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Carroll, E.J. Houghton, G. (1970). Mathematical Reflections on the Analytic Process. Psychoanal Q., 39:103-118.

(1970). Psychoanalytic Quarterly, 39:103-118

Mathematical Reflections on the Analytic Process

Edward J. Carroll, M.D. and Gerald Houghton


The traditional elements of the psychoanalytic process have been modeled in terms of the block diagram algebra of systems theory. Patient-therapist interactions are interpreted mathematically in terms of a behavior equation in which the rates of response are governed by internally conditioned drives shaped by past experiences and genetic inheritance. These motivating drives are activated by stimuli or drive objects in the current environment and are also influenced by the rate of environmental change and time. Integration of the differential behavior equation provides both conscious and unconscious behavior components, the extent and dynamic interaction of which determine the nature and outcome of the therapeutic process. Patient stability has been classified mathematically by analyzing the time-varying modes of response to be found during analytic therapy. Various approaches to the optimization and quantification of the two-person interactions of psychoanalysis have been suggested in the context of their systems-mathematical analogues.

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