To discover the East, Christopher Columbus sailed west. To inoculate people against smallpox, Edward Jenner injected them with pox. Instead of luring the customer to the goods, Jeff Bezos brings the goods to the customer. According to Isaac Newton’s Third Law of Motion, “For every action there is an opposite and equal reaction.” Shakespeare’s Hamlet said, “I must be cruel only to be kind.”
The above contrarian insights exemplify the process of “thinking opposite,” an age-old strategy deeply embedded in the arts and sciences, as well as in industry. If you want to better understand an object or concept, conceive of the opposite. If you want to understand how a machine was put together, disassemble it. If you want to achieve a particular result, define the end goal and then fashion a line of development leading back to the beginning. The practical advantages of oppositional thinking are at least four: first, it allows us to see solutions to problems that we would otherwise not see; second, it makes us more mentally flexible and imaginative; third, it teaches us to be comfortable with ambiguity and paradox; and finally, it often makes us laugh, a sure sign of happiness.
A talent for seeing the importance of opposites is a hidden habit of genius, particularly in science and industry. Why does lightning strike? Because negative and positive charges in the air and ground race to join from opposite directions, as Ben Franklin knew. Why does an airplane go up? Because the wings of a flying plane pull the air above them down, forcing the air below and the plane to go up, as the Wright brothers demonstrated. How can we understand the moment of the “Big Bang” in astrophysics? Play the universe backward until it shrinks into a single incomprehensibly dense atom, as Stephen Hawking suggested.
In 1953, in the famous Cavendish Laboratory at Cambridge University, the team of James Watson and Francis Crick discovered the structure of deoxyribonucleic acid (DNA), the building block of all living things. Their insight involved understanding the principle of opposites. Within each strand of DNA lies hidden a palindrome of molecules. For example:
XXGATCXXXXXXGATCXX—XXCTAGXXXXXXCTAGXX
Together the sequence goes forward and backward. Every living organism has genes with a retrograding pattern. If, as cells multiply, they do not replicate the palindromic process precisely, malignancy or other defects may develop. Understanding this is an important part of today’s biomedical research and genetic engineering. The discovery of the structure of DNA won Watson, Crick, and their colleague Maurice Wilkins a Nobel Prize in Chemistry in 1962.
Occasionally, oppositional thinking is just child’s play. When, in 1785, mathematical genius Johann Carl Friedrich Gauss was eight, his teacher asked him to solve the following problem, just to keep the precocious child occupied for a while: “What is the sum of all the numbers from one to a hundred?” Immediately Gauss came back with the answer: 5,050. Instead of wasting time adding all the numbers, he had a contrarian insight: fifty is the midpoint, and the extremes balance against each other; the sequence of numbers 1, 2, 3, 4, 5, and so on, up to 50, could be set as a palindrome against itself. For those of us who are not geniuses, let’s reduce the problem down from one hundred to just nine numbers. This will enable us to see the insight Gauss experienced; he visualized a reverse pattern that would quickly lead to the solution. In our scheme nine numbers can be set backward against themselves:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 →
9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 ←
Adding vertically, these produce a series of 9 10’s, or 9 × 10 = 90. We’ve doubled the numbers (added a second row that goes backward), so now we have to divide by two to get the answer: 45. Brilliant! But then, thinking inductively, Gauss saw that this procedure could be the basis of a formula for any such problem: Total number T = N(N + 1)÷ 2. Try it by using your own sequence of consecutive numbers. Gauss’s backward insight demonstrated how “thinking opposite” can save a mathematician time.
