2 Seven Hallmarks of Creativity and Two Marks of Genius
The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.
—Albert Einstein5
As Einstein observed, creativity is all about problem solving, and the first step is to find the problem. Let’s look at the seven hallmarks of big-C Creativity and the two marks of genius in more detail and see how they emerge from the lives of great thinkers.
1. The Need for Introspection
Introspection is the ability to sit by yourself and think. Looking inside your own mind, you can increase your own creativity and enhance your intellectual strengths. The best way is to sit in silence, with no distractions.
Luis Alvarez, a Nobel Prize–winning physicist, always followed this suggestion made by his father, an eminent medical researcher: “He advised me to sit every few months in my reading chair for an entire evening, close my eyes, and try to think of new problems to solve. I took his advice very seriously and have been glad ever since that I did.”6
Practitioners of mindfulness and meditation will be well aware that introspection sharpens and clarifies the mind.
2. Know Your Strengths
To make discoveries and enhance creativity, we need to focus, which means homing in on our strengths.
As a child, Einstein enjoyed mathematics, but at university discovered he had no nose for the fundamental problems in the subject. Realizing this, he chose to focus on physics.
Physicist Werner Heisenberg had to abandon a career as a concert pianist to focus on science. He went on to discover quantum mechanics. At a reception at Cambridge University in 1939, a don, doubting Heisenberg’s claims, challenged him to play something. Heisenberg sat down at the piano and, without further ado, played Beethoven’s highly complex Piano Sonata no. 32 from memory, flawlessly.
Marcel Duchamp chose art over his true passion, chess, although he sometimes regretted it. In 1919, during a decade when he was deeply engaged in chess, a game that he claimed energized his creativity, he wrote, “I am absolutely ready to become a chess maniac.”7 He continued to be a committed chess player throughout his life.
Steve Wozniak focused on coding and hardware at Apple, while Steve Jobs stuck to the areas of design and business, which were his strengths. “Jobs was awed by Wozniak’s engineering wizardry and Wozniak was awed by Jobs’ business drive,” writes Walter Isaacson, Jobs’s biographer.8
Investor, cofounder of PayPal, and Silicon Valley provocateur Peter Thiel argues against a multifaceted range of interests if one wants to win in the rough-and-tumble world of start-ups. “Instead of pursuing many-sided mediocrity and calling it ‘well-roundedness,’ a person determines the one best thing to do and does it,” he writes.9
The key lesson is to realize through self-examination where our strengths lie and not to fritter away our talents on hopeless pursuits.
3. Focus, Persevere, and Don’t Be Afraid to Make Mistakes
Focus and perseverance involve the single-minded pursuit of a problem. Highly creative thinkers shut down and exclude everyone around them. There is no creation out of nothing. Artists and scientists work long hours. They encounter dead ends and make endless mistakes. The key lesson is not to be afraid of failure.
As the Danish physicist Niels Bohr said, “An expert is a person who has found out from his own painful experience all the mistakes we can make in a very narrow field.”10 At Bell Labs, AT&T’s premier research laboratory, the number of mistakes a scientist made was taken as a sign of the progress of his research—provided, of course, that he eventually came up with a viable result.
When he was developing rockets for his SpaceX program, Elon Musk bore in mind the many failures of the American and Russian space programs. “I have a lot of respect for those that persevered to produce the vehicles that are mainstays of space launch today,” he says.11 He recommends attempts that will fail quickly so that you can go on to new ones straightaway.12
As Steve Jobs put it, “If you want to live your life in a creative way, as an artist, you have to not look back too much. You have to be willing to take whatever you’ve done and whoever you were and throw them away.”13
4. Collaborate and Compete
“Real technologists wear T-shirts and jeans,” writes Peter Thiel.14 Today’s high-tech geniuses cultivate the casual look. People like Steve Jobs and Mark Zuckerberg, the founder of Facebook, operate in teams, in workplaces purpose-designed with large open areas. Coffee machines, essential to provide fuel, are strategically placed so that teams working on different problems make contact. Milling around the coffee machine, people talk about what they are working on. A member of another team may overhear and chime in that they’ve been thinking about a similar problem and are close to a solution, and the result is a collaboration.
