Evolution , Complex Systems and the Dialectic

The status oflarge scale historical macro-theories is contested both in world-systems theory and in sociology as a whole. I distinguish three types of such dynamic models: evolut ionary models , systems models and dialectical models. I define dialectical models as a family of complex systems models characterized by positive feedback (self:reinforcement or auto-catalysis). Such models lead to processes of accumulation and polarization, leading to system crisis. The games of Monopoly and Risk provide popular examples. This paper investigates the dynamic properties of three examples of such models: Myrdals model of cwnulative causation; Collins's models of Marxian transformations and geopoliti cs; and ChasoDunn and Hall's iterative model of world-systems transformations. A combination of evolutionary, complex systems and dialectical analyses has consideral:fo overlap with chaotic, far-from-e quilibr iwn types of models and with analyses of complex adaptive systems. Such discontinuous, nonlinear dynamic models show great potential for solving problems of dynamic analysis both v,rithin world-systems theory and v,rithin sociology as a whole.


l. Introduction
Within sociology as a whole, the aim of constructing predictive macro-th eories has an ambiguous place, and this ambiguity is even more marked within worldsystcms theory.The distinctive concepts of sociology were quarried out of nineteenth century macro-th eories, particularly those of Marx, Durkheim and Weber (Knapp, 1994), and their theories rested on the larger mass of historical and evolutionary macro-theories by figures such as Bagchot, Comte, Condorcet, Ferguson, Hegel, Maine, Morgan, Saint-Simon, Spencer and Tocnnics.But today, subdisciplincs concerned with social change, such as historical sociology, arc relatively isolated from the mainstream of sociological analysis, which concentrates on such contcmpo rary institutional structures as formal organization, the family, or crime and deviance, taking larger institutional dynamics for granted.This means that for many sociologists, subdisciplincs concerned with social change, such as the Political Economy of World-Sys tems arc treated as relati vely irrelevant to the main theories and the day to day work of sociological analysis.Dynamic large-scale theories of social change are more prominent within world-systems th eory.But approaches to world-systems aiming at a theory of large scale dynamics arc in tension with approaches that arc skeptical about the possibilit y of any such theory , and treat the large scale dynamic as a given context for the analysis of particular historical configurations.
Large scale theories of social change arc often driven by the simple projection of long term secular trends.Some secular trends appear to characterize the demographic, technological and economic spheres, usually conceived by Marxists as parts of the material base.With various oscillations, there has been an inexorable rise in the world's population, and long term increases in literacy, science, technology , productivity and economic production, with manifold further consequences --increas e in transportation, communication and connectedness of the world's population.Th ere has been a rise in th e size and complexity of organizations and political units.Secular trends of this kind have been one of the root<; of evolutionary theories in sociology.Such theories often attempt t o state the implications of such secular trends for the political or cultural spheres (Knapp, 1994).Such trends seem to some theorists to enable other changes in spheres such as inclusive citizenship, ethnic tolerance, gender equality or political democracy and to necessitate other developments.The Marxian conception of the expansion of th e forces of production, and their dialectical fettering by the relations of production (Cohen, 1978) formulated one model of these linkages.The evolutionary conception of mod ernization, differentiation and modern values, formulated another.
[Page 75] Journa I of World-Systems Research Sanderson (1990 ;1997) has stressed the resources of evolutionary theory.He acknowledges that many evolutionary theories are teleological, progr cssivist, overly endogenous, use a specious (functionalist) concept of adaptation, lack an adequat e concept of human agency, and impute too much directionalit y to human history.However, he argues that these flaws are accidental rather than necessary character istics of evolutionary theories .He reports that most sociolo gical respond ents believed that evolutionary theories arc sound in principle, but in need of impro vement (Sanderson, 1997).While few sociologists believe that evolutionary theories arc undeserving of criticism, only about one third believe that they should be abandoned.
The growth of technology, science, complexity, literacy, urbanism or productivity opens up possibiliti es and im poses imperatives on changes in economic, political, cultural and social relations.Social, political and cultural structures which were viable in a prcnuclcar age or in an age when primitive transporta tion and communications could slow the spread of epidemi c diseases, may be entirel y non-viable today.Fundam cn tal disagreements about historical development and social change hinge on such possibilities or imperatives.The abolition of feudalism or of slavery sugg est irrevers ible, dir ectional tendencies .This docs not imply philosoph ical, teleological or ontological necessity, and it is perfectly compatible with the notion that a natural or social catastrophe might reverse millennia of development.However, directional changes arc not a random walk.Th ey reflect an intrinsic dynamic which, for good or ill, will continue as long as the structural sources of that dynamic persist and arc not counteracted.This paper will analyze a family of models of evolution and transformation that arc based on positive feedbacks.Any process that reinforces or feeds on itself can be described as a positive feedback.loop, and such processes tend to produce a secular trend.The positive feedback.loop is one of the simplest and, arguably, most pervasive of feedback.structures.It characterizes autocatalytic or self-reinforcing processes.Positive feedback.is the natural model for processes of accumulation.

