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The authors begin by drawing attention to the problem of the transition from the biological to the psychic, noting that Freud himself, with his background in the neurosciences, grappled with it throughout his career. Certain recent paradigms more commonly applied to the natural sciences, such as in particular chaos and complexity theory, can in their view prove fruitful in psychoanalysis too, and it is shown how these notions are inherent in some of Freud's conceptions. The unconscious is stated to operate like a neural network, performing the kind of parallel processing used in the computing of highly complex situations, whereas the conscious mind is sequential. Dreams, in the authors’ opinion, are organisers of the mind, imparting order to the turbulence of the underlying wishes and unconscious fantasies and structuring them through the dream work. Through dreams, the structured linearity of conscious thought can emerge out of the non-linear chaos of the drives. The dream's navel can be seen as the chaotic link, or interface, between the unconscious wish, which constitutes an attractor, and the conscious thought. The attractor may be visualised as having an hourglass or clepsydra shape, the narrow section being the dream's navel, and, being the same at any scale of observation, has the property of fractality.