When Art Intersects with Mathematics: Constantin Brancusi, M. C. Escher and Cristian Todie

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(Note: this essay is dedicated to my father, the mathematician Henri Moscovici)

It’s only relatively recently in cultural history—during the past hundred years or so–that the disciplines became so highly specialized (and advanced) that it’s nearly impossible for anyone to be “cutting edge” in both the arts/humanities and science/mathematics. But the fields of human knowledge did not used to be so sharply delineated. Plato, for instance, was not only a great writer of dialogues and one of the greatest philosophers of all time, but also an outstanding mathematician. The school he founded in 387 BC, the Academy of Athens, was inspired by Pythagoras and emphasized mathematics as the foundation for all the other fields of inquiry. Likewise, his student, Aristotle, was considered a founder of several empirical branches of science, including physics, astronomy and biology (or natural science, as it was called until the nineteenth century).

Philosopher by Edson Campos

Even as late as the Enlightenment, the French philosophes—particularly Condorcet, Condillac and Buffon–could hope to be at the forefront of scientific discoveries and be well-versed in literature, art and philosophy. One of my personal favorites, the salonnière Emilie (Marquise) du Châtelet, was not only highly cultivated, but also a world-class mathematician and physicist who conducted her own scientific experiments—such as suspending wooden spheres from rafters–to test Newton’s theories.

This confluence of the disciplines—like the ideal of the “Renaissance man” (or woman) who masters all fields–has become only a distant memory in intellectual history. But sometimes there are resonances and intersections between the arts and the sciences even today. Like art and poetry, mathematical innovations are the result of an intuitive process that depends upon inspiration.  As Bertrand Russell eloquently stated in his essay, “The Study of Mathematics”  (1919):

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.”

Just as mathematics is, in some ways, an art form, so the arts and humanities borrow some of their standards of value (and proof) from math and science. In my estimation, the best writing in the humanities and social sciences abides by the standards of logical rigor, valid or plausible premises and “elegant proof” that are upheld in the sciences.  An elegant argument in the humanities, as in mathematics, is one that:

a)   uses a minimum of additional assumptions

b)   is “simple” or succinct

c)    is original, in arriving at new and surprising conclusions

d)   is based on defensible premises

e)   its conclusions are generalizable, in that they can be applied to similar problems

But there are even closer resonances between art and science. If mathematics is, in some respects, an art form—at least in its creative process–the opposite can be said as well: art can be mathematical. Even in the twentieth and twenty-first centuries, when the push for the specialization of the disciplines has reached an extreme, there are artists who illustrate the elegance, beauty and abstraction of mathematics.

Three of the most notable examples that I’d like to discuss here are M. C. Escher—an artist who achieved enormous fame during his own lifetime and remains very popular to this day—Constantin Brancusi and a Romanian-born contemporary artist with whom I’ve had the pleasure of communicating by email, Cristian Todie, whose works are highly appreciated in his host country, France. In a way, this warm reception is not surprising, since France has been an ideal cultural environment for many Romanian writers and artists, including Constantin Brancusi, the sculptor whom Todie cites as his main influence.  So let’s begin with a brief discussion of Brancusi’s works in relation to mathematics and philosophy.

Constantin Brancusi

Constantin Brancusi

Brancusi’s sculptures are mathematical in their geometric designs and their elegance  (understood in the scientific and philosophical sense of the term). His first major work is The Prayer (1907), a minimalist sculpture that reflects the artist’s unique and eclectic mixture of influences: Romanian folkloric peasant carvings, classical sculpture, African figurines and Egyptian art. A very talented craftsman and woodcarver, Brancusi also innovated a new method of creating sculptures: carving them from wood or stone as opposed to modeling them from clay or plaster, as his mentor Auguste Rodin and many of his followers were doing at the time. Most likely deliberately named after Rodin’s The Kiss (1908), Brancusi’s second major sculpture (by the same name) effaces the realism of the lovers, as they embrace to form one rounded, harmonious monolith: quite literally, a monument to love.  Years later, in Bird in Space (1928), the artist conveyed movement, altitude, aerodynamics and flight rather than the external features of the bird itself. The pinnacle of his career and the logical conclusion of capturing feelings and concepts through essential forms, Endless Column  (1938) represents the soaring spirit and heroism of the WWI Romanian civilians who fought against the German invasion.

