FRANCIS SCHAEFFER ANALYZES ART AND CULTURE Part 189 Nancy Pearcey book SAVING LEONARDO Part B Featured artist is M.C. Escher

Francis Schaeffer in 1955 opened up L’Abri in Switzerland where he interact with students about what the Bible had to say about modern day culture and the arts. Nancy Pearcey was one of those unbelieving students who spent time there and later put her faith in Christ. She has written a book called Saving Leonardo: A Call to Resist the Secular Assault on Mind, Morals, and Meaning and it she quotes Schaeffer a great bit. Below are two episodes from Francis Schaeffer’s film series HOW SHOULD WE THEN LIVE? that are referenced in her book and then an interview with her about the book. 



HowShouldWeThenLive Episode 3


HowShouldWeThenLive Episode 4



Saving Leonardo: An Interview with Nancy Pearcey

Neocalvinism — By  on September 1, 2010 at 7:03 am

Nancy Pearcey is perhaps the most famous heir of Francis Schaeffer’s legacy.  Her book Total Truth was both a bestseller and award-winner, which can be a rare combination.  

I was delighted to sit down with her to discuss her latest offering, Saving Leonardo, which is just as unique, thoughtful, and important as her last.

The book is Saving LeonardoIs he in danger?

I wrote the book to be a survival guide to the varieties of secularism that are undercutting freedom and dignity within our culture today.  The reference to Leonardo functions as a metaphor for the way the arts and popular culture channel worldviews deeply into people’s minds and emotions.

The substance of the book is an exploration of the two major “brands” of secularism today.  It’s a little like Ford and Chevy.  We often think of secularism as a single phenomenon, but there are really two strands:  modernism and postmodernism.

Modernism still reigns in the natural sciences, in fields like biology, chemistry, physics, where the dominant worldview is scientific materialism, which treats humans as little more than biochemical machines.  At the same time, postmodernism is rampant in literature, theology, the arts, and similar disciplines.  It is just as dehumanizing because it tends to treat humans as simply the product of social forces, such as race, gender, and ethnic group.  These two streams have created a pincer movement that is crushing human dignity and liberty.

Is there an intellectual connection between modernism and postmodernism, or is it simply historical?

Modernism has its roots in the Enlightenment, and worldviews that aspire to be scientific all cluster under that brand—empiricism, rationalism, logical positivism, analytic philosophy and so on.  These all lead to forms of reductionism that suggest the only world that is real is the world we can see, touch, taste, or measure.  These worldviews deny the spiritual, the moral, and even the emotional, which they reduce to chemical reactions in the brain.

This is where the subtitle of my book comes from.  Modernism assaults “Mind, Morals, and Meaning” by reducing the mind to the brain, reducing morals to our personal preferences, and reducing the universe to a product of blind, material forces, which implies that it has no ultimate purpose or meaning,

This assault lead to a counter-reaction in the Romantic movement.  The Romantics wanted to preserve a sense of the spiritual, but they moved away from orthodox Christianity and toward pantheism.  This stream of thought has given rise to philosophies like existentialism, postmodernism, and deconstructionism.  Saving Leonardo traces the trajectory of these two strands of modern thought.

How does Saving Leonardo relate to Total Truth?

Total Truth is about how truth itself was divided between facts and values.  As I probed this, though, I realized that the division between facts and values was just the tip of the iceberg.  The Enlightenment tradition focuses on the fact realm: what is empirically verifiable and rationally justifiable.  The Romantic stream tended to care about the values realm:  about morality, justice, and the human spirit.  The fact-value dichotomy functions as a sort of hermeneutical key to nearly all of western thought since the Enlightenment.

A lot of people think that modernism came first and postmodernism came later—that the two are sequential.  But in reality they are two types of thinking that exist side-by-side.  People tend to be modernist in many realms of their lives, like in their finances or their business lives, or in dealing with doctors and their health.  But they are postmodern in their theology, ethics, and the arts.  So we’re really dealing with a split mind.

What makes Saving Leonard unique?

Saving Leonardo asks, Who’s writing the script to your life?  Most people are not reading philosophy books; they’re picking up ideas about life from the books they read, the movies they watch, art, literature, and other cultural forms.  That’s where we are most likely to pick up secular ideas—often without realizing it.  So the second half of the book is filled with illustrations and pictures as a way of helping people understand how ideas are communicated through culture.

Let me give you an example.  During the last presidential campaign, ABC news interviewed several teens at a Christian youth rally.  Many of the teens held biblical convictions on current issues—for example most were pro-life.   But the same teens also supported candidates who are in favor abortion.  To the reporter, that sounded like a contradiction.  So he asked the teens, doesn’t that bother you?

