Dynamical Social Psychology: The Next Iteration

Psychological Inquiry 1997, Vol. 8, NO. 2, 152-160

Copyright 1997 by Lawrence Erlbaum Associates, Inc.

AUTHORS' RESPONSE

Dynamical Social Psychology: The Next Iteration

Robin R. Vallacher Department of Psychology Florida Atlantic University

Andrzej Nowak Department of Psychology and Center for Complex Systems

University of Warsaw

We are delighted to have obtained feedback on our target article from such a distinguished and scientifi- cally diverse set of commentators. It is precisely such a confluence of divergent perspectives that is crucial at this point in establishing the viability of the dynamical perspective in social psychology. Our stated aims in the target article were to describe an existing field of sci- ence that could be fruitfully applied to social psycho- logical phenomena, to show what sorts of methods and tools are available and potentially relevant for this purpose, to discuss existing applications, and to point out the potential for new theory and research regarding these and other applications. It was not our intent to argue that all methods and tools from dynamical sys- tems theory are applicable to social psychology, or to state exactly how dynamical social psychology should be done. Such refinement should emerge as a result of divergent perspectives and insights stimulated by, or otherwise relevant to, the ideas presented in the target article. In that very important sense, the commentators individually and collectively fill a critical role in for- warding this perspective and setting the agenda for theory and research in the years to come.

We note with pleasure that all the commentators express appreciation for the central idea that social psychology would profit by being viewed in explicitly dynamical terms. Indeed, several of them extend the dynamical perspective by providing additional argu- ments for its potential utility and developing interesting applications. At the same time, the commentaries differ in their specific reactions to the ideas we presented and in their advice for developing the dynamical perspec- tive. Because these points are largely supportive of our general goal, and because they are well developed in

their own right by the commentators themselves, there is little to be gained by considering them in fine-grained fashion. At a somewhat broader level of analysis, how- ever, the commentaries revolve around one of four basic themes that warrant further comment on our part: (a) Social psychology has always been dynamic, (b) con- temporary social psychology is already dynamic, (c) one should exercise caution in applying dynamical systems to social psychology, and (d) the dynamical perspective should be based on social psychological insights, theory, and data. We consider each of these themes in turn.

Social Psychology Has Always Been Dynamic

We began the target article by noting that social psychology from its very inception has been dynamic. In particular, we noted the emphasis on dynamics cen- tral to the ideas of the field's founding fathers, including James, Mead, Cooley, and Lewin. Several of the com- mentators also stress the dynamic underpinnings of the field and provide more detail than we did concerning the nature of these underpinnings and their role in theory construction. Kruglanski, Clement, and Jost fo- cus on Lewinian field theory, for example, emphasizing its clear and explicit emphasis on internal dynamics and the potential for change and evolution in psychological processes. Messick and Liebrand also note the contri- bution of field theory, and Carver points out classical precedents for the idea that behavior can demonstrate volatility in response to the changing relative salience of multiple motives (e.g., Murray, 1938). Tesser,

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

AUTHORS' RESPONSE

McMillen, and Collins note that classic social psychol- ogy was dynamic in principle, although not necessarily in practice.

We are in complete agreement with the commenta- tors that we are really witnessing what Messick and Liebrand describe as the reemergence of dynamical social psychology. Because of its intuitive and self-evi- dent appeal, dynamism provided an important concep- tual foundation for social psychology as a scientific discipline and shaped the development of subsequent theories. Indeed, one could expand the list of dynami- cally oriented theories relevant to social psychology beyond those cited by us in the target article and by the commentators. Broad perspectives such as general sys- tems theory (von Bertalanffy, 1968) and models based on cybernetic principles (G. Miller, Galanter, & Pri- bram, 1960; Powers, 1973; Wiener, 1948), for instance, stressed the importance of understanding how different elements are put together to form a system, and they expressed many of the key insights of dynamical sys- tems theory, including the potential for internally driven change and feedback loops among system ele- ments. Interestingly, however, the primary legacy of the early dynamic perspectives has been an emphasis on tendencies toward achieving a stable equilibrium rather than on self-sustaining dynamics. Thus, Lewin's (1936) theory inspired a host of theories centering on such notions as cognitive balance, the reduction of cognitive dissonance, and the elimination of incongruity. Even conflict theory (cf. N. E. Miller, 1944), with its empha- sis on the simultaneous prepotence of incompatible response tendencies, focused on the tendency to estab- lish an equilibrium point between the conflicting forces. It is somewhat of an irony, therefore, that the early attempts to express the dynamics of psychological proc- ess ended up emphasizing the static aspects of these processes.

