From the beginning of time, people have assumed there was an invisible world of some sort—of the spirits, the mind, or the world as explored by science. Artists have explored it on canvas and in sculpture, musicians in music, writers in words, and scientists with mathematics. The play between the visible and the invisible has always been at the heart of Western art and scientific thought.
In the fourteenth century, while the painter Giotto was exploring the geometry of planes with horizontal and vertical axes, thus moving toward an understanding of perspective, Nicole Oresme in France was inventing the graph, providing a visual image with which to investigate the laws governing falling objects. Then came the Renaissance. To its great masters, Leonardo da Vinci and Albrecht Dürer, there was no distinction between art and science. They carried out scientific investigations and painted pictures in the same spirit of inquiry and with the same creative fire.
In the seventeenth century, Newton was driven not only by the urge to make scientific developments but by alchemy, mysticism, and religion. His Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), published in 1687, was the culmination of this quest. It gave no hint of its mystical origins, and seemed to offer a way to understand phenomena on the earth and in the heavens using only pure, cold logic. Hereafter, science was to be considered the serious pursuit of truth, while art was seen as merely decorative.
In fact, the flow of ideas between art and science never totally ceased, but it was not until the 1830s that it was renewed with great vigor. The English painter John Constable deeply admired the scientist Michael Faraday and wanted to be considered a scientist as well as an artist. He drew and classified cloud formations and was particularly inspired by the way Faraday used visual images, such as the ghostly lines of electric and magnetic force, to explore electric and magnetic phenomena.
In the 1850s, the Scottish scientist James Clerk Maxwell was beginning to formulate the equations necessary to understand Faraday’s images. To do this, he had to deal with notions in physics that went beyond concepts basic to Newton’s physics, such as weights and velocities. Art, meanwhile, was becoming more abstract, as in J. M. W. Turner’s depictions of London, which astonished his contemporaries.
Then, at the end of the nineteenth century, just as the physics of Newton and Maxwell seemed unassailable, there were three discoveries that threatened to topple this magnificent edifice: x-rays, radioactivity, and the electron. For the first time, scientists had to directly confront phenomena beyond anything they could perceive with their senses—the world of the invisible.
Among much else, Newton had proposed a theory of color showing that white light was made up of red, orange, yellow, green, blue, and violet. Ever after, any discussion of color theory included the question of how we perceive color and whether there could be other theories based on a different set of primary colors. This question interested Johann Wolfgang von Goethe, who considered his own theory of color the best work he had ever done. Georges Seurat, too, was up to speed on the most current work, including the psychological effects of different colors—warm, cool, or arousing. He grouped different colors as dots such that, when viewed from a distance, they coalesced into a scene which conveyed the emotions he wanted to stir. In fact, his experiments with colored dots were experiments in the scientific sense. One of the results was to inspire Gabriel Lippmann to invent color photography.
Around the same time, Paul Cézanne was beginning to play with space in a way that broke with one of the Renaissance’s most firmly established conventions: perspective. He pushed scenes up against the picture plane, thereby transforming a single perspective point into several, focusing on conception—what he knew was there—rather than perception—what he could see with his eyes. His still lifes appear to have been planned mathematically.
All this set the stage for the revolutionary developments of the twentieth century, led by two unparalleled masters: Einstein and Picasso.
Reimagining space and time (1900–18)
One August day in 1914, at the train station in Avignon, two men awkwardly hugged each other. One, in French army uniform of dark coat, red trousers, and a kepi with a rifle slung over his shoulder, was a bear of a man. The other was shorter, solidly built, and swarthy, “a good looking bootblack,” as Gertrude Stein wrote. Georges Braque was going to fight the war to end all wars, while Pablo Picasso had used his Spanish citizenship to avoid it. The two had worked as one. Fired by Picasso’s brilliant ideas, they had created the most influential art movement of the twentieth century: Cubism.
Back in 1905, Picasso was so strapped for funds that he had taken to stealing milk and bread from people’s doorways. But despite his penury, the young Spaniard, just twenty-five years old at the time, was sure that his destiny was to become the toast of the Parisian art scene.
At the time, Émile Loubet, an esteemed orator and honest statesman, was the president of France. France’s great neighbor across the Channel still ruled the waves. Queen Victoria had died in 1901 after a reign of sixty-three years. Her son Edward VII had taken the throne and was now ruling over a decade of decadence.
Freud had recently published The Interpretation of Dreams. The Wright brothers had made their first flight, and France was enjoying the belle époque.
But there were seeds of discontent. Kaiser Wilhelm II in Germany was convinced that France, England, and Russia were plotting to encircle him.
Change was in the air. Europe was swept by an intellectual tidal wave whose proponents dubbed themselves the avant-garde. Their principal concern was to overthrow classical, intuitive notions of space and time—a mission which Picasso took very seriously. The momentum of change affected every aspect of life. The look of the city itself was transformed with the invention of prestressed concrete, which gave architects the freedom to open structures and play with space. Meanwhile, composers such as Erik Satie, Claude Debussy, and Arnold Schoenberg went on sonic adventures, going beyond the rigid structures of Germanic music to develop a new time frame of atonality. In poetry, Guillaume Apollinaire lifted words out of lines and sketched images with them.
Paris was electric with ideas. “We had no other preoccupation but what we were doing and saw nobody but each other. Apollinaire, Max Jacob, Salmon. Think of it, what an aristocracy!” Picasso recalled of this belle époque and of his closest friends who formed the core of his inner circle, his think tank. Their circle included Satie and Alfred Jarry, a literary fantasist who wrote about the fourth dimension and time travel. Jarry’s speciality was demolishing bourgeois literary and social conventions; he was an intellectual agent provocateur.
Another member en marge was Maurice Princet. An insurance actuary by day, by night he hung out with Picasso’s inner circle—la bande à Picasso; he had a penchant for philosophy and advanced mathematics, especially higher-dimensional geometries. “M. Maurice Princet preoccupies himself especially with painters who disdain ancient perspectives,” recalled André Salmon, a close friend of Picasso. Princet was introduced into Picasso’s circle by his notoriously unfaithful mistress, Alice Géry, who at one time had been involved with Picasso, preferring hot-blooded Spanish artists over gray insurance actuaries. Members of la bande à Picasso spoke of him as having a professorial manner but added that he “conceived of mathematics like an artist. [He] was le mathématicien du Cubisme.” It was Princet who introduced Picasso to the great French scientist Henri Poincaré’s writings on geometry. Poincaré would turn out to be the common denominator between Picasso and Einstein; his writings influenced them both.