Well, one of them said, “it’s all a matter of personal preference.”

Where did they pick up such a relativistic concept of morality?  These teens are channeling David Hume, the arch-empiricist who said that if all knowledge is a matter of sensation, then even moral truths are really just sensations—what feels good to you.  Personal preference.

Plato said philosophers should rule the world, and they do—hundreds of years after they die.  Eventually their ideas filter down into the culture, and a major conduit is the arts.

You’re pretty critical of the Enlightenment.  Do you think there’s anything in the period that is worth holding on to?

Certainly.  The best parts of the Enlightenment were rooted in a Christian worldview.  The Enlightenment was based on the scientific revolution, but that came out of a Christian understanding of nature and the world. Historians of science have pointed out that no other culture, east or west, ancient or modern, ever talked about law in relation to nature.  The Enlightenment understanding of the “laws of nature” came from the medieval notion that if God is both Creator and Lawgiver, then the creation must be lawful.

These were deeply Christian themes that the Enlightenment took and ran with.  They wanted God’s good gifts, but didn’t want God.  If you go back and read some of the founders of the scientific revolution, most were devout Christians.

Sociologist Rodney Stark did a wonderful study of the scientific revolution and identified the 52 most significant scientists who were not just theorists but did ground-breaking work at the origin of modern science—the “stars” of science. Then he examined their biographical information, and all but two were clearly Christians (and historians actually disagree about one of them).  The only clear skeptic was Edmund Halley.  Most of the founders of modern science held a Christian worldview, and it inspired their scientific work.

How should Christians respond to living in an increasingly post-Christian world?

In any culture, Christians have an obligation to live out a Biblical worldview in every area of life.  This is not a Christian problem, it’s a human problem—because everyone aspires to live an integrated, consistent life.  The universe as a whole is an integrated unity, and that means truth must also be an integrated unity, and should be expressed in everything we do.

How that is fleshed out politically is primarily in being faithful in your own sphere of influence.  It’s like happiness—you don’t find happiness by pursuing it directly.  You find happiness indirectly through building relationships, meeting your obligations, engaging in meaningful work, and so on.  For Christians who aspire to have an impact on their society, the same principle holds.  It’s often the byproduct of simply having a Christian mindset in whatever your calling is, living and acting consistently with your convictions.

There have been a lot of popular critiques of worldview-centered approaches to culture, most notably James Davison Hunter’s To Change the World. How would you respond?

I had written nearly all of Saving Leonardo before Hunter’s book came out, but in the first chapter I actually quote Hunter saying that the reason Christians have failed to have the social impact they hoped for was that they put all their eggs into the basket of politics.  They overlooked the fact that America’s secular elites had already reached an intellectual consensus on contentious social issues like abortion long before any kind of legal or political measures were taken.  In other words, Hunter himself notes that what came first was shift in worldview.  Ideas are born, nurtured, and developed in the universities long before they step out onto the political stage.

The way I put it in Total Truth is that politics is “downstream” from culture.  And the implication is that it’s time to go “upstream” in order to get a handle on the forces that are shaping politics.

In Saving Leonardo I give the famous quote from Todd Gitlin, former president of the radical SDS.  After the student unrest of the 1960s, he said, the Left “marched on the English department, while the Right took the White House.”  Today we must ask:  Which was the more effective strategy?  The English department is now in the White House.

The implication is that the university is the main shaper of culture today.  The intelligentsia holds the reins of power.  This has not always been the case.  America has historically had a reputation for being non-ideological and pragmatic.  As Calvin Coolidge put it, “The business of America is business.”  And what is America’s only home-grown philosophy?  Philosophical pragmatism.  But we are increasingly a knowledge-based society, and that means whoever is in a position to define what counts as “knowledge” will wield social and political power.

Nancy R. Pearcey is professor of worldview studies at Philadelphia Biblical University. Previously she was the Francis A. Schaeffer Scholar at the World Journal-ism Institute, where she taught a worldview course based on her book Total Truth, winner of the 2005 ECPA Gold Medallion Award for best book on Christianity and Society.


Francis Schaeffer


Today’s feature is on the artist is M.C.Escher

1/2 The Art of the Impossible: MC Escher and Me – Secret Knowledge

2/2 The Art of the Impossible: MC Escher and Me – Secret Knowledge

M.C. Escher Documentary (by CINEMEDIA-NPS-RNTV) [1999]


M. C. Escher

From Wikipedia, the free encyclopedia
M. C. Escher

M. C. Escher in 1971
Born Maurits Cornelis Escher
17 June 1898
Leeuwarden, Netherlands
Died 27 March 1972 (aged 73)
Laren, Netherlands
Nationality Dutch
Education Haarlem School of Architecture and Decorative Arts
Known for Drawing, printmaking
Notable work Relativity, Waterfall, Hand with Reflecting Sphere
Awards Knighthood of the Order of Orange-Nassau

Maurits Cornelis Escher (Dutch pronunciation: [ˈmʌurɪts kɔrˈneːlɪs ˈɛʃər];[1] 17 June 1898 – 27 March 1972), or commonly M. C. Escher, was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints.