Constantin Brancusi

One of the most innovative aspects of Brancusi’s art is that his sculptures capture the essence rather than the form of objects. Relying upon the Platonic and Aristotelian definitions of forms, the artist distinguished his minimalism from abstraction. Brancusi protested: “There are idiots who define my work as abstract; yet what they call abstract is what is most realistic. What is real is not the appearance, but the idea, the essence of things.” For Plato, Forms are the original, essential perfect models—such as goodness, virtue or humanity–for concepts and objects. Aristotle transformed this Platonic notion of Forms, distinguishing between the essential and the contingent, or essence and accident. The essence of the object defines what it is no matter how much it changes its appearance or state. Relying upon this Aristotelian concept, Brancusi was one of the first and best known Modernist artists who sought to capture the essence of the emotions and objects he conveyed: be it love and sensuality or heroism and courage.

M. C. Escher

Escher—the artist I consider, in both content and style, to be the closest precursor to Cristian Todie–remains one of the most popular twentieth century artists, internationally. Recently, the Escher exhibition in Brazil became, according to Blouin Art Info, “the world’s most popular art show,” drawing tens of thousands of viewers. (Blouin Art Info, April 13, 2012) Part of Escher’s continuing popularity can be explained in terms of the universal appeal of his art, which attracts those who love art and those who love mathematics or science alike. Like Picasso and Brancusi, in many respects Escher was an autodidact. He had little formal training in mathematics.

M. C. Escher

In fact, he discovered his passion for geometry, topology and visual paradoxes almost by accident, thanks to his travels to Alhambra, Spain. Escher was fascinated by the intricate, mathematical designs—or tessellations–he saw in the architecture of Alhambra, whose interlocking repetitive patterns of design would inspire much of his artwork.

M. C. Escher tessellation

The word “tessellation” comes from the Latin term “tessera” or small stone cube. “Tessellata” were the mosaic geometric designs of mosques (in which the representation of people or “idols” was strictly forbidden) as well as of Roman floors and buildings in general. Escher’s designs would “interlock” many objects–including his famous representations of fish and various critters–in fascinating patterns that create the magic of optical illusion.

M. C. Escher

Escher’s keen interest in geometric patterns led him to study non-Euclidian geometry. Euclidian and non-Euclidian geometry differ in their representation of parallel lines. Euclid’s fifth postulate states: “Within a two-dimensional plane, for any given line X and a point A, which is not on X, there is exactly one line through A that does not intersect X.” Simply put, in Euclidian geometry two parallel lines will never meet. They will remain at the same distance from one another, to infinity. In non-Euclidean geometry, however, parallel lines can meet, curving towards each other and eventually intersecting. In many of his lithographs, drawings, sculptures and paintings, Escher creates optical illusions that give us a representation of non-Euclidean space. One of his most famous and interesting works, Ascending and Descending, depicts lines of people climbing up and down an infinite loop. This construction is impossible in reality but can be created through playing with perspective.

Escher was also intrigued by topology. This relatively new branch of mathematics, derived from the Greek roots “topos” or “place” and “logos” or “word” and “study of,” analyzes the properties of objects that remain the same even when objects are deformed or stretched. According to  my father, Henri Moscovici (who works in the field of topology), topology can be explained as follows: “Two “objects” (topological spaces) are considered identical if they are homeomorphic, ie there is such a continuous function with continuous inverse between them. For example, a perfect sphere and the surface of potato or a tomato, are homeomorphic.”

In fact, of particular interest to both Escher and Todie are such “homeomorphisms.” One doesn’t have to know much about mathematics, however, to appreciate Waterfall Up and Down, which includes the irregular perspective we find in the Moebius strip.  Escher’s art represents the best of both worlds. For those who love math and science, Escher is one of the rare artists that gives these fields an artistic form. For those of us who don’t, Escher shows us that mathematics can be fun and ingenious.

