In this brief note, we focus attention on a possible implementation of a basic hysteretic pattern (the Preisach one), suitably generalized, into a formal model of unconscious-conscious interconnection and based on representation of mental entities by m-adic numbers.

In the framework of p-adic analysis (the simplest version of analysis on trees in which hierarchic structures are presented through ultrametric distance) applied to formalize psychic phenomena, we would like to propose some possible first hypotheses about the origins of human consciousness centered on the basic notion of time symmetry breaking as meant according to quantum field theory of infinite systems. Starting with Freud's psychophysical (hydraulic) model of unconscious and conscious flows of psychic energy based on the three-orders mental representation, (...) the emotional order, the thing representation order, and the word representation order, we use the p-adic (treelike) mental spaces to model transition from unconsciousness to preconsciousness and then to consciousness. Here we explore theory of hysteresis dynamics: conscious states are generated as the result of integrating of unconscious memories. One of the main mathematical consequences of our model is that trees representing unconscious and conscious mental states have to have dierent structures of branching and distinct procedures of clustering. The psychophysical model of Freud in combination with the p-adic mathematical representation gives us a possibility to apply (for a moment just formally) the theory of spontaneous symmetry breaking of infinite dimensional field theory, to mental processes and, in particular, to make the first step towards modeling of interrelation between the physical time (at the level of the emotional order) and psychic time at the levels of the thing and word representations. Finally, we also discuss some related topological aspects of the human unconscious, following Jacques Lacan's psychoanalytic ideas. (shrink)

In continuation of what has been said in the first part of this two-part paper, herein we present further considerations on symbolism, reconsider some related psychodynamic case reports with some possible variants about their interpretations, and will apply what is said to some further speculations on mathematical symbolism and thought. In this second part, we continue with the numeration of the first part Σύμβολου, 1.

This is the first of a two-part paper in which I would like to propose some possible hypotheses on the early origins of symbolic function, which is the most typical feature of human being, based on disavowal mechanism. Briefly recalling the main stages of the history of symbolism, it will be possible to lay out many of its theories within the framework that we wish to outline with this work, this first part of which is mainly concerned with the basic (...) psychodynamic notion of disavowal and its possible applications, above all in regard to fetishism. (shrink)