VOLUME: IX NUMBER: 22
AN APPROACH TO THE STUDY OF EMOTIONS AS COMPLEX DYNAMICAL SYSTEMS
Universitat Jaime I
The study of emotions has evolved from an analytical perspective based on linear causality and reductionism. This perspective is now giving way to a new approach that grounds the study of emotions in their complexity. For several decades, proposals have been put forward to study emotion mechanisms as systems (Izard, 1971, 1991). The dynamicity and complexity of emotions have recently been added to this systemic approach, thus allowing the study of emotion mechanisms as dynamical systems. A dynamical system is a unit of functional action made up of multiple interconnected elements that change in time and space (Vallacher & Nowak, 1997). This perspective considers that emotions cannot be understood in isolation from other elements of the mind, as response mechanisms integrated in complex structures. The behaviour of these structures cannot be explained without taking into account the processes of change, time and interdependence (Izard, 1991; Munné, 2005; Velasco, 1999). The present study adopts this new approach in order to pose, rather than solve, further questions, through the analysis of the characteristics of dynamical systems and their possible application to the study of emotion mechanisms.
A dynamical system is structured according to three parameters (Beer, 2000): time, the state of the system at a given moment, and an evolution operator that over time transforms the initial state into another state. As Beer (2000) explains, the particularities of a dynamical system may reveal both continuous or discreet time variables, and both numerical or symbolic, or discreet or continuous state variables, or a hybrid of the two which may have finite or infinite dimensions, depending on the total number of variables required to describe the state of the system. Emotions may be considered to be structured as a dynamical system, their evolution dependent on time, involved in the dynamic of an operator that successively transforms each one of their initial states in accordance with the interaction of the multiple variables required to describe each of their states. But what type of system is an emotion system? How can it be defined? What is the nature of this system?
Greenspan (1991) posits that emotions cannot be analysed in isolation from the relationship from which they were generated; that there is no meaning without a context. Similarly, Damasio (2001) argues that information both internal and external to the organism, by itself plays no part in reasoning and decision-making functions. According to Damasio (2001), the knowledge required for reasoning reaches the mind in the form of representations or images, and its manipulation is what constitutes the act of thinking. Emotions are unleashed once the mental content evaluation process has taken place (Damasio, 2001); in other words, the emotion is activated when the information has been thought about, or interpreted and given a meaning (Lazarus & Lazarus, 2000; Schachter & Singer, 1962). The primary and most influential information is sensation, which awakens the organism, activating it to the reality that surrounds it. In this way, the primary emotion emerges from the basic sensation-thought relationship. Sensations such as accelerated heartbeats, irregular breathing, trembling lips, weakness of the knees or gooseflesh correspond to the emotion of fear, but are not the fear emotion itself. In order for these sensations to become an emotion, they must be mentally represented and thought about. The sensation activates the organism, but this energy does not become emotion until the sensation-thought relationship has been interpreted and acquires meaning. The action is inherent to the sensation, the delimitation of the sensation is inherent to thought. The mind is nourished by meaningful, interpreted action based on external signs. This initially presumes that the emotion can dominate the mind through sensations or through information from outside the consciousness. Emotions however do not belong to this external world, but rather they are activated in its presence and take on their identity once it has been interpreted. Thus, emotion appears as an interpretive system, comprised of meaningful action. According to the second law of thermodynamics, interpretation is subject to entropy, to disorder. Entropy is counter-balanced by the information exchange characteristic of open systems. Interpretation is permanently transformed by experience (negentropy), and at the same time it tends to close in on itself in a self-referential process (entropy). This moving interpretive system is necessarily dialectical.