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Positive feedback.processes also have an intrinsic tendency to reach a limit and they often arc characterized by path dependency, instability and amplification of shocks.Thus, such processes and models based on them arc characterized by catastrophic discontinuities, and by chaotic, far-from-equilibrium dynamics (Hallinan, 1997;Wall crstcin, 1997).Such processes often generate tendencies to ward increased inequality and polarization, especially when applied to control of scarce resources such as wealth or land, power or influence.
The archetype of such processes arc those driven by "The Matth ew Principl e" -"To him who hath shall be given and from him who hath not, shall be take away even what he hath," from the parable of the three servants, Matthew 25:29 ( Merton 1973;Cole and Singer 1991;Knapp ct al, 1996).There arc many social processes in which possession of one resource makes it easier to acquire others.The game of Monopoly provides a clear illustration of the systemic dynamic of accumulation, increas ed rents, polarization and increased inequality leading to the collapse of the game when all players but one arc wiped out.The game of Risk, based on the accumulation of territorie s as a source of armies, provides an isomorphic geopolitical illustration.Such processes tend to produc e increased inequality as well as polarization, and thus they arc natural models for Marxian dialectical processes and transitions (Sec Figure 1 ).Although such models have naturnl applications to social dynamics.they arc "nonrccursivc."Variables cannot be arrangc(l in a cm:isal order without loops.Most of our empirical estimation techniques and conccptttal cm:isal images require tl1c assumption of a recursive mo.tel.Nevertheless.tl1c kinds of empirical and tl1corctical problems which we nO\v face may require •tis to tllink in nonrccmSi•-c tcmis.aml in doing ro. it vvill bc-ctscfol to employ a fonn of dialectical analysis.2, i;:,..-oJutionary Theory E volutionaty themy ha~ been an essential point of reference for macrn-social theoty.The otttstanding success ofDa1win's account ofmttural selection in prndncing a nonteleo logical model of organic transformation and speciation has meant that it ha~ !'Crved a~ a recurrent paradigm formacrn-social theories.l\.fore particnlarly.Dmwinian evottttion prnduccd a model of strncttiral change.which occtirs at a different time speed and a different process fu,m the observable actions of organisms.
Ho,,1e,-er. within the social sciences the aim ofmodelingmacro-theory•tqlon that of evohttionaty theozy ha~ always been shaIJlly contested.E vohttionarytheory ha~ been closely tied to Social Dmwinism.which ha~ ideological and theoretical implications deeply antagonistic to those of social science.Moreover.the limitations of Darwinian evohttion a~ a theozy.even in its home sphere of the analysis of biological variation.are rein forced in the sooial sphere.where there are no mechanisms directly analog,m~ to seimal reprnduction.DNA.organism death or selection.Accordingly.evolutionaty model.., of social change arc often diffuse analogies which give no theoretical explanation of the long term secular trends.
[Page 78] Journal of World-Systems Research One of the great virtues of Sanderson's (1991) analysis wa.., to show the interconnection between theories of macro social change and specific, local sociological theories.Sanderson (1997:94) ha.., rightly stressed the fact that the cla..,sic sociological theorists often held evolutionary a ... sumptions.He mentions Durkheim's Division o.lLabor in Society, but it would be equally correct to stress evolutionary themes in Marx, Weber, Mead, Spencer or Park.The fact that early sociologists were concerned to explain powerful, long run directional transformations mean that they had to come to terms with Darwin's evolutionary theory.For example, Marx offered to dedicate Capital to Darwin and the Afterward to the first German edition described the dialectical method in terms of evolutionary theory.There, Marx gave an extended quote from a Russian review which had underscored the aim of establishing objective laws of motion which operate independently of human volition.The review had a ... scrtcd that there is a law of the connection between political-economic phenomena at any time, and that there arc laws of variation governing their development and transition.The review continued that Marx, "proves, at the same time, both the necessity of the present order of things and th e necessity of another order into which the first must pa..,s over; .... Th e old economists misunderstood the nature of economic laws when they likened them to the laws of physics and chemistry.A more thorough analysis of phenom ena shows that social organisms differ among each other a.., fundamentally a.., plants or animals .... Th e scientific value of such an inquiry lies in the disclosing of the special laws that regulate the origin, existence, development and death of a given social organism and its replacement by a higher one."(Marx 1974[188 7]: 17-9) [Page 79] Journal o.l World-Systems Research Marx adopts the reviewer's view that the aim and method of Capital is lik e that of biological evolution ary theory, and he identifies this aim and method a.., that of the "dialectic," commenting, "Whilst the writer pictures what he takes to be actually my method, in this striking and [a.., far a.., concerns my own application of it] generous way, what else is he picturing but the dialectical method ."(Marx ibid .)This virtual identification of dialectic with the method of biological evolutionary theory raises a number of questions, to which we shall return in the fourth section of this paper.However, it is evident that Marx, as well as all the other classical sociological theorists, whatever their admiration for some aspects of Darwinian theory, also maintained a distance from it because of its ideological affiliations, because of the limitations of Darwinian theory as a theory oflong term change, and because of the dis-analogi es between biological and social evolution.
During the late nineteenth and early twentieth centuries, the most influential evolutionary social theories were those associated with Spencer, Darwin, Galton and Sumner, based on conceptions of biological inequality and liberal individualism.World War II, the Holocaust and the New Deal were an abyss for this kind of evolutionary social theory, and the forms of evolutionary theory which reappeared after World War II disassociated themselves from biological assumptions of European genetic superiority.Nevertheless, there remained powerful historical and logical connections between evolution, biological natural selection and justifications of individual and group inequality.Evolutionary theories tend to be drawn to liberalism by a kind of hidden gravitational attraction.And this connection is important because of the resurgence today of ncoracist evolutionary theory (Rushton, 1995;Levin, 1997;Jensen, 1998;Taylor 1998).