His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical ability, he interacted with the mathematicians George Pólya, Roger Penrose, Harold Coxeter and crystallographer Friedrich Haag, and conducted his own research into tessellation.

Early in his career, he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he used as details in his artworks. He traveled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and the Mezquita of Cordoba, and became steadily more interested in their mathematical structure.

Escher’s art became well known among scientists and mathematicians, and in popular culture, especially after it was featured by Martin Gardner in his April 1966 Mathematical Games column in Scientific American. Apart from being used in a variety of technical papers, his work has appeared on the covers of many books and albums. He was one of the major inspirations of Douglas Hofstadter‘s 1979 book Gödel, Escher, Bach.

Early life

Escher’s birth house, now part of the Princessehof Ceramics Museum, in Leeuwarden, Netherlands

Maurits Cornelis[a] Escher was born on 17 June 1898 in Leeuwarden, Friesland, the Netherlands, in a house that forms part of the Princessehof Ceramics Museum today. He was the youngest son of the civil engineer George Arnold Escher and his second wife, Sara Gleichman. In 1903, the family moved to Arnhem, where he attended primary and secondary school until 1918.[2][3] Known to his friends and family as “Mauk”, he was a sickly child, and was placed in a special school at the age of seven; he failed the second grade.[4] Although he excelled at drawing, his grades were generally poor. He took carpentry and piano lessons until he was thirteen years old.[2][3]

In 1918, he went to the Technical College of Delft.[2][3] From 1919 to 1922, Escher attended the Haarlem School of Architecture and Decorative Arts, learning drawing and the art of making woodcuts.[2] He briefly studied architecture, but he failed a number of subjects (partly due to a persistent skin infection) and switched to decorative arts,[4] studying under the graphic artist Samuel Jessurun de Mesquita.[5]

Study journeys

Moorish tessellations at the Alhambra inspired Escher’s work with tilings of the plane. He made sketches of this and other Alhambra patterns in 1936.[6]

In 1922, an important year of his life, Escher traveled through Italy, visiting Florence, San Gimignano, Volterra, Siena, and Ravello. In the same year he traveled through Spain, visiting Madrid, Toledo, and Granada.[2] He was impressed by the Italian countryside, and in Granada by the Moorish architecture of the fourteenth-century Alhambra. The intricate decorative designs of the Alhambra, based on geometrical symmetries featuring interlocking repetitive patterns in the coloured tiles or sculpted into the walls and ceilings, triggered his interest in the mathematics of tessellation, and became a powerful influence on his work.[7][8]

Escher’s painstaking[b][9] study of the same Moorish tiling in the Alhambra, 1936, demonstrates his growing interest in tessellation.

Escher returned to Italy, and lived in Rome from 1923 to 1935. While in Italy, Escher met Jetta Umiker – a Swiss woman, like himself attracted to Italy – whom he married in 1924. The couple settled in Rome where their first son, Giorgio (George) Arnaldo Escher, named after his grandfather, was born. Escher and Jetta later had two more sons: Arthur and Jan.[2][3]

He travelled frequently, visiting (among other places) Viterbo in 1926, the Abruzzi in 1927 and 1929, Corsica in 1928 and 1933, Calabria in 1930, the Amalfi coast in 1931 and 1934, Cargano and Sicily in 1932 and 1935. The townscapes and landscapes of these places feature prominently in his artworks. In May and June 1936, Escher travelled back to Spain, revisiting the Alhambra and spending days at a time making detailed drawings of its mosaic patterns. It was here that he became fascinated to the point of obsession with tessellation, explaining:[5][9]

It remains an extremely absorbing activity, a real mania to which I have become addicted, and from which I sometimes find it hard to tear myself away.[9]

The sketches he made in the Alhambra formed a major source for his work from that time on.[9] He also studied the architecture of the Mezquita, the Moorish mosque of Cordoba. This turned out to be the last of his long study journeys; after 1937, his artworks were created in his studio rather than in the field. His art correspondingly changed sharply from being mainly observational, with a strong emphasis on the realistic details of things seen in nature and architecture, to being the product of his geometric analysis and his visual imagination. All the same, even his early work already shows his interest in the nature of space, the unusual, perspective, and multiple points of view.[5][9]