The interpretation of the sensation-thought relationship does not occur randomly without order; the emotion appears when the interpretation acquires order, as an identity recognised by the mind, a represented identity. Freeman (2000) suggests that this identification process is controlled by consciousness. Consciousness identifies the emotion and its degree of evolution at any given moment. Freeman (2000) understands consciousness as a state of the emotion system that varies with the dynamic of the systemic process and is a unifying link between all the variables in the whole system of the mind. Thus the consciousness represents the identification of the entire state of the emotion system, the framework that gives a sense of unity to the whole system (Freeman, 2000). The first instrument to control the emotion and to find order amongst the fluctuations that dynamise the system is through the identification of the emotion at a higher level. The level of consciousness changes from one state to another because the identity, or the meaning, of the emotion has changed. For this process to make sense, it must be guided in a certain direction, towards somewhere, dialectically. The identity of fear is different from that of love; this is the result of sensations and thought being organised around a principle-guide that gives meaning to the interpretation and allows the experience to be identified as fear or love. A certain order is needed to maintain emotional equilibrium. To maintain the system in this state of equilibrium, neither stability nor instability should predominate. In other words, the system must organise itself in such a way that, by structuring the experiences surrounding an interpretative sense, for instance fear, it can move towards other interpretative senses, for instance love, when the initial sensation is saturated or new conditions make it unstable. According to Powers (1995), underlying this type of organisation is the force to self-regulate the behaviour of the system around its reference values or attractors. Attractors are strange and capricious; they guide the evolution of the system in an unpredictable way, and their freedom/need constantly "attracts" elements that are similar (never the same, never different) to a particular existence (Escohotado, 1999).
Because the attractor is neither intentional nor conscious, it is not a goal (Carver & Scheier, 1998, 2000). Everything a person does, thinks or feels is guided by the force of the attractor, which is the force designed to make sense of experience. The goal however, is guided by values and stimulated by motives, understood as the reasons, or the “why” we act (Locke, 2000). The attractor is the source of motivation, but essentially represents the function of, or the reason for, the action. In systemic terms, the attractor represents the force that guides the direction of the emotion experience at the relational level. Neither is the attractor an objective. For example, the objective of the fear response is to confront a threat; the choice of a response to achieve this objective enables the established goal to be reached in order to resolve the threatening situation. Once the objective has been achieved, fear remains latent as a system that guides the relationship between the internal or external world and the mind, and becomes active when a new situation is interpreted as threatening. Hence, the attractor that guides the fear emotion continues to influence the mind, and is present as one of the references with which to interpret the relation between sensations and information. The attractor, however, can be understood by its effects. Its main effect is to provide cohesion to the structure of meanings, or guide the stability of the system when it faces perturbations. The attractor redirects those perturbed forces of change that move away from the dominant meaning, thus preventing a state of disorder; it forces paths to be taken that guide the interpretation dynamic by clarifying the meanings that arise from all new information that penetrates the system. It is persistent and iterative; it imposes itself as a reference for learning, in such a way that each of the paths it traces is a learning path. As Velasco (1999) states, this dynamic turns the attractor into a mechanism that generates highly stable ordered states, surrounded by instability.
One hypothesis is that the attractor which acts at a higher level of abstraction, shaping the emotion system into a greater organisational hierarchy, is the self. Understood in this way, the ultimate feeling of the emotion system is self-knowledge. From this viewpoint, interpretation is a mechanism of the system that attempts to gain access to the self, which attracts the dialectic process of generating the emergent meaning in the system. The self is the attractor towards which the interpretation of first order human systems would move. But systems are organised in sub-systems that interact with each other and with the environment. Lower order systems have their own attractors. These other attractors possibly represent the force of needs (Grandío, 2005), by shaping subsystems connected in a higher order structure in which the self acts as an interpretive reference. Each system spontaneously generates its own pattern of action, its interpretative order, and is different from the sum of its own parts. This order is generated without any previous planning, and may only be controlled if the self is able to leave the emotion system and observe it without forming part of it.
Because of their interaction, the parts of the system are inseparable. If we analyse the system by breaking it down into its components, our conclusions will deal with the parts and not with the system (Dimitrov, 1999). Sensation cannot be separated from thought if we are to understand the emotion emerging from this relationship. From this unit, the overall activity of each system simultaneously flows in the direction of the higher hierarchical system, and towards the lower hierarchical systems. Each subsystem is a variable of the system that contains it, and to which it adds its properties, forming properties that are not contained in every part. However, each variable bears the qualities of the whole within it. For example, the sensation of increased heartbeats is not fear until it is thought about, although it potentially contains fear. The fear emotion is neither in the sensation described, nor in the thinking about the sensations itself, but the sensation of the heartbeats carries the possibility within it. A set of similar sensations all have the quality of, in this case, fear, and from this potential, they pressurise the system to give them an identical meaning guided by the reference attractor.
