How We Learn

by Benedict Carey

  • • •

  You’re shipwrecked. You swim and swim until finally you wash up on a desert island, a spit of sand no more than a mile around. As you stagger to your feet and scan the coastline, you realize: You’ve read about this place. It’s the Isle of Pukool, famous for its strange caste system. Members of the highest caste never tell the truth; members of the lowest always do; and those in the middle are sometimes honest and sometimes not. Outwardly, the castes are indistinguishable. Your only chance of survival is to reach the hundred-foot Tower of Insight, a holy site of refuge where you can see for miles and send out a distress signal. You follow a winding footpath and arrive at the one intersection on the island, where three Pukoolians are lounging in the heat. You have two questions to ask (Pukool custom, you know) to find your way to that tower.

  What do you ask?

  I like this puzzle for several reasons. It captures the spirit of insight in a visceral way, for one. At first glance, it seems hairy—it echoes a famous problem in math logic, involving two guards and a man-eating lion*2—yet absolutely no math expertise is required. If anything, math expertise is likely to get in the way. A five-year-old can solve it. Better still, we can use it as a way to think about the most recent research on incubation and problem solving, which has branched out like a climbing vine since its duct-tape-and-thumbtack days.

  To review, Wallas’s definition of incubation is a break that begins at the moment we hit an impasse and stop working on a problem directly, and ends with a breakthrough, the aha! insight. Maier and Duncker shone a light on what occurs mentally during incubation, what nudges people toward solutions. The question that then began to hang over the field in the last half of the twentieth century was how. Under what circumstances is incubation most likely to produce that aha! moment in real life? Wallas, Maier, and Duncker had incorporated breaks into their theories, but none specified how long of a break was ideal, or which kind of break was best. Should we hike in the woods, like Helmholtz? Go jogging for forty-five minutes? Stare into space? Some people prefer a nap, others a videogame. And there are students—I wish I were one of them—who will break from the knotty calculation they’re stuck on and turn to their history reading, a different species of break altogether. The religious reformer Martin Luther is said to have had some of his deepest insights on the toilet, as did the prolific French essayist Michel de Montaigne. Should we be parking ourselves there when trying to incubate?

  To try to answer these kinds of questions, psychologists have used old-fashioned trial and error. In more than one hundred experiments over the past fifty years, they have tested scores of combinations of puzzles, incubation durations, and types of study breaks. For instance, are people able to solve more anagrams when they take a five-minute break to play a videogame, or when they take a twenty-minute break to read? Daydreaming for a few minutes might be better than both, one study found; so might a Ping-Pong match. The most productive type of break might change entirely with other kinds of puzzles—riddles, rebus diagrams, spatial problems—and then change again when hints are given. This shifting, multidimensional experience is what scientists are trying to characterize in labs. One well-known experiment will illustrate how they do so.

  This experiment, conducted by two psychologists at Texas A&M University named Steven Smith (whom we’ve met before) and Steven Blankenship, used a simple word puzzle called a Remote Associates Test, or RAT. The subjects were given three words—“trip,” “house,” and “goal,” for example—and the challenge was to find a fourth that completed a compound word with each. (Field was the solution to this one: “field trip,” “field house,” and “field goal.”) Smith and Blankenship chose these puzzles in part because they could easily manipulate the level of difficulty by providing good hints, like “sports” for the example above (two of them are sports-related, and all you need is to find one and try it for the others) or bad hints, in the form of wrong answers, like “road,” which works with “trip” and “house” but not “goal.” The first kind of hint is akin to Maier’s swinging rope. The second is like Duncker’s filled boxes, creating a level of fixedness that is hard to overcome.