Even so-called lone geniuses such as Einstein and Picasso had think tanks that kept them au courant with what was going on in art, literature, philosophy, and science. Einstein’s was an informal study group made up of close friends with a keen interest in philosophy and science who called themselves the Olympia Academy; Picasso’s was a group of mainly young literati who went under the name la bande à Picasso.
In Einstein’s most creative period, his days at the patent office between 1902 and 1909, he sat in an open-plan office, did his work, and daydreamed. He could think wherever he was, he said.
A pioneering example of the move toward open-plan environments was Theo van Doesburg’s studio in 1920s’ Weimar, Germany, where several artists worked together on a common project.
Pixar’s immense success as an animation studio is predicated on close collaboration in an open-plan environment. As Ed Catmull, one of Pixar’s founders, recalled upon seeing a traditional closed office setup, “To put it simply, it struck me as a lousy work environment.”15
There’s considerable controversy over whether open-plan offices are conducive to collaboration or whether in fact they hinder it. A recent study by Harvard University suggested that workers in large open-plan offices talk less and email more.16 But it seems that the Harvard report related mainly to extreme open-plan offices.17 Those that offer a degree of privacy—meeting rooms, breakout spaces, telephone booths—work much better. The debate is ongoing.
In the sciences, collaborative modes of thought came into vogue in the 1920s when the German atomic physicist Max Born in Göttingen and the Danish physicist Niels Bohr in Copenhagen formed groups to work together. But the real breakthroughs were made by individuals sitting alone at their desks. This was how Werner Heisenberg discovered quantum mechanics and his uncertainty principle, and how Erwin Schrödinger nailed his famous equation and later his sometimes alive, sometimes dead cat—though the creative juices that helped with the discovery of Schrödinger’s equation were stirred by an illicit weekend.18
Then there was the Manhattan Project, based in Los Alamos, New Mexico, put together to develop the atomic bomb—a supreme example of a vast, top-level collaborative project. Many of the scientists involved were alumni of the group think sessions in Göttingen and Copenhagen. The periodic get-togethers have become the stuff of legend. Groups working on different parts of the project met to discuss their own work and comment on the work of others. The sessions were entirely democratic—and so was the general atmosphere, which was one of no-holds-barred exchanges. For example, the brash young physicist Richard Feynman felt free to call a suggestion put forth by the great Niels Bohr “a crazy idea.”19
There are many other forms of collaboration in the sciences and the arts: husband-and-wife teams such as Marie and Pierre Curie or Ted Hughes and Sylvia Plath; lovers such as Anaïs Nin and Henry Miller; artists such as Picasso and Georges Braque; writers such as T. S. Eliot and Ezra Pound; musicians such as Aaron Copeland and Leonard Bernstein; string quartets; theater troupes; and the huge number of international collaborators on modern-day, high-energy physics projects such as that at CERN. Successful collaborators bootstrap each other’s creativity.20
In addition to collaboration, competition is often a crucial catalyst. A team at Sussex University searching for the structure of carbon 60 (C60), which occurs on Earth and in the atmospheres of stars, had become bogged down. The team’s work was languishing until its members heard of a group in Germany that claimed to be close to finding the elusive carbon 60 structure. The Sussex group members immediately sprang to life, looked at their data afresh, and realized that the structure of C60 was much like the Buckminster Fuller dome, made famous at the 1967 Montreal Expo. They called it the buckminsterfullerene or buckyball. Harry Kroto, the group’s leader, brought to bear his experience as a graphic artist to deduce a three-dimensional shape from two-dimensional data—to “see” the deep meaning. The discovery of this highly symmetrical molecule opened new areas in chemistry, ranging from phenomena in space to materials on Earth.
5. Beg, Borrow, or Steal Great Ideas
Bach borrowed heavily from the Italian and French baroque, often weaving their melodies into his works, overshadowing composers such as Corelli and Scarlatti for three centuries. Some contend that the scores of his remarkable Prelude 1 in G Major for the keyboard and the melody for his Christmas Cantata 142, Uns ist ein Kind geboren, were lifted from the German composer Johann Kuhnau, a practice that was not unusual in those days when there were no copyright laws.21 It is said that Shostakovich too often lifted from the works of other composers without attribution. He incorporated themes of the fourth movement of Beethoven’s Seventh Symphony into his own Fifth Symphony, for a start.22
Similarly, in the 1920s, Diego Rivera warned young artists in Paris not to let Picasso into their studios because he would steal their ideas—and he probably did.
