Knocking on Heaven's Door - Lisa Randall [193]
In my colleague Marc Kamionkowski’s words, it’s “OK to be ambitious and futuristic.” But the trick is still to determine realistic goals. An award-winning business student present at the Creativity Foundation event I participated in remarked that the recent successful economic growth that had escalated into an economic bubble stemmed in part from creativity. But he noted too that the lack of restraint also caused the bubble to burst.
Some of the most groundbreaking research of the past exemplifies the contradictory impulses of confidence and caution. The science writer Gary Taubes once said to me that academics are at the same time the most confident and the most insecure people he knows. That very contradiction drives them—the belief that they are moving forward coupled with the rigorous standards they apply to make sure they are right. Creative people have to believe that they are uniquely placed to make a contribution—while all the time keeping in mind the many reasons that others might have already thought of and dismissed similar ideas.
Scientists who were very adventuresome in their ideas could also be very cautious when presenting them. Two of the most influential, Isaac Newton and Charles Darwin, waited quite a while before sharing their great ideas with the outside world. Charles Darwin’s research spanned many years, and he published the Origin of Species only after completing extensive observational research. Newton’s Principia presented a theory of gravity that was well over a decade in development. He waited to publish until he had completed a satisfactory proof that bodies of arbitrary spatial extent (not just pointlike objects) obey an inverse square law. The proof of this law, which says gravity decreases as the square of the distance from the center of an object, led Newton to develop the mathematics of calculus.
It sometimes takes a new formulation of a problem to see it the right way and to redefine the boundaries so you can find a solution where, on the surface, none appears possible. Perseverance and faith often make a big difference to the outcome—not religious faith but faith that a solution exists. Successful scientists—and creative people of all kinds—refuse to get stuck in dead ends. If we can’t solve a problem one way, we’ll seek an alternative route. If we reach a roadblock, we’ll dig a tunnel, find another direction, or fly over and get the lay of the land. Here’s where imagination and superficially crazy ideas come in. We have to believe in the reality of an answer in order to continue, and to trust that ultimately the world has a consistent internal logic that we might eventually discover. If we think about something from the right perspective, we can often find connections that we would otherwise miss.
[ FIGURE 81 ] The nine-dots problem asks how to connect all the dots using only four segments without lifting your pen.
The expression “thinking outside the box” doesn’t come from getting outside your work cubicle (as I once thought might be the case), but from the nine-dots problem, which asks how to connect nine dots with four lines without lifting your pen (see Figure 81). No solution to the ninedots problem exists if you have to keep your pen inside the confines of the square, but no one told you that was a requirement. Going “outside the box” yields the solution (see Figure 82). At this point you might realize you can reformulate the problem in a number of other ways too.