Illustration: Lee Wolf
The classic problem we talk about—the one that led to the term “thinking outside the box”—is the nine-dot problem. There is an array of three dots by three dots, and the task is to connect all of them with straight-line segments, not using more than four lines or doubling back. This was done by the psychologist Norman Maier in 1931.
What makes this a tough problem is that you tend to see it as a square, and you strongly want to follow the contours. Then, for whatever reason, you start to say, ‘Do we have to stay in the square?’ You realize you can go outside the lines, and then the problem isn’t so hard, and you can solve it.
Sometimes when you are stumped by a problem, it’s because you either saw something that influenced you and led you to follow one pathway, or you have produced some blocks yourself. But when you sleep on it—or wake up in the middle of the night—you’ve broken that context, and that allows you to see things freshly.
But you don’t need to have to go to sleep to get a break. You just have to do something totally different. You need to work on a problem long enough to really understand it, but sometimes you just need to get away from it, take a walk, do something else, and then the solution may come to you.
Then there are cases where creative people want to do something new and different. But if you’ve seen too much of what other people have done, you may be influenced by the way they saw the problem, and you don’t see the new breakthrough solution.
It’s not surprising that breakthroughs in science come from fields where young people get involved, because in some sense, they are not as well informed about what people have done before, and therefore they look at a problem more freshly. I like to think of it as “creative ignorance.” It’s the white-piece-of-paper approach to trying to solve something.