Albert Einstein finally hit on the core idea underlying his famous theory of relativity one night after months of intense mathematical exercises. He had given himself a break from the work and let his imagination wander about the concepts of space and time. Various images that came to mind prompted him to try a thought experiment: If two bolts of lightning struck the front and back of a moving train at the same time, would an observer standing beside the track and an observer standing on the moving train see the strikes as simultaneous? The answer, in short, was no. The floodgates in Einsteins mind opened, and he laid down an ingenious description of the universe. With his sudden insight, Einstein turned our conceptions of time and space inside out.

Certainly Einstein would not have reached his brilliant notion without his vast knowledge of physics and his ability to think clearly. But the decisive moment arose from his capacity to imagine physical reality from a perspective no one else had ever tried. Einstein was a master at restructuring problems.

We all know how it feels for a solution to a tough problem to suddenly appear in our mind. The chips fall into place, the lightbulb goes on--and the answer seems so obvious that we are amazed we had not noticed it sooner, which is what creates the Aha! feeling. But what happens in the mind to produce this eureka moment? The answer could help all of us be consummate creators.

Knowledge Can Hinder Discovery
Researchers looking for that answer face a daunting methodological problem: how to enable volunteers to systematically produce insights for investigation. The experience is quite subjective. A new point of view arises from an unconscious shift in perception, and the elements of the problem metamorphose into a solution.

Such insights have nothing in common with a computers step-by-step method of solving problems. They are haphazard. Nevertheless, Janet Metcalfe, a psychology professor at Columbia University, devised one way to capture the leaps of understanding. She encouraged volunteers to wrestle with insight problems and asked them while they were thinking to announce periodically whether they were warm or cold--feeling closer to, or still far away from, a solution. She found that even a second before individuals had eureka moments, they felt just as cold as they had at any other time during the endeavor.

If insights feel utterly unintentional, then what brings us to the right idea, if it is not the power of our willful thinking? Psychology professor Stellan Ohlsson of the University of Illinois at Chicago thinks we begin approaching a problem by creating a mental representation of it--a kind of inner model--that includes only certain salient features. At first, we try to look at the features through the lens of our previous experience, which is natural. Yet our very knowledge can prevent us from seeing the features in a new light. Our thoughts go around in circles. We become frustrated. We waste time reapplying methods we already know to be futile. We get nowhere.

Ohlsson believes this mounting failure is precisely what drives us to restructure a problem. The increasingly tense stalemate initiates unconscious processes that change our mental representation of the problem. We look at the features through a new lens. Suddenly, novel possibilities emerge.

The belief that prior knowledge hinders problem solving invokes a bit of a dilemma, however. Taken to its limits, it means that people who possess the least possible knowledge are in the best position to crack a case. Note that it was Einstein, steeped in complex physics, who hit on the theory of relativity, not a contemporary from another discipline, such as Sigmund Freud. Yet although knowledge and experience in the problem area are indispensable, they can be a hindrance if they become so fixed that they block new ideas. Successful experiments begun as early as the 1920s by Gestalt psychologists Karl Duncker and, later, Abraham Luchins demonstrated that habitual use of familiar objects and problem-solving strategies limits the ways individuals employ them.

In 1998 psychologist Jennifer Wiley, then at the University of Pittsburgh, revived this work with a new study investigating the relation between expertise and blindness to alternatives. In one test she gave subjects three words and asked them to find a single, fourth word that would combine with each of three initial words, creating reasonable concepts. For example, given knife, blue and cottage, they could add cheese--as in cheese knife, blue cheese and cottage cheese.

Half of Wileys subjects were chosen because they indicated they considered themselves to be experts on baseball. The other half did not. Wiley gave the group three words, one of which would combine with the added, common word to create a well-known baseball term. The volunteers saw "plate," "broken" and "rest" and were expected to come up with "home" as the matching word: "home plate" (the baseball term), "broken home" and "rest home."

Wiley then started a second test, presenting the words "plate," "broken" and "shot." This time the target word was "glass," which yielded "plate glass," "broken glass" and "shot glass." The baseball experts had more trouble with this second set of terms than the nonexperts. Apparently the aficionados had become so fixated on the term "plate" because of their affinity for "home plate" that it was harder for them to break free of that construct and come up with "glass" for "plate glass." Their knowledge blocked fresh creative insight.

Taking a Novel Perspective
A related question is whether existing knowledge can prevent a person from creatively defining where the solution to a problem might lie. This parameter is perhaps the most important mental factor in setting the stage for reaching a eureka moment.

To study this notion, we created several kinds of tests. In one case, we set up arithmetic problems and gave them to volunteers to solve. We spelled out a mathematical equation on a computer screen, using virtual matchsticks to form the Roman numerals and operators (+, -, =) in an incorrect equation, such as IV = III - I [see box on opposite page for an example]. Our subjects were to envision a solution in which only one matchstick moved to create a correct equation. They then pressed a button when they thought they had figured out the answer. They found certain problems easy to solve, but others proved considerably harder. The reason, we deduced, was an unconscious block imposed by existing knowledge.