Making a rocket booster go up and come back down can save an industrialist money. In 2011, Elon Musk’s SpaceX and the National Aeronautics and Space Administration, formerly frenemies, formed a partnership.1 Henceforth, Musk’s rockets would provide transportation for NASA, taking cargo and astronauts into space. SpaceX had become the dominant force in space transportation by showing that a rocket booster might go round-trip—into space and back down safely to be reused—thereby reducing the cost of each launch by up to 80 percent.2 It took Musk five tries, but he did it. As he said in a 2013 TED Talk, “Physics is really figuring out how to discover new things that are counter intuitive.”3
THINKING OPPOSITE, OR IN CONTRARY MOTION, CAN ALSO PROVIDE structure in the arts. The composer Johann Sebastian Bach saw how a tune could go round-trip, thereby pleasing a king. In 1747, Bach journeyed from Leipzig to Berlin to meet the music-loving King Frederick the Great, who handed Bach a melody and asked him to improvise on it. Bach returned home, cogitated, and then responded with The Musical Offering, in the course of which he turned the royal melody on its head in musical inversion (notes that went up now go down to the same degree) and then employed retrograde motion (pitches of the melody going forward are now made to go backward). Franz Joseph Haydn, Mozart, Beethoven, Franz Schubert, Igor Stravinsky, and Arnold Schoenberg used the same retrograding gambit.
FIGURE 10.1: A twenty-bar melody Mozart wrote in a sketchbook (Sk 1772o) at the age of sixteen when he was learning the art of counterpoint. He wrote only the melody (top part) but indicated by the context that it should be played backward against itself.
Paris, National Library, Mozart Sk 1772o: Craig Wright
Mozart, whose nickname for himself was Trazom, loved creative palindromes. In one case, he fashioned a melody that might go in opposite directions simultaneously, as shown in Figure 10.1. Sometimes he incorporated this oppositional process in a finished composition, but most often he made use of it in his practice sketches. In those he employed oppositional thinking to develop his craft and expand his imagination.
For Mozart, as for us, thinking in opposites is a challenge that can lead to a better outcome. To play a scale in a sonata smoothly, instrumentalists are instructed to practice the scale with exaggerated syncopation. To be a lethal striker in soccer (football), the naturally right-footed kicker is instructed to practice continually with the left. Leonardo da Vinci taught himself how to write both backward and forward, which improved his skill as a draftsman. All such contrarian exercises improve physical flexibility as they promote neuroplasticity.
Leonardo da Vinci belonged to the 10 percent of the general population that is left-handed.4 Within the 100,000 sketches he drew rests evidence that he, too, recognized the creative value of “thinking opposite.” His sketches for his famous painting The Virgin and Child with St. Anne, one of four superb Leonardo works in the Louvre, offer a case in point.5 Around 1478–1480, he imagined two versions of the scene he wanted to create: Virgin and child with a lamb (the cat was a placeholder for the lamb). One faces right (Figure 10.2A), the other left (Figure 10.2B), in near mirror image. In the left-facing composition a second female head appears. About a decade later, a more finished right-facing version appears, but now with the second head (St. Anne) in near mirror image of the Virgin’s (Figure 10.3A). The two stare lovingly at each other. In the finished painting of ca. 1503 (Figure 10.3B), St. Anne’s head is now in alignment with the Virgin’s, but the figures of the Christ Child and the lamb are turned 180 degrees. No viewer standing in the Louvre before Leonardo’s masterpiece would realize that this final version of it was the product of a twenty-year struggle regarding figures in dramatic opposition. Here the process of “thinking opposite,” essential though it is, remains entirely hidden.
FIGURES 10.2A AND B: A: Leonardo da Vinci’s drawing Virgin and Child with Cat, ca. 1478 (Department of Prints and Drawings, British Museum, London).
British Museum Database 1856, 0621.1 recto: Wikimedia Commons
B: His later drawing Virgin and Child with Cat, ca. 1480 (British Museum, London).
British Museum Database 1856, 0621.1 verso: Wikimedia Commons
FIGURES 10.3A AND B: A: Leonardo’s cartoon (finished drawing), ca. 1499 (National Gallery, London).
London, National Gallery, unknown: Wikimedia Commons
B: His painting The Virgin and Child with St. Anne, ca. 1503 (Musée du Louvre, Paris).
Paris, Museum of the Louvre, Dcoetzee: Wikimedia Commons
Walk from The Virgin and Child seventy-five feet northwest in the Louvre, and you will arrive at the world’s most famous painting: Leonardo’s Mona Lisa. It, too, involves a reversal of thinking, but of an even more subtle type. Before the arrival of Leonardo, late-medieval and early-Renaissance painting had been either religious or historical in theme. A painting depicted Christian dogma or left a visual record of reigning kings and queens, and it did so by means of symbols: a dove to announce the coming Christ or a crown to suggest a king. The message in a painting was conveyed from painter to viewer, and the viewer could take it or leave it, believe it or not believe it. In traditional symbolic painting, communication went only one way.