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Moreover, even aside from its ideological affiliations, Darwinian theory has limitations as a theory of long run changes, even in its home sphere.The assumption that mutation s arc random, that modifications build on each other and that adaptation is relative to a given environment means that there is no reason to suppose that an evolutionary process, if repeated, would produce the same outcome.Natural history cannot ground prediction s.While the theory of natural selection provides a framework for analyzing the process by which long run evolutionary trends came about, there is doubt whether the gradual accretion of adaptive changes provides a sufficient or an adequat e account.Gould (1989) has stressed the discontinuous rates of change, with cascades of evolutionary modification, punctuated with mass extinctions.A mammal is "higher," "more adapted," or "more complex" than a cockroach only in a value-laden, ambiguous and und efined sense.Levin & Lewontin ( 1985) have stressed that what evolves is not an organism, subject to a fixed and given environment, but an ecosystem.Theorists of complex adaptive systems such as Kauffman (1993), have stressed that mutual interconn ection and adaptation is subje ct to "red queen effects" (from the scene in Alice In Wonderland in which one must run to stay in place).If one set of organisms is developin g massi ve attack claws and teeth, while another set develops increasingly massive defense armor, then each may be more "adapted," so that organisms without the attack or defense features will be weeded out.But they arc adapted to each other and to a specific environment ; probably "adapted-in-general" is a nonsen se category .Their adaptation, like that of the nation state a.., a war making machine, does not mean that they are adapted to other environments or threats, such a.., climatic changes or disea..,e.