This point is not lost on the commentators, who note that although the early dynamic perspectives clearly had an impact of subsequent theory and research, the dynamical aspects of these theories are not readily apparent in contemporary theory and research. This observation, which is developed most explicitly by Kruglanski et al. and by Messick and Liebrand, leads to some straightforward and troubling questions. In view of the repeated attempts to frame social psychological processes in dynamic terms, why is there not an explicit focus on dynamics in much of contemporary theory and research? More to the point, why should we expect a dynamical perspective to succeed now, given its rather checkered history?

There are two general reasons why the dynamical approach did not have the impact one would have anticipated on the basis of its intuitive appeal. The first,

recognized by virtually all the social psychologist com- mentators, is that appropriate tools and methods for describing and analyzing a system's dynamics were not available at the time of James, Lewin, and the others. What is different this time, as the commentators right- fully acknowledge, is that we now have a powerful set of methods and tools that can be used to capture impor- tant dynamic properties of social psychological sys- tems. We described many of these methods and tools in the target article, of course, and all of the commentators embellish these or offer some of their own. Thus, Eiser and Kruglanski et al. point out the value of the connec- tionist approach, Guastello and Tesser et al. provide examples of structural equation modeling, Carver dis- cusses applications of catastrophe theory, and Gold- stein and Messick and Liebrand discuss the benefits of computer simulation.

The availability of such approaches by no means implies that all the traditional techniques and tools of social psychological research should be abandoned in favor of dynamical tools. Both Carver and Tesser et al. are quite right in noting that some important aspects of social psychological dynamics are captured by well-es- tablished and familiar research strategies. Indeed, al- though new techniques allow one to capture phenomena that eluded earlier analytical techniques and thus can be used to reveal previously hidden characteristics, they may be inadequate for other purposes. If two variables are linearly interdependent, for example, correlation may be the method of choice in describing the relation. Even here, however, our understanding of social psy- chological process would benefit from greater temporal density of measurement, which would reveal the exist- ence of temporal patterns and evolution in the process under investigation (Tesser et al.; van Geert).

The second reason for the limited impact of the dynamic tradition in social psychology is theoretical rather than methodological. In the last few years, our understanding of dynamics has been enriched by the theoretical advances in other disciplines-most nota- bly, mathematics, physics, and biology--concerning the nature of nonlinear dynamical systems. Prior to these developments, descriptions of social psychologi- cal systems were intuitively appealing but did not often lead to unequivocal and testable predictions concerning the behavior and other properties of such systems. We now know, for example, the conditions necessary for the onset of chaos in dynamical systems, the possible types of long-term behavior of dissipative systems (i.e., attractors), and the mechanisms underlying the emer- gence of self-organization in complex systems. We also have formalisms available for the concise description of social psychological systems. Such formalisms in- clude low-dimensional dynamical systems, neural net-

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

VALLACHER & NOWAK

works, and cellular automata, among others. For each type of formal description, it is possible to derive the dynamical properties of the system through analytical techniques and computer simulations. In principle, the advances made in dynamical systems theory in the natural sciences provide for deep theoretical under- standing of dynamical properties and the conditions under which precise, concrete prediction is possible.

At present, we can only speculate about the likely impact of the advances in methodology and theory we described. It is clear, however, that these advances have fostered dramatic breakthroughs in the understanding of a wide variety of phenomena in other scientific disciplines. We believe that by embracing the advances in theory and research on dynamical systems, social psychology will be able to recapture the original in- sights of the classical theories in the field and to do so in such a way that leads to precise description and testable predictions. This renewal of the dynamical perspective also promises to provide a platform for integrating discoveries made in social psychology with those made in the natural sciences.

Social Psychology Is Already Dynamic

There is reason to believe that the dynamical per- spective is well suited to social psychology. With this in mind, several commentators ask what this perspec- tive can offer the field beyond what is already available. In particular, Carver, Kruglanski et al., and Tesser et al. call attention to the fact that important phenomena suggested by dynamical systems theory are already well documented in mainstream social psychology. Hyster- esis, for example, is manifest in primacy effects in various judgment phenomena (e.g., impression forma- tion and attitude change), and the bipolar nature of personal constructs provides an example of discontinu- ous change in judgment. Feedback loops are repre- sented in phenomena that are framed in terms of bidi- rectional causality (e.g., attitudes and behavior, self-regulation). And as Carver reminds us, the concept of statistical interaction, which goes to the very heart of social psychology theory and research, provides aprime example of nonlinear relations between variables.

