by Kevin Ashton
And the Nine-Dot Problem:
Picture three rows of three dots, evenly spaced to resemble a square. Join the dots using only four straight lines without taking your pencil or pen off the paper.
All are solved the same way: by the equivalent of realizing that the faces are also a vase. Charlie is not a person but a fish. Tom is not a person but a cat. Tom knocked over Charlie’s fish bowl, and Charlie died. The prisoner did not “divide” the rope in half widthwise, as we naturally imagine, but lengthwise. The nine dots are joined by drawing lines that extend beyond the “square” created by the dots. This is the source of the cliché “thinking outside the box.”
Does this mean minds leap? We can answer that question with one more problem, the Speckled Band:
Julia sleeps in a locked room. Beside her bed is a bell pull for summoning the housekeeper. Above the bell pull is a ventilator that connects to the room next door. That room contains a safe, a dog leash, and a saucer of milk. One night Julia screams. There is a whistle and a clang. She is found dying with a burnt match in her hand. There are no signs of violence. There are no pets in the house. Her room had remained locked. Her last words are “the speckled band.” How did Julia die?
This is not a psychology problem. It is a summary of a Sherlock Holmes story written by Arthur Conan Doyle in 1892. Julia died from the bite of a poisonous snake trained to crawl through the ventilator and down the bell pull, then return when her murderer whistled. He kept the snake on the leash and fed it the milk. The clang is the sound of him hiding the snake in the safe after the murder. Upon being bitten, Julia lit a match for illumination and glimpsed the snake, which looked to her like a “speckled band.”
Holmes works this out by observing that the only way into the locked room is through the ventilator. He deduces that because Julia died quickly and without obvious signs of violence, she was probably poisoned. Something small and poisonous therefore passed through the ventilator. The dog leash suggests an animal, rather than a gas, and the saucer of milk rules out an insect such as a spider. Julia’s dying words about a speckled band, which initially seem cryptic, now sound like a description of the most likely remaining solution: a snake, trained to respond to its master’s whistle. The clang shows that the snake is in the safe.
Holmes is a fictional character famous for detection, not creation. He describes his process as “observation and deduction: eliminate all other factors, and the one which remains must be the truth.” He does not solve Julia’s murder with a creative leap. The “insight” that begins his process of deduction—that the only way into the locked room is via the ventilator—is an observation. The surprising solution that a snake killed her follows.
Minds do not leap. Observation, evaluation, and iteration, not sudden shifts of perception, solve problems and lead us to creation. We can see this using Duncker’s technique: observing people solving his most famous problem.
3 | STEPS, NOT LEAPS
Many people do not think using words, but we can all verbalize our thoughts without affecting our problem-solving skills. Listening to the mind shows how thinking works. Robert Weisberg asked people to think aloud as they worked on Duncker’s Box Problem. He changed the problem by including nails as well as tacks and substituting a piece of cardboard for the wooden door. The people he worked with had the objects in front of them. They were asked to imagine solutions but not build them.
Here are the thoughts of three people who did not think of using the tack box as a candleholder:
PERSON 1: “Melt the candle and try to stick it up. Candle coming out vertically on a nail, but it will break. Put the candle sideways and nail it up. The candle looks heavy. Put a nail or two nails in the side of the candle, but it might not stay up. I could … no, I couldn’t do that.”
PERSON 2: “I’m looking at the nails, but they won’t penetrate but otherwise how will the candle stick? Put a nail through the vertical candle. Put a nail through the candle held horizontal. Can’t use the matches. Put nails in the wick and under the candle …”
PERSON 3: “I was thinking you could take a nail and bang it through, but that would split the candle, so use the matches to melt enough wax, then use the nails—no good. Bang the nails in close together and put the candle on them.…”
And here are the thoughts of three people who did think of using the tack box to hold the candle:
PERSON 4: “Candle has to burn straight, so if I took a nail and put it through the candle and cardboard …[10 second pause]… if I took several nails and made a row and set the candle on that. If I took the nails out of the box, nailed the box to the wall.”
PERSON 5: “Melt wax and use it to stick the candle up. Take a nail—the nail won’t go through the candle. Put nails around the candle or under the candle to hold it. Put the candle in the nail box—it wouldn’t work, the box would rip.”
PERSON 6: “Light a match and see if I could get wax up on the cardboard. Push a nail through the candle into the cardboard. I’m looking at the matches to see if the idea would work. I’m trying to get more combinations with the nails. Build a base for the candle with the nails like a rectangle. Better yet, use the box. Put two nails into the cardboard, put the box on them, melt some wax and put the candle into the box with the wax and it’ll stand.”
This is how we think. Everyone who thinks of using the tack box gets there the same way. After eliminating other ideas, they think of building a platform out of nails, then think of using the tack box as the platform. There is no sudden shift of perception. We move from known to new in small steps. In every case, the pattern is the same: begin with something familiar, evaluate it, solve any problems, and repeat until a satisfactory solution is found. Duncker discovered this in the 1930s:
“Successful people arrived at the solution in this way: they started from tacks and looked for a ‘platform to be fastened to the door with tacks.’ ”
Evaluation directs iteration. Person 3 decides to “bang the nails in close together and put the candle on them” and evaluates this as satisfactory. Person 4 evaluates this as unsatisfactory so takes one more step: use the tack box. Person 5 also takes this step, the solution Duncker sought for his problem, but makes the opposite evaluation: it won’t work. Person 6 takes the most steps of all and, as a result, improves Duncker’s solution by using melted wax to stabilize the candle.
