Mathematics for Psychoanalysis

Geometry will show the soul towards truth …

All the pictures which science now draws of nature and which nature alone seems capable of according with observational fact are mathematical pictures.

Chaos often breeds life, while order breeds habit.

This paper will propose the development of an intense and intimate interaction between mathematicians and psychoanalysts, especially as related to the study of dynamic psychic or mental phenomena and functions. The pursuit of such efforts, which includes the development of dynamic mathematical models, is an extension of efforts being made in most present-day biological sciences.

Mathematical applications to psychoanalytic data will require dialogues between mathematicians and psychoanalysts. The present paper will focus mainly on the applications of mathematics to psychoanalytic phenomena in general and to the psychoanalytic and psychotherapeutic interactions in particular. The discussions that will be developed in these areas are offered as a model for the interaction between mathematicians and all those engaged in studies of dynamic psychic functioning. It is a central contention of this presentation that there are many clinical and theoretical problems in psychoanalysis that have not been properly understood and resolved using present methods of study. Dynamic mathematical approaches are one possible means of generating new levels and forms of understanding with which to resolve many of these issues. There is reason to believe that such efforts will make substantive inroads into the current uncertainties in psychoanalytic thinking.

Some Basic Premises

Three premises form the foundation of the creation of mathematical models of dynamic processes.

First, there is the postulate that mental functioning and phenomena, including conscious and unconscious communicative interactions, as well as psychopathological symptoms at the most elementary level, are psychobiological transactions and expressi