With Leonardo’s Mona Lisa, painting took a quantum turn. The lines of communication are reversed. Instead of the artist telling us something, the lady in this painting wants to engage in a dialogue with the viewer. Her question, in the form of her quizzical smile, is a provocation. Here painting ceases to be monodirectional dogma and becomes bidirectional engagement. To understand the Mona Lisa, we must accept that the meaning of a painting may not rest in the work itself as much as it does in the viewer. Art historians call this “reverse perspective.”
Psychologists define the term “reverse psychology” as a strategy by which saying one thing is designed to produce the opposite effect. Writers sometimes employ “reverse chronology” as a storytelling technique, and they have done so for dramatic effect as far back as Virgil’s Aeneid. The composer Richard Wagner used reverse chronology when crafting the libretto of his seventeen-hour-long musical drama The Ring Cycle; he began with the death of his gods and heroes (Twilight of the Gods), worked backward through the events of their earlier lives (Siegfried and The Valkyrie), and finally prefaced this trilogy with a context-setting preview (Rhinegold). George Lucas proceeded similarly in his Star Wars films, following up an opening trilogy with three “prequels” that went back in time. In 1922, F. Scott Fitzgerald published a short story, “The Curious Case of Benjamin Button,” in which the life of the protagonist unfolds in reverse chronological order: he is born an eighty-year-old, becomes middle-aged, then becomes youthful, and then dies as a child.
“I always know the end of the mystery before I begin to write,” says the bestselling murder mystery writer P. D. James.6 Mystery writers often establish “who done it,” where, and how and then go back to the beginning to lead the reader through their story. Indeed, “murder mysteries are backward creatures,” wrote the mystery writer Bruce Hale in “Writing Tip: Plotting Backwards.”7 We are speaking of mystery novels here, but the principle can be widely applied. Any aspiring author might do well to ponder first: What will be the ending? Indeed, “Think backward” is good advice for anyone making a public presentation, written or spoken, be it a corporate report or a wedding speech. Look over the material, save the best and most persuasive for last, and structure everything else to lead there. Not only will the material stay “on point,” but, equally important, the audience will appreciate the “big bang” conclusion.
A RAY IS, BY DEFINITION, A STRAIGHT LINE, LIKE THE FIRST FEW feet of water shot from a squirt gun. A wave is a curve, like ripples emanating from a stone tossed into a pond. If not exact opposites, “ray” and “wave” are very dissimilar. That light could be both a ray and a wave is a paradox, from the Greek paradoxon, “contrary opinion.” “Thinking opposite” sometimes requires being comfortable with paradox.
More than once Albert Einstein wrestled with conditions that were paradoxical. In 1905, he resolved a long-standing debate between opposing theories regarding the nature of light: Is light a stream of particles (a straight line), or is it a wave? Isaac Newton had previously opted for particles; he called them “corpuscles.” Newton’s near contemporary Christiaan Huygens (1629–1695) argued for waves. Newton’s theory seemed to prevail until James Maxwell (1831−1879) put the wave description onto more solid ground with his unified laws of electromagnetic waves (1865).8 In 1905, Einstein showed how these oppositional theories might be reconciled, with his theory of wave-particle duality. Waves of light hit a material, which then emits a stream of photoelectrons (Einstein’s photoelectric effect). “We have two contradictory pictures of reality,” he said. “Separately neither of them fully explains the phenomena of light, but together they do.”9 This duality became part of quantum physics—a new orthodoxy made of paradox. In addition, the photoelectron’s energy is always inversely proportional to the light’s wavelength—an embedded antithesis. Illuminating the conundrum of light brought Einstein the Nobel Prize in 1921.
