The Mathematics of M.C. Escher's Art

A Dutch graphic, tessellation-, print-, woodcut-, lithograph-, mezzotintmaker, Maurits Cornelis Escher (1898 - 1972), is known for his impeccably construed worlds of impossibility, infinity, and  visual paradoxes, which integrate mathematics into art. Exploring the shape and logic of space, and ultimately capturing hyperbolic space on a two dimensional plane, his works use both the mathematical perfection and distorition of some of the spatial and geometric relations. 

(Relativity)

Among other concepts, Escher employed and further developed H.S.M. Coxeter and Poincare's circle model, George Pólia's seventeen plane symmetry groups, and Roger Penrose's geometric tilings and figures. Furthermore, Escher was fascinated by the Moorish Alhambra Palace in Granada, Spain, where all symmetry patterns are present. On the other hand, his works inspired many others, such as J.F. Schouten, J.W. Wagenaar, or crystallographers concerned with polychromatic symmetry. Escher's tessellations usually feature sets of invariant tiles which interlock with copies of themselves; they represent either local or global regularity, and encompass orderly, algorythmic, self-similar repetition outside traditional symmetry groups. What is more, if colouring is employed, although it is compatible with symmetry, more often than not, there is no ballance with the four-fold rotation symmetry, or four colour theorem. 

(Lizzard Square)

Escher played with the perspective, used multiple points of view, applied shifting vanishing points, manipulated shadow and light, made background become figure and vice versa. He employed infinite loops (called strange loops by Hofstadter), stairs, reflective surfaces, windows, and geometric figures, and in order to create optical illusions, or visual paradoxes, he used different kinds of reflections and symmetries, colour and shape combinations, rotations, and translations. 

(Convex and Concave)

He employed and mixed different kinds and senses of symmetry. His best-known lithograph, Drawing Hands, for instance, does not represent a literal symmetry, but balance with respect to center point, and left and right. He used an absolute, as well a non-absolute, yet dynamic symmetry of halves, i.e. the application of a perfect point symmetry and a rotation by 180 degrees called anti-symmetry, counter-change, or half-turned symmetry. Not surprisingly, one of the most important features of Escher's works is duality, i.e. the counterbalance of two opposing notions in the broadest sense of a dualistic nature of entities: one defining the other, figure becoming ground, light dissolving into shadow, etc. 

(Day and Night)

Another aspect of Escher's art is his specific depiction of order and its disruption. His favourite shapes and figures were Penrose polygons (see for instance his use of Penrose triangle in Waterfall), Necker cube (e.g. in Belvedere), Möbius Strip (e.g. in Swans), and last but not least, polyhedra (see for instance a stellated dodecahedron used in Gravity or in Order and Chaos). 

(Order and Chaos)

To sum up, Escher's lithograph print, Raptiles, represents probably all types and senses of symmetry (many of them not explicitly mentioned in the present text) which Escher put to use. The print features symmetry as ballance, duality, order, regularity, invariance, compatibility, economy, and closure.  

(Raptiles)

For further information, see:

- a video lecture entitled Symmetry in the works of M.C. Escher given by Doris Schattschneider at Moravian College;

- an article by Doris Schattschneider entitled Escher: a mathematician in spite of himself based on a talk given in July 1986 at the Eugene Strens Memorial Conference on Intuitive and Recreational Mathematics held at the University of Calgary;

- Douglas Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid (New York: Basic Books, 1979).

A Kiss as a Snapshot Photography Trope

A kiss has always been, though rather inconspicuously and sporadically, a recurrent theme of what might be labeled artistic snapshot photography. Some of the most famous photographs depicting a kiss follow.

Robert Doisneau is recognized as a witty, humorous, yet emphatic photographer of Parisian street life, and many of his photographs are viewed as the icons of French lifestyle. Although eventually revealed as posed [1], the photograph entitled Le baiser de l'hôtel de ville has come to be read as a story of boisterous love, lust, and spontaneity.

(Robert Doisneau: Le baiser de l'hôtel de ville)

(Robert Doisneau: Les amoureaux de Paris)

Henri Cartier-Breson is often pronounced the most capable street photographer. He believed in the time-stop, individual history preservative effect of photography, and with the patience of a fisherman, observed the surrounding him life in order to capture “les moments décisifs”.

(Henri Cartier-Breson: Café de Flore)

Alfred Eisenstaedt became famous by means of taking pictures of the famous (both in culture and politics), as well as by pioneering an available light photography. Nonetheless, the photograph for which he is known world-widely is a picture of a sailor passionately kissing a young woman on V-Day in Times Square. This snapshot not only became one of the symbols of the U.S. jubilant victory, but also one of the photographs that contributed to the definition of American photojournalism.

(Alfred Eisenstaedt: V-Day Kiss)

Eliot Erwitt is known for his candid look at the everyday city life, his portraits of people (often juxtaposed with some static objects), and (arguably) predominantly, for his witty photographs of dogs. His photograph California Kiss is considered one of the finest American snapshots from the 1950’s.

