The frequently asked questions (FAQs) presented here were written to highlight the essential points of the dynamical perspective on social experience, with an eye toward the implications of this perspective for the understanding and potential resolution of intractable conflict. We wish to emphasize that this particular perspective represents an adaptation of basic principles and methods of dynamical systems and complexity science to social psychology developed by Vallacher and Nowak. Accordingly, we list below some basic readings we have published that describe various features of this perspective and its empirical base. These readings provide the basis for the FAQs and thus are recommended for readers who wish to go beyond the short answers we have provided to these questions.
- 01. Aren’t social psychological processes inherently dynamic? Why do we need dynamical social psychology?
- The intuition that all social psychological processes are inherently dynamic was the guiding principle at the beginning of social psychology in the early 1900s. The founding fathers of the field—most notably, James, Cooley, Mead, Lewin, and Asch—all emphasized in different ways the multiplicity of interacting forces operating in individual minds and in social groups, the potential for sustained patterns of change resulting from such complexity, and the tendency for individuals and groups to strive for mental and interpersonal coherence. Indeed, the very notion of dynamic social psychology can be traced directly to the seminal contributions of Kurt Lewin. However, Lewin and others could not find appropriate formal tools (because such tools didn’t exist) to analyze the dynamics of human experience in a rigorous and systematic fashion. As a result, the subsequent research spawned by early social psychology reduced personal and interpersonal processes to simple causal relations, in which dynamics were defined as a one-step change between the cause and the effect.
New discoveries in the natural sciences (e.g., statistical mechanics, non-linear dynamics, computer simulations and visualization) in the 1980s provided tools to capture the complexity and dynamism of many real-world phenomena in chemistry, biology, and physics. Only in the last decade or so have psychologists found ways to adapt these tools to the unique subject matter of social psychology. The modern tools associated with the dynamical approach allow psychologists to capture the deep insights that launched the field in its nascent stage but to do so with the rigor normally associated with the natural sciences. With these developments, it is fair to say that in the early years of the 21st century we are witnessing the re-emergence of dynamical social psychology as articulated by the field’s founding fathers at the turn of the last century.
- 02. How is dynamical systems theory different from general systems theory?
- Both approaches emphasize the basic role of interactions among elements comprising a system. A number of basic principles, including the operation of positive and negative feedback loops and the organization of elements at different levels of system function, are common to the two approaches. They differ, however, in a number of critical respects. General systems theory, derived within the cybernetic tradition, emphasizes the regulation of system function based on feedback loops among system elements. It focuses on the maintenance of stable states rather than basic patterns of temporal evolution and change in a system. In contrast, dynamical systems theory, based on formalisms developed in mathematics and physics, concentrates on how systems composed of interacting elements change in time. In its simplest interpretation, a dynamical system is a set of difference or differential equations describing temporal change.
Dynamical systems have been the primary tool of physics since the time of Isaac Newton. In the early 1980s, however, discoveries concerning non-linear dynamical systems revolutionized scientists’ understanding of how many diverse phenomena change and evolve in time. Most important, it was shown that when the mutual influences among elements are non-linear, amazingly complex phenomena may appear as a result of interactions among the elements. Such phenomena as chaos, self-organization, emergence, bifurcation, and unpredictability were observed in systems composed of a small number of very simple elements. General systems theory lacks the most fundamental insight of non-linear dynamical systems: emergence and self-organization.
An important discovery of the dynamical systems approach is that otherwise distinct phenomena conform to a small set of universal properties. Attractors provide an example of such universality. An attractor is state or pattern of changes to which a system tends to evolve (i.e., is “attracted to”) over time and to which the system returns if perturbed by an outside influence. Despite the enormous diversity of phenomena in different domains and at different levels of reality, only three types of attractors are possible: fixed-point (convergence to a stable state), periodic (sustained oscillation between two or more states), and chaotic (complex pattern of changes that never repeats, yet is not random).
- 03. How is dynamical systems theory different from catastrophe theory?