Later life

In 1935, the political climate in Italy (under Mussolini) became unacceptable to Escher. He had no interest in politics, finding it impossible to involve himself with any ideals other than the expressions of his own concepts through his own particular medium, but he was averse to fanaticism and hypocrisy. When his eldest son, George, was forced at the age of nine to wear a Ballila uniform in school, the family left Italy and moved to Château-d’Œx, Switzerland, where they remained for two years.[10]

The Netherlands post office had Escher design a semi-postal stamp for the “Air Fund” in 1935[11] and again in 1949 he designed Netherlands stamps. These were for the 75th anniversary of the Universal Postal Union; a different design was used by Surinam and the Netherlands Antilles for the same commemoration.[12][13]

Escher’s last work, Snakes, 1969

Escher, who had been very fond of and inspired by the landscapes in Italy, was decidedly unhappy in Switzerland. In 1937, the family moved again, to Uccle (Ukkel), a suburb of Brussels, Belgium.[2][3] World War II forced them to move in January 1941, this time to Baarn, Netherlands, where Escher lived until 1970.[2] Most of Escher’s best-known works date from this period. The sometimes cloudy, cold and wet weather of the Netherlands allowed him to focus intently on his work.[2] After 1953, Escher lectured widely. A planned series of lectures in North America in 1962 was cancelled after an illness, and he stopped creating artworks for a time,[2] but the illustrations and text for the lectures were later published as part of the book Escher on Escher.[14] He was awarded the Knighthood of the Order of Orange-Nassau in 1955.[2]

In July 1969 he finished his last work, a large woodcut with threefold rotational symmetry called Snakes, in which snakes wind through a pattern of linked rings. These shrink to infinity toward both the center and the edge of a circle. It was exceptionally elaborate, being printed using three blocks, each rotated three times about the center of the image and precisely aligned to avoid gaps and overlaps, for a total of nine print operations for each finished print. The image encapsulates Escher’s love of symmetry, of interlocking patterns, and at the end of his life, of his approach to infinity.[15][16][17] The care Escher took in creating and printing this woodcut can be seen in a video recording.[18]

Escher moved to the Rosa Spier Huis in Laren in 1970, an artists’ retirement home in which he had his own studio. He died there on 27 March 1972, aged 73.[2][3] He is buried at the New Cemetery in Baarn.[19][20]

Mathematically-inspired work

Escher’s work is inescapably mathematical. This has caused a disconnect between his full-on popular fame and the lack of esteem with which he has been viewed in the art world. His originality and mastery of graphic techniques is respected, but his works have been thought too intellectual and insufficiently lyrical. Movements such as conceptual art have to a degree reversed the art world’s attitude to intellectuality and lyricism, but this did not rehabilitate Escher because traditional critics still disliked his narrative themes and his use of perspective. However, these same qualities made his work highly attractive to the public.[21] Escher is not the first artist to explore mathematical themes: Parmigianino (1503–1540) had explored spherical geometry and reflection in his 1524 Self-portrait in a Convex Mirror, depicting his own image in a curved mirror, while William Hogarth‘s 1754 Satire on False Perspective, foreshadows Escher’s playful exploration of errors in perspective.[22][23] Another early artistic forerunner is Giovanni Battista Piranesi (1720–1778), whose dark “fantastical”[24] prints such as The Drawbridge in his Carceri (“Prisons”) sequence depict perspectives into complex architecture with many stairs and ramps, peopled by walking figures.[24][25]Only with 20th century movements such as Cubism, De Stijl, Dadaism and Surrealism did mainstream art start to explore Escher-like ways of looking at the world with multiple simultaneous viewpoints.[21] However, while Escher had much in common with, for example, Magritte‘s surrealism, he did not make contact with any of these movements.[26]


In his early years, Escher sketched landscapes and nature. He also sketched insects such as ants, bees, grasshoppers and mantises,[27] which appeared frequently in his later work. His early love of Roman and Italian landscapes and of nature created an interest in tessellation, which he called Regular Division of the Plane; this became the title of his 1958 book, complete with reproductions of a series of woodcuts based on tessellations of the plane, in which he described the systematic buildup of mathematical designs in his artworks. He wrote “Mathematicians have opened the gate leading to an extensive domain.”[28]

Hexagonal tessellation with animals: Study of Regular Division of the Plane with Reptiles (1939). Escher reused the design in his 1943 lithograph Reptiles.