What impressed Picasso most about science was x-rays, with their mind-bending message that what you saw was not necessarily what you got. Picasso’s love of movies and photography provided the technical background that enabled him to play with images, and with reality.
He was especially interested in mathematics, and in particular the geometry of four dimensions—the three dimensions of our everyday world (length, depth, and width) with an extra spatial dimension. If the artist could glimpse the four-dimensional world, he would be able to see all perspectives of a scene at once: a god’s-eye view; blooming, buzzing confusion. But how to project these perspectives onto the two-dimensional canvas?
Some artists even attributed mystical attributes to the fourth dimension, seeing it as a place where one could communicate with the dead or tap one’s powers of intuition; it was a world of ideas generated purely by thought, where the irrational moment of creativity occurred.
Princet introduced Picasso to concepts from four-dimensional geometry. He showed him a book on the subject written by Esprit Jouffret, a keen amateur mathematician who was also a friend of Poincaré. The equations meant nothing to Picasso, but the illustrations did. They were projections from the fourth dimension onto the two-dimensional page, showing complex polyhedrons as if the viewer was walking around them, viewing one perspective at a time. This was the way Poincaré had suggested for showing the fourth dimension, as Picasso knew from Princet’s lectures on Poincaré’s best-selling book Science and Hypothesis. Picasso, however, disagreed. “Why not project all perspectives at once?” we can imagine him asking Princet in a smoky bistro. He unveiled his response to the conundrum in 1907, in his revolutionary and groundbreaking Les Demoiselles d’Avignon, using all he had learned of mathematics, science, and technology to depict the fourth dimension in the face of one of the women.
Les Demoiselles d’Avignon was met with nothing but an embarrassed silence. Most of Picasso’s friends and colleagues thought he had gone mad, and to make things worse his mistress, Fernande Olivier, walked out on him. For several months Picasso was severely depressed. The painting was not seen again for three years, when a photograph of it appeared in an architectural journal under the title “Study by Picasso.” Commenting on the “terrible picture [that looms] through the chaos [in Picasso’s atelier],” the author of the article, Gelett Burgess, asked Picasso whether he had used models: “ ‘Where would I get them?’ grinned Picasso.”
The painting was not publicly exhibited until 1916, when art critics trashed it as “a nightmare,” “overwhelming,” and “yet another big daub by Picasso.” Nine years passed before Picasso finally sold it to a wealthy Parisian art collector who promised to have it hung in the Louvre. The collector never did. On his death in 1938, his family sold it to the Museum of Modern Art in New York for the even then paltry sum of $28,000. For many years, only Picasso realized its worth and importance.
As we now know, Les Demoiselles d’Avignon was the foundation of Cubism.
IN 1905, WHILE Picasso was seeking his style, in a city not far in distance but light-years away in culture, another young man, two years older, had already found his. Intense and handsome, with a passion for the violin, Albert Einstein had the “kind of beauty that caused havoc,” as a female admirer recalled. There were many similarities between the two, on both the personal and creative fronts, in particular the fact that the most creative periods of their lives spanned the same years: 1902–09.
At the time, both were involved in tempestuous relationships: Picasso with his flamboyant and flirtatious mistress, Fernande Olivier, and Einstein with his sultry and moody wife, Mileva Marić. And both struggled to make ends meet.
Born in 1879, in 1905 Einstein was a complete unknown. At his high school in Munich, his Greek teacher had told him he would not amount to anything—and indeed he didn’t, at least in Greek. But Einstein did not waste his time. By the age of twelve, he had taught himself advanced mathematics and physics.
He then left Germany for Switzerland, which had managed to remain a peaceful place. Luckily for him, the Swiss Polytechnic Institute in Zürich did not require a high school diploma for entry. Nevertheless, when Einstein graduated in 1900, the Institute refused to give him a letter of recommendation. By now he had renounced his German citizenship.
Finally, in 1902, with the help of a friend’s father, he got a job as a patent clerk third class at the Swiss federal patent office in Bern, an intellectual backwater. “[At the patent office I] was set free to produce my best creative work,” he recalled. For culture, Einstein had a study group which consisted of himself and two pals, Conrad Habicht and Maurice Solovine. They called themselves the Olympia Academy, and took all knowledge as their province. Among the books they studied was Poincaré’s Science and Hypothesis, which left them “spellbound,” as a former member recalled. This was Einstein’s think tank. “This group had a considerable influence on my development,” he later recalled.
Three years later, at white heat, with no forewarning, Einstein published four papers that would change the course of science as well as of nations.
Since he was fifteen, Einstein had been mulling over the state of physics and had grown increasingly unhappy with it. He found certain of its inconsistencies “unbearable.” In that era, he wrote, the equations of physics were interpreted in a way that “led to asymmetries that do not appear to be inherent in the phenomena.”
He concluded that physics was riddled with redundant explanations and extraneous concepts that had led to these asymmetries, and pared all these away using a minimalist aesthetic. This led him to the discovery of his relativity theory in 1905. It was a response to aesthetic discontents. Thus he introduced the notion of symmetry into twentieth-century physics.
Einstein’s theory opened the way to revealing a universe that was astounding, contradicting all our intuitions as experienced in daily life. There were no true times, just as there were no true lengths, for there was no one true perspective of any physical phenomenon. It was exactly what Picasso and the Cubists were discovering at almost the same moment.
“A consequence of the work on electrodynamics has suddenly occurred to me,” Einstein wrote. This was that mass and energy were equivalent, that every mass is equivalent to a huge amount of energy. Thus the equation E = mc2 made its appearance in September 1905. Einstein even suggested a way to release this energy by using radioactive processes.
Most physicists were convinced that Einstein’s relativity theory was at odds with experimental data. Like Picasso, Einstein alone realized the worth of his work and persevered in claiming that the data were wrong, as indeed they turned out to be. Just about every physicist failed to spot the significance of what he had accomplished, asserting that Einstein had merely substantiated an already existing theory of the electron. Later, he recalled of the leading physicists of that era that “they were theorizing out of their depth,” a rather audacious statement for a patent clerk. Like Picasso, he was confident of his destiny.