- Catastrophe theory describes how the equilibria of a system change as a function of changes in the settings of the system’s control parameters. It was developed within the field of topology and thus does not address any state other than those corresponding to system equilibria. The theory is presented in geometrical terms as shapes of surfaces on which the equilibria reside. In contrast, dynamical systems theory describes the dynamics of any state in the system, whether at equilibrium or not.
The closest counterpart to catastrophe theory from a dynamical perspective is bifurcation theory, which describes how the attractors of a dynamical system change as a result of changes in the setting of control parameters. It subsumes the fixed-point attractors that correspond to equilibria in catastrophe theory, but also describes periodic and chaotic attractors. With respect to fixed-point attractors, bifurcation theory goes beyond catastrophe theory in that it describes the behavior of the system in the vicinity of an attractor. For example, a system may converge on a fixed-point attractor by a direct trajectory or by a spiral trajectory—neither of which can be derived from catastrophe theory. Bifurcation theory also describes how a fixed-point attractor may transform under certain conditions into a periodic attractor, which in turn may transform into a chaotic attractor. In catastrophe theory, the fate of a system that departs from an equilibrium is undetermined.
- 04. Is dynamical systems theory the same as chaos theory?
- Chaos theory is an especially well-publicized subset of dynamical systems theory. In many non-linear systems, the precisely determined interaction of a few elements leads to a very complex temporal trajectory that never repeats itself. The state of the system cannot be predicted, since minimal changes in the initial states of the elements can promote very different temporal trajectories. This results in a practical inability to predict the state of the system, despite the deterministic rules governing the systems. In the 1980s and early 1990s, this scenario became very popular, both in science and the general public, as an increasing number of phenomena that were assumed to be random were found instead to reflect deterministic rules that produce chaotic trajectories. The philosophical revolution was in understanding that complexity is the flip side of simplicity rather than its antithesis. Systems may be very simple at the level of their component elements, yet very complex at the level of the system’s global properties and behavior.
Dynamical systems theory, though, is considerably broader than chaos and different dynamic scenarios are currently attracting more attention in the scientific community. In particular, self-organization, the universal properties of networks, and scenarios in which extremely rare and localized events govern the global dynamics of a system are at the forefront of contemporary work in dynamical systems.
- 05. What exactly does `non-linear` mean?
- Linearity refers to proportionality between a source of influence (e.g., a cause) and the resultant change (e.g., the effect). Non-linearity refers to any other type of influence relation. In a threshold function, for example, a cause has no effect until a particular level of intensity is reached, beyond which the effect appears at full-strength. Other examples of non-linearity include inverted-U functions, in which moderate values of a cause have greater effects than do extreme values of the cause, and U functions, in which both extremes of a cause promote the same extreme effect, while moderate values of the cause produce no (or minimal) effect.
- 06. If all the elements in a dynamical system influence each other and the state of the system, how can one possibly limit the scope of an investigation to just a few variables?
- Focusing on a small set of variables is viable in two scenarios: dynamical minimalism and the search for control and order parameters. In the approach of dynamical minimalism, the goal is to identify the most important qualitative properties of the phenomenon and to construct the simplest possible model capable of reproducing the phenomenon. Attainment of this goal involves stripping the phenomenon of non-crucial properties. Computer simulations are particular useful in this regard, because they may reveal that very complex properties unexpectedly emerge from non-linear interactions among simple elements over time. Emergence accounts for substantial growth in the complexity of a system’s processes and properties. Because of emergence, then, very complex systems may often be described by very simple models. Functions of the human brain may be reproduced, for example, by a system composed of interacting binary elements (artificial binary neurons interconnected in a network).