After his 1936 journey to the Alhambra and to La Mezquita, Cordoba, where he sketched the Moorish architecture and the tessellated mosaic decorations,[29] Escher began to explore the properties and possibilities of tessellation using geometric grids as the basis for his sketches. He then extended these to form complex interlocking designs, for example with animals such as birds, fish, and reptiles.[30] One of his first attempts at a tessellation was his pencil, India ink and watercolour Study of Regular Division of the Plane with Reptiles (1939), constructed on a hexagonal grid. The heads of the red, green and white reptiles meet at a vertex; the tails, legs and sides of the animals exactly interlock. It was used as the basis for his 1943 lithograph Reptiles.[31]

His first study of mathematics began with papers by George Pólya[32] and by the crystallographer Friedrich Haag[33] on plane symmetry groups, sent to him by his brother Berend, a geologist.[34] He carefully studied the 17 wallpaper groups, and created periodic tilings with 43 drawings of different types of symmetry.[c] From this point on he developed a mathematical approach to expressions of symmetry in his art works using his own notation. Starting in 1937, he created woodcuts based on the 17 groups. His Metamorphosis I (1937) began a series of designs that told a story through the use of pictures. In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif. He extended the approach in his piece Metamorphosis III, which is four metres long.[9][35]

In 1941 and 1942, Escher summarized his findings for his own artistic use in a sketchbook, which he labeled (following Haag) Regelmatige vlakverdeling in asymmetrische congruente veelhoeken (“Regular division of the plane with asymmetric congruent polygons”).[36] The mathematician Doris Schattschneider unequivocally described this notebook as recording “a methodical investigation that can only be termed mathematical research.”[34] She defined the research questions he was following as

(1) What are the possible shapes for a tile that can produce a regular division of the plane, that is, a tile that can fill the plane with its congruent images such that every tile is surrounded in the same manner?
(2) Moreover, in what ways are the edges of such a tile related to each other by isometries?[34]


Multiple viewpoints and impossible stairs: Relativity, 1953

Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—his art had a strong mathematical component, and several of the worlds which he drew were built around impossible objects. After 1924, Escher turned to sketching landscapes in Italy and Corsica with irregular perspectives that are impossible in natural form. His first print of an impossible reality was Still Life and Street (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as Relativity (1953). House of Stairs (1951) attracted the interest of the mathematician Roger Penrose and his father the biologist Lionel Penrose. In 1956 they published a paper, “Impossible Objects: A Special Type of Visual Illusion” and later sent Escher a copy. Escher replied, admiring the Penroses’ continuously rising flights of steps, and enclosed a print of Ascending and Descending (1960). The paper also contained the tribar or Penrose triangle, which Escher used repeatedly in his lithograph of a building that appears to function as a perpetual motion machine, Waterfall (1961).[37][38][39][40]

Escher was interested enough in Hieronymus Bosch‘s 1500 triptych The Garden of Earthly Delights to recreate part of its right-hand panel, Hell, as a lithograph in 1935. He reused the figure of a Mediaeval woman in a two-pointed headdress and a long gown in his lithograph Belvedere in 1958; the image is, like many of his other “extraordinary invented places”,[41] peopled with “jesters, knaves and contemplators”.[41] Escher was thus not only interested in possible or impossible geometry, but was in his own words a “reality enthusiast”;[41] he combined “formal astonishment with a vivid and idiosyncratic vision.”[41]

Escher 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. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals.[42]

Escher was also fascinated by mathematical objects like the Möbius strip, which has only one surface. His wood engraving Möbius Strip II (1963) depicts a chain of ants marching for ever around over what at any one place are the two opposite faces of the object—which are seen on inspection to be parts of the strip’s single surface. In Escher’s own words[43]

An endless ring-shaped band usually has two distinct surfaces, one inside and one outside. Yet on this strip nine red ants crawl after each other and travel the front side as well as the reverse side. Therefore the strip has only one surface.[43]

The mathematical influence in his work became prominent after 1936, when, having boldly asked the Adria Shipping Company if he could sail with them as travelling artist in return for making drawings of their ships, they surprisingly agreed, and he sailed the Mediterranean, becoming interested in order and symmetry. Escher described this journey, including his repeat visit to the Alhambra, as “the richest source of inspiration I have ever tapped.”[9]

Escher’s interest in curvilinear perspective was encouraged by his friend and “kindred spirit”[44] the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a “thinking artist”[44] alongside Piero della Francesca, Leonardo da Vinci, Albrecht Dürer, Wenzel Jamnitzer, Abraham Bosse, Girard Desargues, and Père Nicon.[44] Flocon was delighted by Escher’s Grafiek en tekeningen (“Graphics in Drawing”), which he read in 1959. This stimulated Flocon and André Barre to correspond with Escher, and to write the book La Perspective curviligne (“Curvilinear perspective“).[45]

Platonic and other solids

Sculpture of the small stellated dodecahedron as in Escher’s 1952 work Gravitation. University of Twente