But such “theft” is never mere plagiarism. The likes of a Bach or a Picasso use the ideas of others to stimulate their ever-fertile minds. What they see or hear soon becomes theirs, woven into their own pattern of ideas and elevated to a level far beyond the original. We are constantly absorbing the ideas of others. They are stored in our memory banks and over time become our own.
In principle, of course, no one is wholly original. Accumulation—building upon what you and others have accomplished—is part and parcel of creative activity. But some people see the world in an entirely new way. Galileo saw the motion of a pendulum not as a swinging back and forth but as a falling and rising, which gave him a way to test his revolutionary theory of falling bodies, based on falling through a vacuum, a concept that went against the scientific and religious doctrines of his day—the horror vacui, the fear of empty space, devoid of God. Thus he confirmed his theory that the speed of a falling body is independent of its weight and that the distance through which a body falls is directly proportional to the time it takes, squared.
Einstein saw the physics of 1905 in a dramatically different way from just about everyone else, as a subject riddled with asymmetries that, in his opinion, did not appear in nature. The spectacular result was his discovery of the theory of relativity.
Bach often plagiarized himself, recycling parts of scores. So did Mozart, some of whose pieces for clarinet or flute are almost identical.
In the 1970s, the early days of Microsoft, Bill Gates offered to find a program that would manage all of a computer’s hardware and software—in other words, an operating system that would be standard for IBM computers. At the time, IBM was falling behind in producing mainframes and feared it would soon be overtaken in the fledgling business of personal computers, too. Gates realized that whatever operating system IBM chose would become the standard system and would dominate the computer industry. He began preliminary discussions with a company that was producing one possible system, but negotiations soon fell through—so he decided to have a go at finding a system by himself.
Gates and his partner, Paul Allen, turned to a struggling start-up company that had built an operating system called QDOS—Quick and Dirty Operating System. They convinced the developer to sell it to them for $50,000, free and clear, to be used however they wanted. They did not, however, tell the owner what they had in mind. They made a few changes and turned it into MS-DOS, which would dominate the software industry for three decades.
Microsoft is now among the world’s largest software companies. As Gates recalled, “An innovator is probably a fanatic, somebody who loves what they do, works day and night, may ignore normal things to some degree and therefore may be viewed as a bit unbalanced. Certainly in my teens and 20s I fit that model.”23 He certainly did. In fact, based on this quote alone, Gates ticks many of the boxes of my hallmarks of big-C Creativity, such as focus, perseverance, and not being afraid to make mistakes.
Steve Jobs famously “borrowed” a revolutionary graphical interface developed at Xerox PARC. As Jobs put it, “We have always been shameless about stealing great ideas.”24 He liked to quote Picasso as saying, “Good artists copy, great artists steal.”25 Perhaps he considered Picasso a buccaneer like himself.
Jobs said of Xerox, “They were copier-heads who had no clue about what a computer could do.”26 So Jobs’s action was no mere theft. He saw the possible uses of the interface—and Apple went on to improve the initial concept enormously.
A legendary story is that of the origins of Facebook. From an early age, Mark Zuckerberg, its founder, was a wunderkind at programming. As an interviewer writes, “Some kids played computer games. Mark created them.”27 Friends who were artistically inclined came over to his house with pictures they had drawn, and he would create games about them. Zuckerberg had long been interested in linking computers to transmit messages. At Harvard, he developed various social networking sites, which brought him to the attention of Divya Narenda and twins Cameron and Tyler Winklevoss, who asked him to help them develop their site.
At this point, the stories differ. Zuckerberg’s is that he tired of assisting them and created his own site, which went on to become Facebook. It took off almost immediately, and he dropped out of Harvard to run it. He claims that whereas Narenda and the Winklevosses’s website emphasized dating, his focused on networking.