The participants, like most of us, learned in school that solving arithmetic problems is a matter, above all, of manipulating quantities. Most subjects began by moving only the matchsticks that changed the numbers, for example, by taking away the first matchstick forming the "one" in the Roman numeral IV, changing it to V. This strategy worked with certain problems but failed for others. In the failed cases, the problems could be solved only by moving a matchstick that changed an operator, for example, by taking away the top matchstick in =, leaving a minus sign. The ingrained knowledge that the operators of an equation should remain unchanged brought most of our participants to a standstill. Only when they changed their perspective about where the solution might lie did they open up new possibilities for solving what had seemed to be an intractable problem.

We also measured the eye movements the subjects made while working. At the outset, they looked longer and more often at the numbers, paying almost no attention to the operators. Once they realized that a problem seemingly could not be solved by manipulating the quantities, their eye movements typically slowed. Some people would stare at the same spot on the screen for five to 10 seconds, whereas normally their eyes changed fixation points about three times a second. These people were staring into a blind alley.

We could tell successful problem solvers from unsuccessful ones merely by analyzing their gaze patterns. Those who stared longest at the numbers failed. Those who looked longer at the operators figured out the answer sooner or later--even though they, too, felt at some point that the problem was impossible. The success rates and gaze times both provided evidence for the idea that insight comes about through unconscious processes.

The Right Hemisphere Solution
Researchers are also examining the brains structures to learn how we reach insights. This work is difficult because the standard instruments of cognitive neuroscience, such as electroencephalography and functional magnetic resonance imaging, measure neuronal processes that last from a few milliseconds to a few seconds. Solving problems often takes minutes or hours. Furthermore, many different cognitive processes are in play at once. Investigators therefore use indirect methods to infer which brain regions help to restructure problems and generate insight.

Cognitive neuroscientists Mark Jung-Beeman and Edward Bowden of Northwestern University recently probed the question of whether both halves of the brain are equally involved. For most people, the left hemisphere is primarily responsible for conscious processing of speech, and the right hemisphere takes care of the unconscious perception of space. (Recent research has shown that this crude division varies for many people, but some partitioning of labor does seem to exist.)

Jung-Beeman and Bowden assumed that step-by-step problem solving took place mainly in the left hemisphere, through the conscious application of logical rules, which would rely on deliberate language. The right hemisphere, they figured, played a critical role in solving insight problems, which require restructuring--a spatial task. Individuals would experience a eureka moment only when the right hemisphere sent the solution to the left hemisphere, thereby putting the solution into discernible terms.

To start, subjects had to try to solve various insight problems. The scientists recorded which exercises each person failed to solve. They then exploited the fact that the left eye sends its images to the right hemisphere and the right eye to the left hemisphere. They sat each subject in front of a computer and controlled which eye could see the screen. They briefly flashed the solution to an insight problem the person had failed. Sometimes the solution was shown only to the right eye, sometimes only to the left eye. The subjects perceived the solutions much more frequently when they were seen by the left eye and thus the right hemisphere. Apparently the unconscious processes that lead to insight tend to take place in the right brain.

Sleep and Good Cheer
As investigators learn more about what is happening in the brain during the exact moment of insight, all of us will want to know what we can do to maximize the conditions that allow us to have brilliant thoughts. Clinically proven advice might be a while in coming. Yet anecdotal work suggests that some simple steps can raise our chances.

You do have to start with sufficient knowledge to solve your problem. Without it, Einstein would not have succeeded. Then, if you have indeed been working on a problem for a long time and are stuck, get away from it. Take a break. A nap would be even better. Many studies have shown that important insights come in dreams or daydreams or follow short naps. The famous example often cited is of German chemist Friedrich August Kekulé von Stradonitz, who in the late 1800s is reported to have said he discovered the round shape of the benzene ring after working in the lab for hours, then dreaming of a snake swallowing its own tail. Commercial production of benzene sparked the rise of the fossil-fuel industry.

Neuroendocrinologist Ullrich Wagner of the University of Luebeck in Germany has demonstrated that sleep promotes insight. He gave subjects number sequences and two logical rules for manipulating them. But the sequences could also be solved by using a simple hidden rule that the test takers might discover as they worked. The examinees practiced problems and were then told to take a break before they had discovered the trick. Some slept during the interlude, and others did not. When they returned to do more problems, the individuals who had slept found the "hidden rule" much more often than subjects who had not. Wagner attributes the improvement to a process of consolidation of information that takes place in the hippocampus during sleep; new data are connected with knowledge already in memory.

If you cannot take a nap during the workday, it is often helpful to let your thoughts wander. Or break away briefly and do something that puts you in a good mood--have an ice cream cone or play ping-pong. Plenty of research has shown that a positive attitude helps the unconscious brain look at a problem from a different angle, improving your chances of solving it.