part, Escher interacted with the work of mathematicians such as Penrose (who has tilings named after him; interestingly, his uncle Roland was a famous art critic - whose biographies of Picasso and Miro I have greatly enjoyed) and Coxeter (who did pioneering research on reflection groups).


The methods Escher used included sketches on paper, lithographs (printing using stone or metal), and woodcuts. His output contains arresting realistic details, along with - what a physicist might call - local as well as global symmetries, and very original perspectives on the subject matter.


His work involves, for example,


i) optical reflection (and this one too)

ii) the tiling of space or tessellation (he was inspired by the patterns in the Alhambra and Mezquita mosques) - this is an example of his famous realization of hyperbolic geometry

iii) morphing from one pattern to another (and this one too)

iii) symmetry

iv) illusions resulting in two-dimensional drawings of structures logically impossible to construct in three dimensions


Some rather interesting films on Escher are available here. In them, one of his sons describes how favorite activities of Escher included building mazes in the family living room, playing Bach on the gramophone, and working obsessively on ideas which came to him in the middle of the night (during this time he would lock his door, and get upset if he was disturbed).


Other films show Escher at work, describing his specific love of southern Italian landscape, along with his observation that although he lived in Rome for 12 years he did not relate to its architecture.


My favorites were the two clips narrated by Sir Roger Penrose describing Escher's work, their collaboration (on the 'art of the impossible'), and a brush (sic) between Escher and Mick Jagger (very amusing).


Inspired by Escher's example, I looked into some other 'mathematical' artists as well. See what you think of them:



I thought they were all interesting, but I hope you will agree that Escher's appeal is quite unique.


Bonus video: The Museum of Illusions in Prague.





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