Cristian Todie

Today, Cristian Todie enjoys a similar universal appeal, intriguing those who appreciate math and the arts and humanities alike. Born in 1954 in Constanta, Romania and living in France for many years, Todie creates non-Euclidian sculptures and designs that catch the eye and fascinate viewers. He sees himself as perpetuating, for our times, the “minimalist” sculpture of Brancusi, particularly in its geometric designs and (Aristotelian) emphasis upon capturing the inner essence of objects rather than their changing, accidental properties.

Cristian Todie

If you take a look at his website, called Art Théorique, you’ll also see that, as for Escher, mathematics lies at the basis of Todie’s art: in an intuitive and visual manner that any viewer can enjoy, without needing advanced mathematical training.

http://www.art-theorique.com/

In Todie’s digital photography, however, you’ll also detect a strong Dadaist influence. This is somewhat surprising, since historically this art movement set itself against math and science. Founded by a Romanian poet, Tristan Tzara, Dada was born in the wake of the bloodshed and devastation of WWI. Many of the writers and artists associated with this movement rejected “logic” and “reason,” blaming them for the technological breakthroughs that made the ravages of war possible. Like Surrealism, the art movement that grew out of it, Dadaism is whimsical, free and imaginative. It’s defined not as much positively, in terms of what it is, as negatively, in terms of what it is not. As Hugo Ball famously stated, “For us, art is not an end in itself… but it is an opportunity for the true perception and criticism of the times we live in.”

Cristian Todie

In the online exhibit called One Man Show, many of Todie’s images congruously combine a fascination with topology, optical illusions of non-Euclidean geometry with Dadaist absurd or whimsical images that transpose our daily, familiar reality into the domain of playfulness and imagination.

http://www.art-theorique.com/content/one_man_show/index.html

Cristian Todie

Todie’s innovative topological art confirms Henry David Thoreau’s famous saying: “It’s not what you look at that matters, it’s what you see.” And part of what you’ll see in Todie’s sculptures and photographs—much like in the works of his precursors, Brancusi and Escher–is a world where the sharply separated and largely parallel domains of mathematics and art intersect in the imaginative shapes of non-Euclidian space.

Claudia Moscovici, postromanticism.com

http://www.amazon.com/Romanticism-Postromanticism-Claudia-Moscovici/dp/0739116754

Art and Emotion

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aesthetics, Art and Emotion, art criticism, art history, Bernini The Ecstasy of Saint Teresa, Classical Sculpture by Philiip Scott Johnson, Claudia Moscovici, Claudia Moscovici's Romanticism and Postromanticism, emotion in art, fineartebooks, Michelangelo The Dying Slave, Myron's Discobolos, postromanticism, postromanticism.com, Rodin The Kiss, Romanticism, Romanticism and Postromanticism, the role of emotion in art

We tend to associate art and emotion. The Romantic notion of art as the product of an emotive, sensitive and inspired artist who creates masterpieces to move the public has not altogether disappeared from the popular imagination. Yet, in recent history—particularly since the movement of art for art’s sake in the nineteenth century and the formalist and conceptual currents of the twentieth century—emotion has almost disappeared from art itself. Even in the movement of conceptual art most closely associated with emotion and spirituality—abstract expressionism—emotion is a part of the process of artistic creation and palpable in the moving effect of art upon (some) viewers rather than readily recognizable in the artistic object itself. There is, of course, no eternally valid rule that dictates that emotion should be an inherent part of a work of art—or of any part of the artistic process, for that matter. And, in fact, art has not always existed as separate from artifact and artistic objects have not always been valued for their expressive powers.

For the ancient Egyptians, to offer one notable example, art served a largely symbolic and religious function. Tombs, busts and paintings were used as a means of preserving and glorifying the souls of kings, queens and other privileged members of society. E.H. Gombrich tells us that, appropriately enough, one Egyptian word for sculptor was “He-who-keeps-alive.” Egyptian artists depicted the human figure not as they saw it, nor to express or provoke emotion, but to capture the essence of an important person’s spirit for the afterlife by representing his or her body from its most characteristic angles. The face was shown in profile; the eye from the front; the shoulders and chest from the front; the legs from the side, with the feet seen from the inside and toes pointed upward. (The Story of Art, 60-1). For millennia Egyptian figures had a frozen and immobile, non-expressive look that strove to freeze the souls of powerful men and women in time and to safeguard their happiness in the afterlife.

