Managing the Project

How does one approach a large, difficult problem? By definition the solution to the problem is ill-defined, and the path to the solution is even more obscure. The poor definition of the problem does not, however, imply the complete lack of operational strategies. It is not sufficient to throw up our hands in despair and go fishing to await divine inspiration. The resolution of difficult problems—and of easy ones—can be facilitated by a coherent strategy. This “rational” nature of problem solving applies to the realm of scientific discovery: . . . However romantic and heroic we find the moment of discovery, we cannot believe either that the events leading up to that moment are entirely random and chaotic. . . . We believe that finding order in the world must itself be a process impregnated with purpose and reason. We believe that the process of discovery can be described and modeled, and that there are better and worse routes to discovery—more and less efficient paths. . . . Purposive activity enhances creative problem solving not only in science, but in nontechnical arenas as well. This chapter discusses a number of strategic issues and techniques for addressing challenging problems. Some failures are productive while others are not. An active failure is one that serves to advance the state of knowledge. Such a result may be used to modify a tentative hypothesis, whether through refinement or outright rejection. Active failures may in turn be classified into two types: definitive or mixed. A definitive failure is a strong result that may be used to overturn a proposition by showing it to be false. To illustrate, consider the question, “Are there stars in our galaxy that are over 15 billion years old?” Suppose that a means were found to give a definitive answer, and the resulting answer was “No.” This type of failure is actually a positive result for the opposite hypothesis. In other words, the negative response is actually a positive confirmation of the query, “Are there no stars in our galaxy over 15 billion years old?” In fact, a statistician might well have begun the investigation with the null hypothesis, “No star in our galaxy is over 15 billion years old.”