A man in a town married twenty women. There have been no divorces or annulments, and everyone in question is still alive and well. The man is not a bigamist, and he has broken no laws. How is this possible?

This is the so-called marrying-man problem, which psychologists often use to study creative insight: the process by which we suddenly figure out the answer to something that had previously stumped us. A problem makes no sense at first. But then we turn it around in our minds and, presto, the answer comes. So, naturally, Mark Beeman, a cognitive neuroscientist at Northwestern University, who studies insight and creativity, likes to pose questions like this one to applicants who want to work in his lab. (The answer to this particular conundrum is that the man is a priest.)

Beeman studies insight because it’s a key component in how creativity works—the main subject of his research. Creativity is the whole process of how we come up with new ideas; insight is just a step along the way, albeit an important one. A composer who writes a new, beautiful song has done something creative; the moment when she realized that she could end it on a minor chord was insight. In general, creativity seems to come when insight is combined with the hard work of analytical processing. A person can’t discover the theory of general relativity in a dream if he isn’t a physicist who’s done some heavy thinking about the subject beforehand.

In the field of psychology, there’s long been a certain haziness surrounding the definition of creativity, an I-know-it-when-I-see it attitude that has eluded a precise formulation. During our conversation, Beeman told me that he used to be reluctant to tell people what his area of study was, for fear of being dismissed or misunderstood. What, for instance, crosses your mind when you think of creativity? Well, we know that someone is creative if he produces new things or has new ideas. A choreographer, an artist, a writer, a scientist, or a mathematician with a novel discovery—these are the creatives, the people who bring something new into the world. And yet, as John Kounios, a psychologist at Drexel University who collaborates frequently with Beeman, points out, that view is wrong, or at least not entirely right. “Creativity is the process, not the product,” he says.

To illustrate, Beeman offers an example. Imagine someone who has never used or seen a paperclip and is struggling to keep a bunch of papers together. Then the person comes up with a new way of bending a stiff wire to hold the papers in place. “That was very creative,” Beeman says. On the flip side, if someone works in a new field—Beeman gives the example of nanotechnology—anything that he produces may be considered inherently “creative.” But was the act of producing it actually creative? As Beeman puts it, “Not all artists are creative. And some accountants are very creative.”

Insight, however, has proved less difficult to define and to study. Because it arrives at a specific moment in time, you can isolate it, examine it, and analyze its characteristics. “Insight is only one part of creativity,” Beeman says. “But we can measure it. We have a temporal marker that something just happened in the brain. I’d never say that’s all of creativity, but it’s a central, identifiable component.” When scientists examine insight in the lab, they are looking at what types of attention and thought processes lead to that moment of synthesis: If you are trying to facilitate a breakthrough, are there methods you can use that help? If you feel stuck on a problem, are there tricks to get you through?

In a recent study, Beeman and Kounios followed people’s gazes as they attempted to solve what’s called the remote-associates test, in which the subject is given a series of words, like “pine,” “crab,” and “sauce,” and has to think of a single word that can logically be paired with all of them. They wanted to see if the direction of a person’s eyes and her rate of blinking could shed light on her approach and on her likelihood of success. It turned out that if the subject looked directly at a word and focussed on it—that is, blinked less frequently, signalling a higher degree of close attention—she was more likely to be thinking in an analytical, convergent fashion, going through possibilities that made sense and systematically discarding those that didn’t. If she looked at “pine,” say, she might be thinking of words like “tree,” “cone,” and “needle,” then testing each option to see if it fit with the other words. When the subject stopped looking at any specific word, either by moving her eyes or by blinking, she was more likely to think of broader, more abstract associations. That is a more insight-oriented approach. “You need to learn not just to stare but to look outside your focus,” Beeman says. (The solution to this remote-associates test: “apple.”)

As it turns out, by simply following someone’s eyes and measuring her blinks and fixation times (how long she looks at something before either looking away or closing her eyes), Beeman’s group can predict how someone will likely solve a problem and when she is nearing that solution. Although that’s not an entirely new ability—the study replicates earlier work that relied on fMRI and EEG, which found similar patterns and showed that both the moment of insight and the preparatory phases are marked by distinct neural patterns, and it builds on a 2012 study of attention and verbal problem solving—it’s a more easily observable and potentially trainable approach. “This is less anatomical, but it’s more directly linked to attention,” Beeman says. “Your state of attention both before you get a problem and when you’re solving it matters.”

That’s an important consideration for would-be creative minds: it helps us understand how distinct patterns of attention may contribute to certain kinds of insights. I’ve written before about the link between caffeine and creativity. This work suggests that being caffeinated may facilitate the analytical part of the creative process but impede the insight-finding part, by honing your focus but dulling your ability to think more diffusely.

It suggests, too, that timing is important. If you aren’t focussed when the problem is presented, for instance—that is, if your attention is already diffuse when “pine,” “crab,” and “sauce” first flash across the screen—you may find it harder to reach an insightful solution because you haven’t done enough conscious, analytical processing. You need to take the time to understand all aspects thoroughly before you try to facilitate your mind-wandering or daydreaming. In other words, don’t go for a walk or hop in the shower or take a nap immediately after getting a new problem. First, reach for that cup of coffee to make sure you don’t miss any details.

Now Beeman and his colleagues are trying to see if their findings apply equally to people who have already accomplished something creative: Are the attention patterns that they’ve identified telling us something about creative achievement and not just creative potential, or, more specifically, the potential to come up with insightful solutions? To accomplish this, they are testing people who are advanced in fields that are traditionally considered creative and in fields that can be either creative or analytic, depending on how you approach them, like the creative arts, architecture, and advertising. What they want to know is whether these advanced-career individuals show the same creative-processing patterns as undergraduates. “We can’t study how they got creative,” Beeman says. “But we can see how their brains work.”