By the spring of 1909, Einstein’s career had become meteoric. Walther Nernst, the impresario of physics in Berlin, visited him in Zürich, where he was an associate professor at the university, to consult him on his research into the way in which heat courses through matter, based on the still controversial quantum theory discovered barely ten years earlier by Nernst’s colleague Max Planck. Einstein’s research moved Planck’s work from theory into the laboratory. At the same time, Einstein was working on expanding his theory of relativity to a point where scientists could use it to explore why the universe is as it is. The new so-called general theory of relativity began as one man’s view of the cosmos. Ten years later, in 1919, its verification would result in his deification as genius incarnate.
The world meanwhile had suffered the cataclysm of war. Einstein used his immense prestige to advertise his long-held pacifist views, which had led him to renounce his German citizenship when he was living in Switzerland. He reacquired it in 1919 as a show of support for the liberal government of the Weimar Republic. He would renounce it again in 1933.
Picasso, too, was busy in his new atelier in Montmartre, creating paintings, photographs, and sculptures, and carrying out further researches into Cubism—reducing natural forms to geometry, the aesthetic he had discovered in 1907 with Les Demoiselles d’Avignon. He also photographed some of his Cubist paintings and laid the negatives one on top of the other to produce prints that were Cubism upon Cubism, Cubism to the nth degree, which he thought of as a higher order of Cubism. He made a multifaceted sculpture, Head of Fernande, and his portraits of her also had a true three-dimensionality. He was “as overworked” as God, he recalled.
New trends in both art and science were emerging, set in motion by the breakthroughs made by Picasso and Einstein. Ironically, both men would find it impossible to follow these through to their logical conclusions. At bottom Einstein was a classical physicist who clung to a view of the universe that was essentially an updated version of Newton’s science of motion, and Picasso’s bent was always toward an abstract figuratism. The two were determined to maintain a visual imagery in their work that connected with what we see in our daily lives.
Beyond reality (1918–30)
Whereas Einstein and Picasso were reluctant to follow to the extreme the avenues that their magnificent breakthroughs had opened, other artists were not. Wassily Kandinsky, for one, had no problem moving totally away from reality as we see it with our eyes and stepping out into the void. “The work of art is born of the artist in a mysterious and secret way,” he wrote in 1912.
Born in Moscow in 1866, Kandinsky was inspired to become an artist when he went to an exhibition in Moscow in 1895 and saw how the French Impressionists played with color and light. He was particularly struck by Monet’s Haystacks. “That it was a haystack the catalogue informed me. I could not recognize it. . . . I wondered if it would not be possible to go further in this direction,” he wrote. He was twenty-nine at the time. Until then, he had had a successful law practice and even as a young painter he still looked like a lawyer—neatly dressed, hair combed, with wire-rimmed glasses, eager to provide a logical analysis of any situation at hand. This businesslike façade, however, concealed an intense belief in Russian mysticism which inspired his lifelong fascination with color and music.
In 1906 in belle époque Paris, Kandinsky met up with a group of artists famous for their extravagant use of pure colors and exaggeration of forms. They were known as Fauves, or “wild men,” and among them was Henri Matisse. Kandinsky was dazzled. To him the works of Picasso and Braque, conversely, with their emphasis on objects, materials, and geometric representation, smacked of science. In these, he wrote, “natural form is often forcibly subjected to geometrical construction, a process which tends to hamper the abstract.” He wanted to find the “spiritual existence,” which meant exploring the unseen “absolute forces” behind material objects. The artist should strive “toward the abstract, the non-material,” for only in this way could he express his inner emotions.
“The harmony of the new art,” he continued, “appeals less to the eye and more to the soul.” He used bright colors to “symbolize feelings” and evoke the “inner glory” of nature—to probe consciousness itself.
Nevertheless, he was impressed by Einstein’s relativity theory and the equivalence of mass and energy, E = mc2, which asserts that everything we see and touch is simply energy. Kandinsky interpreted this as the mystical aspect of modern science—that everything is amorphous. His 1910 painting Improvisation was completely abstract: it did not refer to any naturally occurring object or even any geometrical form. Kandinsky had discarded form altogether.
Around the same time, a group of Parisian artists was also looking for ways to probe emotion and consciousness using line and color, but in addition they wanted to bring in a scientific element. In particular, they wanted to communicate the dissolving of substance into energy, to suggest that all forms were products of the mind. Picasso’s friend the poet Apollinaire dubbed this movement Orphism after Orpheus, who sought pure music. Just as Picasso had emphasized conception over perception, Apollinaire did too, describing Orphism as the art of painting “with elements borrowed not from visual reality, but entirely created by the artist.”
The Orphists met in the Parisian suburb of Puteaux, at the house of the three Duchamp brothers: Raymond Duchamp-Villon, Jacques Villon, and Marcel Duchamp, and thus were known as the Puteaux Group. Apollinaire was the poet of the group, which included Jean Metzinger and Albert Gleizes, who painted in a sort of academic style of Cubism and participated in group showings in salons. To Picasso’s annoyance, Gleizes and Metzinger proclaimed themselves the founders of Cubism.
Like Kandinsky, these artists were very interested in developments in science and technology. Electromagnetic waves emanate forcefully from Robert Delaunay’s Eiffel Tower, while in his Nude Descending a Staircase, Duchamp explores movement in space and time.
Meanwhile, in Italy, a group of artists had sprung up who threw off all ties with the past and celebrated a new world grounded in modern technology, with the emphasis on the violence and beauty of speed. They called themselves the Futurists. Their images were stimulated by technology and fired by extremist rhetoric. “We want no part [of the past]. We spit every day on the Altar of Art,” wrote their chief propagandist, Filippo Marinetti, who called himself “the caffeine of Europe.” The Futurist manifesto of 1909, which he had a hand in writing, minced no words: “We will glorify war—the world’s only hygiene.” Then came the carnage of the First World War, which put a stop to the Futurists’ belligerent propaganda. Marinetti would go on to write speeches for Mussolini.
