How We Learn (17 page)

None of these quotes is especially informative or illuminating by itself. Read too many of them, one after another, without the benefit of expertise in the fields or the precise calculations the person is working out, and they begin to sound a little like postgame comments from professional athletes:
I was in the zone, man; I felt like I was seeing everything in slow motion
.

Wallas saw, however, that the descriptions had an underlying structure. The thinkers had stalled on a particular problem and walked away. They could not see an opening. They had run out of ideas. The crucial insights came after the person had abandoned the work and was deliberately
not
thinking about it. Each insight experience, as it were, seemed to include a series of mental steps, which Wallas called “stages of control.”

The first is
preparation:
the hours or days—or longer—that a person spends wrestling with whatever logical or creative knot he or she faces. Poincaré, for example, spent fifteen days trying to prove that Fuchsian functions could not exist, an extensive period of time given his expertise and how long he’d played with the ideas before sitting down to construct his proof. “Every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and
reached no result,” he wrote. Preparation includes not only understanding the specific problem that needs solving and the clues or instructions at hand; it means working to a point where you’ve exhausted all your ideas. You’re not stalled, in other words. You’re stuck—ending preparation.

The second stage is
incubation
, which begins when you put aside a problem. For Helmholtz, incubation began when he abandoned his
work for the morning and continued as he took his walk in the woods, deliberately
not
thinking about work. For others, Wallas found, it occurred overnight, or during a meal, or when out with friends.

Some mental machinations were clearly occurring during this downtime, Wallas knew, and they were crucially important. Wallas was a psychologist, not a mind reader, but he ventured a guess about what was happening: “Some kind of internal mental process,” he wrote, “is operating that associates new information with past information. A type of internal reorganization of the information seems to be going on without the individual being
directly aware of it.” That is to say, the mind works on the problem
off-line
, moving around the pieces it has in hand and adding one or two it has in reserve but didn’t think to use at first. One way to think of this is in terms of a weekend handiwork project. There you are, for example, replacing an old, broken door handle and casing with a new one. It looks like an easy job, but there’s a problem: The casing sits off-center, the bolt and latch don’t line up right. You don’t want to cut new holes, that’ll ruin the door; you futz and futz and see it’s not going to happen. You give up and break for lunch, and suddenly think … wait, why not use the
old
casing, put the new hardware in that? You threw the old casing away and suddenly remembered you still had it—in the garbage.

That’s the general idea, at least, and in Wallas’s conception, incubation has several components. One is that it’s subconscious. We’re not aware it’s happening. Another is that the elements of the problem (the Pencil Problem, for example, presented at the school) are being assembled, taken apart, and reassembled. At some point “past information,” perhaps knowledge about the properties of triangles we hadn’t initially recalled, is braided in.

The third stage of control is called
illumination
. This is the aha! moment, the moment when the clouds part and the solution appears all at once. We all know that feeling, and it’s a good one. Here’s Poincaré again, on the Fuchsian functions problem giving up its secrets:
“One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. By the next morning …
I had only to write out the results.”

The fourth and final stage in the paradigm is
verification
, checking to make sure those results, indeed, work.

Wallas’s principal contribution was his definition of incubation. He did not see this as a passive step, as a matter of the brain resting and returning “fresh.” He conceived of incubation as a less intense, subconscious continuation of the work. The brain is playing with concepts and ideas, pushing some to the side, fitting others together, as if absentmindedly working on a jigsaw puzzle. We don’t see the result of that work until we sit down again and notice an entire corner of the jigsaw puzzle is now complete—revealing a piece of the picture that then tells us how to work with the remaining pieces. In a sense, the letting go allows people to get out of their own way, giving the subconscious a chance to toil on its own, without the conscious brain telling it where to go or what to do.

Wallas didn’t say how long incubation should last. Nor did he specify what kinds of downtime activity—walks, naps, bar-hopping, pleasure reading, cooking—were best. He didn’t try to explain, in scientific terms, what might be happening in our brains during incubation, either. The goal wasn’t to lay out a research agenda, but to establish a vocabulary, to “discover how far the knowledge accumulated by modern psychology can be made useful for the improvement of the thought-processes of a working thinker.” He expressed a modest hope that his book could induce others “to explore the problem with greater success
than my own.”

He had no idea.

• • •

The subsequent study of creative problem solving was not your typical white-coated lab enterprise. In the early days, in fact, it was
more like shop class. To study how people solve problems, and to do so rigorously, psychologists needed to devise truly novel problems. This wasn’t easy. Most of us grow up on a steady diet of riddles, jokes, wordplay, and math problems. We have a deep reservoir of previous experience to draw on. To test problem solving in the purest sense, then, scientists needed something completely different—ideally, not “academic” at all. So they settled on puzzles that demanded the manipulation not of symbols but of common household objects. As a result their labs looked less like labs than your grandfather’s garage.

One of the more inventive of these shop class labs belonged to the University of Michigan psychologist Norman Maier, who was determined to describe the mental machinations that directly precede seeing a solution. In a 1931 experiment, Maier recruited sixty-one participants and brought them into a
large room one at a time. Inside, each participant found tables, chairs, and an assortment of tools, including several clamps, a pair of pliers, a metal pole, and an extension cord. Two ropes hung from the ceiling to the floor, one in the middle of the room and the other about fifteen feet away next to a wall. “Your problem is to tie the ends of those two ropes together,” they were told. The participants quickly discovered that it wasn’t possible to grab one rope and simply walk over and grab the other; it didn’t reach far enough. Maier then explained that they were free to use any object in the room, in any manner they chose, to tie the two together.

The puzzle had four solutions, some more obvious than others.