Escher often incorporated three-dimensional objects such as the Platonic solids such as spheres, tetrahedons and cubes into his works, as well as mathematical objects like cylinders and stellated polyhedra. In the print Reptiles, he combined two and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality:[46]

The flat shape irritates me – I feel like telling my objects, you are too fictitious, lying there next to each other static and frozen: do something, come off the paper and show me what you are capable of! … So I make them come out of the plane. … My objects … may finally return to the plane and disappear into their place of origin.[46]

Escher’s artwork is especially well liked by mathematicians like Doris Schattschneider and scientists like Roger Penrose, who enjoy his use of polyhedra and geometric distortions.[34] For example, in Gravitation, animals climb around a stellated dodecahedron.[47]

The two towers of Waterfall‘s impossible building are topped with compound polyhedra, one a compound of three cubes, the other a stellated rhombic dodecahedron known as Escher’s solid. Escher had used this solid in his 1948 woodcut Stars, which also contains all five of the Platonic solids and various stellated solids, representing stars; the central solid is animated by chameleons climbing through the frame as it whirls in space. Escher possessed a 6 cm refracting telescope and was a keen enough amateur astronomer to have recorded observations of binary stars.[48][49][50]

Levels of reality

Escher’s artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. His interest in the multiple levels of reality in art is seen in works such as Drawing Hands (1948), where two hands are shown, each drawing the other. The critic Steven Poole commented that[41]

It is a neat depiction of one of Escher’s enduring fascinations: the contrast between the two-dimensional flatness of a sheet of paper and the illusion of three-dimensional volume that can be created with certain marks. In Drawing Hands, space and the flat plane coexist, each born from and returning to the other, the black magic of the artistic illusion made creepily manifest.[41]

Infinity and hyperbolic geometry

Doris Schattschneider‘s reconstruction of the diagram of hyperbolic tiling sent by Escher to the mathematician H. S. M. Coxeter[34]

In 1954, the International Congress of Mathematicians met in Amsterdam, and N. G. de Bruin organized a display of Escher’s work at the Stedelijk Museum for the participants. Both Roger Penrose and H. S. M. Coxeter were deeply impressed with Escher’s intuitive grasp of mathematics. Inspired by Relativity, Penrose devised his tribar, and his father, Lionel Penrose, devised an endless staircase. Roger Penrose sent sketches of both objects to Escher, and the cycle of invention was closed when Escher then created the perpetual motion machine of Waterfall and the endless march of the monk-figures of Ascending and Descending.[34] In 1957, Coxeter obtained Escher’s permission to use two of his drawings in his paper “Crystal symmetry and its generalizations”.[34][51] He sent Escher a copy of the paper; Escher recorded that Coxeter’s figure of a hyperbolic tessellation “gave me quite a shock”: the infinite regular repetition of the tiles in the hyperbolic plane, growing rapidly smaller towards the edge of the circle, was precisely what he wanted to allow him to represent infinity on a two-dimensional plane.[34][52]

Hyperbolic tessellation: Circle Limit III, 1959

Escher carefully studied Coxeter’s figure, marking it up to analyse the successively smaller circles[d] with which (he deduced) it had been constructed. He then constructed a diagram, which he sent to Coxeter, showing his analysis; Coxeter confirmed it was correct, but disappointed Escher with his highly technical reply. All the same, Escher persisted with hyperbolic tiling, which he called “Coxetering”.[34] Among the results were the series of wood engravings Circle Limit I–IV.[34] In 1959, Coxeter published his finding that these works were extraordinarily accurate: “Escher got it absolutely right to the millimeter.”[53]


The Escher Museum in The Hague. The poster shows a detail from Day and Night, 1938

Escher’s special way of thinking and rich graphics have had a continuous influence in mathematics and art, as well as in popular culture.

In art collections

The Escher intellectual property is controlled by the M.C. Escher Company. Exhibitions of his artworks are managed separately by the M.C. Escher Foundation.[e]

The primary institutional collections of original works by M.C. Escher are the Escher Museum in The Hague; the National Gallery of Art (Washington, DC);[56] the National Gallery of Canada (Ottawa);[57] the Israel Museum (Jerusalem);[58] and the Huis ten Bosch (Nagasaki, Japan).[59]


Poster advertising the first major exhibition of Escher’s work in Britain. Dulwich Picture Gallery, 14 October 2015 – 17 January 2016. The image is based on Hand with Reflecting Sphere, 1935.[f]