Two years later, in 1911, the Futurists arrived in Paris. With their dapper dress, Italian good looks, and panache, they took the Parisian art community by storm, especially the women. Picasso had been looking for an excuse to dump Fernande, and found it when she had an affair with one of them. The Futurists revered Picasso and Braque, but had nothing but disdain for Picasso’s followers—Duchamp and his friends, the Puteaux Group.
In 1916, yet another new art movement emerged, the brainchild of the Romanian expatriate, poet, and performance artist Tristan Tzara, this time in Zürich. Zürich had become a focal point for artists, writers, and political figures, including Lenin, as well as Picasso’s longtime German dealer and friend, Daniel-Henry Kahnweiler, all seeking refuge from the war. The credo of the new movement was that it was time to put an end to the hierarchy that condoned the war and all the artistic trends associated with it, starting with good taste and rational thinking and moving on to Futurism and even Cubism, whose productions the new artists referred to as “Cathedrals made of shit.” These iconoclasts were intellectual shock troops. They called their movement Dada and themselves Dadaists.
Meanwhile, Kandinsky’s countryman Kazimir Malevich was striving to depict the cosmos in other ways. An intense, broad-shouldered, powerful man, in his early works he had been influenced by Fauvist colors and Cubist geometry, but wanted to go beyond this into purely abstract painting, as Kandinsky had. While designing the sets for the Cubist–Futurist opera Victory over the Sun, he was struck by the way in which three-dimensional stage props became basic two-dimensional forms under the spotlights. Perhaps, he thought, both the world about us and the unseen world might be built out of supremely one-dimensional forms—straight lines.
The first painting Malevich produced in this new experimental style—Suprematism—was a black square on a white background, in which the square, with its four straight sides, represented stability.
Next he painted a circle, reasoning that if a circle was expanded to fill the universe, its perimeter would become essentially a straight line. Then he painted a black cross constructed of five squares. To prove that these geometrical forms encompassed the whole cosmos, Malevich turned to science. In a series of writings and artworks focusing on magnetism, he convinced himself that geometrical forms had played a key role in James Clerk Maxwell’s model of how magnets and wires carrying an electric current affected the space around them, which scientists in Maxwell’s day believed was filled with a ghostly substance called the ether, another extraneous notion leading to asymmetries that Einstein got rid of using his minimalist aesthetic.
Like Picasso with Jouffret’s book, Malevich could not understand the equations in Maxwell’s writings. It was the images that dazzled him, among them the patterns formed by iron filings on a piece of paper placed near a magnet. Maxwell and his predecessor, Michael Faraday, had abstracted from these patterns to depict the unseen space around the magnet—the nonobjective world, which to Malevich was the only possible source of art. Inspired by these, he made a drawing of space using only straight lines.
By 1918, Malevich had moved beyond electromagnetism to depict the world about him as ultimately formless and colorless energy. That year he produced his first white-on-white painting, a white cross on a white canvas. The square had shed its material being and merged with infinity in a glare of pure whiteness. Malevich had entered the fourth dimension, achieving a sort of cosmic consciousness, a nirvana.
Into the atom
For many years, scientists refused to embrace abstraction. They tried to describe the physical world in images drawn from everyday phenomena and dealt with objects in the atomic realm in the same way as those in our daily world, treating electrons as if they were charged billiard balls and obeyed the same laws of motion.
Then in 1905, Einstein suggested that light was emitted in indivisible bursts, or packets. He called these light quanta. Dazzlingly, he pointed out for the first time that the “profound formal distinction” made by scientists between waves and particles was unwarranted. Why assume that light was both particle and wave when, in specific phenomena, only one of these two was needed? He then applied his minimalist aesthetic to choose the particle aspect of light in order to deduce the law of the photoelectric effect, later put to practical use in developing devices that automatically open doors.
Most scientists dismissed Einstein’s light quanta as seriously weird, useful only for doing calculations that could not be done using a theory of light as waves. How could a theory of light particles explain how two sources of light could interfere with each other? How could particles interfere with one another?
In fact, the whole issue of how electrons behaved in atoms baffled scientists until Niels Bohr investigated it. Einstein wrote of him, “He is like a sensitive child and walks about this world in a kind of hypnosis.” Born in Copenhagen in 1885 into a highly intellectual family, Bohr was heavy-set, physically strong, yet clumsy—not one to get into a fight with—and very smart. He mumbled, speaking very softly and without enunciating clearly. From an early age he was exposed to the arcane world of Danish philosophy. He became steeped in Søren Kierkegaard’s views on why we exist at all and Paul Martin Møller’s tale of the boy who thinks about what he’s thinking about and so on ad infinitum. Bohr’s father, an eminent professor of physiology at the University of Copenhagen, had a wide intellectual circle which often met at his home, so Niels heard these topics explored in depth by Denmark’s leading thinkers.
Bohr completed his PhD in 1911. That same year, laboratory experiments revealed that the atom seemed to behave like a miniature solar system with a positively charged nucleus at the center, like a sun, around which negatively charged electrons circulated like planets. This image of a minuscule solar system was most exciting, for it suggested that the atomic world was a reflection of the cosmos itself. Two years later, Bohr supplied the mathematics to back it up. His theory was immensely successful in making sense of many properties of atoms, in particular, of the sort of light they emitted, which formed their “fingerprint.”
EIGHT YEARS LATER, as the First World War came to a close, science and art began to brush up against each other more closely than ever before.
In 1919 the English scientist Arthur Stanley Eddington set out to verify Einstein’s generalization of relativity by testing the theory’s startling prediction that starlight would bend near massive objects, i.e., other stars. He sailed to the tiny Portuguese island of Principe, off the west coast of Africa, and there carried out a spectacular experiment. His aim was to measure the extent that light from stars was bent in the sun’s vicinity. To do so he photographed stars close to the edge of the sun during a total eclipse and compared their positions with those from star catalogues, with the sun removed, and found that the same stars were in distinctly different positions. He was thus able to measure how much a star’s light was deflected by the sun’s huge gravitational field. He concluded that Einstein was correct, and as a result of this dramatic proof relativity became a household word. Thanks to the explosion of interest, the public learned that we actually live in a world of four dimensions, where the fourth dimension is time. That same year, 1919, El Lissitzky, Malevich’s colleague at the Artistic Institute in Vitebsk (Belarus), set out to incorporate science into his art.