“When does a woman falling from a building not fall?” Answer: “When everything else is falling with her.” When Albert Einstein solved that hypothetical riddle, he found the answer to another. In 1907, Einstein was vexed by the apparent opposition of two theories: Newton’s theory of celestial gravity, which states that objects are pulled in a straight line to other objects, and his own Theory of Special Relativity, which states that objects are governed by the rules unique to their context. “One is dealing here,” he noted, “with two fundamentally different cases, [which] was for me, unbearable.”10 Visualizing a situation in which everything was falling at once produced “the happiest thought of my life” and removed the unbearable burden. How can stasis and motion exist at one and the same time? “Because,” Einstein said, “for an observer in free fall from the roof of a house there is during the fall—at least in his immediate vicinity—no gravitational field. Namely, if the observer lets go of any bodies, they remain relative to him, in a state of rest.”11 The force of gravity might be at work, but another might act with it both conterminously and equally. In the language of science, there was a “complete physical equivalence and simultaneity of the opposite effect, of a uniform gravitational field.”12 In layman’s terms, forces could pull in a straight line and a curve depending on the speed of the object and the force of the gravitational field. Newton wasn’t wrong, but his theory of gravity was not accurate under all circumstances. Newton’s apple might fall straight down, but in Einstein’s space-time it would curve. Similarly, the fact that a single atom can behave like two separate atoms under certain circumstances is the fundamental logic behind the emerging field of quantum computing and the computer of the future.13
“THE COLDEST WINTER I EVER SPENT,” MARK TWAIN SAID, “WAS A summer in San Francisco.” We were expecting Twain to elaborate on a winter experience and instead are jerked around to summer. But long before Twain’s 180-degree pivot, William Shakespeare had used the same gambit in the opening lines of his play Richard III: “Now is the winter of our discontent, made glorious summer by this sun of York.” Shakespeare fashions not only a play of opposites (winter yielding to summer) but a pun—the “sun of York” was Edward, son of the Duke of York and now the brightest sun in the York dynastic firmament. Richard III is a dark political tragedy, yet one full of humor owing to opposing views of Richard: the citizens see him as a malevolent force; he—being delusional—views himself as benevolent. The most famous example of Shakespeare’s antipodal scenes is when the murderer Macbeth yields to the comically drunken porter. When negative and positive forces connect, drama strikes the stage like a lightning bolt.
Most of Shakespeare’s poetry is built on analogies, metaphors, and similes—two related concepts joined in a pair. Poetic pairing can be all the more effective when the pair is an antithesis. To appreciate what makes genius, consider a passage spoken by Romeo in Shakespeare’s Romeo and Juliet. Here the lover experiences a knot of contradictory feelings that come double time—fourteen in eight lines. Some might be expected: “sick health” and “cold fire”—you or I might have thought of these. But “brawling love” and “feather of lead”—there’s the hidden genius!
Here’s much to do with hate, but more with love.
Why, then, O brawling love! O loving hate!
O any thing, of nothing first create!
O heavy lightness! Serious vanity!
Mis-shapen chaos of well-seeming forms!
Feather of lead, bright smoke, cold fire, sick health!
Still-waking sleep, that is not what it is!
This love feel I, that feel no love in this. [I love her, but she loves me not.]
Finally, consider the staying power of Shakespeare’s most succinct oxymoron, one in which he juxtaposes two opposite and incompatible existential conditions: “To be or not to be.”
HENRY FORD REVOLUTIONIZED FACTORY WORK AND THE CAR INDUSTRY when he began to mass-produce the inexpensive Model T in 1913 by means of an assembly line. A visit to a slaughterhouse in Chicago had impressed him with the speed and efficiency with which a dead steer could be disassembled to nothing, hanging from its heels and pulled along a steel chain. If disassembly might occur so quickly, he thought, could not the process be reversed in additive fashion?
The contrarian Elon Musk took the opposite approach to Ford when it came to pricing his cars. When Musk took the helm at Tesla, instead of introducing an inexpensive car and working up to expensive models, he started with the Roadster in 2011 (price $200,000), next introduced a Model X in 2015 ($80,000), and finally brought out the Model 3 in 2017 ($35,000). Thus, at the moment, Tesla is transitioning from being a high-price, low-volume company to being a low-price, high-volume one. As Musk announced loudly in a public post of 2006 titled “The Secret Tesla Motors Master Plan,” his agenda was to:
Build sports car
Use that money to build an affordable car
Use that money to build an even more affordable car. . . .