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Moreover, even if the process of natural selection were an adequat e and suffici ent account of biological evolution, there are powerful differences between biological and social evolution.Processes of social, cultural and political change ar e often Lamarkean rather than Darwinian and operate on an immensely shorter time scale.Van Parijs (1987) shows that even restricting consideration to the two processes of blind selection and of reinforcement (and diffusion), the combination oflocal equilibria and interaction may produce a highly discontinuous, unpredictable process.Sanderson detaches evolutionary theory from progressivism and teleology at the cost of making it nonpredictiv c, by arguing that societies are not adapted, but individual behavior is adaptive.How ever, this risk.., merely saying that people do what they do because it seems to them like a good idea at the time.It is unclear that this generates a theoretical explanation of any long run directional trends, particularly consequential material trend ....

Complex Systems
A central insight of sociological theory, in opposition to the liberal individualism typified by Spencer, wa.., that social structures have properties which are not ea..,ily or obviously a function of the individuals who are members of those social structures.The dynamics of a hurricane are not well-analyzed in terms of the trajectories and dynamics of individual rain drops (Mahew, 1980).Social structures may reproduce or perpetuate themselves independently of the awareness and intentions of individual....One of the ba..,ic attractions of biological evolution a.., a model of large scale change wa.., the promise to provide a model of macro-structural change.Similarly, one of the ba..,ic insights of world systems theory, in opposition to modernization theory, wa.., that the structure of the world system exists and reproduces itself independently of the position of various societies, states and regions within it.

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During the twenti eth century, systems theories have been an important body of analytical techniques that are relev ant to such holistic properties of structures.Since its origin in engineering analysis, systems theory has developed into a numb er of heterogeneous bodies of analysis with separate jou rnals, methodologies and almost non-o verlapping literatures.For example, general systems theory was an ambitious programs for a general theory of all holistic structures (Von Bertalanffy, 1968).It inspired subsequent attempts to model system needs of organizations on those of all living systems (Miller, 1995).Cybernetics (Weiner, 1965) generated a va..:;t array of analyses of information systems.Systems dynamics constitutes a family of techniques for simulating feedback models in the investigation of organizations, urban or ecological processes (e.g.Forrester 1969;1971;Collins, 1995) Systems analysis and operations research constitute a wide variety of ways of breaking down an organizational structure or proc ess (Cortes, 1974).Thes e and similar bodies of theory have demonstrated the possibility of powerful counterintuitive dynamic effects of system structure, and in the pa..:;t decades, the technical capacities of computer modeling have led to a powerful explosion of simulations of complex system dynamics (Collins, 1995;Bar-Yam, 1998).
The dynamics of a system can always be represented in at lea..:;t two ways: a..:; a set of causal relations operating between parts, and a..:; a trajectory in a pha..:;c-spacc.Even very simple deterministic nonlinear systems may generate non-repeating, unpredictabl e trajectories that exhibit discontinuous shifts from one region to another of the pha..:;c space (Lewin, 1992).
The potential for constructing dynamic holistic models of social structures hav e been one of the main promises of systems theories.However, those promises have been largely unfulfilled.Burns and his collaborators (Burns & Bueldcy 1976) distinguish 11 morphosta..:;is, 11 systemic processes operating within a given structure, maintaining that structure, and "morphogcnsis" the kinds of processes operating to transform the structure.In principle, both kinds of processes can be investigated with systems methods, concept..:; and simulations.In practice, systems models have concentrated almo st exclusively on "morphosta..:;is" and have great difficulty dealing with the genesis and transformation of systems .Dynamic simulations that treat the structures and relations a..:; given often a..:;sumc away precisely those processes that most sociologists would consider "dynamic. 11Empirical analysis of (nonrccursi vc ) models with feedbacks raises formidable technical problems.For example, such feedbacks will violate a..:;sumptions of uncorrelat ed error terms, which allow simple lea..:;t squares estimation, and they will often produce identification problem..:;, which make empirical estimation of causal effects impossible.While there arc technical solutions to many of these problems, such a..:; two stage lea..:;t squares estimation techniques (Berry, 1984;Brown, 1995), they arc inconv eni ent and make demands for data and rigorous theory which we often lack.

