Baird et al. do a simple experiment demonstrating how mind wandering can facilitate creative incubation, that the basement stuff that is dinking around in the absence focused effort more easily makes novel associations:
Although anecdotes that creative thoughts often arise when one is engaged in an unrelated train of thought date back thousands of years, empirical research has not yet investigated this potentially critical source of inspiration. We used an incubation paradigm to assess whether performance on validated creativity problems (the Unusual Uses Task, or UUT) can be facilitated by engaging in either a demanding task or an undemanding task that maximizes mind wandering. Compared with engaging in a demanding task, rest, or no break, engaging in an undemanding task during an incubation period led to substantial improvements in performance on previously encountered problems. Critically, the context that improved performance after the incubation period was associated with higher levels of mind wandering but not with a greater number of explicitly directed thoughts about the UUT. These data suggest that engaging in simple external tasks that allow the mind to wander may facilitate creative problem solving.