Narenda and the Winklevosses, however, claimed that Zuckerberg stole their idea. They eventually reached a settlement, but litigation continues. So there may well be a grain of truth on both sides.
The point is that art and science are Darwinian enterprises: only the fittest survive. There is no copyright on ideas. One must fight for one’s place in the sun.
6. Thrive on Ambiguity
In periods of ambiguity, geniuses thrive while others go quiet.
By mid-1925, all the viable theories of atomic physics had been demolished, and it seemed as if the subject lay in ruins. Bohr himself tried to rework the foundations of his original theory, which postulated that the atom was like a miniscule solar system, but he got nowhere. Then he and his coworkers tried abandoning the laws of conservation of energy and momentum—cornerstones of physics—as being inexact. This too was refuted by experiments. One major physicist, Wolfgang Pauli, wanted to disappear into Hamburg café society, perhaps even produce movies. Others, having tried everything and failed, were on the verge of nervous breakdowns. It seemed that atomic physics had hit a dead end. Ambiguity reigned.
But Pauli’s colleague, Werner Heisenberg, an unassuming young German physicist, thrived in such situations. That June, after salvaging parts of past attempts, he hit on the solution: the new atomic physics, quantum mechanics.
Sometimes areas are thrown into turmoil after a milestone work appears. Such was the case in art after cubism came on the scene and in music after the appearance of works by Satie and Stravinsky. Stravinsky’s 1913 Rite of Spring caused riots in Paris of a magnitude not even matched by Satie’s Parade, as Stravinsky himself recalled with pride.
Karlheinz Stockhausen, Steve Reich, and Philip Glass caused turmoil again and initiated an entirely new phase in music. The twenty-first-century avant-garde electronic music they inspired often mixes sound and image, both generated by creative algorithms. One does not leave these concerts whistling a tune; instead, they provide cerebral and visceral experiences.
So if your idea seems out of step, it could be because everyone else is heading in the wrong direction. Have faith in yourself and your instincts!
7. The Need for Experience and Suffering
Being “out there,” encountering the world both professionally and personally, is essential to prime the mind to make creative breakthroughs in art, literature, music, and science. Breakthroughs are made by thinkers who have a well-rounded intellectual background, who have read outside their field and can bring this knowledge to bear, however indirectly.
Einstein was only twenty-six when he discovered relativity theory, in 1905, but he had certainly lived. By this time, he had had at least two intense romantic relationships. One was with Marie Winteler. He boarded with her family when he attended preparatory school in Aarau, Switzerland, to bone up on subjects he had done poorly on in high school in order to enter the Swiss Polytechnic Institute in Zurich. He had already rebelled against the Prussian high school system, been asked to leave, and traveled on his own through Northern Italy. When he moved to Zurich, Marie wrote that she would come and visit, to see where “my darling lives.”28 Soon afterward, Einstein ended the relationship.
Marie subsequently married and divorced, eventually dying in a mental asylum. A family member asserted that her unhappy affair with Einstein “confused her” and ruined her life.29 But their love letters reveal that for him, she was an inspiration.
The woman Einstein rejected her for was Maleva Marić, a fellow physics student. They married in 1901, but by 1905 he had tired of her too. Maleva’s influence on his relativity paper was distinctly negative; he succeeded despite her. He may not have suffered hugely himself, but he certainly imposed suffering on others.
Essential to Einstein’s discovery of relativity theory was his insistence that its equations be beautiful so as to reflect the symmetries of nature. His aesthetic feel for nature was probably nurtured by his romantic attitude. By 1905, he was also well versed in philosophy—particularly that of Immanuel Kant, who analyzed how the brain constructs concepts of space and time. Without such intellectual and social maturity, he may not have succeeded in developing the penetrating critique of the state of science in his day that was required for his new theory of space and time.
At moments of extreme concentration, geniuses tend to focus to such an extent that they shut out those around them. In the course of their work, they are often vampires, sapping energy from those who share their lives.