Born in 1890 in a small Jewish community near Smolensk, Lazar Markovich Lissitzky, better known as El Lissitzky, was swarthy and handsome, with close-cropped hair and an intense intellectual stare. In 1917 he began to focus on graphic art and architecture and to make a name for himself. Two years later, Marc Chagall persuaded him and Malevich to come to his institute in Belarus, which specialized in graphic art. It was there that Lissitzky decided to rewrite Malevich’s style of art—Suprematism—by incorporating relativity into it. He was particularly influenced by the way in which in relativity theory the three dimensions of space were combined with time into four-dimensional space-time, as the Russian mathematician Hermann Minkowski had demonstrated in 1907.
Minkowski had a stern Prussian bearing with a manicured handlebar mustache, high-collared shirt, and pince-nez glasses, and had been one of Einstein’s teachers in Zürich. To describe Einstein’s work, he used poetical statements such as, “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” In his scientific papers Minkowski included two-dimensional diagrams of space-time. As in the four-dimensional world of the artist, where the fourth dimension was a spatial one, if a scientist could visualize this four-dimensional space he would be able to see every possible measurement of a phenomenon.
From 1921 onward, themes related to Minkowski’s diagrams began to feature in Lissitzky’s art, in particular in his collage Vladimir Tatlin, Working on the Monument. His choice of Tatlin was both symbolic and dramatic. Tatlin was a central figure in postrevolutionary Russian art. His first constructions had been abstract, like Picasso’s, but after the 1917 October Revolution he began to incorporate rivets, iron, glass, and airplane wings to express the dynamic unfolding of forces. He argued that Socialist art should not be abstract and rejected the mysticism and abstraction of Malevich’s work. Tatlin’s art became known as Constructivism.
His most famous work, which inspired Lissitzky’s collage, was his Monument to the Third International, a Constructivist tower designed to be erected in St. Petersburg after the Bolshevik Revolution of 1917, as the headquarters of the Comintern, the Third International. It was an extraordinary construction of industrial materials—iron, glass, steel—and a symbol of modernity. In shape it was a bit like Brueghel’s Tower of Babel: a twin helix of girders which would spiral up 1,300 feet, higher than the Eiffel Tower, containing four geometric glass structures which would rotate at different speeds. It was conceived as a visual representation of Leninist dialectical materialism: but it was never built and was probably unbuildable.
Lissitzky believed that art was not meant to be merely art but to enhance society as a whole and that, to accomplish this, artists should take their place alongside scientists and engineers. Tatlin was his “new man,” the architect of a new reality founded on relativity theory made concrete.
While Lissitzky was working on his Tatlin collage, he visited Weimar, in Germany, where he met the Dutch artist Theo van Doesburg. Van Doesburg had established an abstract art movement along with Piet Mondrian, among others. They produced a professional journal which they entitled De Stijl (The Style).
Van Doesburg intended De Stijl to be more than merely another art movement: it was to lead the way toward a new humanity and a new society. He conceived this lofty goal in 1915 when he saw Mondrian’s abstract paintings and immediately contacted him.
Mondrian took a deep interest in science. “There are ‘made’ laws, ‘discovered’ laws, but also laws—a truth for all time,” he wrote. “These are more or less hidden in the reality which surrounds us and do not change. Not only science but art also, shows us that reality, at first incomprehensible, gradually reveals itself, by the mutual relations that are inherent in things.” This was a call for the artist and the scientist to work together to seek the true, unchanging laws of nature that lie in a realm beyond what we can perceive with our senses.
Van Doesburg admired the pureness of Mondrian’s abstraction. But to his eyes it lacked modern scientific punch or scientific content. Its fourth dimension was static because it was a purely spatial dimension. Van Doesburg wanted to develop Mondrian’s work and incorporate it into his De Stijl movement.
Whereas Mondrian was slow-moving and casually dressed, van Doesburg was the opposite. In his new approach to art and creativity there was no place for the romantic, bohemian image of the lonely, impoverished, poorly dressed artist starving in his freezing atelier. The new art van Doesburg envisioned was one that would integrate new technology and science and was practiced by men in suits and ties working in spotless offices.
In 1920, van Doesburg was already incorporating science into his art, using poems he called “X-images,” where “X” stood both for “x-ray” and for the unknown in an equation. Then Lissitzky introduced him to relativity, with its four-dimensional space-time. This gave him the material to push Mondrian’s style of art into modern times. He even proposed a plan for a university to be built in Amsterdam, with designs styled after Minkowski’s space-time diagrams on its ceilings and walls, similar to Lissitzky’s work in the Tatlin collage. It did affect the final design for the University of Amsterdam, built in 1923.
By the 1930s a battle was going on between exponents of nonfigurative and figurative art, centering on the term “relative.” Mondrian wrote in an essay: “It is necessary to point out that the definitions ‘figurative’ and ‘nonfigurative’ are only approximate and relative. For every form, even every line, represents a figure; no form is absolutely neutral. Clearly, everything must be relative, but, since we need words to make our concepts understandable, we must keep to these terms.” The term “relative” had taken on a life of its own, apart from its rigorous use in relativity theory. Here Mondrian wondered whether there can be a truly abstract art.
Strange worlds (1930–50)
With the First World War over, the Roaring Twenties were in full swing. But there was industrial decline in Britain, the German economy was suffering rampant inflation, and the great crash of 1929 was looming on the horizon.
By now artists were releasing their hold on reality and creating fully abstract works; but scientists still tried to maintain either some visual imagery that could be abstracted from phenomena we can actually witness, or nothing at all. They were torn between figuration and abstraction. To make matters worse, by 1924 it had become clear that Bohr’s theory could not accommodate the wealth of data on the atom that had accrued since he proposed it in 1913. It was totally apparent by now that atoms did not actually behave as if they were minuscule solar systems. The Austrian physicist Wolfgang Pauli wrote succinctly, “We do not want to clap the atom into the chains of our bias but on the contrary, we must adjust our concepts to experience.” Instead of clinging to an outmoded image of the atom, scientists would be better off trying to understand the situation as it really was—listening to nature with a sympathetic ear attuned to the music of the spheres.