The search for simplicity may take a different tack. Often, macroscopic properties of systems composed of many interacting elements may be described by a small number of variables, referred to as order parameters. In a bottle of gas, for example, there are 1023 molecules for every liter. But the macroscopic properties of the gas may be almost fully described by its temperature and pressure. Most complex systems have order parameters, so finding them is a major goal in the understanding of the system. In cognitive systems, for example, evaluation provides a critical order parameter, in that it tends to remain stable despite a rapid turnover of specific thoughts and because it provides the key to understanding the system’s behavioral tendencies. It is also the case that of the many variables affecting a system’s dynamics, only a few are of critical importance, it that they can change the system’s dynamics in a qualitative, as opposed to a merely quantitative, fashion. These critical variables represent the control parameters of the system. By describing the dynamics of the system in terms of the relation between control parameters and order parameters, one can specify with just a few variables and equations the dynamics of extremely complex systems consisting of a very large number of elements and the micro variables describing the state of each of these elements.
- 07. How does a control parameter differ from any other external influence on a system’s behavior?
- The behavior of a system depends on some factors that are usually constant in time and represent either external influences or the mode of functioning in the system. Since changing the values of these parameters controls the dynamics of the system, they are referred to as control parameters. Control parameters decide about the general dynamical properties of the system, such as the type and positions of the system’s attractors. They may represent significant external influences or conditions in which the system is working, or they may represent internal factors that determine modes of interaction among system elements. With respect to the dynamics of response to provocation, for example, both external factors such as environmental stress (e.g., heat, noise) and internal factors (e.g., emotions such as happiness and anger) dictate the interaction among specific thoughts and feelings that may eventually result in a behavioral response.
The system may also be subjected to myriad momentary and incidental influences. Such influences and perturbations are usually represented collectively as “noise.” Whereas control parameters decide about the global dynamics of a system, the momentary external influences affect the state of the system. In a conflict with a business partner, for example, the dynamics of a person’s thoughts and behaviors might be influenced by distractions and incidental factors (e.g., telephone ringing, passersby, etc.). When such factors are considered collectively, there combined influence approximates a random distribution and thus can be considered noise. It should be noted, though, that the overall magnitude of noise is considered an important control parameter for most dynamical systems in nature.
- 08. How can one identify a system’s control parameters?
- In principle, a multitude of variables influence the states and dynamics of a system. In non-linear dynamical systems, however, only a small subset of these variables play a critical role in changing the dynamics of the system in a qualitative way. These variables represent the control parameters of the system. The effects of the other variables are usually small and quantitative in nature. When building simple models of complex phenomena, one should try to include only the system’s control parameters. Establishing the critical control parameters for a system is a major step in understanding the phenomenon and in theory construction.
Converging on a final set of control parameters often entails a combination of theoretical insight, experimentation, and computer simulations. Theory, based on prior research, may suggest which variables are critically important for the dynamics of a phenomenon. With respect to cognitive processes, for example, theory suggests that emotions play a critical role in the dynamics of thought. In the experimental approach, by varying many factors one can identify which factors are critical in that they qualitatively change the dynamics of the phenomenon. In computer simulations, one can systematically vary combinations of all the parameters describing a model.
Computer simulation models of the formation of public opinion, for example, have identified a small set of control parameters (e.g., issue importance, locality of social interactions, opinion leaders) that qualitatively change the dynamics and outcome of the process. Local influence, for example, has been shown in simulations to be critical to the survival of minority opinions in clusters. If influence is global, such clustering cannot occur and minority opinions decay in a society. With the existence of strong leaders, minority opinion clusters can survive even in the presence of relatively high levels of noise. Other factors (e.g., the weight attached to one’s own opinion) are less important and determine quantitative features, such as the size of the clusters.
- 09. How does emergence take place in a dynamical system?
- Demonstrating the process of emergence was one of the major accomplishments of modern science. With the use of computer simulations, it was discovered that very simple but non-linear rules governing the interaction among very simple elements can result in complex and totally unexpected properties and spatial and temporal patterns at the system level. In simulations of brain function, for example, extremely simple binary elements (similar to switches) connected into networks can perform complex tasks such as pattern recognition, error correction, prediction, optimization, and generalization. Complex functions and patterns can emerge in the process of self-organization, as a result of low-level elements influencing each other without the influence of a higher-order agent.