Clearly, many elements of a dynamical systems approach to social psychology are already in place. Our point is that the dynamical systems perspective may allow us to assemble those elements into a coherent whole. So, although a statistical interaction is proof of a nonlinear relation between two (or more) variables, it does not tell us much about the properties of the system that produced the interaction. Would such a system, for example, display intrinsic dynamics? If so, what pat- terns would be exhibited in such dynamics? How would

such a system respond to external disturbance? Would it return to its original state, jump to a different equilib- rium, or begin a process of sustained evolution toward a new equilibrium? Would such evolution be regular or would it be characterized by abrupt changes? How can one change the properties of the system to make it regular or irregular? The dynamical systems approach may enable us to pull together knowledge concerning interactions among known variables and thereby de- scribe the dynamical properties of the system.

Even if one cannot specify all the relations among the system's variables and thus build a comprehensive quantitative model, important insights into the nature of the system can be provided by building models of qualitative understanding. As van Geert notes, formal models should not attempt to explain the phenomenon in question in all its natural complexity. Their function is to provide the greatest possible simplification of the phenomenon while providing an explanation that ac- counts for a significant amount of the phenomenon's important properties. Van Geert makes a strong case that such models should not be considered inferior to models that attempt to provide full descriptions of a phenomenon. Models of qualitative understanding and their role in social psychology were discussed at length in the target article, of course, and in Nowak, Lewen- stein, and Vallacher (1994).

Beyond the task of assembling elements into a work- ing system, the dynamical approach allows one to ana- lyze the behavior of a system in time. As van Geert notes, most social psychological research involves sin- gle-step models and hence conceals the effects of re- peated iteration of the dynamic process at work. Be- cause of the iterative nature of dynamics, an essential causal factor in a psychological process is the process itself (van Geert). This means that the state of the system at any moment in time is determined by the state of the system at the preceding moment. Observation of suc- cessive states of a system over time is thus necessary to reveal the system's intrinsic dynamics. It may turn out that the most important stable feature of a system is the type or pattern of dynamics displayed by the system. So even if one wants to derive a static description of a system, it may be impossible to do so without analyzing the patterns of change in the system. Goldstein picks up on this point and recommends the construction of phase diagrams in which the value of an order parameter (i.e., the variable that characterizes the system's dynamics) is plotted as a function of control parameters.

In collapsing across the dimension of time (e.g., by looking at average values), social psychology stacks the deck in favor of static solutions to dynamic processes. Thus, despite the feel for iteration and open-ended phenomena in the works of Lewin, James, and the other

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

AUTHORS' RESPONSE

founding fathers, their intellectual descendants empha- size forces toward achieving equilibrium. In Heiderian balance theory, for example, people are said to find a stable solution to unbalanced triads. In dissonance the- ory, the tension associated with incompatible thoughts is eventually resolved with the ascendance of one cog- nitive element at the expense of the other. The dynami- cal perspective, however, suggests that the tendency toward a stable equilibrium is but one of several possi- ble system tendencies. As noted in the target article, for example, our research showed that people sometimes achieve dynamic rather than static integration in judg- ment, alternating between two (or more) conflicting means of integrating information. Goldstein makes the case that dynamic integration may represent a highly general phenomenon, with many types of systems dis- playing the ]potential for the emergence of multiple integrative frames competing for prepotence over sus- tained periods of time.

Another valuable insight from dynamical systems is the notion of intrinsic dynamics (Nowak et al., 1994; Vallacher & Nowak, 1994b; Vallacher, Nowak, & Kaufman, 1994). We emphasized this concept in the target article because of its clear relevance for social psychological processes. Intrinsic dynamics refer to changes in the values of variables describing the state of the system when parameters describing external influence are constant. On this view, some psychologi- cal processes do not need external explanations for their occurrence; instead, they can be explained in terms of previous states of the system and its internal properties. As van Geert notes, this feature of dynamical systems may be extremely important for understanding the na- ture of causation in social psychology. Thus, the notion that people's thoughts, feelings, and actions may act as causal factors in generating other thoughts, feelings, and actions is likely to prove central to our under- standing of many social psychological phenomena (Vallacher, Nowak, Markus, & Strauss, in press). Beek, Verschoor, and Kelso prefer a different understanding of intrinsic dynamics. For them, this notion refers to a pattern of changes within a system, regardless of the internal versus external source of these changes. The distinction between internal and external causation may not be of crucial importance in the study of motor coordination, but as Goldstein and van Geert note, it is clearly essential to understanding human thoughts, feel- ings, and actions. From the very beginning, the issue of internal causation has played a crucial role in theory and research on many topics in social psychology, and as Carver notes, this issue goes to the very heart of theory and research on personality.