Despite wide popular interest, Escher was for long somewhat neglected in the art world; even in his native Netherlands, he was 70 before a retrospective exhibition was held.[41][g] In the twenty-first century, major exhibitions have been held in cities across the world.[62][63][64] An exhibition of his work in Rio de Janeiro however attracted more than 573,000 visitors in 2011;[62] its daily visitor count of 9,677 made it the most visited museum exhibition of the year, anywhere in the world.[65] No major exhibition of Escher’s work was held in Britain until 2015, when the Scottish National Gallery of Modern Art ran one in Edinburgh from June to September 2015,[63] moving in October 2015 to the Dulwich Picture Gallery, London.[60] The exhibition moved to Italy in 2015–2016, attracting over 500,000 visitors in Rome and Bologna, before moving to Treviso[64] and then Milan.[66]

In mathematics and science

Wall tableau of one of Escher’s bird tessellations at the Princessehof Ceramics Museum in Leeuwarden

Doris Schattschneider identifies 11 strands of mathematical and scientific research anticipated or directly inspired by Escher. These are the classification of regular tilings using the edge relationships of tiles: two-color and two-motif tilings (counterchange symmetry or antisymmetry); color symmetry (in crystallography); metamorphosis or topological change; covering surfaces with symmetric patterns; Escher’s algorithm (for generating patterns using decorated squares); creating tile shapes; local versus global definitions of regularity; symmetry of a tiling induced by the symmetry of a tile; orderliness not induced by symmetry groups; the filling of the central void in Escher’s lithograph Print Gallery by H. Lenstra and B. de Smit.[34]

Gödel, Escher, Bach by Douglas Hofstadter,[81] published in 1979, discusses the ideas of self-reference and strange loops, drawing on a wide range of artistic and scientific sources including Escher’s art and the music of J. S. Bach.

The asteroid 4444 Escher was named in Escher’s honor in 1985.[82]

In popular culture

Escher’s fame in popular culture grew when his work was featured by Martin Gardner in his April 1966 Mathematical Games column in Scientific American.[83] Escher’s works have appeared on many album covers including The Scaffold‘s 1969 L the P with Ascending and Descending; Mott the Hoople‘s eponymous 1969 record with Reptiles, Beaver & Krause‘s 1970 In A Wild Sanctuary with Three Worlds; and Mandrake Memorial‘s 1970 Puzzle with House of Stairs and (inside) Curl Up.[h] His works have similarly been used on many book covers, including some editions of Edwin Abbott‘s Flatland which used Three Spheres; E. H. Gombrich‘s Meditations on a Hobby Horse with Horseman; Pamela Hall’s Heads You Lose with Plane Filling 1; Patrick A. Horton’s Mastering the Power of Story with Drawing Hands; Erich Gamma et al.’s Design Patterns: Elements of Reusable Object-oriented software with Swans; and Arthur Markman’s Knowledge Representation with Reptiles.[i] The “World of Escher” markets posters, neckties, T-shirts, and jigsaw puzzles of Escher’s artworks.[86] Both Austria and the Netherlands have issued postage stamps commemorating the artist and his works.[13][87]