Creating is taking steps, not making leaps: find a problem, solve it, and repeat. Most steps wins. The best artists, scientists, engineers, inventors, entrepreneurs, and other creators are the ones who keep taking steps by finding new problems, new solutions, and then new problems again. The root of innovation is exactly the same as it was when our species was born: looking at something and thinking, “I can make this better.”
Six undergraduates talking their way through a puzzle is not enough for generalization, nor is twenty-five, which is how many Weisberg asked to talk out loud, nor even 376, which is how many tried the Box Problem in his experiment. But these results do undermine a vital premise of the creativity myth: that creating requires leaps of extraordinary thinking. It does not. Ordinary thinking works.
4 | AHA!
There is an alternative to the theory that creation comes from ordinary thinking: the idea, proposed by psychologists Pamela Auble, Jeffrey Franks, and Salvatore Soraci, writer Jonah Lehrer, and many others, that many of the best creations come from an extraordinary moment of sudden inspiration, sometimes called the “eureka effect” or “aha! moment.” Ideas start as caterpillars of the conscious mind, become cocoons in the unconscious, then fly out like butterflies. This moment results in excitement and possibly exclamation. The key to creating is to cultivate more of these moments.
People who believe this will have many reasonable objections to the proposal that creation comes from ordinary thinking. There are documented cases of great creators having aha! moments. Many people have experienced frustration with a problem and set it aside only to have the solution come to them. Neurologists
seeking the source of such moments are discovering interesting things. The aha! moment is woven into our world. Oprah Winfrey has trademarked it. How can ordinary thinking explain this?
The most frequently cited story of an aha! moment was first made famous by a Roman architect named Vitruvius.
Vitruvius says that when the Greek general Hiero was crowned king of Syracuse, in Sicily, twenty-three hundred years ago, he celebrated by giving a craftsman some gold and asking him to create a golden wreath. The craftsman duly delivered a wreath with the same weight as the gold that Hiero had provided, but Hiero suspected that he had been tricked and that most of the wreath was made of silver. Hiero asked Syracuse’s greatest thinker, a twenty-two-year-old named Archimedes, to find the truth: was the wreath pure gold or a mixture of gold and silver? According to Vitruvius, Archimedes then took a bath. The lower he sank, the more the water overflowed. This gave him an idea. Archimedes ran home naked, shouting, “Eureka, eureka!”—“I have found it, I have found it!” He made two objects that were both the same weight as the wreath, one in gold and one in silver, and submerged each of them in water and measured how much water overflowed. The silver object displaced more water than the gold object. Then Archimedes submerged Hiero’s “golden” wreath into the water. It displaced more water than the same weight of pure gold, proving that it had been adulterated with silver or some other substance.
This story about Archimedes, which Vitruvius told two centuries after the fact, is almost certainly not true. The method Vitruvius describes does not work, as Archimedes would have known. Galileo pointed this out in a paper called “La Bilancetta” (“The Little Balance”), which calls the method of comparing gold and silver Vitruvius describes “altogether false.” The tiny differences in the amount of water displaced by the gold, the silver, and the wreath would have been too hard to measure. Surface tension and drops of water that remained on the wreath would have caused other problems. Galileo’s paper shows the method Archimedes probably used, based on Archimedes’s own work: weighing the wreath underwater. Buoyancy, not displacement, is the key to solving the problem. Overflowing a bath is unlikely to have inspired this.
But let’s take Vitruvius’s story at face value. He says that Archimedes, “while the case was still on his mind, happened to go to the bath, and on getting into a tub observed that the more his body sank into it, the more water ran out over the tub. As this pointed out the way to explain the case in question, without a moment’s delay, and transported with joy, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for as he ran he shouted repeatedly in Greek, ‘Eureka, eureka.’ ”
Or: Archimedes’s eureka moment came from an observation he made while thinking about the problem. At best, the bath is like the platform of nails in the Weisberg experiments: it is the one thing that leads to another. If it happened at all, Archimedes’s legendary shout of “Eureka” did not come from an aha! moment but from the simple joy of solving a problem with ordinary thinking.
Another famous example of an aha! moment comes from Samuel Taylor Coleridge, who claimed his poem “Kubla Khan” was written in a dream. According to Coleridge’s preface:
In the summer of the year 1797, the Author, then in ill health, had retired to a lonely farmhouse. An anodyne had been prescribed, from the effects of which he fell asleep in his chair at the moment that he was reading, “Here the Khan Kubla commanded a palace to be built, and a stately garden thereunto. And thus ten miles of fertile ground were inclosed with a wall.” The author continued for about three hours in a profound sleep during which time he could not have composed less than from two to three hundred lines without any sensation or consciousness of effort. On awaking he eagerly wrote down the lines; at this moment he was unfortunately called out by a person on business from Porlock and on his return to his room, found all the rest had passed away.