More generally, although many concepts and meth- ods of traditional social psychology are directly rele-

vant to the dynamical perspective, at present they are dispersed and unrelated. Without a coherent dynamical perspective, it may prove impossible to integrate the relevant features of traditional social psychology. Mes- sick and Liebrand point out, for example, that their knowledge of the rules of individual behavior con- stantly misled them regarding the group-level conse- quences of these rules. Only through computer simula- tion were they able to derive the group-level consequences of individual strategies in the Prisoner's Dilemma situation. A similar claim can be made for the value of formal models based on differential or differ- ence equations. In his commentary, for instance, van Geert provides a detailed example of how a simple model of attitude change, when formalized in terms of difference equations, may have unexpected dynamical properties that are impossible to derive from a verbal description alone. We hope that the dynamical perspec- tive will enable us to identify and integrate the relevant concepts and methods; supplement them with new con- cepts, methods, and understanding of system dynamics; and in this way form a coherent paradigm with specific theories, research strategies, and analytical tools. As Kruglanski et al. suggest, such a paradigm holds prom- ise for establishing both integration within the field and unprecedented cross-fertilization with other scientific disciplines.

Caution Is Required in Applying Dynamical Systems to Social

Psychology

The dynamical systems perspective provides a set of rich metaphors and fascinating qualitative insights into complex phenomena. Largely because of this feature, the dynamical perspective has captured the attention of many people in recent years. It is clearly tempting to speculate about avariety of things that might be chaotic, fractal, ever changing, self-organizing, or unpre- dictable. As Eiser notes, such speculation is entirely reasonable, even desirable, during the context of dis- covery. It is important to remember, however, that the dynamical systems approach derives from rigorous methods and equations of mathematics and physics. Hence, one must be careful to ensure that scientific rigor does not give way to speculation, particularly during the context of proof. We expounded on this point at some length, of course, toward the end of the target article.

In response, several of the commentators point out the generative value of the dynamical perspective gen- erally and of specific approaches tailor-made for differ- ent applications (Beek et al.; Eiser; Goldstein; Guas-

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

VALLACHER & NOWAK

tello; Messick & Liebrand). Eiser is especially adamant in arguing that too strong an emphasis on rigor can stifle creativity in the initial stages of the development of a new perspective. On the other hand, the commentators from outside the field of social psychology (Beek et al.; Burlingame & Hope) stress the need to maintain rigor and caution in applying dynamical ideas to social psy- chological phenomena. In developing this point, both of these commentaries offer valuable advice regarding limitations and precautions, as well as specific recom- mendations concerning techniques of application. The issue here is obviously one of achieving balance be- tween these opposing concerns, apoint we tried to make in the target article and which is recognized by several of the commentators (e.g., Eiser; Goldstein; Guastello).

In addressing this issue, the most fundamental ques- tion is whether the state of the field justifies the appli- cation of the dynamical systems paradigm to interper- sonal processes. The commentators, as a group, clearly appreciate the potential for application of this paradigm. The most skeptical position is presented by Burlingame and Hope. They caution us, first of all, regarding the use of nonlinear tools and advocate the use of linear models. We agree in principle that claims about nonlinear dy- namics underlying observed phenomena need to be made with caution. By the same token, however, cau- tion should be applied when claiming linearity. After all, assuming that all the relations in a given system are linear until proven otherwise carries with it very strong implications. Such a system, for instance, cannot ex- hibit hysteresis, chaotic behavior, or statistical interac- tions among variables. Indeed, the claim of linearity is much stronger than the claim of nonlinearity because linearity assumes a very specific formal relation be- tween variables, whereas nonlinearity includes an infi- nite set of possible relations (e.g., quadratic, sinusoidal, threshold, etc.), the only common characteristic of which is that they are not linear. And whereas several linear relationships can exist in a nonlinear system, the converse is not true--even a single nonlinear relation means that the system is nonlinear rather than linear.

Second, Burlingame and Hope make the strong claim that virtually no empirical evidence exists to support nonlinear dynamical patterns in psychological datasets, although they do not rule out the existence of such patterns in principle. Such a sweeping generaliza- tion ignores numerous demonstrations of nonlinear phenomena in psychology, some of which are noted by the other commentators. The demonstrations of hyster- esis and phase transitions in movement coordination (e.g., Kelso, 1995) and visual perception (e.g., Haken, 1977), for instance, were developed within the frame- work of synergetics. More to the point, perhaps, within social psychology a variety of nonlinear phenomena,

including hysteresis (e.g., primacy effects), threshold effects, and statistical interactions, have been thor- oughly documented, as noted earlier, and are consid- ered standard fare in the field. We noted some of these effects in the target article, and several of the commen- tators remind us of others (see Carver; Guastello; Kruglanski et al.; Tesser et al.).