The man who finally found a way out was Werner Heisenberg, the German physicist who would later work on the German atomic bomb project. Heisenberg had the look of “a simple farm boy with short, fair hair, clear blue eyes, and a charming expression.” He first encountered atomic physics in 1919, at the age of eighteen, while lying on a rooftop at the University of Munich, reading Plato’s Timaeus. He was doing guard duty for the Free Corps, a hard-line conservative group made up mainly of disgruntled war veterans. A Communist uprising was in progress and Austria and Germany were in political turmoil.
Heisenberg was entranced by Plato’s description of atoms as geometrical solids. He knew this was a fantasy, but he admired the way in which ancient Greek scientists had been prepared to consider even the most unlikely speculations. Perhaps he could do the same. A year later he formally entered the university and promptly began to make his mark in physics.
He set out to reshape Bohr’s theory of the atom but finally decided that it was a dead end. Then, while recovering from hay fever in May 1925 on Heligoland, a small pollen-free archipelago in the North Sea, everything suddenly snapped into place. “I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy,” he wrote. There and then Heisenberg rewrote atomic physics. Physicists dubbed his new theory “quantum mechanics.”
Quantum mechanics solved many problems that had eluded the Bohr theory, but nevertheless physicists were uncomfortable because it could not be visualized. The mathematics it employed was unfamiliar and it was difficult to use. It was like trying to visualize infinity. To Heisenberg, this was not a problem. It meant that his theory was unencumbered with outdated visual imagery, like that of the solar system atom, which had led to confusion.
In quantum mechanics, electrons were treated as invisible particles. The year before, however, in 1924, the French physicist Louis de Broglie put forward convincing arguments that electrons could be waves as well as particles, just as Einstein had shown that light could be a particle as well as a wave.
At the end of 1925, the rakish Austrian physicist Erwin Schrödinger was on an illicit skiing weekend with a paramour when he had an epiphany. He worked out an equation and made it the basis of a new atomic physics in which electrons were waves surrounding the nucleus. He then carried out some of the calculations which had previously been done using Heisenberg’s quantum mechanics but in a much simpler and more direct way using his theory, which employed visual imagery from classical physics—waves—and whose mathematics was familiar to all physicists, namely differential equations (in this case, his own—Schrödinger’s—equation).
Schrödinger wanted to find a version of atomic theory that was different from Heisenberg’s quantum mechanics. “Inspired by [de Broglie’s suggestion that electrons were waves, I] felt discouraged not to say repelled by [quantum mechanics], which appeared very difficult to me and by the lack of visualizability,” he wrote. Schrödinger’s was an aesthetic choice—waves over particles; Heisenberg’s choice of particles over waves was equally aesthetic. Schrödinger’s wave mechanics took the world of physics by storm and overnight atomic physics went figurative again.
Heisenberg went apoplectic. “The more I reflect on the physical portion of Schrödinger’s theory the more disgusting I find it. . . . What Schrödinger writes on the visualizability of his theory I consider crap,” he wrote to that most incisive and critical of physicists, Wolfgang Pauli. Thus began what Heisenberg dubbed the battle between the waves and the particles.
In 1927, Bohr took the first steps toward resolving this knotty issue. He drew from his wanderings through the labyrinth of Danish philosophy and his knowledge of Eastern thought, bearing in mind the counterintuitive consequences of the high speed of light which means that time is relative. For Bohr, the key lay in the incredible minuteness of the atomic world, which is measured using an unimaginably tiny scale based on Planck’s constant, 6.6 · 10-34. (By contrast, the scale of relativity, used for high speeds and the vast universe, is based on the enormous speed of light, 3.0 · 108.)
In their atomic theories, Bohr argued, Heisenberg (quantum mechanics) and Schrödinger (wave mechanics) had each considered only one-half of the real world. Both the wave and the particle modes of existence were necessary in order to fully understand the ambiguous world of the atom. Bohr argued that it was necessary to opt for full symmetry, to take the electron as both wave and particle. The wave and particle aspects of an electron could be complementary in the yin-yang sense but at the same time mutually exclusive, which meant that only one side could ever be “seen” in an experiment. In other words, however you looked at an atomic entity, that was precisely what it was—either wave or particle, but never both at the same time. Bohr dubbed his new view “complementarity.”
Bohr was widely read and highly cultured, with interests that went far beyond science into art. He seems to have had a particular interest in Cubism, as evidenced by the fact that, when he was given carte blanche by the Carlsberg Foundation to furnish his study in any way he wished, he chose a painting by Jean Metzinger, a member of the Puteaux Group. Cubism was in fact one root of his powerful notion of complementarity.
Perhaps he had read Metzinger and Gleizes’s manifesto On Cubism. A Cubist painting, they wrote, represented a scene as if the observer were “moving around an object in order to seize it from several successive appearances.” It was this that most impressed Bohr about Metzinger’s painting. Mogens Anderson, a Danish artist and friend of Bohr, recollected Bohr’s pleasure in giving “form to thoughts to an audience at first unable to see anything in it—They came with a preconceived idea of what art should be.” Bohr’s idea of complementarity offered a motif for the world of the atom that had striking parallels to the multiple perspectives offered by Cubism, providing a way of glimpsing beyond and behind the world of perceptions.
Heisenberg went on to conduct research into nuclear physics in 1932, still pursuing the correct imagery for the atomic domain, but it remained elusive. He did, however, come up with an important suggestion: to let the mathematics of the quantum theory decide the proper imagery.
IN 1921, THE French writer André Breton read a translation of Einstein’s popularization Relativity: The Special and the General Theory. Breton was twenty-five at the time and his imagination was fired by what he read. “ ‘One event can be the cause of another only if they both can be brought within the same point of space,’ Einstein tells us. . . . I love at a certain altitude; what would I do even higher?” he wrote, playing with relativity theory—in which clocks at higher altitudes run slower than clocks at lower altitudes—as a way of looking into emotions and states of mind.
Breton and his circle were eager to examine states of mind using Freudian psychoanalysis and automatism to tap into the unconscious. They began to experiment with automatic writing, supposedly a key to the unconscious, in which artists drew spontaneously, without censoring their thoughts. To name the emerging movement and to describe his lyrical approach to his own creations in art and literature, Breton adopted a word coined in 1917: “sur-realism.” It was a magical word.