- 10. Can the nature of an emergent property be predicted?
- The human mind cannot model the functioning of non-linear systems. Thus, even very simple non-linear interactions among very simple elements often have effects that are totally unexpected and surprising for the researcher. Since computers do not have this limitation, the use of computer simulations is ideally suited for investigating emergence in non-linear systems.
- 11. How does an attractor differ from more familiar notions, such as “schema,” “goal,” “attitude,” “habit,” or “disposition”?
- An attractor describes the long-term dynamics of a system. Each of the other concepts can thus be conceptualized as an attractor for a specific type of system. In traditional approaches, however, these phenomena are commonly investigated as fixed structures, with little consideration to their dynamic properties. By framing them in terms of attractors, we can recapture the dynamics that are often lost in theoretical accounts.
A schema, for example, constrains the dynamics of perception and thinking, causing the stream of thought concerning an object or event to converge on a specific set of values (i.e., default values). A goal, in turn, represents an attractor in that it steers actions toward the attainment of particular state. The concept of attitude, for example, describes the values of thoughts, feelings, and actions that are most often experienced in contact with the attitude object and to which a set of psychological mechanisms promote convergence after perturbation. Having a positive attitude toward a person, for example, does not rule out the possibility of experiencing negative feelings on specific occasions, but rather suggests that such feelings are intrinsically unstable and infrequent. In similar fashion, a disposition does not describe a single value on a dimension of personality, but rather the attractor for a system of interacting mechanisms producing and controlling thoughts, feelings, and behaviors in a certain domain.
Reframing these familiar notions in explicitly dynamical terms highlights their common properties and thus provides theoretical unity across otherwise diverse domains and levels of experience. A dynamical account also suggests how higher-order properties and processes develop (e.g., emergence via self-organization) and change both quantitatively and qualitatively (e.g., noise, settings of control parameters). Investigating schemas, goals, and the like from a dynamical perspective thus may illuminate the origin, evolution, and transformation of the collective states that provide stabilization of people’s thoughts, feelings, and actions. It is worth emphasizing, too, that a dynamical system may have more than one attractor governing its dynamics. Identifying the structure of attractors in a system thus provides insight into the possible co-existence of different (and potentially conflicting) schemas, goals, attitudes, habits, and dispositions governing a person’s functioning under different conditions. A radical change in an attitude or a behavioral pattern, for example, can be understood as the movement of a system from the basin of one attractor to the basin of another (previously latent) attractor.
- 12. If a system moves between two (or more) different states over time, how can one tell whether this signifies the presence of two (or more) fixed-point attractors or one periodic (or quasi-periodic) attractor?
- In both scenarios, the system will be observed frequently in the vicinity of two (or more) points. In the case of periodic evolution, the switching between points will be very regular and the system will depart a point soon after reaching it, because the intrinsic tendency of the system is to oscillate between (among) them. In the case of two (or more) fixed-point attractors, the timing of the switching between the points will be irregular and the system will have a tendency to rest at a point after reaching it. Only internal noise or external perturbations will cause such a system to depart from one attractor and converge on the other.
Cognitive and social systems usually operate in the context of high levels of noise. The influence of noise can disrupt the regularity of periodic evolution and can also cause relatively rapid switching between fixed-point attractors. In such cases, more subtle criteria are necessary to distinguish between the fixed-point and periodic scenarios. In recent years, sophisticated software has been developed that can make this distinction.
- 13. What is chaos?
- Chaos is a very complex pattern of dynamics that can be observed in non-linear dynamical systems. A small number of variables interacting in a non-linear manner give rise to an extremely complex temporal trajectory (change of momentary states) of a system. Despite the operation of deterministic rules, the system’s trajectory is unpredictable over a long time interval. Chaos is characterized by sensitivity to initial conditions, so that even the slightest change in the state of the system result in a very different temporal trajectory of the system’s behavior over a long time span. Chaos is also characterizing by mixing, such that two points that were initially very similar may drastically diverge from one another and become similar to points that initially were very different. In this process, the similarity relation of states is disrupted by the system’s temporal evolution. Two friends who are highly similar to each other in high school, for example, may adopt very different life patterns and become similar to people with whom they initially had little or no similarity. If many elements evolve according to a chaotic rule, any initial order among them becomes disrupted as the pattern of their similarities becomes mixed.