Picasso’s life was a series of disastrous liaisons, not unlike Einstein’s. In 1907, when he painted Les Demoiselles d’Avignon, he was living with Fernande Olivier. Theirs was a tempestuous and argumentative relationship, in which they frequently broke up and came together again. As Einstein did with Mileva, Picasso learned to harness Fernande’s moods to his vision, and his passions provided some of the dynamics for his greatest creations. This cycle would continue throughout his life.
Erwin Schrödinger famously enjoyed an open marriage and often travelled with both his wife and his current girlfriend. There were always affairs with others too, lurking in the background. This psychological stress spurred rather than hindered his scientific creativity.
In general, Werner Heisenberg led an idyllic family life, but he went through a period of great turmoil in 1927 when he was trying to convince his mentor and father figure, Niels Bohr, of the veracity of the uncertainty principle, perhaps his greatest discovery. Their ferocious arguments often drove Heisenberg to tears. Bohr’s tenacious skepticism turned out to be crucial in shaping the uncertainty principle’s final form.
Alma and Gustav Mahler’s marriage was always in turmoil. Gustav forbade Alma to compose. Although he suspected she continued to do so, he never asked to see her work. “I played through my compositions again, my piano sonata, my many Lieder,” Alma wrote to a friend. “I feel again: this is what I want. I long for creativity. My present life is a delusion. I need my art!”30 As a result, Gustav had to suffer the affairs of his beautiful young wife.
Ted Hughes and Sylvia Plath suffered a tortured marriage, an explosive mix of her mental illness and his affairs, culminating in Plath’s suicide. Its stresses and strains and their later reverberations drove both to creative heights.
Steve Jobs often behaved tyrannically against those he suspected of mediocrity and lack of preparation. Ed Catmull, one of the founders of Pixar, recalls Jobs’s direct approach: “These charts are bullshit! This deal is crap!”31 “He could be rough on people he didn’t think were smart,” recalled Steve Wozniak, Jobs’s partner at Apple.32 In this way, he could drive people beyond what they thought were their limits. Occasionally someone stood up to him, which he respected if what they had to say had validity.
Elon Musk, a billionaire entrepreneur whose successes include the Tesla electric car and the SpaceX space shuttle, worries that his children will not suffer as he has done. He feels that suffering gave him the will to succeed, no matter how adverse the circumstances. “They might have a little adversity at school, but these days schools are so protective,” he says. Musk’s solution was to create “artificial adversity” at home by insisting that his children spend more time reading than they do playing video games and by restricting the length of time they can play—a brave attempt, though it doesn’t sound like the greatest of suffering.33
Although they often profess concern for humanity at large, geniuses often care little for those closest to them. Gandhi, the voice of the Indian masses, had difficulties with his own family. His oldest son rebelled against everything Gandhi taught and believed in. Gandhi’s closest relationships were with people he would never meet, such as top-level politicians, with whom he communicated by letter.
The Indian astrophysicist Subrahmanyan Chandrasekhar, discoverer of black holes, was very close to his students and colleagues but paid scant attention to his wife, who had hoped for a career alongside him in physics. Her disappointment ended up tormenting both of them, she told me.34
The experiences of intellectual powerhouses such as these can inspire us lesser mortals to build up our emotional dimension not only socially but through literature, music, and philosophy, as these people did. To make an important scientific discovery, create a dramatic work of art, or write a breakthrough novel, you will have to have lived—and you will probably need to focus obsessively on your work to the exclusion of family and friends.
The Two Marks of Genius
1. The Essence of Creativity: Finding the Problem
Problem discovery is the remarkable ability, possessed by only a select few, to identify a specific problem—a problem that will open a bold new avenue of thought and that is usually antithetical to what just about everyone else in the field is working on. Entrepreneur Peter Thiel has these words of advice for those planning tech start-ups: “The next Bill Gates will not build an operating system. The next Larry Page or Sergey Brin won’t make a search engine. And the next Mark Zuckerberg will not create a social network. If you’re copying these guys you aren’t learning from them.”35
A stunning example is Einstein, who in 1905 realized that all the scientists toiling on the frontier of physics were trying to solve the wrong problem. They were concerned with how the electron is structured, whereas he realized that they should have been looking at the nature of space and time. For six years, no one understood the importance of his relativity theory. When appreciated at all, it was usually for the wrong reasons, because it was assumed to add rigor to the then-popular theory of the electron.