  This experiment used the second kind, the bad clue. Smith and Blankenship wanted to know whether a short incubation break affects people differently when they’re given bad hints—when they’re “fixed,” if you’ll excuse the expression—versus when they’re not. They recruited thirty-nine students and gave them twenty RAT puzzles each. The students were split into two groups. Half were given puzzles that had misleading words in italics next to the main clues (DARK light … SHOT gun … SUN moon), and the other half worked on the same puzzles, but without words next to the clues (DARK … SHOT … SUN). Both groups had ten minutes to solve as many puzzles as they could, and neither group did very well. Those who worked on the fixed ones solved two, on average, compared to five for the unfixed group.

  The psychologists then gave their participants another ten minutes to work on the puzzles they hadn’t solved the first time through. This time around, each group was subdivided: half took the retest immediately, and the other half got a five-minute break, during which they read a science fiction story. So: Two groups, one fixed and one not. Two conditions within each group, incubation and no incubation.

  The result? The incubation break worked—but only for those who got the bad clues. They cracked about twice as many of their unsolved puzzles as the unfixed group who got a break.

  The authors attributed the finding to what they called “selective forgetting.” A fixating (misleading) word temporarily blocks other possible answers, they argued, but “as more time elapses, after the initial failed attempts, the retrieval block may wear off.” It’s as if the students’ brains were temporarily frozen by the bad hints and the five-minute break allowed for some thawing out. This occurs all the time in normal daily life, most obviously when we get unclear directions—“the pharmacy is right at the end of Fowler Road, you can’t miss it”—and we arrive at the given spot, backtracking, circling, rechecking the street names: no pharmacy. We’re sure we’re missing it somehow. Finally, we sit down on a bench, stare at the birds for a few minutes, and it hits us: Oh, wait: maybe he meant the other end of Fowler Road. Or, the pharmacy moved. Or he has no idea what he’s talking about. The initial assumption—the pharmacy must be around here, somewhere—no longer has a stranglehold on our mind. Other options have floated in. Romantic entanglements are another classic example: We become infatuated, we think we’re in love, but time loosens the grip of the fixation. We come to see exasperating flaws. Maybe she’s not the one, after all. What was I thinking?

  In previous chapters, we’ve seen how forgetting can aid learning actively, as a filter, and passively, allowing subsequent study to ramp up memory. Here it is again, helping in another way, with creative problem solving.

  As Smith and Blankenship were quick to note, selective forgetting is only one possible explanation for incubation, in these specific circumstances (RATs, fixed words, five-minute reading break). And theirs was just one experiment. Others have produced slightly different results: Longer breaks are better than shorter ones; playing a videogame is as good as reading; writing may help incubation for certain kinds of problems, such as spatial ones like the Pencil Problem. In each case—in each specific study—scientists have floated various theories about what’s happening in the buildup to that aha! moment. Maybe it’s selective forgetting. Maybe it’s a reimagining of the problem. Maybe it’s simple free-associating, the mind having had time to wander in search of ideas. No one knows for sure which process is the most crucial one, and it’s likely that no one ever will. Our best guess? They all kick in at some level.

  What does that mean for us, then? How do we develop a study strategy, if scores of experiments are saying various, often contradictory, things?

  To try to make sense of the cacophony, let’s return to the Isle of Pukool. How to find our Tower of Insight? The three Pukoolians are pointing in different dir
ections, after all. It’s hard to know who’s being honest and who’s not.

  What to do?

  Easy. Look up. The tower is one hundred feet tall, and the island is flat, and the size of a city park. No complex math logic required: The tower is visible for miles. Try this on a group of friends when they’re in the mood. You’ll notice that some people see the answer right away, and others never come close. I didn’t come close. I spent hours concocting absurd, overly complex questions like, “Which way would those two fellow islanders say that you would say …?” I wrote out the various possible answers on paper, using a math notation I’d forgotten I knew. When I finally heard the solution, it seemed somehow unfair, a cheap trick. On the contrary. Taking a step back and looking around—seeing if we’ve used all the available information; attempting to shake our initial assumptions and start from scratch; doing a mental inventory—is a fitting metaphor for what we have to do to make sense of the recent work on incubation. Looking at each study individually is like engaging the Pukoolians one-on-one, or staring so closely at a stereogram that the third dimension never emerges. You can’t see the forest for the trees.