Greek art was perhaps the first—and certainly the most influential art in the Western tradition–to capture the essence not only of the human spirit, but also of the human form, with all its movement and powers of expression. In Greek art, we feel, even the body seems infused with a soul. Myron’s famous sculpture of the discus thrower, Discobolos (c. 450 B.C), which is of the same era as the better known works of the sculptor Pheidias, displays the beauty, poise, force and movement of a young man’s efforts to launch the discus he holds in his hand. The sculpture is not entirely naturalistic—in the sense that athletes who would try to assume the same position would not be able to throw the discus very far. Nonetheless, it captures the elegance and athleticism of the male body in the first blush of youth. Part of this sculpture’s naturalism lies in the way it conveys movement and emotion through the positioning and poise of the body. This artistic video on classical sculpture by Philip Scott Johnson highlights this phenomenon:

More generally, classical Greek and Hellenistic sculptures rarely look stiff or contrived because of the way in which the human form is balanced: often in a position of counterpoise, with the weight shifted upon one leg, which allows sculptors to reveal the muscular curvatures of the body.

While classical Greek sculpture tends to focus upon the beauty of the human form, Hellenistic art—the art of the empires founded by Alexander the Great’s followers—places increasing emphasis upon the expression of emotion. The kinds of feelings represented in Hellenistic sculpture, however, are not those of everyday people in ordinary circumstances. Rather, Hellenistic art usually exhibits the emotions of extraordinary individuals engaged in tragic conflicts. To offer one well-known example, the sculpture Laocöon and his sons (175-50 B.C.)—executed by Hagesandros, Anthenodoros and Polydoros of Rhodes–immortalizes the story of a priest who is being punished by the gods for forewarning the Trojans not to accept a giant horse which, as it turns out, carried inside it enemy soldiers.

This sculpture was rediscovered in Rome in 1506 and many art historians believe that what was found was not the original sculpture, but a Roman copy. Whether or not it is the original work, The Laocöon Group made a strong impression upon Italian Renaissance sculptors, especially Michelangelo. Laocoon is frozen in an image of terrible anguish since his punishment consists of having to witness two gigantic snakes emerge from the sea and suffocate with their coils his beloved sons. Hellenistic art, at least in this representative sculpture that would become a favorite during the Renaissance and the Neoclassical periods, privileges the expression of a kind of emotion that is at once mythical and dramatic: mythical in its literary and religious references, dramatic in its depiction of human tragedy.

The painting and sculpture of the Renaissance masters continues to focus upon the expression of emotion on a grand scale and to grapple with the connection—as well as the hiatus–between the human and the divine. Michelangelo’s The Dying Slave (1513), for example, reveals the moment when the slave lets go of earthly life as his soul escapes toward heavenly existence.

Despite the twists and turns of his beautiful, muscular form, the slave’s body reflects the resignation, tranquility and spirituality of the transition from life to death. Emotive expression, Michelangelo shows so well, is not necessarily primarily located in the face. The whole body, every movement and gesture, expresses the feelings and attitudes reflected in the face.

This total, eloquent expressivity of sculpture reaches its apex, many believe, in Lorenzo Bernini’s The ecstasy of Saint Teresa (1645-52). The sculpture represents the sixteenth century mystic in a state of rapture. We witness the moment when the angel of God pierces the young nun with a golden arrow, provoking the paradoxical feelings of pleasure mixed with pain and of sensual abandon mixed with divine illumination. As she swoons, half-closing her eyes and slightly opening her lips with ecstasy, Saint Teresa becomes the very embodiment of religious fervor, spiritual attunement and passion. Even the drapery that enfolds her body swirls and twists around her with the same mixture of passive yet passionate frenzy visible on her face.