The emotions that form part of higher order systems are not only transformed when the properties of the system to which they belong change, but their very transformation also influences the higher levels. The interaction between the numerous variables continuously creates new patterns of action that, when transmitted, affect the path of the system’s overall state. For example, fear interacts with desire to generate a new system of meanings. A feeling of control may emerge from the desire to obtain satisfaction and the fear of losing it, which is defined by parameters other than those of fear and desire, but configured by their qualities. This new feeling is established at a lower order of interpretation to that of fear and desire. However, the feelings of control generate new action patterns that interact with the current patterns in the same and higher levels. The original fear and desire are transformed when they interact and are affected by the new control-based order. The subsystem attractors therefore contribute information for self-knowledge. Yet this may be limited because of the dominance of the emotions through the feelings, and the dominance of the mind through the emotions. This chain of dependencies may present a problem for self-knowledge, by creating an illusion that the self is the feelings, and the external information is the self. Indeed, many of the studies on the self claim that one of the most common ways it can be recognised is by using this external information (Smith & McKie, 1995). The dependence on this mental illusion leads to a distancing from the dynamic of the system. In this context, Freeman (2000) puts forward the hypothesis that the role of the conscience, as a higher level control mechanism, is to prevent precipitated interpretations by regulating the chaos coming into the system. Control of the emotion system involves at least two tasks: on the one hand, mental recognition of the influence in the interpretative process of sensations and learning; and on the other, the identification of the sensation underlying the attractor that guides the emerging meanings in the system.
Actions have their reasons and explanations, but they are emotional (Freeman, 2000, Damasio, 2001). Emotions are configured with their own rationalising dialectic logic, from which the interaction of the structural variables makes up a pattern of global activity. At the same time, this pattern restricts the activity of the variables themselves. The combination of fear and threat may mean survival, but it may evolve towards the meaning of holding on to an achieved social position. Changes in interpretation cause the direction of the system to shift, either towards a new meaning, or towards clarification of the original meaning. To understand the system’s dialectic movement, we should consider three properties: 1.- the extreme sensitivity of the initial conditions; 2.- the stabilising and cohesive force of the meanings, of the dissipative structures; 3.- the fluctuations, governed by the law of entropy, that lead the system to change the links between its components and guide it towards new attractors, thus questioning stability.
An emotion system is sensitive to the initial conditions. These conditions define the system in a state and at the moment in which it is detained by the observer (Velasco, 1999). The state represents the level of meaning reached by the interpretive dynamic, the meaning of the emotion at that moment as it is represented in the mind. Under the impact of a new condition, the whole system may become destabilised and shift towards a new state, forming a path from one state to another. Subsequent changes in the path of the emotion are determined by a state. This path has structure and order; in other words, chaos makes the path traced by the emotion and the new meanings it adopts essential, but it is determined by an underlying order that conditions the dynamic of the system. This order is arranged in a structure that restricts the system’s behaviour according to the patterns that move it regularly, and the rules that establish the way in which it must move.
The determinism of the initial conditions guarantees that the effect of a new condition will be restricted by the rules that dominate the initial state. However it does not guarantee an accurate prediction of the next state with regard to the meaning the emotion adopts. The emotion may give rise to new, lower order emotions with their own emergent patterns or rules. The interaction of the initial state with a new condition may also generate new patterns of action that will involve modification of the original rules, but this type of change is slower. For example, one of the main rules of the emotion system is that all interpretation is rational. This is a higher hierarchical level rule, and therefore is unlikely to transgress when interpreting the new conditions. The initial state conditions the subsequent interpretations to be rational, but does not prevent the possible emergence of new rules, such as the rule of persistence that pressurises to continue the interpretation based on the original meaning. In addition, the image or representation that symbolises the meaning interpreted from the emotion does not always have the same form. Within the same structure, the forms of expression change more flexibly and unpredictably than the underlying structures. If we take cognitive dissonance as an example, we see how dissonant behaviour leads to sensations that are thought of as unpleasant. The interpretation of the new information as tense and unpleasant generates a new order based on the “tension avoidance” rule. Under the “rationalise” behaviour pattern, the system guides new action patterns that obey the reference “tension avoidance” rule. In this way, a dominant rule may act as a guide and condition subsequent responses, but the forms the interpretation of the situation may adopt are extremely varied, and unpredictable even in the short term.