Journa I of World-Systems Research
The result of thes e problems is that system..:; models arc often static analyses by stipulati on.A set of components and of causal forces is a..:;sum cd and treated a..:; given; their simula tion is not connected to empirical evidence that the causal forces arc a..:; a..:;sumcd in the model.Such simulations may be useful in showin g implications of theoretical a..:;sumptions or the sensitivity of a dynamic to variation in som e component parameter (Hanneman and Collins, 1987;Collins, 1995).Sometimes simulations show that no plausible variation in some inputs or causal connections makes much difference to the operation of such system.Forrester constructed well-known simulations suggesting that all the currently considered solutions to some problem were bound to fail (1969; 1971 ), either because the proposed solutions generate feedback incr ca-;cs in the initial problem, or because alternative paths make changes in some inputs or par amctcrs ineffective.
Thus, even without quantitative estimation, the qualitative structure of causal relations, is often far more important than the quantitative size of its component parameters.For example when variables arc part of a mutually reinforcing complex, sorting out the quantitative effects of any one of them is often both ferociously difficult and practically irrelevant.Often, what is important dynamically is the net mutual reinforcement of th e complex, which may lead to qualitative system dynamics such a-; path depend ence, instability and amplification of small differences in initial conditions.Moreover, systems of positive feedback often have two properties which arc extremely useful in explaining structural change: they often produce a secular trend, and they often produce incrca-;cd inequality and polarization.In both cases the dynamic reaches a limit, either external or internal.We shall consider three examples of systems of positive feedback: Myrdal's analysis of cumulative causation, Collins's models of Marxian crises; and Cha-;c-Dunn and Hall's iterati ve model of world-systems transformations.Each of them can be understood a-; an evolutionary dialectical process.

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Journa I of World-Systems Research a) Myrdal: In An American Dilemma (1944), Myrdal argued that minority group disadvantages encoura ge white racism ( e.g.white supremacy, segregation and stereotyping) which reinforce minorit y disadvantages.Myrdal developed the conception of group advantages or disadvantag es a-; a mutually reinforcin g, auto-catalytic proc ess.He suggested that group characteristics such a-; mean education, job skill -;, percent employed, incom e, wealth, health, credit rating, political influence, marital stability, or law-abidingn css arc mutually reinforcing.Advantag es promote other advantages; disadvantages promote other disadvantages.The result is a vicious cycle that tend-; to produce greater inequality , polarization and segregation .
Myrdal's Nobel prize wa-; ba-;cd on the idea that cumulative causation (both as vicious cycles of poverty and a-; beneficent cycles of develop ment) is central to the analysis of development and institu tional transforma tion (1968;1970;Agrcsano, 1997).Th e mutual reinforcement of advantages or disadvantages, often called the Matthew Effect in sociology (Merton, 1973), operates at several levels of analysis (Knapp ct al. 1996) .An individual's charac teris tics may affect his or her life chances; they may affect a-;pirations and identity ; and the characteristics of an individual's neighb orhood, ne twork, famil y, racia l or ethnic group may affec t the individu al's life chances, either directly or by influcnci11g the resp_,nses of others.A whole society may have advantages or disadvantages which c,,Qn,,ll.atcabsohltely or relatively.Because each element reinforces the otl1ers i11 tl1e complex., in the absei1ce of othei• force, such as go .... -emmei1t polity, su.ch a system will teml towanl increased i11eq,,ll.llityand pola1iz.ation.