But what about the expression of more modest, individuated feelings? In the modern period, few artists were as thoughtful and successful in showing the relation between human form and feeling as Auguste Rodin. Despite the religious allusions of The Gates of Hell, Rodin brings emotion down to earth by materializing a passion that functions not only as a connection between the human and the divine, but also as an intimate and profound connection between earthly lovers. Perhaps no one else has described Rodin’s most sensual and moving sculpture, “The Kiss,” as eloquently as his friend, the art critic Gustave Geffroy:

“The man’s head is bent, that of the woman is lifted, and their mouths meet in a kiss that seals the intimate union of their two beings. Through the extraordinary magic of art, this kiss, which is scarcely indicated by the meeting of their lips, is clearly visible, not only in their meditative expressions, but still more in the shiver that runs equally through both bodies, from the nape of the neck to the soles of the feet, in every fiber of the man’s back, as it bends, straightens, grows still, where everything adores—bones, muscles, nerves, flesh—in his leg, which seems to twist slowly, as if moving to brush against his lover’s leg; and in the woman’s feet, which hardly touch the ground, uplifted with her whole being as she is swept away with ardor and grace.”

Rodin revealed human love and life as a process of mutual creation between women and men. Passion is not only a union with those we desire and adore, but also an elevation through shared feelings and sensuality which is always in process, never complete. His representations of the fragility of our mutual creation were as inchoate, vulnerable yet compelling as the material shapes that seemed to emerge only part-finished from the bronze or blocks of stone. In the expression of the beauty, erotic fervor and intensity of human emotion, postromanticism carries on Rodin’s artistic legacy.

We have seen that art can serve many different purposes in different contexts such that it’s impossible to define it in relation to any set of common qualities, including emotion. Yet, as I have also suggested, when emotion is materialized in art, it renders artistic objects all the more poignant, moving and palpable for viewers. The expression of emotion not only touches us, but also enables us to connect to artistic creation in a way that’s unique and irreplaceable. This is why postromantic art continues the Romantic legacy of expressing the fragility, contingency and intensity of human emotion at each stage of the creative process: the feelings and inspiration of the artist; the expressivity of artistic representations, and the emotional impact upon viewers. Emotion and art don’t have to be interconnected. Yet what beautiful and meaningful art is produced when they are!

Claudia Moscovici, postromanticism.com

http://www.amazon.com/Romanticism-Postromanticism-Claudia-Moscovici/dp/0739116754

Paola Minekov’s Painting for The Seducer: A Novel

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Anna Karenina, Anna Karenina staring Keira Knightley, Anna Karenina the movie, Claudia Moscovici The Seducer, dangerous relationships, fatal passion, illicit love, Keir Knightley Anna Karenina, painting of The Seducer by Paola Minekov, Paola Minekov, passion, psychopathic seduction, social predators, The Seducer by Claudia Moscovici, The Seducer painting, The Seducer: A Novel, Tolstoy

The Seducer painting by Paola Minekov

My friend, the artist Paola Minekov, recently finished a beautiful painting for my new novel, The Seducer. This painting captures perfectly the novel’s main theme– psychopathic seduction–by a social predator who comes on strong and poses, initially, as a romantic Prince Charming or Mr. Right. In Paola’s painting, as in my novel, the victim, Ana seems to hesitate between her strong attraction to her captor and the fear and anxiety their illicit passion provokes. His shadowy figure lurks, ominous yet attractive, like a dangerous lure.  A current of crimson red runs throughout the painting: simultaneously the red of passion and the red of blood, as they become one and the same in this novel about a fatal love.

Psychopathic seducers, as social predators, target countless victims. But they attach like parasites, for a long time, to comparatively few: only to their most promising hosts. I think that promising victims give off a scent of vulnerability, of unfulfilled desires that are perfect lures for pathologicals in need of control.  However many women they seduce and conquer; however many individuals they con; however much power they acquire, they still aren’t satisfied and need more. That’s because, emotionally, psychopaths are hollow human beings. The emotions, caring, money and time anyone pours into them seeps through them like through a bottomless hole.

Narcissists are very similar psychologically, only instead of control what they desire even more is validation. Narcissistic personalities often become famous artists, writers, scholars, movie producers or politicians. They have the drive and dedication to get to the top, but their thirst for validation is far greater than their periodic success. It is only temporarily satisfied and, in some respects, fundamentally unachievable. Success is fleeting and being at the top of the charts–be it as a singer, producer or best-selling writer–quickly turns into yesterday’s news. Narcissistic individuals often end up in an endless rat race, spinning in place, both emotionally and psychologically, no matter how rich or famous they become.