  Thankfully, scientists have a method of stepping back to see the bigger picture, one they use when trying to make sense of a large number of varied results. The idea is to “pool” all the findings, positive and negative, and determine what the bulk of the evidence is saying. It’s called meta-analysis, and it sometimes tells a clearer story than any single study, no matter how well done. In 2009, a pair of psychologists at Lancaster University in the United Kingdom did precisely this for insight-related research, ransacking the available literature—even hunting down unpublished manuscripts—and producing a high-quality, conservative meta-analysis. Ut Na Sio and Thomas C. Ormerod included thirty-seven of the most rigorous studies and concluded that the incubation effect is real, all right, but that it does not work the same in all circumstances.

  Sio and Ormerod divided incubation breaks into three categories. One was relaxing, like lying on the couch listening to music. Another was mildly active, like surfing the Internet. The third was highly engaging, like writing a short essay or digging into other homework. For math or spatial problems, like the Pencil Problem, people benefit from any of these three; it doesn’t seem to matter which you choose. For linguistic problems like RAT puzzles or anagrams, on the other hand, breaks consisting of mild activity—videogames, solitaire, TV—seem to work best.

  Sio and Ormerod found that longer incubation periods were better than short ones, although “long” in this world means about twenty minutes and “short” closer to five minutes—a narrow range determined by nothing more than the arbitrary choices of researchers. They also emphasized that people don’t benefit from an incubation break unless they have reached an impasse. Their definition of “impasse” is not precise, but most of us know the difference between a speed bump and a brick wall. Here’s what matters: Knock off and play a videogame too soon and you get nothing.

  It’s unlikely that scientists will ever give us specific incubation times for specific kinds of problems. That’s going to vary depending on who we are and the way we work, individually. No matter. We can figure out how incubation works for ourselves by trying out different lengths of time and activities. We already take breaks from problem solving anyway, most of us, flopping down in front of the TV for a while or jumping on Facebook or calling a friend—we take breaks and feel guilty about it. The science of insight says not only that our guilt is misplaced. It says that many of those breaks help when we’re stuck.

  When I’m stuck, I sometimes walk around the block, or blast some music through the headphones, or wander the halls looking for someone to complain to. It depends on how much time I have. As a rule, though, I find the third option works best. I lose myself in the kvetching, I get a dose of energy, I return twenty minutes or so later, and I find that the intellectual knot, whatever it was, is a little looser.

  The weight of this research turns the creeping hysteria over the dangers of social media and distracting electronic gadgets on its head. The fear that digital products are undermining our ability to think is misplaced. To the extent that such diversions steal our attention from learning that requires continuous focus—like a lecture, for instance, or a music lesson—of course they get in our way. The same is true if we spend half our study time on Facebook, or watching TV. The exact opposite is true, however, when we (or our kids) are stuck on a problem requiring insight and are motivated to solve it. In this case, distraction is not a hindrance: It’s a valuable weapon.

  As for the kid in the auditorium on the morning of my presentation, I can’t know for sure what it was that helped him solve the Pencil Problem. He clearly studied the thing when I drew those six pencils side by side on the chalkboard—they all did. He didn’t get it right away; he was stuck. And he had several types of incubation opportunities. He was in the back with his friends, the most restless part of the auditorium, where kids were constantly distracting one another. He got the imposed break created by the SEQUENC_ puzzle, which held the audience’s attention for a few minutes. He also had the twenty minutes or so that passed after several students had drawn their first (and fixed) ideas, attempting to put all the triangles onto a flat plane. That is, he had all three types of the breaks that Sio and Ormerod described: relaxation, mild activity, and highly engaging activity. This was a spatial puzzle; any one of those could have thrown the switch, and having three is better than having just one, or two.

