This chapter tries to establish a crucial difference in the psychoanalytical work: the difference of vertex between the state of mind of the psychoanalyst and the state of mind of the analysand and its relations to intuition in apparently opposed states of mind, dreaming and awake, and the caesura between those states. It is about searching for a well-succeeded psychoanalytical language: a language derived from the use of intuition to describe the emotional turbulence and the transformations caused by the meeting of different vertices. Bion (1970) named this language the Language of Achievement. The psychoanalyst attempts to create such working language through the use of his intuition, trying to put what it informs through his imagination. It means to allow himself to develop imaginative conjectures and rational conjectures.