Abstract: The psychological dynamics is governed by the "observable-unobservable" systemic ratio. The psychological insight represented by the (unobservable) psychological soft component obeys the functional models which define the psychological system. The functionality of the psychological system depends on the functionality of psychological instances.
What is essential and what is variable in transactional "challenge-response"? The pointing out of the essential feature presupposes the coming into play of an equivalence class of a ratio in which the engaged resources oppose a certain destructive potential. Technically speaking, in this ratio a certain tolerance of the entropy of psychological measures and a certain capacity to adjust this entropy are involved. This means that different situations could be treated in an equivalent manner. But this fact proves the myth of psychological invincibility! At the conscious level, a new structure is needed, which has to bring out the problematic situations. This structure should have the behaviour of a special consciousness which has to distinguish between the potentials of using its products. The interpretive potential of the conscious instance is recorded by the tensional effort – a weak structure which preserves the equivalence class – mentioned above – specific to a person. The reason for preserving it is to assure the simultaneous functioning of strong and weak psychological structures and, of course, of psychological instances. At the psychological level, the entropy and the adjustment of entropy are assembled in different structures. The structures must be compatible, meaning that these are acting on the basis of certain formulae which have to assure the accurate functioning of the psychological system. The variability of the psychological energy suggests for the unconscious instance equivalence class type structures, functioning on the basis of a constant "anti-entropy/entropy" ratio and for the conscious instance and its peripheral instance, the special type structures functioning on the basis of the "anti-entropy + entropy" formula. The functioning of the psychological system presupposes the existence of a certain control structure of the functioning of psychological instances along predefined formulae.
The approach based on the mathematical theory of invariants clarifies the problem of the nature of the tensional habituation process, the behaviour of the need for psychological stimulation in conditions of psychological equilibrium and the relation between the subjective perception of the psychological tension and the amplitude of the tensional states.
Trying to find a similitude between the physical and the psychological world of the attraction laws, the theory of the germination processes of tensional states is posited.
The future purpose of the mathematical approach is to create an unifying theory between the functionality of the psychological soft and of the physiological hard.


Brief Biography of the Speaker:
Alin Gilbert SUMEDREA, Ph.D in Psychology (1993), Ph.D in Statistics (1993), is Professor and Head of the Department of Psychology, Faculty of Science, Lucian Blaga University of Sibiu, ROMANIA. He is also Head of the Psychological Research Centre, Sibiu, ROMANIA.
The scientific activity is represented by 60 published scientific papers and 9 books. Research activity: 17 finalized research projects. He was director for 5 research projects.
Current research interests include: Applications of differential geometry in psychology; Mathematical modeling of psychological processes.