Change cannot be predicted from the initial conditions essentially because the relation between two variables does not only depend on the values the two take, but also on those taken by other system variables, which gives rise to non-linearity and explains the extreme sensitivity of human systems in initial conditions (Kelso, 1995; Schöner & Kelso, 1988). The dynamic of living systems with large numbers of elements has been explained in the theory of organised criticality put forward by Bak and Chen (1991), in which the behaviour of complex systems is characterised by the possibility that small deviations may cause large changes, and large deviations, small changes. But this unpredictability is also due to the fact that initial conditions do not always show emotion variables in a single state. At times, emotions, as system variables, are found in a state known as hysteresis (Kelso, 1995), according to which we may observe fear in two or more states simultaneously. In the case of fear, the moment in which we observe fear tells us what state the emotion is to be found in. If we observe the fear of a person facing an attacker, we may assume that at this moment the fear activated in this state will be defined by the threat to his or her life (state one), but it may also be defined at the same time by the threat to the lives of his or her children (state two), and/or the threat to his virility (state three).
The way system variables behave is similar to that described by Heisenberg in his principle of uncertainty: we can observe the state of fear or its position at a given moment, but we cannot simultaneously establish the speed at which the nature of the fear changes (how much it will alter or how). It is not possible to simultaneously measure how fear changes, and the state of fear. The prediction measures the future state of one of its variables from its initial state or from other variables. As it is not possible to simultaneously measure how the emotion will change from one state to another, the accuracy of this prediction will depend on the stability of the rules that lend cohesive meaning to the emotion. The speed of change is not the same from one emotion to another, nor among the parameters that identify an emotion. Higher order systems, which have more stable structures, change more slowly than those located at lower levels. Likewise, a system that has developed very stable internal structures follows a slower change process than others with more unstable structures. The longer the time period we consider between two states, the more obvious this characteristic of the system becomes, in such a way that the strong relationships between variables mean probability predictions can be made on the evolution of one or another, and the shorter the time separating them, the more accurate the prediction will be. If the structures that hold the system variables together and enable its definition are strong, the system can maintain the same type of behaviour, the same action patterns, over long periods of time. This does not imply that no change occurs, but simply that as it takes place more slowly, it is less perceptible and more difficult to detect.
Stability in the strict sense is not possible, as change is the only stable feature of all human systems. The higher the emotion’s hierarchical level, the more complex it will be. At this level, the emotion is more unstable in the subsystems, but more stable in the dominant system. Human systems are by nature open systems, and it is the inclusion of new information that by tensing the internal structures, causes changes. The more environmental variables there are interacting with the emotion, the greater the likelihood of change in the values that regulate interpretation. The task of the system, as a whole, will be to improve cohesion in the interdependence of its components. This cohesion is brought about by a self-organisation mechanism that manages communication and cooperation within the system (Kossman & Bullrich, 1997). Self-organisation is the management mechanism that brings order out of chaos, by structuring a person’s experiences according to rules of interpretation and action. Self-organisation is responsible for the emergence of action patterns. This dynamic follows the principle of autopoiesis described by Maturana and Varela (2000), according to which the organisation of the emotion structure depends on the behaviour of the elements it is composed of, and not on the behaviour of the environment. According to Maturana and Varela (1988), systems are open in terms of content, but operationally closed.
