Formal foundations for the origins of human consciousness
Résumé
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 consciousmental states have to have different 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 concepts.