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In the dissipative quantum model of brain memory recording is modeled as coherent condensation of certain quanta in the brain ground state. The formation of finite size correlated domains allows the organization of stored information into hierarchical structures according to the different life-times of memories and the size of the corresponding domains. The openness of the brain to the external world (dissipation) implies the doubling of the brain system degrees of freedom. The system obtained by doubling, the Double, plays the role of the bath or environment in which the brain is permanently embedded. It is suggested that conscious as well as unconscious activity may find its root in the permanent dialogue of the brain with its Double.