Abstract
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.