Clearly, as Tesser notes, some nonlinear effects are easier to demonstrate than are others. The use of sophis- ticated methods to deal with the more difficult cases requires caution, as Burlingame and Hope suggest. As an example, they cite a number of considerations, in- cluding statistical tests, that should be performed if the results of the Grassberger-Procaccia method are to be used as the sole evidence of nonlinear dynamics in a system (Guastello also expresses reservations about this method). They also argue that it is safer to rely on conclusions reached by methods with a proven track record, such as Fourier analysis, than to rely on ad- vanced methods specifically designed to capture non- linear dynamics. Although we agree that time-proven methods may provide stronger proofs than would more advanced methods, we feel that the use of new methods should not be discouraged, provided, of course, that relevant assumptions are met. In order to develop the dynamical paradigm in social psychology, one needs to know which tools can best capture the dynamics of complex social phenomena. Although traditional tools may be safer, in many cases they may be insufficiently sensitive to the subtle and complex dynamics of human thought and behavior in social contexts. Until these methods are tried, we will not know which of them are useful and should be retained and which are useless or misleading and should be rejected.

Nonlinear dynamical models are usually associated with differential or difference equations. Noting this, Beek et al. point out that there are no dynamical models corresponding to empirical data in social psychology. We agree that the use of nonlinear equation models is rare in social psychology, although we do note one such model in the target article (Lewenstein, Nowak, & Latant, 1993). Although equations are commonly used to build formal models of physical and certain social (e.g., demographic, economic) systems, the develop- ment of computer simulations is presently the most common technique of formalizing the rules governing the dynamics of social psychological systems. Indeed, as suggested by Messick and Liebrand and by Gold- stein, computer simulation is arguably the most impor- tant new method for capturing the dynamics of complex social processes. Both Burlingame and Hope and Beek et al. take a reserved stance with respect to this ap- proach. The apparent concern is that computer simula- tions can blur the line between hard experimental data

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

AUTHORS' RESPONSE

and metaphor. One can build computer simulation mod- els on the basis of untested assumptions and then use the results of the simulations as proof of the phenome- non under investigation. This is a very legitimate con- cern. Just because one can simulate a process on the computer does not mean the process exists anywhere in nature. When used appropriately, however, computer simulations are among the strongest tools in the non- linear dynamical systems approach and are crucial to major discoveries in this field.

Therefore, the question is, What distinguishes un- warranted use from the proper use of these techniques? As Goldstein notes, it all depends on how well the assumptions of computer simulation are tested and what kinds of conclusions are derived on the basis of the simulations. To begin with, computer simulations may be used to investigate the implications of existing the- ory. For example, one might have a well-specified theory (developed independently of computer simula- tions) concerning the rules governing individual behav- ior and may use computer simulation to investigate the emergent properties of a system composed of N such individuals. A,s Messick and Liebrand point out, with- out the use of computer simulations, the derivation of group-level properties may be virtually impossible. By itself, the simulation does not prove whether the rules assumed on the individual level are true or false. How- ever, by comparing results of the computer simulation to empirical data on the group level, one can assess the plausibility of individual-level assumptions.

Computer simulations may also be treated as mod- els of real-world phenomena. In this approach, the requirements of computer simulations are no different from those of any other form of social theory. Com- puter simulations simply provide a language in which models are written. Thus, the knowledge of social psychologicall laws and mechanisms is essential in building simnlation models that accurately reflect the phenomenon under investigation. In social psychol- ogy, there is considerable knowledge concerning the mechanisms driving personal and interpersonal sys- tems. Hence, computer simulation models in many cases can be evaluated against existing theories and empirical data. We advocated this approach in the target article, of course, and provided examples of how it has been implemented in social psychology to date (e.g., Latant, Liu, Nowak, Bonevento, & Zheng, 1995; Nowak, Szamrej, & LatanC, 1990).

Whether one chooses to formalize dynamic proper- ties in terms of equation systems or computer simula- tion models, an important issue needs to be addressed. There can be little doubt that social psychology has managed to identify the key features of interpersonal thought and behavior. Whatever shape dynamical so-

cial psychology ultimately achieves, such concepts as intrinsic motivation, self-awareness, planning, emo- tion, mental control, goals, and attitudes will certainly play a prominent role. What is less clear is how these concepts will be measured and what kinds of models will be developed to capture them. Because of the complexity of social psychological phenomena, it is unlikely that we will ever be able to incorporate all the variables operating on all levels of social reality into a single theoretical model. A complete description of even a simple social interaction, after all, can be under- stood with recourse to myriad situational, dispositional, and historical factors that may interact in nonlinear fashion, and the nature of such interactions may them- selves change with successive iterations of the process (Vallacher & Nowak, 1994a). Hence, the main ques- tion, as posed by Beek et al., is how social psychology can choose among relevant variables when constructing dynamical models.