Unlike the chaos and iconoclasm of Dada, Breton considered Surrealism to be constructive. Picasso thought otherwise. “The Surrealists never understood what I intended when I invented the word,” he wrote. (In fact, the word had been Apollinaire’s invention.) “Something more real than reality, a resemblance deeper and more real than the real, that is what constitutes the sur-real.”
Picasso considered automatic writing and automatic drawing to be trivia. Although from time to time he used surrealistic effects, he detested being classified as a Surrealist. He was, however, on friendly terms with Breton throughout the 1920s and 1930s, although he never took him seriously as the almighty leader of a movement, as Breton liked to think of himself. Picasso always said that he was strange, and some letters that he purchased, from Breton to an ex-mistress, bore this out. Showing them to a friend, Picasso pointed to stains on one of them and asked, “What do you think this is?” “Hydrochloric acid?” the friend suggested. “No, it’s sperm,” Picasso told him. “That’s how Breton was. A weird type.”
But Picasso did agree on one aspect of Surrealism. “The Surrealists were right,” he told his dealer and friend Daniel-Henry Kahnweiler. “Reality is more than the thing itself. I always look for its super-reality.” Indeed, Picasso had done just that in Les Demoiselles d’Avignon, completed a decade and a half before the inception of Surrealism.
It was relativity, not quantum theory, that dazzled the Surrealists because there were still no readable popularizations of quantum theory in the 1920s and 1930s. Eddington’s books on relativity theory, on the other hand, held them spellbound, with insightful and poetic explanations of abstruse scientific ideas such as, “Human personalities are not measurable by symbols any more than you can abstract the square root of a sonnet.” Even to the Surrealists, this was surreal.
Einstein visited Spain in 1923 and translations of his works were published there. José Ortega y Gasset wrote an introduction to the printed version of Einstein’s lecture in Madrid, positioning relativity theory in the history of Western thought, and also translated Freud’s works into Spanish. Both Einstein and Freud greatly influenced the young Spanish artist Salvador Dalí.
“The difference between a madman and me is that I’m not mad,” Dalí famously said.
“The new geometry of poetic thought demands a physical revision and accommodation of the order of those to which Einsteinian physics subjects all measurements,” he wrote. Dalí painted figures and forms so precisely that they become otherworldly, placing them in highly imaginative renderings of a world oozing with flaccidity, sex, melancholy, and morbidity. What interested him most were the psychological aspects of relativity that he could draw out through psychoanalysis.
He demonstrated this in his 1931 painting The Persistence of Memory, with its drooping clocks, each in a different place and displaying a different time. He described it as “this harrowing and colossal question of Einsteinian space-time [as] a soft, extravagant, and solitary paranoiac-critical Camembert of time and space”—a typical Dalí-esque amalgam of relativity and psychoanalysis (and food). What he meant by “paranoiac-critical” was the Surrealist goal of extending the physical world, looking at one thing and seeing another, which Picasso referred to as super-reality and had been striving for himself when he painted Les Demoiselles d’Avignon.
Symmetry in art, symmetry in physics
“I think it is probable that negative protons can exist, since as far as the theory is yet definite, there is a complete and perfect symmetry between positive and negative electric charge, and if this symmetry is really fundamental in nature, it must be possible to reverse the charge on any kind of particle,” said the English physicist Paul Dirac in 1933, when he received the Nobel Prize.
Dirac’s greatest achievement was his prediction that every particle has a partner that is its antiparticle, opposite in charge but with the same mass, such that if the two came into contact they would annihilate in a blaze of light. He derived this startling conclusion from an equation he discovered which bears his name. The year before he won the Nobel Prize at the age of thirty-one, the antiparticle of the electron had actually been discovered in the laboratory. As Dirac said, it simply had to be the case. His certainty echoed Einstein’s on receiving the news that Eddington had verified his general theory of relativity on his spectacular trip to the island of Principe in 1919: “I knew that the theory is correct. [If the results had come out otherwise] then I would have been sorry for the dear Lord. The theory is correct.”
Four hundred years earlier, the astronomer and mystic Johannes Kepler had written about the “harmonies of the spheres.” And in 1904, Poincaré wrote of scientists’ “quest for this especial beauty, the sense of the harmony of the cosmos . . . just as the artist chooses from among the features of his model those which perfect the picture and give it character and life.” “The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful,” he went on. In his 1905 paper on relativity, Einstein had called for scientists to seek theories that revealed symmetries of nature. It was this that led scientists in the twentieth century to take up this quest.
Artists seldom defined symmetry as beauty, but this was not the case for scientists. In science, an equation has symmetry and is considered beautiful when it remains unchanged in form even if certain of its components are altered. If they are, for example, flipped from left to right, it is said that the equation exhibits mirror symmetry. A major symmetry occurs when an equation is unchanged in form even when its space and time coordinates are altered, as prescribed by Einstein’s relativity theory. Such an equation is valid throughout the universe; there is a democracy between every laboratory, be it on the earth or in a star system a trillion miles away.
In art, on the other hand, symmetry is a balance that is pleasing to the eye between different elements on a canvas or in a sculpture. Artists have long understood the use of asymmetry. Picasso’s Three Musicians, for example, is eye-catching due to Picasso’s violation of just about every rule of symmetry.
The Surrealists discover quantum physics
In the 1930s, popularizations of quantum mechanics began to appear. Surrealist artists were particularly influenced by The New Scientific Spirit by the French philosopher Gaston Bachelard. With a flowing white beard, long uncombed hair, and a generally disheveled appearance, Bachelard looked every inch the sage. Originally educated in physics and chemistry, he decided that the philosophy of science was his true calling, to which he brought theories of literature and psychoanalysis.
In The New Scientific Spirit, Bachelard wrote that developments in quantum theory “confront us with suggestive dilemmas.” This was territory for the psychoanalyst because “psychologically the modern physicist is aware that the rational habits acquired from immediate knowledge and practical activity are crippling impediments of mind that must be overcome in order to regain the unfettered movement of discovery.” He used the term “psychoanalysis” to mean an examination of the imagination in which the limitations imposed on it by logical thought were discarded.
Bachelard’s writings led Breton to conclude that “modern scientific and artistic thought present us with identical structures.” Breton went further in claiming that, according to Surrealism, “today, reason goes so far as to propose the continuous assimilation of the irrational.”
