A recent experiment led by the German neuroscientist Ullrich Wagner demonstrates the potential for dream states to trigger new conceptual insights. In Wagner’s experiment, test subjects were assigned a tedious mathematical task that involved the repetitive transformation of eight digits into a different number. With practice, the test subjects grew steadily more efficient at completing the task. But Wagner’s puzzle had a hidden pattern to it, a rule that governed the numerical transformations. Once discovered, the pattern allowed the subjects to complete the test much faster, not unlike the surge of activity one gets at the end of a jigsaw puzzle when all the pieces suddenly fall into place. Wagner found that after an initial exposure to the numerical test, “sleeping on the problem” more than doubled the test subjects’ ability to discover the hidden rule.