One strategy recommended in the target article is to use order parameters for the description of the system's behavior. In addressing this idea, Beek et al, recom- mend a potentially useful strategy that derives from the theory of synergetics (Haken, 1977). The idea is that analysis of a system's instabilities may provide a key to establishing the order and control parameters in the system, which in turn describe the global dynamics of the system. We very much agree with this approach and have advocated its use in social psychology (Nowak et al., 1994). According to Beek et al., one cannot be certain whether an order parameter has been identified unless it changes qualitatively as a result of merely quantitative changes in a control parameter. We agree with Beek et al. that those variables that best reflect changes in patterns of system dynamics are order pa- rameters, but we are not quite sure what is meant by the requirement that changes in order parameters be "quali- tative." Order parameters change abruptly during phase transitions of the first order. During phase transitions of the second (or higher) order, however, order parameters may change in a gradual rather than an abrupt fashion in the immediate vicinity of the phase transition, de- pending on the value of the so-called critical exponent (see Landau & Lifshitz, 1964; Schuster, 1984). So, although abrupt change in a variable can suggest that it is an order parameter for a system, gradual change does not necessarily mean that a variable is not an order parameter.

The approach to identifying order parameters es- poused by Beek et al. is clearly useful, but there are other legitimate and potentially useful means of identi- fying order parameters, some of which are discussed by Haken (1977). In introducing the concept of order parameter, Haken describes thoughts as order parame-

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

VALLACHER & NOWAK

ters of the brain. Such a conclusion clearly follows from theoretical considerations and intuitions about the cru- cial properties of the human brain, not from an analysis of instabilities in brain function. It is also the case that whenever onecan write a formal model of the phenome- non, order parameters can be determined by analyzing the dynamics of the equation without having to rely directly on empirical methods (Naken, 1977). Another potentially valuable suggestion of synergetics is to look at the time scale underlying the evolution of variables in the system. Those variables that evolve on short time scales immediately following a change in the value of an order parameter may be eliminated from the descrip- tion of the system. With respect to the cognitive system, for example, this suggests that one may disregard the rapid turnover in individual thoughts when describing the global properties of the mind and may focus instead on global evaluation as a likely order parameter for the system (Vallacher Ck Nowak, 1994b).

It should be noted that order parameters may have a recursive structure in that the parameters at one level of description may become dynamical variables at a higher level of anaIysis. Following Haken's example, thoughts may be order parameters for brain states, evaluation may be an order parameter for thoughts, and dynamic versus static integration may be an order pa- rameter for evaluation. Higher level order parameters can be defined in this example if one broadens the scope to consider the coordination of evaluation among inter- acting individuals. In particular, the degree of clustering of attitudes in a social group may be considered an order parameter for group-level evaluations. The idea that order parameters can be arrayed in a functional hierar- chy is reminiscent of models in social psychology that attempt to depict the structure of various phenomena, such as self-regulation (Carver & Scheier, 1990), action identification (Vallacher & Wegner, 1987), and social cognition (cf. Fiske & Taylor, 1991). This is another instance in which social psychology has shown appre- ciation for the complexity of phenomena without the help of the work on nonlinear dynamical systems. At the same time, however, hierarchical models in psy- chology often have a somewhat arbitrary feel to them (e.g., the number of levels specified, the label attached to each level) and are correspondingly difficult to vali- date. With the insights and tooh provided by such models as synergetics, it may be possible to develop functional hierarchies for individual- and group-level phenomena with greater certainty and precision. The ordering of levels, for example, may be derived from the time scales found1 to be associated with the various elements in the system under investigation as well as from the nature of the interdependencies among the elements (Vallacher et al., in press).

Dynamical Social Psychology Should Start With Social Psychology

One point that all the commentators seem to agree on is that the dynamical systems approach by itself will not serve as a panacea for social psychology. We agree with this assessment. Although the work on nonlinear dynamical systems in the natural sciences has yielded an extensive and rich set of concepts, such ideas cannot substitute for intimate knowledge of social psychologi- cal theory and research. The dynamical approach offers only methods, tools, and understanding about possible types of behavior in complex systems. Such techniques and principles can help to delimit the range of likely effects to expect in social processes and can suggest the general form of invariant principles underlying seem- ingly distant phenomena, but any theory developed within this framework must be informed by the collec- tive insight and knowledge of social psychology as a scientific field.