Selected works

  • Trees, ink (1920)
  • St. Bavo’s, Haarlem, ink (1920)
  • Flor de Pascua (The Easter Flower), woodcut/book illustrations (1921)
  • Eight Heads, woodcut (1922)
  • Dolphins also known as Dolphins in Phosphorescent Sea, woodcut (1923)
  • Tower of Babel, woodcut (1928)
  • Street in Scanno, Abruzzi, lithograph (1930)
  • Castrovalva, lithograph (1930)
  • The Bridge, lithograph (1930)
  • Palizzi, Calabria, woodcut (1930)
  • Pentedattilo, Calabria, lithograph (1930)
  • Atrani, Coast of Amalfi, lithograph (1931)
  • Ravello and the Coast of Amalfi, lithograph (1931)
  • Covered Alley in Atrani, Coast of Amalfi, wood engraving (1931)
  • Phosphorescent Sea, lithograph (1933)
  • Still Life with Spherical Mirror, lithograph (1934)
  • Hand with Reflecting Sphere also known as Self-Portrait in Spherical Mirror, lithograph (1935)
  • Inside St. Peter’s, wood engraving (1935)
  • Portrait of G.A. Escher, lithograph (1935)
  • “Hell”, lithograph, (copied from a painting by Hieronymus Bosch) (1935)
  • Regular Division of the Plane, series of drawings that continued until the 1960s (1936)
  • Still Life and Street (his first impossible reality), woodcut (1937)
  • Metamorphosis I, woodcut (1937)
  • Day and Night, woodcut (1938)
  • Cycle, lithograph (1938)
  • Sky and Water I, woodcut (1938)
  • Sky and Water II, lithograph (1938)
  • Metamorphosis II, woodcut (1939–1940)
  • Verbum (Earth, Sky and Water), lithograph (1942)
  • Reptiles, lithograph (1943)
  • Ant, lithograph (1943)
  • Encounter, lithograph (1944)
  • Doric Columns, wood engraving (1945)
  • Balcony, lithograph (1945)
  • Three Spheres I, wood engraving (1945)
  • Magic Mirror, lithograph (1946)
  • Three Spheres II, lithograph (1946)
  • Another World Mezzotint also known as Other World Gallery, mezzotint (1946)
  • Eye, mezzotint (1946)
  • Another World also known as Other World, wood engraving and woodcut (1947)
  • Crystal, mezzotint (1947)
  • Up and Down also known as High and Low, lithograph (1947)
  • Drawing Hands, lithograph (1948)
  • Dewdrop, mezzotint (1948)
  • Stars, wood engraving (1948)
  • Double Planetoid, wood engraving (1949)
  • Order and Chaos (Contrast), lithograph (1950)
  • Rippled Surface, woodcut and linoleum cut (1950)
  • Curl-up, lithograph (1951)
  • House of Stairs, lithograph (1951)
  • House of Stairs II, lithograph (1951)
  • Puddle, woodcut (1952)
  • Gravitation, (1952)
  • Dragon, woodcut lithograph and watercolor (1952)
  • Cubic Space Division, lithograph (1952)
  • Relativity, lithograph (1953)
  • Tetrahedral Planetoid, woodcut (1954)
  • Compass Rose (Order and Chaos II), lithograph (1955)
  • Convex and Concave, lithograph (1955)
  • Three Worlds, lithograph (1955)
  • Print Gallery, lithograph (1956)
  • Mosaic II, lithograph (1957)
  • Cube with Magic Ribbons, lithograph (1957)
  • Belvedere, lithograph (1958)
  • Sphere Spirals, woodcut (1958)
  • Circle Limit III, woodcut (1959)
  • Ascending and Descending, lithograph (1960)
  • Waterfall, lithograph (1961)
  • Möbius Strip II (Red Ants) woodcut (1963)
  • Knot, pencil and crayon (1966)
  • Metamorphosis III, woodcut (1967–1968)
  • Snakes, woodcut (1969)

See also


  1. Jump up^ “We named him Maurits Cornelis after S.’s [Sara’s] beloved uncle Van Hall, and called him ‘Mauk’ for short …”, Diary of Escher’s father, quoted in M. C. Escher: His Life and Complete Graphic Work, Abradale Press, 1981, p. 9.
  2. Jump up^ The circled cross at the top of the image may indicate that the drawing is inverted, as can be seen by comparison with the photograph; the neighbouring image has a circled cross at the bottom. Likely, Escher turned the drawing block as convenient while holding it in his hand in the Alhambra.
  3. Jump up^ Escher made it clear that he did not understand the abstract concept of a group, but he did grasp the nature of the 17 wallpaper groups in practice.[9]
  4. Jump up^ Schattschneider notes that Coxeter observed in March 1964 that the white arcs in Circle Limit III “were not, as he and others had assumed, badly rendered hyperbolic lines but rather were branches of equidistant curves.”[34]
  5. Jump up^ In 1969, Escher’s business advisor, Jan W. Vermeulen, author of a biography on the artist, established the M.C. Escher Foundation, and transferred into this entity virtually all of Escher’s unique work as well as hundreds of his original prints. These works were lent by the Foundation to the Hague Museum. Upon Escher’s death, his three sons dissolved the Foundation, and they became partners in the ownership of the art works. In 1980, this holding was sold to an American art dealer and the Hague Museum. The Museum obtained all of the documentation and the smaller portion of the art works. The copyrights remained the possession of Escher’s three sons – who later sold them to Cordon Art, a Dutch company. Control was subsequently transferred to The M.C. Escher Company B.V. of Baarn, Netherlands, which licenses use of the copyrights on all of Escher’s art and on his spoken and written text. A related entity, the M.C. Escher Foundation of Baarn, promotes Escher’s work by organizing exhibitions, publishing books and producing films about his life and work.[54][55]
  6. Jump up^ The poster for the exhibition is based on Hand with Reflecting Sphere, 1935, which shows Escher in his house reflected in a handheld sphere, thus illustrating the artist, his interest in levels of reality in art (e.g., is the hand in the foreground more real than the reflected one?), perspective, and spherical geometry.[23][60][61]
  7. Jump up^ Steven Poole comments “The artist [Escher] who created some of the most memorable images of the 20th century was never fully embraced by the art world.”[41]
  8. Jump up^ These and further albums are listed by Coulthart.[84]
  9. Jump up^ These and further books are listed by Bailey.[85]

Further reading



  • Escher, M. C. The Fantastic World of M. C. Escher, Video collection of examples of the development of his art, and interviews, Director, Michele Emmer.

External links

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