The first was to tie one rope to a chair and then walk the other rope over. Maier put this in the “easy” category. He considered two others slightly more difficult: Tie the extension cord to one of the ropes to make it long enough to reach, or use the pole to pull one rope to the other. The fourth solution was to swing the rope in the middle of the room like a pendulum and catch it as it neared the wall. Maier considered this the most advanced solution, because in
order to make it happen you had to tie something heavy (like the pliers) to the rope so it would swing far enough.

After ten minutes, 40 percent of the students had landed on all four solutions without any help. But it was the remaining 60 percent that Maier was interested in: those who got at least one of the possibilities but not the hardest one, the weighted pendulum. At the ten-minute mark, they were stumped. They told Maier they’d run out of ideas, so he gave them a few minutes’ break. In Wallas’s terminology, these students were
incubating
, and Maier wanted to figure out what exactly was happening during this crucial period of time. Did the fourth solution appear as a completed whole? Or did it reveal itself in stages, growing out of a previous idea?

To find out, Maier decided to nudge the stumped students in the direction of the pendulum solution himself. After the break, he stood up and walked toward the window, deliberately brushing against the rope in the center of the room, causing it to swing ever-so-slightly, taking care to do so in full sight of the participants. Within two minutes, almost all of the participants were creating a pendulum.

When the experiment was over, Maier asked them how they arrived at the fourth answer. A few said that they’d had a vague notion to move the rope somehow, and the hint simply completed the thought. The solution appeared to them in stages, that is, and Maier’s nudge made it click. Nothing new in that, we’ve all been there. Think of the game show
Wheel of Fortune
, where each letter fills in a blank of a common phrase. We feel ourselves nearing a solution, letter by letter, and know exactly which letter lights the lamp.

The rest of the group’s answers, however, provided the real payoff. Most said that the solution appeared in a flash, and that they didn’t get any hints at all—even though they clearly had. “I just realized the cord would swing if I fastened a
weight to it,” one said. The solution came from a previous physics class, said another. Were these participants just covering their embarrassment? Not likely, Maier argued. “The perception of the solution of a problem is like the perceiving
of a hidden figure in a
puzzle-picture,” he wrote. “The hint was not experienced because the sudden experience of the solution
dominated consciousness.” Put another way, the glare of insight was so bright, it obscured the factors that led to it.

Maier’s experiment is remembered because he’d shown that incubation is often—perhaps entirely—subconscious. The brain is scanning the environment, outside of conscious awareness, looking for clues. It was Maier who provided that clue in this experiment, of course, and it was a good one. The implication, however, was that the incubating brain is sensitive to any information in the environment that might be relevant to a solution: the motion of a pendulum clock, a swing set visible through the window, the swaying motion of the person’s own arm.

Life is not always so generous with hints, clearly, so Maier hadn’t completely explained incubation. People routinely generate creative solutions when no clues are available at all: with their eyes closed, in basement study rooms, in tucked-away cubicles. Successful incubation, then, must rely on other factors as well. Which ones? You can’t ask people what they are, because the action is all offstage, and there’s no easy way to pull back the curtain.

But what if you—you, the scientist—could block people from seeing a creative solution, in a way that was so subtle it went unnoticed. And what if you could also discreetly
remove
that obstacle, increasing the odds that the person saw the answer? Would that reveal anything about this hidden incubation? Is it even possible?

A young German psychologist named Karl Duncker thought so. Duncker was interested in how people became “unblocked” when trying to crack a problem requiring creative thinking, too, and he’d read Maier’s study. In that paper, remember, Maier had concluded, “The perception of the solution of a problem is
like the perceiving of a hidden figure in a puzzle-picture
.” Duncker was familiar with picture puzzles. While Maier was conducting his experiments, Duncker was studying in Berlin under Max Wertheimer, one of the founders of
the Gestalt school of psychology. Gestalt—“shape,” or “form” in German—theory held that people perceive objects, ideas, and patterns whole, before summing their component parts. For example, to construct a visual image of the world—i.e., to see—the brain does a lot more than piece together the patches of light streaming through the eyes. It applies a series of assumptions: Objects are cohesive; surfaces are uniformly colored; spots that move together are part of the same object. These assumptions develop early in childhood and allow us to track an object—a baseball, say—when it disappears momentarily in the glare of the sun, or to recognize a scattering of moving spots behind a thicket of bushes as our lost dog. The brain “fills in” the form behind the bushes, which in turn affects how we perceive the spots.

Gestalt psychologists theorized that the brain does similar things with certain types of puzzles. That is, it sees them as a whole—it constructs an “internal representation”—based on built-in assumptions. When I first saw the Pencil Problem, for instance, I pictured an equilateral triangle on a flat plane, as if drawn on a piece of paper, and immediately began arranging the remaining pencils around that. My whole life, I’d worked geometry problems on paper; why should this be any different? I made an assumption—that the pencils lie in the same plane—and that “representation” determined not only how I thought about possible solutions, it also determined how I interpreted the given
instructions
. Many riddles exploit just this kind of automatic bias.
^*1

Duncker suspected that Gestalt-like biases—those “mental representations”—could block people from seeing solutions. His innovation was to create puzzles with built-in—and removable—
“curtains,” using everyday objects like boxes, boards, books, and pliers. The best known of these was the so-called candle problem.
In a series of experiments, Duncker had subjects enter a room—alone—that contained chairs and a table. On this table were a hammer, a pair of pliers, and other tools, along with paper clips, pieces of paper, tape, string, and small boxes filled with odds and ends. One contained thumbtacks; another contained small candles, like you’d see on a birthday cake; others had buttons, or matches. The assignment: fasten three of the candles to the door, at eye height, so they could be lighted, using anything from the table. Each participant was given ten minutes to complete the assignment.