But even those of us who are neither psychopaths nor narcissists, which is to say, even more or less normal human beings experience an insatiable longing: the insatiable longing for love. This is what I describe in my new novel, The Seducer, through the character of Ana, modeled after my favorite heroine by the same name from Tolstoy‘s novel, Anna Karenina (which, incidentally, remains very relevant and is being launched soon as a film starting Keira Knigthley).  If some of us are tempted to cheat on or deceive those we love; if we are lured by the temptation of instant passion, happiness and commitment promised by dangerous social predators, it’s because within us, someplace, somehow, there’s an insatiable longing for love. This need can be a wound from previous betrayals or trauma, or simply an unrealistic, fantasy-driven yearning that can’t be fulfilled in reality.

Real love takes patience, constant nurturing and work. It depends on commitment and strength. It sometimes takes self-sacrifice. Psychopaths can tempt us with instant fulfillment, instant commitment, instant passionate love that require no work, because we’re “meant for each other,” because this is “the love of our lives”. This promise is not only a false and dangerous illusion, but also rests upon a fundamental repudiation of true love and of reality, flaws and all.

In my novel The Seducer I attempted to offer a psychologically accurate and in-depth sketch of three common forms of emotional insatiability: 1) the insatiable need for control and power over women of Michael, the psychopath; 2) the insatiable need for validation that keeps Karen, his needy and narcissistic fiancee, indefinitely caught in his clutches, and 3) the insatiable need for love of Ana, who represents the force, the need, the empty part that propels each and every victim into the arms of a dangerous social predator.

Any woman can become a tragic heroine like Ana if she gives in to a secret longing that has no realistic outlet or satisfaction. Written in the tradition of my favorite nineteenth-century novels, Anna Karenina and Madame Bovary–but with a contemporary psychological twist–The Seducer shows that true love can be found in our ordinary lives rather than in flimsy fantasies masquerading as great passions.

Claudia Moscovici, The Seducer: A Novel

http://www.amazon.com/Seducer-Novel-Claudia-Moscovici/dp/0761858075/ref=sr_1_1?s=books&ie=UTF8&qid=1326297451&sr=1-1

An Archaeology of Contemporary Life: The Art of Gianluca Capozzi

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An Archaeology of Contemporary Life: The Art of Gianluca Capozzi, art blog, art criticism, art reviews, Claudia Moscovici, contemporary art, contemporary painting, fine art, Gianluca Capozzi, hyper-realism, Italian art, painting, pop art, postmodern art, postromanticism.com, Surrealism

Born in Avellino, Italy, educated at the prestigious Academy of Fine Art in Florence, the contemporary artist Gianluca Capozzi shows an amazing versatility. Her paintings range from hyper-realism to a kind of minimalist Surrealism to Pop art. Gianluca Capozzi’s artwork offers an archaeology of contemporary life.

If anyone were to discover her works decades or even centuries later, they’d see our societies as they are: fragments of our every day lives, be it enjoying a day at the beach or walking on crowded city streets, on the way to work. But for the modern viewer, her artwork holds unexpected visual surprises that give us–quite literally–a fresh perspective on our daily activities: such as images that are off-center, where the focal point is the people dispersing into the city streets from an empty center or a young woman standing in the foreground with a fire blazing right behind her.

One of my favorites, called Pinup, featured below, captures perfectly the nearly inseparable fetishism–a longstanding cliché of the media machine–between women’s sexual allure and cars.

On the other hand, the painting entitled Office, below, is demurely realist and traditional. In a manner reminiscent of Degas’ voyeuristic framing, the viewer is invited to peek inside our mundane reality of “just another day at the office” as if we were mere external observers to our own everyday lives. This painting effectively defamiliarizes the familiar through its perspective rather than its style.

Finally, the painting entitled Sunday Afternoon, featured below, superposes a black and white image of a man working on his car with whimsical, colorful streaks of color. Both the car and the man have a retro look about them, but the splashes of color framed in white render them very fresh, ornamental and modern.

Gianluca Capozzi has the talent to render the familiar unfamiliar for the viewers of today while also making it more memorable for the viewers of tomorrow. You can see more of Gianluca Capozzi’s contemporary and versatile art on her blogspot, at the link below:

http://www.capozzigianluca.blogspot.com

Claudia Moscovici, postromanticism.com