(Eliot Erwitt: California Kiss)

John Kimmich-Javier is a trained as an architect photographer who is rather unknown to wider public. His photograph, The Kiss, quite neatly documents Kimmich-Javier’s novel depiction of ancient buildings and their interiors.

(John Kimmich-Javier: The Kiss)

In 1968, Rocco Morabito, a former Jacksonville Journal photographer, was awarded Pulitzer Prize for Spot Photography for his photograph entitled The Kiss of Life. The picture captures an apprentice lineman, Champion, who is hanging unconscious having received a high voltage jolt, and another apprentice lineman, Thompson, who breathes life into Champion, and eventually rescues him.

(Rocco Morabito: The kiss of life)

Finally, Nan Goldin is an American photographer known for her documentary(-like) photographs of transsexual and gay communities, drug addicts, and people with AIDS. In spite of the fact that her pictures more often than not burst with the aggressive search for identity, violence in relationships, and rough sexuality; falling into the category of (memento) AIDS and gay photographs, the photograph entitled Gotscho Kissing Gilles affectionately represents a farewell kiss to a lover, a tender kiss of loss.

(Nan Goldin: Gotscho Kissing Gilles)

Chilly Chinese Contemporary Paintings

Chinese contemporary art is said to be one of the most exciting and diverse art scenes in the world. It ingeniously fuses expressionistic and realistic imagery with the grotesque, as well as it amalgamates collective, political, and personal statements, creating thereby uniquely turbulent worlds of the painted narratives... Cold Sweat?

(Zhang Xiaogang)

(Fang Li Jun)

(Zhao Bo)

(Li Li)

(Yue Minjun)

(Wang Ke)

For more Chinese contemporary artists, see: 

http://www.chinesecontemporary.com/

http://www.artscenechina.com/

http://www.newchineseart.com/

Poetics of the ParkeHarrisons

A multidisciplinary production process, comprising numerous photography techniques (such as darkroom, photomontage, collage, or varnishes), as well as painting, drama theatre (see staged scenes or fabricated props) and sculpture (see versized objects), has been applied in Robert and Shana ParkeHarrison's photographs in order to create photographs that, in spite of touching the surreal, attempt to picture a disturbing actual man-nature relation, primarily focusing on the human impact on nature, destruction and rehabilitation.

"I want to make images that have open, narrative qualities, enough to suggest ideas about human limits. I want there to be a combination of the past juxtaposed with the modern. I use nature to symbolize the search, saving a tree, watering the earth. In this fabricated world, strange clouds of smog float by, there are holes in the sky. These mythic images mirror our world, where nature is domesticated, controlled, and destroyed." Robert ParkeHarrison, The Architect's Brother (Santa Fe, NM: Twin Palms, 2000).

(Forestbed)

The ParkeHarrisons' work may be divided into two distinct periods: (1) the older works that might be distinguished by their monochrome (sepia or black-and-white) tonality, laboriously constructed sets of damaged or hollow landscapes, and the character of an "archetypal", black-suit-clad figure of "Everyman", who is patiently executing obscure, improbable and futile acts and rituals, and uses crude machines in attempt to communicate with the earth, to help it in its work, and to heal its wounds; and (2) the newer works, which are characterized by subdued colour palette; bare, grey walls or ground; blindingly white snow or contrejour (i.e. backlight); and by showing only parts of human body: there is no full man/woman portrayed.

(Cloud Burst)

(Pollination)

The photographs appear to me strangely poetic, and beautifully rendered ambiguous: they are witty and ironic, as well as unnerving and gloomy. In a highly organized fashion, they tell the story of chaos of a struggling (?), angry (?) and confused (?) existence.

(Grey Dawn)

(The Scribe)

Digital Legerdemain of Loretta Lux

Critics have responded in a number of ways to the digital legerdemain of Loretta Lux, a former German painter and currently a photographer creating rather formal, quasi-portraits of children. Her creations - utilizing photography, painting, and Photoshop technique of digital manipulation - have been described as disquieting, disturbing, repellent, displaying barely sublimated eroticism, creepy, kitschy, and monstrous, as well as charming, arresting, lovely, fashion-magazine-photography-like, fascinating and beautiful.

(Study of a Boy 1)

The genre of portraiture is undermined by means of showing children who "do not belong to themselves": the portrayed children do not represent themselves, they are awkwardly distant, anonymous and unengaged figures of children, dressed in vintage clothes and willed into existence. The surreal, doll-like, emotional opacity of the children's gazes evokes what is missing, yet the artifice is not hidden but accentuated, creating thereby eerily enigmatic air of obscure, carefully composed inconsistency superficially nearing oddly smooth perfection of calculated charm. The photographed subjects are slightly altered: they have distended hands and limbs, enlarged heads and eyes, their faces wear distinctive deathly pallor, their hair is silky, and their skin translucent.