Don’t tell anyone.14
As a young data manager at the hedge fund D. E. Shaw & Co. during the early 1990s, Jeff Bezos was comfortable hedging a bet: correctly positioning one economic asset as a counterpoise to another. Bezos saw that internet usage was expanding at the astounding rate of 2,300 percent each year and recognized that global growth was “the big picture.” The challenge was how to link it to the little guy and make money, so he went in search of a problem that he could monetize. Thinking opposite, he found one: shopping. A consumer drives around looking for things but often comes home empty-handed. Why not reverse the process, use the internet to find the goods, and have the goods go to the consumer, thereby saving time and money? He did, and today Amazon controls 40 percent of e-commerce in the United States.15 In 2005, Bezos said, “Sometimes people see the problem and the problem is really annoying them, and they invent a solution. Sometimes you can work this from the backwards direction. And in fact in high tech I think a lot of the innovation sometimes comes from this direction. You see a new technology or there’s something out there, . . . and you work backwards from a solution to find the appropriate problem.”16 Bezos’s current obsession: “We have to go into space to save Earth.”17
TO BE FUNNY, “THINK OPPOSITE.” HUMOR INVOLVES IRONY, CONTRADICTION, or counterintuitive thinking. So does sarcasm. When we say, “Boy, that was smart,” we actually mean the opposite. Creative comedians are philosophers who sometimes reveal the truth, as they show us, ironically, that we have the wrong target because the real one is hidden. The following shtick appears in Chris Rock’s stand-up comedy special “Bigger and Blacker”:
Gun control? We need bullet control! I think every bullet should cost five thousand dollars. Because if a bullet cost five thousand dollars, people would start to think before they shoot, wondering if they can afford it. . . . We wouldn’t have any more innocent bystanders, or if we did, the shooters would be going around saying “Give me my property back!” [condensed and sanitized]
A paradox can be an oxymoron with a moral, and that is what Rock has constructed here by setting a perceived truth against a truth: guns don’t kill, bullets do. Maybe we should just outlaw bullets. Rock has also said, “Comedy is the blues for people who can’t sing.” He understands that jokes explore the polar opposites of human experience and allow us to laugh along the way. As Freud argued in his The Joke and Its Relationship to the Unconscious (1905), jokes reveal the foibles, fears, and contradictions within all of us. The joke here: Freud’s book on jokes is the least funny book you will ever read.
Below are some one-liners from geniuses past and present. They are funny because they involve opposites, a misunderstanding, a logical impossibility, or a repositioning of words.
Shakespeare: “O villain! Thou wilt be condemned into everlasting redemption for this!” (Much Ado About Nothing)
Benjamin Franklin: “If we don’t all hang together we surely will all hang separately.”
“I probably should be proud of my humility.”
Charles Darwin: “[Thomas] Carlyle silenced everyone by haranguing during the whole London dinner party on the advantages of silence.”
Mark Twain: “Wagner wouldn’t sound nearly so bad if it weren’t for the music.”
Albert Einstein: “To punish me for my contempt of authority, Fate has made me an authority.”
Will Rogers (in Texas during a drought): “The Rio Grande is the only river I’ve ever seen that needs irrigation.”
Winston Churchill: “The farther backward you look, the farther forward you can see.”
Martin Luther King, Jr.: “Our scientific power has outrun our spiritual power. We have guided missiles but misguided men.”
Elon Musk: “When people ask me why I started a rocket company, I say, ‘I was trying to learn how to turn a large fortune into a small one.’”
“The best kind of service is no service at all.”
N. C. Wyeth: “It is the hardest work in the world to try not to work!”
Jack Vogel: “You get what you don’t pay for.”
Oscar Wilde: “Work is the curse of the drinking class.”
“True friends stab you in the back.”
“To lose a parent is a great misfortune; to lose both looks like carelessness.”
“I can resist everything except temptation.”
J. K. Rowling: “We bought two hundred copies of ‘The Invisible Book of Invisibility’—cost a fortune and we never found them.” (The Prisoner of Azkaban)
Oscar Levant: “What the world needs is more geniuses with humility. There are so few of us left.”
Jokes are funny, but the reason is hidden from us: it’s “thinking opposite.”
