The role of a story
Evocative example of stories and flow as elements of problem solving from Town of Cats, a Haruki Murakami story in the New Yorker. Note: emphasis mine.
He had been regarded as a math prodigy from early childhood, and he could solve high-school math problems by the time he was in third grade. Math was, for young Tengo, an effective means of retreat from his life with his father. In the mathematical world, he would walk down a long corridor, opening one numbered door after another. Each time a new spectacle unfolded before him, the ugly traces of the real world would simply disappear. As long as he was actively exploring that realm of infinite consistency, he was free.
While math was like a magnificent imaginary building for Tengo, literature was a vast magical forest. Math stretched infinitely upward toward the heavens, but stories spread out before him, their sturdy roots stretching deep into the earth. In this forest there were no maps, no doorways. As Tengo got older, the forest of story began to exert an even stronger pull on his heart than the world of math. Of course, reading novels was just another form of escape-as soon as he closed the book, he had to come back to the real world. But at some point he noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of math. Why was that? After much thought, he reached a conclusion. No matter how clear things might become in the forest of story, there was never a clear-cut solution, as there was in math. The role of a story was, in the broadest terms, to transpose a problem into another form. Depending on the nature and the direction of the problem, a solution might be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. It served no immediate practical purpose, but it contained a possibility.