Creative problem-solving is a free-for-all, as creative problem-solvers know.
It's toilsome work that British psychologist Graham Wallas said, in his 1926 book The Art of Thought, unfolds in four stages:
Preparation. The problem-solver acts like a hunter/gatherer, finding and grabbing materials she can use to construct new ideas.
Incubation. The problem-solver takes an indefinite time out. "The period of abstention may be spent either in conscious mental work on other problems, or in a relaxation from all conscious mental work," Wallas says.
Illumination. The problem-solver arrives at the eureka moment. That moment, Wallas says, is "the culmination of a successful train of association, which may have lasted for an appreciable time, and which has probably been preceded by a series of tentative and unsuccessful trains."
Verification. The problem-solver hunkers down to serious work "in which the results of the inspiration are verified and the consequences deduced."
The four-fold process may be serial, but creative problem-solving isn't, Wallas says.
Creative problem-solving proceeds like music, with wandering and overlapping parts.
"In the daily stream of thought these four different stages constantly overlap each other as we explore different problems. Even in exploring the same problem, the mind may be unconsciously incubating on one aspect of it, while it is consciously employed in preparing for or verifying another aspect."