This gave the poem—subtitled “A Vision in a Dream”—an aura of mystery and romance that continues to this day. But Coleridge is misleading us. The anodyne, or painkiller, which he says he had been prescribed was opium dissolved in alcohol—a substance to which Coleridge was addicted. A trance of three to four hours is a classic opium-induced state, which can be euphoric and hallucinogenic. Coleridge’s movements in the summer of 1797 are well known. He had no time to retire to a lonely farmhouse. The person from Porlock may have been fictitious and an excuse for not finishing the poem. Coleridge used a similar device—a fake letter from a friend—to excuse the incompleteness of another work, his Biographia Literaria. The preface claims the poem was composed during sleep, then written automatically. But in 1934, an earlier manuscript of “Kubla Khan” was found that differs from the published poem. Among many changes, “From forth this Chasm with hideous turmoil seething” became “And from this chasm, with ceaseless turmoil seething”; “So twice six miles of fertile ground / With Walls and Towers were compass’d round” was changed to “So twice five miles of fertile ground / With walls and towers were girdled round”; “mount Amora” was rewritten as “mount Amara”—a reference to Milton’s Paradise Lost—then, finally, “mount Abora.” The origin story changed, too. Coleridge says the poem was “composed in a sort of reverie brought on by two grains of opium” in the fall, rather than appearing complete during a sleep in the summer.
These are minor changes, but they show conscious thought, not unconscious automation. “Kubla Khan” may or may not have started in a dream, but ordinary thinking finished it.
A third frequently told story about an aha! moment comes from 1865, when chemist August Kekulé discovered the ringlike structure of benzene. Twenty-five years after making this discovery, Kekulé said, in a speech to the German Chemical Society:
I was sitting writing at my textbook but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gamboling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by repeated visions of the kind, could now distinguish larger structures of manifold conformation: long rows, sometimes more closely fitted together all twining and twisting in snake-like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the consequences of the hypothesis.
Robert Weisberg points out that the word Kekulé used was halbschlaf, or “half-sleep,” which is often translated as “reverie.” Kekulé was not sleeping. He was daydreaming. His dream is often described as a vision of a snake biting its tail. But Kekulé says he saw atoms twisting in a snake-like motion. When he later describes one of the snakes seizing its tail, he is referring back to his analogy. He is not seeing a snake. This is a case of visual imagination helping solve a problem, not an aha! moment happening in a dream.
A sudden revelation has also been attributed to Einstein, who was stuck for a year while developing the special theory of relativity and went to a friend for help. “It was a beautiful day when I visited him with this problem,” he said. “I started the conversation with him in the following way: ‘Recently I have been working on a difficult problem. Today I come here to battle against that problem with you.’ We discussed every aspect of this problem. Then suddenly I understood where the key to this problem lay. Next day, I came back to him again and said to him, without even saying hello, ‘Thank you. I’ve completely solved the problem.’ ”
Was this a flash of inspiration? No. In Einstein’s own words: “I was led to it by steps.” All stories of aha! moments—and there are surprisingly few—are like these: anecdotal, often apocryphal, and unable to survive scrutiny.
And there has been a lot of scrutiny: in the last few decades of the twentieth century, many psychologists believed that creation comes from a period of unconscious thinking they called “incubation,” followed by an emotion they called “the feeling of kno
wing,” followed by an aha! moment, or “insight.” These psychologists conducted hundreds of experiments designed to validate their hypothesis.
For example, in 1982, two researchers at the University of Colorado tested the feeling of knowing with thirty people in an experiment lasting nineteen days. They showed the subjects pictures of entertainers and asked them to recall the entertainers’ names. Only 4 percent of memories were recovered spontaneously, most of them by the same four people. All the other memories were recovered by ordinary thinking: gradually working through the problem by remembering, for example, that the entertainer was a movie star in the 1950s, that he had appeared in an Alfred Hitchcock movie where he was chased by a crop duster, that the movie was called North by Northwest, and, finally, that his name was Cary Grant. The study’s conclusion? Even the “spontaneous” memories had probably also come from ordinary thinking, and there was no support for unconscious mental processing as a way of recovering memories. Other studies into the feeling of knowing have had similar results.
And what of incubation? An academic named Robert Olton spent many years at the University of California, Berkeley, trying to prove that incubation exists. In one experiment he sorted 160 people into ten groups and asked them to solve an insight problem called the Farm Problem, which involves dividing an L-shaped “farm” into four parts of the same size and shape. The solution is novel—you have to make four smaller L shapes in various orientations. Every subject was tested individually and given thirty minutes to solve the problem. To see if taking a break from thinking—that is, incubating—made a difference, some subjects were given a fifteen-minute break. During this break, some people could do whatever they wanted; others were given mental work like counting backward in threes, or were asked to talk about the problem out loud, or were told to relax in a room with a comfortable chair, dim lights, and soft music. Each activity tested a different idea about how incubation works.