The dominant action patterns automatically reinforce the most valid options available to deal with information exchange and the need to dissipate turbulences. This is done through repetition, an expression of the persistence of the attractor as the guide that gives the system meaning. Interaction with the environment involves the constant redefinition of the relationship with it, but the rules that determine the meaning of the emotion attempt to continue and maintain the achieved level of organisation. If this fails, it may lead to a crisis, or a period of chaos, which may present a learning opportunity, although it may also open the way to the disintegration of the system. Possible changes have been described in accordance with the occurring operational level. We can thus distinguish between first and second order changes (Prigogine & Stengers, 1984; Watzlawick, Weakland & Fisch, 1974). First order change occurs when the fluctuations, or the tendency to instability, are absorbed and adjusted without affecting the structure of the system. These fluctuations are thoughts and sensations whose interpretation has no order; they harass, or almost attack the system, with the potential to destabilise it, until dissipation places them within the established order. Thus, the fear of death that activates the behaviour of fleeing is easily justified, and the thought of cowardice is dissipated by the strategic thought, which fits better in a system where fear interacts with, for example, pride. Yet at times, the complexity of the system is extremely high, to the extent to which interaction with the environment generates turbulences that disturb the order of the system, particularly in the subsystems that lie furthest from the hierarchical core of the dominant system. In this case, the elements of the system are forced to reorganise into new patterns and rules of interaction, thus manifesting a second order change. In this change, fear may be reorganised into, for instance, shame, and new rules of behaviour appropriate to this new emotion are established. Dissipation of the fluctuations creates a new order. Emotion is inherent to the individual, and never dies, but emotions are also ephemeral, in such a way that fear may disappear, to be replaced by another emotion, such as happiness, which is the absence of fear.
A stable system gives cohesion to the internal relations of the system by repeating the action patterns, thus reducing complexity. Order, which is created through cooperation between the components, restricts the behaviour of these components, thereby establishing a determinism as a result of the intrinsic undetermined nature of feedback (Rosch, 1994). The system’s behaviour is caused by itself, from its initial conditions, and not by environmental influence. In other words, the emotion is the beginning and the end of each act, it repeatedly returns to its origin. But the repetition of the rules and patterns that control the organisation of the system is relative, since once a change has occurred, there is no going back (Kossman & Bullrich, 1997). Prigogine (1980) argues that a system moves in repetitive patterns because of the dissipative structures inherent to its dynamic of change. In the case of the fear observed at an initial stage characterised by the “flee” rule, the dissipative structures will tend to strengthen this rule, even in the face of new interpretations that push to establish the new “shame” feeling. While “fleeing” previously fitted into a fear-pride pattern that rationalised the rule as a strategy, now it may fit into a new fear-shame pattern, where fleeing is characteristic of cowards who should feel ashamed of themselves. If they are successful, the rule will be strengthened and the emotion will settle around the “flee” rule, the fear becomes simplified by a dominant response that gives meaning to the experience that activates it, whether it interacts with pride or with shame. The flee rule, as the initial condition, conditions a self-similar interpretation when facing a new condition arising from interaction with the environment. In this way, the fear emotion tends to reproduce itself and to increasingly resemble itself. The dominant rule is reiterated, but it is not the same from one state to another. The feeling of fear is displaced. The fear is now more intense, or more secure, more shameful or more proud, but it is not the same as that of the initial state. The dissipative structures generate a dynamic of circular causality that affects all the orders of the system’s organisation, capable of shaping repetitive patterns similar to those described as fractal structure.
Fractals involve a behaviour that stays at the boundaries of the system, and remains within them, and as such, they always reflect its identifying structure, thus the way this identity is expressed is never repeated. The essential property of the fractal is self-similarity, meaning that the part is similar to the whole (Mandelbrot, 1987, 2003; Munné, 1995). In this way, no behaviour is ever the same, but it is always of the same type as the previous one. The more fear changes, the more it resembles the original fear; the more the flee rule is reiterated, the more the fear behaviour will resemble itself. It must be borne in mind that every time any dynamical system manifests itself, it leaves fractal marks. These provide information on the system’s qualities, and on its parts due to the self-similarity effect (Wegner & Tyler, 1995). When a small part of an emotional manifestation is observed, we can expand it to obtain a general sense of the emotion in the system.