It is interesting in this regard that the more cautious comments about the introduction of dynamical systems principles and methods to social psychology are made by the researchers outside social psychology (Beek et al; Burlingame & Hope). These commentators claim that the dynamical systems approach may prove diffi- cult to apply to specific phenomena, let alone to the field as a whole, because the critical dynamical variables in social psychology are not identified or well understood. They argue as well that the mathematical theory of dynamical systems alone will not establish these vari- ables. According to Beek et al., establishing these vari- ables will require adopting a suitable theory of complex behavior in a system, such as synergetics. We agree that dynamical systems theory alone is unlikely to establish the key variables for social psychology. However, we suspect that even more specific theories alone, such as synergetics, are inadequate to the task. Establishing the key variables of dynamical social psychology requires intimate knowledge of social psychological phenom- ena, theories, and data. This situation actually is not all that different from the situation in the natural sciences. Thus, although mathematics is an indispensable tool in theory construction in physics, chemistry, and biology, it cannot substitute for knowledge of the subject matter in these disciplines.

There are encouraging signs that dynamical notions can be created on the basis of existing knowledge in social psychology. In social judgment, for example, global evaluation represents a likely candidate as an order parameter for the information-processing system (Vallacher et al., 1994). In a similar fashion, there are strong theoretical reasons derived from work in the social sciences to consider clustering as an order pa-

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

AUTHORS' RESPONSE

rameter for several types of group-level and societal phenomena (G. Haag, personal communication, March 14, 1996; Latant, Nowak, & Liu, 1994; Lewenstein et al., 1993). Baron, Amazeen, and Beek (1994) suggested that level of commitment is an order parameter for both close relationships and group socialization. In each of these instances, dynamical systems theory generally, or its various theoretical manifestations (e.g., synergetics, neural networks, chaos theory, bifurcation theory), can be used to determine which of these variables or their characteristics can be used to build adynamical descrip- tion of the phenomenon in question, and to suggest procedures for assembling these variables into a system. But the initial focus on evaluation, clustering, and com- mitment is based on intimate knowledge of the subject matter in question, not on knowledge of analytical techniques.

Ultimately, the development of dynamical social psychology will depend on how well the insights and tools from dynamical systems theory can be adapted to describe social psychological phenomena and how well social psychological theory and research can be recast in dynamical terms. These two sources of growth are strongly interdependent in a positive feedback loop. This interdependence of social psychological theory and dynamical systems is explicitly recognized by sev- eral of the commentators (Eiser; Goldstein; Guastello; Kruglanski et al.; Tesser et al.). This point is developed in the most concrete terms by Guastello, who presents a wide range of social psychological applications, sev- eral of which he personally developed. These include group productivity, organizational change, the relation between international polarization and war, and eco- nomic problems regarding unemployment and infla- tion. Although dynamical concepts (e.g., catastrophe models) and tools (e.g., structural equation modeling) were used to shape the nature of these applications, the focus and predictions in each case represent an under- standing of the subject matter in question. More gener- ally, dynamical systems concepts, methods, and tools provide ameans by which social psychologists can give explicit attention to the complexity of thought and behavior in an interpersonal context, and to the tempo- ral patterns by which such complexity is revealed.

It is axiomatic in science that method shapes theory as much as theory shapes method (Kaplan, 1964). The growth and refinement of a new perspective clearly requires coordinated feedback between the advances made on both fronts. From this vantage point, there is reason to be optimistic about the emergence of dynami- cal social psychology as a primary paradigm for the field. Social psychology and dynamical systems theory each has its own momentum; the coupling of their respective concepts and tools may well, through suc-

cessive iterations, produce a synthesis that is uniquely able to integrate the fragmented topical landscape that characterizes present-day social psychology. Equally important perhaps, such a synthesis is likely to promote a positive feedback loop between social psychology and other areas of science that have begun to embrace the dynamical systems perspective.

Summary

It is often said that the human brain is the most complex physical system in the universe (e.g., Edel- man, 1992; Kelso, 1995). If any system is more com- plex than the human brain, it is a set of interacting brains. The subject matter of social psychology, there- fore, is arguably the most complex of all the sciences, certainly more complex than that of physics, chemistry, or biology. We made this point early in the target article, and several of the commentators emphasize the com- plexity of social phenomena as well. It is interesting in this fight to note that several key notions that are pre- cisely defined in nonlinear dynamical systems were discussed decades ago in the context of individual- and group-level phenomena. Emergence, internal causa- tion, feedbackloops, and unpredictability, for example, are represented in a number of perspectives in classic social psychology. Only very recent developments in the understanding of complex dynamics have made it possible for the natural sciences to capture and measure these concepts in a formal and precise fashion.

From this perspective, the failure of classic social psychology to provide rigorous understanding for con- cepts such as emergence is not a reflection on the softness of social psychology; rather, it is a reflection on the inability of the tools of natural science at that time to capture the complexity of social psychological processes. In this respect, social psychology may have the potential for leading, rather than following, devel- opments in the natural sciences with respect to the description of extremely complex phenomena. For this potential to be realized, however, it is imperative that the insights generated from within social psychology be recast in terms of the most advanced concepts and tools in modern science. If the resultant theory can maintain the depth of insight offered by social psychology and the precision associated with the natural sciences, social psychology may well assume a prominent role in the emerging synthesis of science.