- 14. How can one distinguish chaos from randomness in a system’s behavior?
- Chaos and randomness may look very similar, because both are irregular and unpredictable. Randomness is a stochastic process in which elements do not obey deterministic rules and the number of variables necessary to describe the system cannot be reduced. Chaos, in contrast, is a deterministic process in which a small number of variables, interacting in a non-linear fashion, produce a very complex, yet orderly trajectory that can resemble randomness. There are specific ways to display such a trajectory to reveal its orderly fashion (e.g., a phase space or return map). There are also specific mathematical techniques that allow one to distinguish between random and chaotic trajectories (e.g., the Grassberger-Procaccio and Kaplan-Glass algorithms).
- 15. How are attractors formed?
- In dynamical systems, the state of the system at a given moment in time depends on the state of the system at the preceding moment. If a system operates without external perturbations, its long-term dynamics may follow one of a small number of scenarios. In one scenario, the values of the variables describing the system may go to infinity (essentially, an “explosion” of the system) when the prevalent tendency is unconstrained exponential growth. Alternatively, the values may go to zero in an exponential decay if nothing prevents this decay. In a large class of systems, other long-term scenarios are possible and described by attractors. An attractor is formed when many initial conditions of the system converge after some time (the transient regime) on a small number of states or patterns. In this sense, the formation of an attractor is due to the nature of dynamic interactions of variables as described by the equations specifying the dynamics of the system.
In real systems, there are many mechanisms (which could be described by equations) specifying the interactions. Fixed-point attractors (e.g., stable equilibria), for example, may result from the principle of energy minimization. The dynamic principle is that at each moment, the system will adopt a state that minimizes its energy. Such dynamics may be conceptualized as a descent from a hill to a valley, where the valley represents the attractor. At some moment, the system will reach a state associated with a local energy minimum. A departure from this state (e.g., caused by external perturbation) will result in an increase of energy. The energy minimization principle, however, will bring the system back to its minimal energy state.
In artificial neural networks, for example, the energy of the system is defined as the sum of the discrepancies between the actual states of all the neurons and the states dictated by the signals coming across excitatory and inhibitory signals from other neurons. The dynamics of the system is such that each neuron adopts a state that is closer to the one dictated by states of the other neurons, thereby decreasing the energy of the whole system. Over time, the system evolves in the direction in which the dictated and actual states of the neurons are the same. Since high discrepancy may be interpreted as incoherence and low discrepancy as coherence, the principle of energy minimization results in an evolution from incoherent states to coherent states. Theses coherent states represent the attractors of the system. A reversal of this principle can account for dynamics of optimization. Optimal levels of stimulation, incongruity, and satisfaction, for example, can be described by this principle if one represents optimal states as those at which the system’s energy is minimal.
Fixed-point attractors may also be formed by the principle of balance of forces. The relative strength of the forces acting on a system dictate in which direction the system will evolve, with the stronger force having greater effect. The approach-conflict provides a clear and well-documented example of this scenario. The concept of energy is not necessary because simple comparison of the strength of the forces provides the basis for attractor formation.
In systems with self-regulatory capacities, an attractor represents the standard of regulation for the system. Goals, norms, values, and so forth provide examples of self-regulatory attractors in human systems. Any departure from such standards engages regulatory mechanisms that bring the system back to the standard. In cybernetics, this scenario is epitomized by the functioning of a thermostat. In psychology, this scenario has been employed to describe self-regulation and goal attainment.
In principle, all three scenarios may be described in equivalent terms as energy minimization. Each of them, however, stems from a different tradition and is associated with different theories and research paradigms.
- 16. What are the basic properties of an attractor?