Systems that are far from equilibrium are more open to multiple and varied interactions with the environment. Their structures are less stable and more likely to become disorganised when tension in favour of change increases (Kossman & Bullrich, 1997). But it is this instability that grants them a greater capacity for reorganisation. Self-organisation is responsible not only for configuring the structures that provide the emotion’s meaning with stability, but also for maintaining the system at levels of stable equilibrium. A system remains at equilibrium if it does not close itself off from its environment, and exists side by side with instability while at the same time controlling it to prevent it from destroying the system. To reach this equilibrium, the order created by self-organisation acts to restrict the structural patterns that define the meaning of the emotion, thus establishing a circular determinism. The dissipative structures work against instability; they are designed to reject the information that the system’s logic cannot adjust, the information whose relation with the emotions defines a logic other than stability. They are counter-balanced by the principle of fluctuation that tends to move the system towards chaos (Prigogine, 1980; Prigogine & Stengers, 1984). When the fluctuations are slight, the dissipative properties cause the order of the system to prevail. In the case of grief from bereavement, for instance, one type of fluctuation is inevitability. Dissipation leads inevitability to cause undetectable qualitative changes in the short term, but these become essential changes over time, until they reach a critical level from where the grief is reorganised. But large-scale fluctuations can destabilise the system to the extent that a chaotic dynamic is generated that has no defined order. The bereaved person can create a block against inevitability, if it is not dissipated, in such a way that the inability to accept the inevitable can cause the system to disintegrate in a person for whom the confirmation of the inevitable is unbearable. The inevitable is information that penetrates in the form of fluctuation and is dissipated or filtered, in order that the grief can progress towards acceptance of loss. The need for emotional changes to occur without traumas, with a certain level or order, is what determines the constant search for stability in a system (Velasco, 1999).
Dissipative structures act as sophisticated control mechanisms by working to promote stability and self-similarity. Thus, a system based on grief will tend to become more stable and coherent over time, guided by its reference attractor. The more stable it is, the more predictable it will be. As Velasco (1999) states, we can predict the system’s behaviour regarding the relational structure that lends it meaning, and regarding the action patterns that reflect this relational structure, but not regarding external fluctuations that affect the system, as these are random in the long term. We can therefore make predictions about how the system will behave so long as its action patterns are reiterative and its self-similar behaviour is more regular. However, a system that does not allow fluctuations to penetrate its boundaries will eventually be dissipated, and will come so close to equilibrium that entropy will be at a maximum and information will flow at random. While dissipation represents persistence, the fluctuations represent critical interpretation and diversity. Grief reiterates its pattern of sadness and desolation, but this is threatened by exposure to the external world, from whence new feelings come that are capable of erasing the boundary that separates grief from the ability to forget.
The boundaries separate the system from its environment and establish a frontier. The frontier between the system and its surroundings retains an ambivalence of separation and exchange. This differentiation allows the emotion to be autonomous. When this autonomy is extreme, the system reaches equilibrium. A system at equilibrium keeps its boundaries closed and there is no information exchange. The boundaries act as an unstable filter, alternating open phases and phases of separation when it is closed to its surroundings. This alternation represents the degree of permeability between states, thus maintaining the equilibrium between dissipation and fluctuation. The more porous a system is, the fuzzier its limits will be. Dissipation clearly outlines the boundaries whereas fluctuation erases them. In an emotion of fear structured on the basis of panic, the system boundaries are clear. When fear is structured on the basis of reflection, of diversity in the parameters of interpretation, the boundaries of fear will be more diffuse, its extension fuzzier. Fuzzy logic maintains the principle that everything is a question of degree, is typical in systems whose rules are not based on linear causality, and the links between its components are undefined (Kosko & Isaba, 1993). The boundary of a fuzzy system is diffused, in such a way that a sensation or a thought may belong to more than one emotion at the same time. The same statement may be both true and false (Kosko, 1995). But this multiple act of belonging is not established randomly. The thought about heartbeats may pertain to fear or love, in different degrees. One condition of fuzzy sets is that the sum of the degrees of belonging represents the whole of the condition (Kosko, 1995; Kosko & Isaba, 1993). The interpretation of the relation between the heartbeats and the thought about the heartbeats, and a given reference situation, may include varying percentages of the fear emotion, the love emotion and even the shame emotion. Whatever the distribution might be, the total sum of all that belongs must represent the whole interpretation. If one has 50% fear, one also has 50% absence of fear; one may be frightened and not be frightened at the same time. This is not a contradiction in fuzzy logic.