Notes

The preparation of this article was supported in part by National Science Foundation Grant SBR 95-1 1657.

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010

VALLACHER & NOWAK

We thank Marek Kus, Maciej Lewenstein, and Michal Zochowski for their helpful comments on an earlier draft.

Robin R. Vallacher, Department of Psychology, Florida Atlantic University, Boca Raton, FL 3343 1. E-mail: VALLACRR @ ACC.FAU.EDU

References

Baron, R. M., Amazeen, P. G., & Beek, P. J. (1994). Local and global dynamics of social relations. In R. R. Vallacher & A. Nowak (Eds.), Dynamical system in socialpsychology (pp. 11 1-138). San Diego, CA: Academic.

Carver, C. S., & Scheier, M. F. (1990). Origins and functions of positive and negative affect: A control-process view. Psycho- logical Review, 97, 19-35.

Edelman, G. M. (1992). Bright air, brilliantfire. New York: Basic Books.

Fiske, S. T., & Taylor, S. E. (1991). Social cognition (2nd ed.). New York: McGraw-Hill.

Haken, H. (1977). Synergetics: An introduction. Berlin: Springer- Verlag.

Kaplan, A. (1964). The conduct of inquiry. New York: Harper & Row.

Kelso, J. A. S. (1995). Dynamic patterns. Cambridge, MA: MIT Press.

Landau, L. D., & Lifshitz, E. M. (1964). Statisticalphysics. Ox- ford, England: Pergamon.

Latank, B., Liu, J., Nowak, A., Bonevento, M., & Zheng, L. (1995). Distance matters: Physical space and social influence. Personality and Social Psychology Bulletin, 21, 795-805.

Latank, B., Nowak, A., & Liu, J. (1994). Measuring emergent social phenomena: Dynamism, polarization, and clustering as order pa- rameters of social systems. Behavioral Science, 39, 1-24.

Lewenstein, M., Nowak, A,, & Latank, B. (1993). Statistical me- chanics of social impact. Physics Review A, 45,703-716.

Lewin, K . (1936). A dynamic theory ofpersonality. New York: McGraw-Hill.

Miller, G., Galanter, E., & Pribram, K. (1960). Plans and the struc- ture of behavior. New York: Holt, Rinehart & Winston.

Miller, N. E. (1944). Experimentall studies of conflict. In J. M. Hunt (Ed.), Personality and the behavior disorders (pp. 431-465). New York: Ronald Press.

Murray, H. A. (1938). Explorations in personality. New York: Ox- ford University Press.

Nowak, A,, Lewenstein, M., & Vallacher, R. R. (1994). Toward a dynamical social psychology. In R. R. Vallacher & A. Nowak (Eds.), Dynamical systems in social psychology (pp. 279-293). San Diego, CA: Academic.

Nowak, A., Szamrej, J., & Latank, B. (1990). From private attitude to public opinion: A dynamic theory of social impact. Psycho- logical Review, 97, 362-376.

Powers, W. T. (1973). Behavior: The control ofperception. Chi- cago: Aldine.

Schuster, H. G. (1984). Deterministic chaos. Vienna: Physik Verlag. Vallacher, R. R., & Nowak, A. (1994a). The chaos in social psy-

chology. In R. R. Vallacher & A. Nowak (Eds.), Dynamical systems in social psychology (pp. 1-16). San Diego, CA: Academic.

Vallacher, R. R., & Nowak, A. (1994b). The stream of social judg- ment. In R. R. Vallacher &A. Nowak (Eds.), Dynamical sys- t e m in social psychology (pp. 251-277). San Diego, CA: Academic.

Vallacher, R. R., Nowak, A., & Kaufman, J. (1994). Intrinsic dy- namics of social judgment. Journal of Personality and Social Psychology, 67, 20-34.

Vallacher, R. R., Nowak, A,, Markus, J., & Strauss, J. (in press). Dynamics in the coordination of mind and action. In G. Weary, M. Kofta, & G. Sedek (Eds.), Personalityfunctioning and social cognition: An action control view. New York: Ple- num.

Vallacher, R. R., & Wegner, D. M. (1987). What do people think they're doing? Action identification and human behavior. Psy- chological Review, 94, 3-15.

von Bertalanffy, L. (1968). General systems theory. New York: Braziller.

Wiener, N. (1948). Cybernetics. Cambridge, MA: MIT Press.

Downloaded By: [Vallacher, Robin][Florida Atlantic University] At: 14:12 6 May 2010