- Attractors are points or patterns of temporal evolution to which a system tends and to which it returns when perturbed. Fixed-point, periodic, and chaotic attractors can be characterized in terms of different properties. With respect to fixed-point attractors, three basic properties have been identified: basin of attraction, depth, and shape.
The basin of attraction refers to the range of values surrounding the attractor that eventually converge on the attractor. The wider the basin, the larger the range of nearby values that converge on (are “attracted” to) the attractor. Someone who is optimistic, for example, might react to news that is neutral or even moderately negative with evidence of his or her tendency to see the world in positive terms. If the basin is very wide, covering the entire range of values that can be adopted, the system will converge on the attractor regardless of its starting value. For a highly optimistic person, even devastating news (e.g., the loss of his or her job) might be seen in positive terms (e.g., an opportunity to take on a new job). An attractor with a narrow basin will attract a smaller range of nearby values. A person might have a tendency to stabilize on a high degree of optimism, for example, but display this tendency only in reaction to positive events. When the person is in a pessimistic or even a neutral mood, his or her optimism may not be evident.
Depth represents the force required to move the system out of the equilibrium. A deep attractor can resist relatively strong forces in the direction of some other value outside the basin of attraction. For a person whose attractor for optimism is very deep, strong inducements from outside are required to change his or her mental state if he or she is within the basin of attraction. A shallow attractor is more readily destabilized by forces associated with a contradictory influence. So if a person’s optimism is not especially well-entrenched, even a brief encounter with a skeptical person might be sufficient to dampen the person’s rosy view of the world.
Shape describes how the system reacts to various deviations from its attractor, and how strongly each deviating state will be pulled back to the attractor. Some attractors react very weakly to small deviations, but react in a disproportionately stronger fashion for larger deviations. Such an attractor would allow the optimistic person to move almost freely through a range of positive moods, but strongly restrict him or her from moving into a range of negative moods. A contrasting example is an attractor in which the forces returning the system to its equilibrium are very strong in the immediate vicinity of the attractor, but become progressively weaker with increasing distance from the attractor. An optimistic person may very strongly stabilize on a very positive view of the world, for example, but once the person is induced to adopt a moderately optimistic view, he or she may be less inclined to resist an outright negative worldview.
- 17. How are attractors changed?
- One should distinguish between changing which attractor in a given structure currently characterizes the system’s dynamics and changing the structure of attractors (the attractor landscape). In the first case, external influences can move a system between the system’s attractors. A married couple, for example, may have two attractors governing how the parties interact with one another: conflict and suspicion or love and affection. Depending on many factors (e.g., household stress, positive or negative interactions with other people), the couple can move from one state to another. However, only those states will be relatively stable for the relationship. The parties may find it impossible, for example, to interact in an emotionally neutral fashion for an extended period of time.
In the second case, the attractor landscape of a system may undergo a qualitative change under certain scenarios. As a result of marital therapy, for example, the married couple may develop new forms of interaction other than conflict and affection. The new forms represent different modes of influence among each party’s thoughts, feelings, and actions concerning the other party, with these modes promoting the emergence of qualitatively different configurations of stable states (attractors). In dynamical systems, a change in the structure of attractors follows well defined rules specified by bifurcation theory. In particular, several scenarios have been identified in which fixed-point and periodic attractors can transform into chaotic attractors (e.g., period-doubling scenario). Catastrophe theory also specifies how fixed-point attractors can change. The cusp catastrophe (corresponding to pitch-fork bifurcation), for example, describes how an initial attractor may lose its stability in response to increasing values of a splitting parameter, diverging into two attractors, with the original attractor becoming a repellor.
In general, attractors change as a result of change in the control parameters of the system. If a social relationship revolves around non-important matters, the attractor for interaction is likely to reflect moderately positive values and be relatively weak, allowing for flexible reactions to one another’s behavior. If the relationship grows in importance and begins to involve personally engaging issues (e.g., finances) and occurs in an environment of increasing stress, this increase in the value of the splitting factor is likely to produce a bifurcation of the attractor into one characterizing highly positive interactions (e.g., mutual support, affection) and one characterizing highly negative interactions (e.g., antagonism, distrust, conflict).