The artist’s freedom to change an object was stunningly used by the American artist Man Ray. His photographs, with their undulating forms, dazzlingly display the Surrealist style of playing with images from the world of perceptions, such as in Violin d’Ingres, his dazzling photograph of his lover Kiki de Montparnasse’s back transformed into a violin, or his series of photographs entitled Mathematical Objects, depicting models of surfaces generated by mathematical equations. Ray’s work influenced, among others, Max Ernst and Henry Moore.
Alongside Bachelard’s provocative essays on quantum theory, Louis de Broglie—the French physicist who had discovered that electrons, like light, possessed a schizoid personality of both wave and particle—began writing in a reflective manner. In contrast to Bohr and Heisenberg, de Broglie continued to seek visual images of the atomic world that were abstractions from phenomena we see every day. But Bohr, Heisenberg, and particularly Pauli, all forceful and formidable adversaries, offered such strong criticism that it silenced de Broglie, a mild-mannered man. He did not argue his views again until after Pauli’s death in 1958. Nevertheless, the Surrealists found the wave-particle duality with its counterintuitive ambiguities irresistible and read de Broglie assiduously.
In 1935 Christian Zervos, an influential French art collector, writer, and founder of the magazine Cahiers d’Art, wrote that the time had come to absorb quantum physics into art. His suggestion was taken up by younger Surrealists such as the Chilean artist Roberto Matta and the Austrian Wolfgang Paalen, who, in the 1940s, was to break with Surrealism for the very reason that it was not up-to-date on quantum theory. These artists looked for new images generated by the new physics, based in part on Freudian psychoanalysis, yet not abstract as Kandinsky had been. In this way they hoped to capture the tensions in physics (wave versus particle) as well as in psychoanalysis (id/ego/superego).
Matta was a notoriously difficult person but, nevertheless, remained faithful to the cause of Surrealism. His strongly expressed political views gave him the cachet of having been on the hit lists of both Franco in Spain and Pinochet in Chile. The American Abstract Expressionist Robert Motherwell was greatly influenced by Matta’s art. He recalled, “Matta wanted to show the Surrealists up as middle-aged gray-haired men who weren’t zeroed into contemporary reality.”
Matta produced images, lines, and curves similar to Man Ray’s photographs of mathematical surfaces but with added color. Duchamp put it well: “Matta’s first and most important contribution to Surrealist painting was the discovery of regions of space hitherto unexplored in the realm of art.”
Paalen was more critical than Matta of Surrealism. “It seems to me that we have to reach a potential concept of reality, based as much on the new directives of physics as on those of art,” he wrote. Surrealism was not up to the task because “it tries to poeticize science, which can only lead to mysticism.” Unlike Matta, Paalen wanted more concrete images along the lines of what de Broglie had described.
Like Matta, Paalen was both artist and thinker. He decided to take on the challenge of representing the wave-particle duality head-on. He wanted to be seen as an advocate of the need for science to influence art and for artist and scientist to seek a new worldview together, as Mondrian had done. His depictions of the wave-particle duality were, however, sadly, less than striking—essentially swirls and vortices.
Dalí caught the mood when he wrote:
In the Surrealist period I wanted to create the iconography of the interior world—the world of the marvelous, of my father Freud. I succeeded in doing it.
Today the exterior world—that of physics—has transcended the one of psychology. My father today is Dr. Heisenberg.
It is with pi-mesons and the most gelatinous and indeterminate neutrinos that I want to paint the beauty of the angels and of reality.
Dalí realized that quantum theory, with its notions of probability and axioms such as Heisenberg’s uncertainty principle, had shattered the classical cosmos with its insistence that all processes developed in a continuous manner and could be described with unlimited accuracy. But it was not until after 1945, when the atomic bombs were dropped on Japan, that Dalí put his thoughts onto canvas. In The Disintegration of the Persistence of Memory, he produced dramatic images of a fragmented universe.
From the start, Dalí was a renegade who considered Breton a dogmatic fool. Dalí espoused fascism instead of communism, chose figuration over abstraction, and spoke glowingly of the atomic bombs that had been dropped on Japan and the bright future promised by nuclear energy. He pushed Breton and his strong left-wing beliefs to his limit. In 1952, Breton threw him out of the Surrealist movement. But by that time Surrealism had run its course and Breton also would soon throw in the towel.
Visualizing the invisible
By 1932, physicists had realized that an as yet undiscovered particle with no electrical charge at all existed inside the nucleus. They called it the neutron.
In a flight of inspired fancy, Heisenberg imagined that a neutron might be made up of an electron and a proton. Inside the nucleus the neutron could split into its component proton and electron. The electron would then move to another proton in the nucleus and the two fuse to become a new neutron. In this “exchange” the “migrating” electron would “transmit” an attractive force, which would explain why the nucleus was stable.
It soon became clear that in fact neutrons could not be made up of an electron and proton, but nevertheless some sort of exchange process would have to be dreamed up. The image of particles engaging with one another by exchanging other particles was extremely helpful. This unexpected scenario was exactly what Heisenberg had suggested as a way of finding the proper imagery for the atomic domain: to let the equations of quantum theory generate it—in other words, as Plato had suggested two thousand years earlier, to let mathematics guide the scientist into realms that could not be expressed in images derived from our everyday world.
Finally, in 1949, the American physicist Richard Feynman worked out the proper imagery for the atomic world: Feynman diagrams. “A half-assedly thought out semi-vision thing,” was how he described his discovery. In the diagrams, Feynman replaced Bohr’s iconic solar system image of the atom with lines indicating how an atom moves through space and time and how particles interact with one another by exchanging other particles, just as Heisenberg had suggested. The diagrams provide a glimpse of how objects that can be both a wave and a particle are able to interact with one another, in a visual form that seems to echo Mondrian’s call for the “destruction of a particular form [and its replacement with] mutual forms of free lines.”
Art and physics had reached the same juncture at about the same time: representing the world in the fullest sense of the term, encompassing both seen and unseen. Although Mondrian kept up with events in science, Feynman’s interest in art was limited to sketching naked women in pole-dancing establishments, so we must attribute his great advance solely to the increasingly abstract nature of theories of elementary particles.