There have been many claims of dreams enabling individuals to obtain insight about their emotional and interpersonal life (e.g.,Freud, 1953/1900; Rycroft, 1979; Blechner, 2001). However, much of the evidence here is anecdotal, or based on case-studies, and scientific investigation is difficult. There have also been claims about scientific discoveries being derived from dream experiences (Barrett, 1993), for example, that Kekulé's dream or vision of “whirling snakes” led him to insight regarding the structure of the Benzene ring, and that a dream of Mendeleev led him to his structure for the periodic table of the elements (Barrett, 2001, with critical account by Baylor, 2001). Whilst it is difficult to validate claims that some scientific insights are attributable to dream experiences, numerous cognitive experiments have been devised to assess the relationship between sleep and insight. Wagner et al. (2004) used a mathematical task, the number reduction task (NRT), which can be solved either by a relatively lengthy calculation method, or by more sudden insight into a hidden rule. In the study initial training on the NRT was followed by 8 h of either nocturnal sleep, or nocturnal wakefulness, or daytime wakefulness. At subsequent retesting, more than twice as many subjects gained insight after sleep than after wakefulness. The authors concluded that sleep, by restructuring new memory representations, facilitates extraction of explicit knowledge, and results in insightful behavior.