A Mathematical Law of Emotions ALIN

The psychological dynamics exists if there is a consciousness capable of discovering it. Therefore, the psychological complexity is discernible to the consciousness despite the existence of its filters. The identification of the psychological mechanisms presupposes the knowledge of the reason for the existence of psychological components. The psychological system is endowed with specific programs, functioning on the basis of certain interpretation languages which are capable of assigning optimally the psychological resources and also of preserving its components. There is such a program which supports the dynamics of emotions. The emotions mentally translate a present failed state into a satisfied state. These are attenuated by the adjustment mechanism of the psychological experience as defense mechanism. Taking into account the capacity of emotions to describe tensional states, the mathematical approach starts from the partial differential equation of the tensional psychological dynamics [14]. The separated solutions of this equation can be expressed in certain coordinate systems. The capacity of the coordinate systems to maintain the equation mentioned above leads to the idea that these define in fact the emotional mechanism which has to preserve the tensional psychological state. The mathematical law of emotions was obtained in such a way that the coordinate systems preserve the Helmholtz type equation. Key–Words: Coordinate systems, Emotion, Mediated reality, Subjective reality, Symmetry group, Symmetry operators. 1 The Support of the Psychological Defense Mechanism The dynamics of the psychological experience records deviations from an optimal register which has to favour the transformation of the personality towards the saturation formulae. At the psychological level, the internalisation of the references develops the entropy capacities with destructive and restoration valences. The transformation of the inner representation into behaviour acts dissociates the reference type reality in the subjective reality as an image of a self – created scenario and in the mediated reality which has to maintain the self – created scenarios. The alteration of the subjective reality inhibits the dynamics of the personality but it activates the psychological resources, directing them towards the maintaining of the affected subjective reality. The formulae of the psychological structuration pressupose the existence of certain equilibriums between the elements of the mediated reality which necessitate the existence of a restoration and self generation capacity. The deletion of the self generation capacity as an effect of self – satisfaction determines the activation of certain germination processes of the elements of subjective and mediated reality. At the level of the subjective reality, the appearance of the unspecific contents involves an entire affective emotional regression caused by the priority of their interpretation. Moreover, the subjective reality changes into a potential reality determined by the approach of identifying of certain specifics which do not exist! The lack of identification of the authentic subjective reality engages the psychological system in the rebuild approach but without the above mentioned elements. If the approach becomes effective, the subjective reality will be changed into an altered mediated reality which does not maintain the self – created scenarios. The chance of restoration consists in the act of maximal dissociation of the altered subjective reality, followed by the correct interpretation of the specific elements and their structuration in the class of subjective reality. The persistence of the subjective realities amplifies the inner communication up to saturation. The subjective reality and the mediated reality define the interpretative elements of the pure desire (personal) and of the negotiated desires (resulted and interpreted from the communication with the environRECENT ADVANCES in NEURAL NETWORKS, FUZZY SYSTEMS & EVOLUTIONARY COMPUTING ISSN: 1790-5109 60 ISBN: 978-960-474-195-3 ment). The psychological system has certain specific codification resources which assign a psychological experience to each element of the subjective and mediated reality. The dynamics of the psychological experience is determined by the changes of the elements of the two types of realities. The using of the realities, subjective and mediated, is determined by the commutators supervised by the sensors of detection and transformation of the psychological tonus not used in needs [14]. The reason for the existence of the psychological defense mechanism [1], [2], [3], [6], [7], [8], [9] is given by the presence of a dynamics of psychological experience which has to be adjusted in the integrity area of the psychological system. The adjustment is done by choosing certain languages which change the elements of the realities, subjective and mediated, into modulators of psychological experience more accessible for the psychological system. But the psychological defense mechanism is not in any way the magic element which generates the psychological dynamics. Simultaneously with the dynamics of the subjective and mediated realities, there exists a dissonant reality between the final act and the initial one, which functions virtually and generates new commutators or uses the commutators of the elements of reality. The commutators, as interpretative devices, mediate the relation between the cognitive dissonance and the organic behaviour retort. These are in fact the interpretative equalizing languages of these two acts. The effective overlapping is realized by the emotional act which constitutes the support for the psychological defense mechanism. The invincibility of the psychological system is explained through its endowment with invariant elements which maintain the antagonistic constructions, having for their main task the assurance of the functionality of autonomy. The dynamics of the situations shows forms of the psychological defense mechanism meant for the adjustment of the psychological experience. However, all the psychological mechanisms constitute devices of psychological integrity. The emotional act constitutes a mechanism of the psychological availability which has the capacity to eliminate the discrepancy between the image of the satisfied desire and the present psychological image. This one is in fact a transformation act of a present psychological state into a future psychological state. The dissociation of the experiential dowry into essential facts and detail type facts is noticed by the psychological system in the conscious and the unconscious plane. The filters of consciousness are incapable of identifying the logic of the essential, which is additionally constituted by the elements of mediated reality that hide the discernible logic of the emotional poles specific to subjective reality. The asymmetric orientation of the emotional act towards the future shows its optimistic facet, which is discernible to the unconscious state. Moreover, the emotional act is specialized, at the level of the unconscious state, in identifying the essential facts. The crystallization of the personality is realized through the acting of the essential references which endow the psychological system. The activation is produced through the experiential act. The experiences generate tensional states and these are determined by desires. The emotion as a support of desire maintains the tensional states. Therefore, the emotion manifests itself as a tensional psychological state and as a mechanism in which the transformations of the parameters of the psychological dynamics have to preserve the tensional state. The main consequence of this statement results in the existence of two laws: one for the tensional psychological dynamics (see the equation (1)) and the other for emotions. Both equations must be preserved by the transformations of the parameters of the psychological dynamics which define in fact the emotional mechanism. In the following chapters we will determine and analyze the laws of the emotional mechanism and the law of emotions. 2 A Mathematical Theory of Emotional Mechanism The equation (see [13], [14])