Jonah Lehrer uses the example of Bob Dylan to explain creativity from a neuroscience perspective. Dylan was burnt out from his performance schedule, and wanting to quit music, he retired to a cabin in Woodstock to relax and do nothing:

It took a few days to adjust to the quiet of Woodstock. Dylan was suddenly alone with nothing but an empty notebook. And there was no need to fill this notebook – Dylan had been relieved of his creative burden. But then, just when Dylan was most determined to stop creating music, he was overcome with a strange feeling. "It's a hard thing to describe," Dylan would later remember. "It's just this sense that you got something to say." What he felt was the itch of an imminent insight, the tickle of lyrics that needed to be written down. "I found myself writing this song, this story, this long piece of vomit," Dylan said. "I'd never written anything like that before and it suddenly came to me that this is what I should do." Vomit is the essential word here. Dylan was describing, with characteristic vividness, the uncontrollable rush of a creative insight. "I don't know where my songs come from," Dylan said. "It's like a ghost is writing a song." This was the thrilling discovery that saved Dylan's career: he could write vivid lines filled with possibility without knowing exactly what those possibilities were. He didn't need to know. He just needed to trust the ghost.

This "vomit" of insight comes from the left hemisphere of the brain. While the right side is responsible for conscious anaysis, the left side makes subconscious connections, unexpected ones that provide a different perspective on a puzzle or problem, and can come into play when the right side can't solve it. That insight (insight because it's unconscious) depends upon the groundwork laid by the conscious, analytic side of the brain. It doesn't really pop out of nowhere. Again, it's just looking at the same parts of a puzzle, but from new perspectives and seeing new connections.

Interestingly, constraints stimulate the creative process. Lehrer gives the example of poets writing sonnets and haikus, which have strict structural requirements.

Instead of composing freely, poets frustrate themselves with structural constraints. Unless poets are stumped by the form, unless they are forced to look beyond the obvious associations, they'll never invent an original line. They'll be stuck with clichés and conventions, with predictable adjectives and boring verbs. And this is why poetic forms are so important. When a poet needs to find a rhyming word with exactly three syllables or an adjective that fits the iambic scheme, he ends up uncovering all sorts of unexpected connections; the difficulty of the task accelerates the insight process.

So, creativity needs frustration—giving up hope that a solution is possible—to come into play. And apparently, it also involves a relaxing and putting aside of the problem.

It reminds me of sometimes going to sleep without solving a problem and waking up in the morning with the solution in my mind.

It also reminds me of what I've gleaned from the writings of Idries Shah. A student of Shah, Doris Lessing writes,

In a Sufi school you first learn what is being taught and, above all, how. Sufi books are designed to be read differently from our usual habit: quietly, non-argumentatively, willing to absorb what is there, noticing how a question in one part may be answered in another, observing juxtapositions and intimations of the unexpected, above all not interposing screens of 'received ideas' between the author and one's best self.

"Received ideas" point to the rational mind attempting to resolve a problem while the "unexpected" points to the insight of creativity stemming from forming new connections. Note that this enlightenment is not some supernatural phenomenon but instead is the normal process of creativity, of the ability to look at a problem or situation anew.

The approach of reading "quietly, non-argumentatively, willing to absorb what is there" reminds me of Peter Elbow's "The Believing Game".

the believing game is the disciplined practice of trying to be as welcoming or accepting as possible to every idea we encounter: not just listening to views different from our own and holding back from arguing with them; not just trying to restate them without bias; but actually trying to believe them. We are using believing as a tool to scrutinize and test. But instead of scrutinizing fashionable or widely accepted ideas for hidden flaws, the believing game asks us to scrutinize unfashionable or even repellent ideas for hidden virtues. Often we cannot see what's good in someone else's idea (or in our own!) till we work at believing it. When an idea goes against current assumptions and beliefs--or if it seems alien, dangerous, or poorly formulated---we often cannot see any merit in it.

Now, the believing game is not quite the same as Sufism (and to be fair to Elbow, he uses it to counterbalance the dominating "doubting game" in academia). That is, one is not "interposing screens of 'received ideas'"—whether believing or doubting. Instead, one is being open to seeing unexpected connections between ideas. It's a neutral stance rather than a "welcoming" one.

It would be interesting to develop a non-argumentative approach to writing the required argumentative papers in composition with the goal of seeing if creativity is stimulated.