  Let’s reset the problem, then: Given six identical pencils, create four equilateral triangles, with one pencil forming the side of each triangle. If you haven’t solved it already, try again now that you’ve been at least somewhat occupied by reading this chapter.

  Got the answer yet? I’m not going to give it away, I’ve provided too many hints already. But I will show you what the eleven-year-old scratched on the board:

  Take that, Archimedes! That’s a stroke of mad kid-genius you won’t see in any study or textbook, nor in early discussions of the puzzle, going back more than a hundred years. He incubated that one all on his own.

  * * *

  *1 Here’s a famous one that used to crease the eyebrows of my grandparents’ generation: A doctor in Boston has a brother who is a doctor in Chicago, but the doctor in Chicago doesn’t have a brother at all. How is that possible? Most people back then just assumed that any doctor must be a man, and thus came up with tangled family relations based on that mental representation. The answer, of course, is that the doctor in Boston is a woman.

  *2 You find yourself in a stadium, in front of a crowd, a pawn in a cruel life-or-death game. The stadium has two closed doors, a guard standing in front of each one. All you know is that behind one door is a hungry lion, and behind the other is a path out of the stadium—escape. One guard always tells the truth, and the other always lies, but you don’t know which is which. You have one question you can ask of either guard to save your life. What’s the question?

  Chapter Seven

  Quitting Before You’re Ahead

  The Accumulating Gifts of Percolation

  I think of incubation, at least as scientists have described it, as a drug. Not just any drug, either, but one that’s fast-acting, like nicotine, and remains in the system for a short period of time. Studies of incubation, remember, have thus far looked almost exclusively at short breaks, of five to twenty minutes. Those quick hits are of primary interest when investigating how people solve problems that, at their core, have a single solution that is not readily apparent. Geometric proofs, for example. Philosophical logic. Chemical structures. The Pencil Problem. Taking an “incubation pill” here and there, when stuck, is powerful learning medicine, at least when dealing with problems that have right and wrong answers.

  It is hardly a cure-all, though. Learning is not reducible to a series of discrete puzzles or riddles, after all; it’s not a track meet where we only have to run sprints. We have to complete decathlons, too—
all those assignments that require not just one solution or skill but many, strung together over time. Term papers. Business plans. Construction blueprints. Software platforms. Musical compositions, short stories, poems. Working through such projects is not like puzzle solving, where the solution suddenly strikes. No, completing these is more like navigating a labyrinth, with only occasional glimpses of which way to turn. And doing it well means stretching incubation out—sometimes way, way out.

  To solve messier, protracted problems, we need more than a fast-acting dose, a short break here and there. We need an extended-release pill. Many of us already take longer breaks, after all—an hour, a day, a week, more—when working through some tangled project or other. We step away repeatedly, not only when we’re tired but often because we’re stuck. Part of this is likely instinctive. We’re hoping that the break helps clear away the mental fog so that we can see a path out of the thicket.

  The largest trove of observations on longer-term incubation comes not from scientists but artists, particularly writers. Not surprisingly, their observations on the “creative process” can be a little precious, even discouraging. “My subject enlarges itself, becomes methodized and defined, and the whole, though it be very long, stands almost complete and finished in my mind, so that I can survey it, like a fine picture or a beautiful statue, at a glance,” reads a letter attributed to Mozart. That’s a nice trick if you can pull it off. Most creative artists cannot, and they don’t hesitate to say so. Here’s the novelist Joseph Heller, for example, describing the circumstances in which valuable ideas are most likely to strike. “I have to be alone. A bus is good. Or walking the dog. Brushing my teeth was marvelous—it was especially so for Catch-22. Often when I am very tired, just before going to bed, while washing my face and brushing my teeth, my mind gets very clear … and produces a line for the next day’s work, or some idea way ahead. I don’t get my best ideas while actually writing.”