MANY OF THE WORLD’S GREAT RELIGIONS INVOLVE A THEOLOGY embracing a constant cycle of beginnings and endings, or an endless pull of opposing forces. In Buddhism, contrary and unified forces coexist as nirvana, the end of the cycle of rebirth, and samsara, the endless series of incarnations and reincarnations of living things.18 Nirvana, the ultimate state, itself is both nondeath and nonlife. Within Taoism, yin and yang are opposite yet universal moral principles, operating together as a single force. The Hebrew word אמת, meaning “truth,” one of the names of God in Judaism, uses the first (aleph) and last (taw) letters of the Hebrew alphabet. Satan and the angels of God do battle in Christian eschatology. Ego sum alpha et omega, the first and last letters of the Greek alphabet, symbolize God as described in the Book of Revelation.
Martin Luther King, Jr., was graduated from Crozer Theological Seminary in 1951 and earned a Ph.D. in theology at Boston University four years later. He knew about alpha et omega, beginning and end, and he employed this antithesis in his most famous speech, “I Have a Dream” (1963).
Much has been written about King’s “I Have a Dream,” the defining moment of his career and a tipping point for Americans’ thinking about race. The simple point here is that the rhetorical power of the speech derives from not only the relentless pursuit of a single refrain (anaphora) but also the relentless use of contradictory images (oxymoron). Rhetoric marches ahead directly, while poetry alternates between opposites.
Now is the time to rise from the dark and desolate valley of segregation to the sunlit path of racial justice. . . .
This sweltering summer of the negro’s legitimate discontent will not pass until there is an invigorating autumn of freedom and equality.
Nineteen sixty-three is not an end but a beginning. . . .
In the process of gaining our rightful place we must not be guilty of wrongful deeds.
Let us not seek to satisfy our thirst for freedom by drinking from the cup of bitterness and hatred. . . .
We shall always march ahead. We cannot turn back. . . .
I have a dream that one day, on the red hills of Georgia, the sons of former slaves and the sons of former slave owners will be able to sit down together at the table of brotherhood.
I have a dream that one day even the state of Mississippi, a state sweltering with the heat of injustice, sweltering with the heat of oppression will be transformed into an oasis of freedom and justice. . . .
I have a dream that one day every valley shall be exalted, every hill and mountain shall be made low, the rough places will be made plain and the crooked places will be made straight. . . .
With this faith we will be able to transform the jangling discords of our nation into a beautiful symphony of brotherhood.19
In college, King encountered Indian religious beliefs and studied the life of Mahatma Gandhi, and in 1959 he went to India to learn from Gandhi’s disciples about passive resistance. As the leader of the Southern Christian Leadership Conference, King then used nonviolence as a weapon against violence in the streets. The water cannon and police dogs directed against women and children in Birmingham, Alabama, had the opposite effect; they created a public backlash. In 1964, King’s contrarian approach won him the Nobel Peace Prize.
IN SUM: THE GENIUSES OF THIS CHAPTER SUGGEST THAT THE MORE a person can exploit the contradictions of life, the greater his or her potential for genius. Great artists, poets, playwrights, musicians, comedians, and moralists embed oppositional forces in their work for dramatic, and sometimes comic, effect. Brilliant scientists and mathematicians seemingly do not go in search of contradictions but are comfortable when they find them. Transformative entrepreneurs look for contrarian solutions. Bach used counterpoint to fashion his greatest works. Bezos worked backward from a solution to a problem. King used oxymoronic words and vigorous inaction to change public opinion about race in the United States.
We can all employ this strategy. After telling a child a bedtime story, reverse the process and have the child tell you one—encourages visionary thinking on the part of both teller and auditor. Before launching a new company, hold a “premortem,” working backward to see why the venture might fail. To write a better company report or give a better speech, look over the material and get the end in place first. Simplify your argument; less may be more. To reduce personal bias and reasoning errors when making a big decision, write a list of the pros and cons.20 To test the validity of your position, find a devil’s advocate; arguing with your spouse or partner can be a good thing and will provide an opportunity to exercise passionate restraint. To be witty in conversation, think of an opposite rejoinder. While the strategy of “thinking opposite” may go unobserved, the improved outcomes will be obvious.