(Girl With Marbles)

The sense of staginess is dramatized by the serene, shadowless, light background, into which the children - in heavily mannered poses - are set. By virtue of such Photoshop devices as Gaussian blur, unsharp masking and level control as well as thanks to the use of manual coloring, the subtle color palette is impeccable and the composition of forms is carefully structured, underlying thus the lurking element of fantasy.

(The Green Room)

Numerous influences, especially among Renaissance and German Romantic painters (some of whom have been cited by the artist herself) might be noted. They include: Agnolo Bronzino, Diego Velázquez, Francisco de Goya, Balthasar Kłossowski de Rola (known as Balthus), Piero della Francesca, Caspar David Friedrich, Philipp Otto Runge, etc. Lux's photographs also resemble those of a German photographer, August Sander.

(Bronzino: Bia, the Illegitimate Daughter of Cosimo I de' Medici)

(de Goya: Don Manuel Osorio Manrique de Zunica)

(Runge: The Hulsenbeck Children)

(Velázquez: Las Menians [a fragment])

Robert Browning's Dramatic Monologue

On the ground of its unique narrative qualities, the form of poetry that has recently appealed to me most is a form called dramatic monologue. It was invented and practiced principally by Robert Browning, and it is fundamentally characterized by having an explicit - often unreliable - speaker and an implied auditor. Glenn Everett describes Browninesque dramatic monologue as having the following three basic characteristics: (1) the reader acting as a silent listener, (2) the speaker's argumentative tone, (3) the completing of the dramatic scene by the actual reader from within, by means of using conjecture and imagination [adapted from Glenn Everett, "'You'll Not Let Me Speak': Engagement and Detachment in Browning's Monologues". Victorian Literature and Culture 19 ( 1991): 123-142]. One of the best examples of an unreliable narrator in Browning's poetry features in a poem entitled Porphyria's Lover. (For a case study of the ambiguities in dramatic monologues, see "Porphyria's Lover" by George P. Landow.)

Porphyria's Lover

The rain set early in tonight,

The sullen wind was soon awake,

It tore the elm-tops down for spite,

And did its worst to vex the lake:

I listened with heart fit to break.

When glided in Porphyria; straight

She shut the cold out and the storm,

And kneeled and made the cheerless grate

Blaze up, and all the cottage warm;

Which done, she rose, and from her form

Withdrew the dripping cloak and shawl,

And laid her soiled gloves by, untied

Her hat and let the damp hair fall,

And, last, she sat down by my side

And called me. When no voice replied,

She put my arm about her waist,

And made her smooth white shoulder bare,

And all her yellow hair displaced,

And, stooping, made my cheek lie there,

And spread, o'er all, her yellow hair,

Murmuring how she loved me — she

Too weak, for all her heart's endeavor,

To set its struggling passion free

From pride, and vainer ties dissever,

And give herself to me forever.

But passion sometimes would prevail,

Nor could tonight's gay feast restrain

A sudden thought of one so pale

For love of her, and all in vain:

So, she was come through wind and rain.

Be sure I looked up at her eyes

Happy and proud; at last l knew

Porphyria worshiped me: surprise

Made my heart swell, and still it grew

While I debated what to do.

That moment she was mine, mine, fair,

Perfectly pure and good: I found

A thing to do, and all her hair

In one long yellow string l wound

Three times her little throat around,

And strangled her. No pain felt she;

I am quite sure she felt no pain.

As a shut bud that holds a bee,

I warily oped her lids: again

Laughed the blue eyes without a stain.

And l untightened next the tress

About her neck; her cheek once more

Blushed bright beneath my burning kiss:

I propped her head up as before,

Only, this time my shoulder bore

Her head, which droops upon it still:

The smiling rosy little head,

So glad it has its utmost will,

That all it scorned at once is fled,

And I, its love, am gained instead!

Porphyria's love: she guessed not how

Her darling one wish would be heard.

And thus we sit together now,

And all night long we have not stirred,

And yet God has not said a word!

Josef Bolf's Childhood World of Anxiety

Only recently have I discovered obscure paintings by a contemporary Czech painter, Josef Bolf. Most of his pictures from 2006 onwards have been made by means of using a childly "naive" technique of scraping off of a layer of black drawing ink dabbed on a pink wax-crayoned layer. This technique by itself introduces the theme of childhood which is developed throughout. There is the surreal merging with the real, half-human and half-animal, comics stylization verging into prodigious precision, the spell of the omnipresence of ambivalence and disunity hovering over the world of childhood. There is no idealization, no safety, no carelessness, no innocence; there is perennial sense of depression and vulnerability and an obsessive longing for self-destruction. The pictured world seems to be conquered by sadness, anxiety, uprootedness, death and pain.

(Josef Bolf)