- 18. What is a latent attractor?
- Several attractors may co-exist in a system. At any one time, only one attractor will capture the dynamics of the system. The existence of other attractors will not be visible in the system’s dynamics and thus can be considered latent as opposed to manifest. In a stable environment with a constant balance of forces, the system will remain at the current attractor despite the presence of the latent attractors. When conditions change, however, the system may be moved out of the basin of this attractor to the basin of a latent attractor. When this happens, the system’s behavior will appear to change suddenly as the system’s dynamics converge on the previously latent attractor.
- 19. How can one purport to characterize very different processes in terms of the same principles, yet provide deep insight into each process?
- Each area of science is defined in terms of its own issues and concepts. Because of this specificity, the laws governing the phenomena in each area cannot be generalized to other areas. One of the most important discoveries in non-linear dynamical systems, however, is the universality of basic dynamical processes. In systems consisting of a large number of interacting elements, the system’s dynamics depend on the structure of the system and the nature of influence among the elements. The exact nature of the elements is of secondary importance. Systems that are very different may therefore exhibit highly similar patterns of dynamics. The growth of vegetation in arid regions, for example, is governed by the same principles as the growth of an economy and the dynamics of the immune response in animals. By understanding the basic nature of interactions among elements and the crucial variables governing the system’s dynamics and the resultant pattern, one can develop deep insights into how the system works.
Often the knowledge of how a system works can be highly informative about other systems that share the same interaction patterns and variables. For example, the dynamics of cognitive systems such as the self-structure follow the same basic principles as those governing interactions among individuals in the formation of public opinion. In both cases, the state of each element (i.e., thought vs. person) depends on the influence of related (neighboring) elements. On the macro level, in both cases one can observe the formation of clusters of similar elements, a reduction in the number of less popular states, and increase in the system’s coherence. Both processes share similar control parameters. The distribution of the strength of elements, the locality of interaction, and the amount of noise in the system have qualitative effects on the system. Because of these basic dynamical commonalities, the patterns of change in both cognitive and social systems follow similar scenarios.
- 20. What is the role of causation in dynamical social psychology?
- This question can be answered at two levels. With respect to fast-changing (dynamical) variables that capture changes in the momentary state of the system, the current state of the system is directly caused by the preceding state of the system. More precisely, the state of each variable in the current moment is caused by the states of other variables in the previous moment and by the value of its own previous state. Because the state of every variable is the effect of all the relevant variables in the previous moment, and because every variable is one of the causes determining the state of the other variables in the next moment, a dynamical system is characterized by bi-directional causality. Each variable is both a cause and an effect as the dynamics are iterated over time. This chain of cause and effect gives rise to patterns of intrinsic dynamics.
External factors also play a causal role in dynamical systems. Such factors can influence the momentary state of the system, but they do so by interacting with the intrinsic dynamics of the system. Sometimes their effect may be minimal or short-lived, as the system returns to its attractor after perturbation. At other times, an external factor may have a disproportionately large and non-linear effect if it moves the system out of the basin of one attractor to the basin of another attractor. In this “threshold” scenario, even a very slight change in the magnitude of an external factor can promote a dramatic and wholesale effect on the state of the system.
Some external factors go beyond influencing the momentary state of system, reconfiguring instead the dynamics of the system. Such factors are the system’s control parameters. By changing the value of control parameters, patterns of intrinsic dynamics and system-level properties may change dramatically. For example, the number, type, and basins of attraction of attractors may change. From this perspective, one may treat the pattern of dynamics as a state (e.g., cooperative or competitive activity). Changes in the value of a control parameter can thus be represented as a cause, with the resulting pattern of dynamics representing the effect. This level of analysis provides a way to reframe the traditional notion of causation in the social sciences.
Prepared for annual meeting of International Association of Conflict Management, Budapest, Hungary (July, 2007).