Picasso wanted to create an entirely new form of art that broke completely with impressionism, with the past. The problem he focused on was how to reduce nature to geometrical forms. Cézanne had moved in this direction, but only tentatively. Picasso decided to take it to the extreme. The result was his breakthrough painting of 1907, Les Demoiselles d’Avignon, which contained the seeds of cubism. Like Einstein’s relativity theory, cubism would not be accepted worldwide for some six years. As for the painting itself, it went unsold for almost twenty years. When Picasso first showed it to friends and colleagues, they thought he had lost his mind.
Physicist Mitchell Feigenbaum wanted to solve the problem of how systems become disordered—like a wave breaking into droplets or smoke rings breaking up in the air. Looking at vast swirling canvases by J. M. W. Turner, he saw there patterns of dynamic fluid motion and what would come to be called Mandelbrot sets and fractals. Looking at a painting of a scene in a park, he realized that the best way to understand the background was to get close up and look at every small detail, then work back out to the whole panorama. Applying this to his scientific work, it struck him that everyone else in his field was trying to understand chaotic systems in their totality right from the start. Applying his newfound method of scaling down, he began by searching for the patterns within apparently random systems. This was the key to his discovery of modern chaos theory: to deal with complex systems by exploring how “big details relate to little details.”36 Thus, according to chaos theory, a butterfly fluttering its wings in Brazil might cause hurricanes in the northern hemisphere.
At the beginning of the twentieth century, Erik Satie used to play the piano at the Els Quatre Gats bistro in Montmartre, where Picasso sketched him. The problem of the day, as he saw it, was how to liberate French music from what he saw as the straitjacket of Germanic compositional style. His friend Claude Debussy had already attempted this, but Satie wanted to create an entirely new style of music with its own menu of problems. A short man, shabbily dressed, with an unkempt beard and a famously sharp tongue, Satie looked like a sack of potatoes, according to poet Jean Cocteau. Unprepossessing though he was, he produced haunting melodies from chords that seemed too complex to yield anything but atonality. To the undiscerning listener, these melodies seem to repeat themselves. But in fact there are subtle differences, a technique that Philip Glass picked up. Satie was the personification of the Parisian avant-garde, and in 1917 he went on to collaborate with Picasso, Cocteau, and Sergei Diaghilev on short ballet pieces, most notably Parade. His score incorporated cowbells, typewriters, foghorns, milk bottles, and a pistol to produce the sounds of everyday life in Paris—which, combined with Picasso’s cubist costumes, caused a riot in the theater.
Regal and moody looking, Karlheinz Stockhausen was at the forefront of the radical new trends in music that commenced after World War II. The problem he set himself was to break completely with all previous avant-garde music, including twelve-tone music. To do so, he explored the possibilities of electronic music, partly using mathematical statistics, as well as concrete music, for which he took sounds from just about anywhere, including the human voice, the environment, and computer-based signal processing. His groundbreaking work continues to be controversial.
Steve Reich went yet further. The problem he posed for himself was how to produce new sounds with the minimal use of musical instruments. He experimented with tape loops to create phasing patterns, sometimes accompanied by voices and clapping hands. His repetitive compositions with their slow harmonic rhythms marked the beginning of minimal music.
Which brings us to Philip Glass. Tall and wild-haired, he thrived in the New York art world of the 1960s. The problem he flirted with was to find a new approach to minimalism in music, beyond that pioneered by Satie, Stockhausen, and Reich. He was chief among the musicians who picked up on Satie’s repetitive atonal melodies to craft the dominant sound of the late twentieth century.
Although it can’t be taught, we all have these leaps of imagination. Perhaps the lesson is to practice introspection to give such leaps a chance to emerge, then to trust in them and go along with them when they do.
2. Spotting Connections
In 1905, Einstein realized there was a connection between the structure of the laws of thermodynamics (which deal with the flow of heat) and the nature of space and time. What could seem further apart?
The theory of light as it stood in 1905 predicted that the speed of light, when measured in a laboratory on Earth, should vary due to the earth’s motion. But very accurate measurements showed otherwise: the speed of light always remained the same. To explain away the discrepancy between the theory and the experiments, scientists resorted to piling on hypotheses—suggesting, for example, that moving objects become deformed when in motion.
