Knocking on Heaven's Door - Lisa Randall [194]
[ FIGURE 82 ] Possible creative solutions to the nine-dots problem include “thinking outside the box,” folding the paper so the dots align, or using a very thick pen.
These solutions aren’t cheating. They would be only if you have additional constraints. Education unfortunately sometimes encourages students not only to learn how to resolve problems, but also to second-guess the teacher’s intention—narrowing the range of correct answers and potentially also the students’ minds. In The Quark and the Jaguar,73 Murray Gell-Mann cites Washington University physics professor Alexander Calandra’s “Barometer Story,”74 in which he tells of a teacher who wasn’t sure he should give a student credit. The teacher had asked his students how they might use a barometer to determine the height of a building. This particular student answered that you could attach a string to the barometer, lower it to the ground, and find out how long the string was. When he was told to use physics, he suggested measuring the time it took for it to fall from the top of the building, or measuring the shadow at a known time of day. The student also volunteered the nonphysics solution of offering the superintendent the barometer in exchange for being told the height of the building. These answers might not have been what the teacher was looking for. But the student astutely—and humorously—recognized that the teacher’s constraints weren’t part of the problem.
When other physicists and I started thinking about extra dimensions of space in the 1990s, we not only went outside the box, we went outside three-dimensional space itself. We thought of a world in which the very stage in which we solved the problems was bigger than we had originally assumed. In doing so, we found potential solutions to problems that had plagued particle physicists for years.
Even so, research doesn’t arise in a vacuum. It is enriched by the many ideas and insights that others have thought of before. Good scientists listen to one another. Sometimes we find the right problem or solution just by very carefully listening to, observing, or reading someone else’s work. Often we collaborate to bring in different people’s talents, and also to keep ourselves honest.
Even if everyone wants to be the first to solve an important problem, scientists still learn from and share with one another and work on common topics. Occasionally other scientists say things that contain the clues to interesting problems or solutions—even unwittingly. Scientists might have their own inspiration, but they will often also exchange ideas, work out the consequences, and make adjustments or start again if the original idea doesn’t work. Imagining new ideas and keeping some while shooting others down is our bread and butter. That’s how we advance. It’s not bad. It’s progress.
One of the most important roles I can play as an adviser to graduate students is to be alert to their good ideas, even when they haven’t yet learned how to express them—and to listen when students find loopholes in my suggestions. This back-and-forth is perhaps one of the best ways to teach—or at least foster—creativity.
Competition plays an important role as well—in science as well as in most any other creative endeavor. In a discussion of creativity, the artist Jeff Koons simply told those of us in the room that when he was young, his sister did art—and he realized that he could do it better. A young filmmaker explained how competition encourages him and his colleagues to absorb each other’s techniques and ideas and thereby refine and develop their own. The chef David Chang expressed a similar thought a little more bluntly. His reaction after going to a new restaurant is, “That’s delicious. Why didn’t I think of that?”
Newton waited to publish until his results were complete. But he might also have been wary of his competitor Robert Hooke, who knew about