In a 2004 paper published in Nature, Jan Born, a neuroscientist at the University of Lübeck, described the following experiment:
A group of students was given a tedious task that involved transforming a long list of number strings into a new set of number strings. This required the subjects to apply a painstaking set of algorithms.
However, Born had designed the task so that there was an elegant shortcut, which could only be uncovered if the subjects saw the subtle links between the different number sets. When left to their own devices, less than 25 percent of people found the shortcut, even when given several hours to mull over the task.
When Born allowed people to sleep between experimental trials, they suddenly became much more clever: 59 percent of all participants were able to find the shortcut. Born argues that deep sleep and dreaming “set the stage for the emergence of insight” by allowing us to mentally represent old ideas in new ways.