Fuzzy systems are multi-valued, in such a way that the meaning only partially belongs to them. The interpretation of a situation may belong to the fear system, but it may also partially belong to other systems such as that of pride. This partial belonging and the extent to which it belongs may lead to confusion with the differing concept of probability (Kosko & Isaba, 1993). Probabilities measure the extent to which a specific thing may be expected to happen. Fuzziness measures how much something is happening now, or the extent to which a certain condition is being fulfilled. The operations in a fuzzy system construct possible reasonings of a qualitative nature (Munné, 1995). This is because fuzziness describes the mechanisms people use to understand each other and the world around them by constructing an interpretive process that blurs meanings (Dimitrov, 1999). When the system is faced with an interpretation that is proportionally shared between different emotions, the whole system carries out a clarification process that transforms the fuzzy interpretation into a single emotion. The interpretation chooses one alternative from the various available options, and this is not done at random. When a new input of information activates an emotion system, the values that regulate interpretation change slightly, and this change constitutes the system’s learning. The change is qualitative, not quantitative. The boundaries’ fuzziness makes it easier for the fluctuations to penetrate, generating discontinuities in the evolution of the emotion system, doubts and uncertainty. The self-organisation process re-establishes order, but qualitative changes are required if this is to be possible. These changes modify the system internally, without changing the variable values either significantly or perceivably. Like adaptive fuzzy systems, the emotion system learns to recognise the regular patterns present in the new information that comes into the system. The qualitative changes and discontinuities challenge the patterns and rules that regulate the emotion until a significant change is brought about. This change occurs when the system reaches a critical point, after which reorganisation is required to keep the system far from equilibrium and chaos. As multiple, sufficiently valid solutions are available, the system opts for one of the possible paths. The resulting discontinuity, representing the potential paths the change might take, is known as bifurcation.
The attractors force the system to spontaneously re-create its boundaries with cascades of bifurcations, and a solution is eventually found in the dominant internal order (Escohotado, 1999). Bifurcations are sudden changes in the system’s pattern of behaviour, also known as critical phenomena or dynamic phase transitions (Kelso, Ding & Schöner, 1991). Bifurcations lead to operative instability within a context of structural stability, and offer a new path when the fluctuations apply pressure to fit a new order in. These phenomena are studied by catastrophe theory (Zadeh, 1965). Catastrophe theory, which has been shown to be applicable to the study of human behaviour (Zeeman, 1977), allows changes to be analysed in relation to structural stability (Woodcock & Davies, 1978). Catastrophe theory studies the qualitative changes that emerge in the dynamic of the system in an attempt to understand the disorder of discontinuity (Thom, 1983). The function of the sudden alterations in the nature of the system, deriving from a bifurcation, is to alter its nature so as to maintain constancy (Munné, 2005). The bifurcations represent the points of discontinuity, qualitative deviations from the interpretation. They may be caused by the amplification of a small internal fluctuation, or by an external perturbance, when the system is in an unstable situation. The bifurcations drive the system towards a configuration, the path of which may be perfectly determined, but which is not the only one possible, and which are foreseeable but not unpredictable. In the case of grief, the bifurcations may take the system towards new interpretation systems based either on love, on recovery, on loneliness, chronic sadness or profound grief.
The analysis of emotions as complex dynamical systems brings into question the way in which changes are measured. In this type of analysis, accurate measurement is not a good way of improving knowledge. According to Kosko (1995), the more accurate the measurement of a complex dynamical system, the further it is from being understood. Furthermore, we cannot trust reliable measures. Change means that the measurement is not stable, and the measurement obtained cannot be guaranteed to be the same in another occasion. Qualitative changes do not necessarily have to be quantitatively identifiable, and therefore the variables may have the same values from one state to another, yet the system has altered significantly. Moreover, measurements of an eminently mathematical nature are valid for mathematical phenomena, but whether they would be so for dialectic phenomena is questionable. Consequently, perhaps more qualitative ways of approaching the analysis of emotions are required to understand their interpretative dynamic.
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