Mulling these over, and dissatisfied at the lack of any systematic explanation for the suggestions, Einstein suddenly recalled an interesting feature of the laws of thermodynamics: they don’t explain, they simply insist. The first law of thermodynamics is that energy is conserved in every physical process. Never mind how; it just is.
So, Einstein concluded, why not simply assert that the speed of light is always the same, no matter where or how it is measured? He added another assertion: that measurements taken in laboratories in uniform relative motion are unaffected by the laboratory’s motion—the principle of relativity.37 His theory of relativity followed from these two statements or postulates. This new theory of space and time either eliminated or systematically deduced hypotheses that earlier scientists had proposed with no basis in theory.
At pretty much the same time, Picasso turned not to the latest developments in art but to contemporary developments in science, technology, and mathematics for inspiration. The problem he set himself was how to represent all perspectives of a scene at once. Images from a book on four-dimensional geometry—geometry with four spatial dimensions—and what he had learned about the science of X-rays gave him hints as to how to go about it. He learned about these subjects from members of his think tank.38 The result was Les Demoiselles d’Avignon, which brought art decisively into the twentieth century.
In 1968, the twenty-four-year-old Italian physicist Gabriel Veneziano was working at CERN and MIT. Studying the equations for how particle collisions are represented in physics, he found that these apparently unrelated equations could be brought together with the Euler beta function, an exotic mathematical formula seemingly of use only in pure mathematics. Further study of this unexpected connection between mathematics and physics led physicists to hypothesize that elementary particles can be represented as vibrating strings, which in turn led to string theory.
Forever playing games, revising rules, or inventing new ones, mathematician John Horton Conway studied the patterns that emerge as one places and removes tiles in the Chinese board game Go. This inspired him to invent the Game of Life, a mathematical grid of cells in which simple rules about a cell becoming “live” or “dead” produce a riot of patterns. The Game of Life is primarily a game, but it also turned out to be an important tool for studying the evolution of spiral galaxies and in the development of chaos theory.
The key lessons here are to be broad rather than narrow in one’s interests; to take on board all sorts of ideas, no matter how unlikely; and to be alert for connections.
Intent, Imagination, and Unpredictability
There are three qualities, three states of mind, that thread through the seven hallmarks of creativity and the two marks of genius: intent, imagination, and unpredictability.
Anyone launching into a creative endeavor—an artist, a poet, a scientific researcher—begins with intent, with the desire to solve a problem or at least a line of pursuit.
Next they think about how to solve it, which may involve going well beyond the original approach. To do this, they may well dream up—that is, imagine—an entirely new approach to the problem.
This leap could come out of the blue and be entirely unpredictable.
Unpredictability—going beyond logic—is an essential element in creativity. To rephrase Toulouse’s words, quoted at the beginning of this part, the mathematician Poincaré’s way of thinking was more akin to a dream than to a rational approach, seemingly most suited to “works of pure imagination.”
Great discoveries are made not by logic alone, but often by spotting links between things or areas or ideas or philosophies that at first sight have nothing to do with each other. This can happen suddenly and unpredictably, when the mind rearranges the information at hand in a totally new way.
Samuel Taylor Coleridge claimed he was inspired to write his much beloved poem “Kubla Khan” while in an opium dream, in which he heard a voice intoning the first lines. But there is never creation from nothing. There is always some material to begin with. And in Coleridge’s case, he later revealed that he had been reading about Xanadu just before he went to sleep.
The poem may have been dreamed up in his unconscious, but it required artistry to get it down on paper. To build his rich word picture, he began with iambic tetrameters, then moved on to other rhyming schemes and made much use of the sonic qualities of the words. In other words, he reinterpreted the traditional verse form and used it in new ways. Dream or not, Coleridge still pushed the boundaries of the rules of poetry that held sway in his day, added to which he was already an accomplished poet and used all his skill in his work. His problem was to get the poem down before he forgot it—but in the process he employed intent and imagination, finally breaking into unpredictability, to dramatic effect.