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The psychotic part of the personality is seen as a multidimensional mental realm that is fully comprehensible only through intuition and tolerance of approximations, transience, and the notion of infinity. It is suggested that a major differentiating factor between the psychotic and nonpsychotic parts of the personality is the capacity to tolerate the infinite complexity of the human mind. With the use of mathematical concepts, Bion tries to describe the state of mind required of the analyst who endeavors to tread on psychotic territories of the personality. Bion is in effect trying to describe the intensity, violence, and fortitude of the transformation of the emotional experience generated by the psychotic as opposed to the nonpsychotic part of personality. Viewed from this vertex, transference is the path by which the unrepressed and unrepresentable unconscious can evolve and express itself. It is the function by which the individual can live through for the first time aspects of his mental life that have never been experienced. This is illustrated with a number of clinical vignettes highlighting different aspects of our capacity to get in touch with this nonsensuous realm of the psychoanalytic encounter.