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The central model is related to the core MCM' model from Capital.Profit-making leads to the incrca-.ingorganic composition of capital a-.well a-. to the concentration of capital, the decline in the numb er of capitalists and an incrca-.e in the rate of unemployment (the reserve army).In the standard run, this leads to uncrca-.cdunemployment, depressio n, inequality, and the erosion of the power ba-.e of capitalists and loss of state pow er --th e ela-.sicscenario of Marxian revolution.The further dynamics of Collins's model flow from its a-.sumption that, since capital accumulation is funded out of profits, the loss of state power by the capitalist cla-.shalts capital accumulation, leading to the stagnation of the economy, and the furth er rise of unemployment.Thus, Collins and Hanncman's second model of the post-revolutionary situation avoids this stagnation by having the state function a-. an organ of planning and capital accumulation -leading to a statcmanagcd economy.But what is possible in the post-revolutionary situation, Collins and Hanneman suggest, is also possible under capitalism, and so they construct a third model, in which the rise of unemployment and capital concentration is avoided by the development of a welfare state .
Thus, Collins produces a single model of accumulation, whose developmental dynamic branches into three trajectories: revolution followed by collaps e; revolution followed by state-planing ; or avoidance of revolution by a welfare state.The concept-.arc unremarkable ; the paramete r specifications are debatable; th e traj cctorics do not appear to exhaust all possibilities.But what is importan t is that the analysis derives substanti vely important alternative outcomes often conceived a-.representing fundamentally different causal stru ctures, a-.branching paths from the same model , given relati vely small chang es in some param eters.
The central divergences of the models result from shifts in state power, and the authors do not elaborate their a-.sumptions with respect to this parameter.Th e substance of t he analysis requires further investigation.A fundamental virtue of the model is that it shows that reasonable assumptions about ways that unemployment and inequality result from the self-reinforcing cycle of capital accumulation and about the impact of unemployment and inequality on political mobilization make it possible to develop plausible dynamic model.., of social transformations producing substantively interesting diverging traj ectorics.

Journal of World-Systems Research
It is interesting that Collins fails to relate this endogenous system model to the intcrsocictal, geopolitical model that Collins claims is the central explanation of the transformation and dissolution of the Soviet block (Collins,1992).In that model, expansion arises from the feedback loop in which the territorial size of th e conquering state leads to greater resources, which lead.., to military advantage and regime legitimacy .
The expansion hits limits (represented by negative feedback loops) when the expanding state attains a central position (king of the mountain, eliminating marchland advantage) and to logistical overload.., (1992: 1560).Collins maintains that in the 1970s, the former Soviet Union wa.., reaching those limits, leading to unravelin g and collapse.He suggests that the geopolitical model, at the largest time scale, can be usefully connected to internal dynamic models, such a.., Tilly's, in which military success lead.., to intensive resource extraction, which lead.., to state organization which lead.., to military success .
The self-reinforcing character of Collins's geopolitical arguments (1992) can be simply represented by a positive feedback loop of domination, directly analogous to the positive feedback of advantage and accumulation.Control of population, coercive reso urccs or strategic area.., may help a power to acquire further resources.The game of Ri sk in which territories yield armi es, and armies yield territories, is a simplifi ed archetype of this dynamic.Myrdal stress es that the loop of cumulative causation is unstable --the way up is the way down.The amplification of advantages generates a beneficent cycle, but if anything brings that proc ess to an end the amplification of deficits will generate a vicious cycle (unless one happens to end on the knife edge of an unstable equilibrium ).The process of domination is unstable and path dependent in the same way.The accumulation loop generates inequality, which is reinforced by the transfers of reso urces from th e poor to the afllu cnt, and the process of domina tion should generat e pow er inequalit y and concentration of power in the same way.(1997).A central construct of world-systems theory has been the self-maintaining reproduction of inequality between core and periphery, which produces a powerful dynamic over the la<;t 500 years.The system ha<; depended importantl y on the incorporation of new groups and new area<; into the world economy.Those proce sses inexorably approach limits when 100% of the world's population and territory is incorporated.At those limits the irresistible force of incorporation hit<; the immovable object of global limits, producing systemic crises.An idiographic answer to the question what happens next is that system dynamics can only predict that there will be a crisis, but outcomes arc necessarily invisible.A more theoretical approach extends the theoretical definition of world-systems from the modern, global, capitali st world system to prior world-systems Though not global, they were world-systems in exhausting or nearly exhausting the reach of commercial, political and cultural networks.Thus they constitute a rca<;onably large universe of inter-societal systems that came into existence, expanded and then been merged or incorporated into larger systems.Cha<;c-Dunn and Hall 's analysis of the dynamics governing the "rise and demise" of such systems marries a theory of scmipcriphcral institutional innovation to the model of circumscription developed by Carneiro, Harris, and Cohen (Cha<;c-Dunn & Hall 1997;Sanderson, 1995).The theory of scmipcriphcral innovation ha<; roots in Trotsky's concept of uneven and combined development, Gcrshcnkron's analysis of the "advanta ges of backwardness," Service's distinction between adaptation and adaptivity, and Quigley's concept of the institutionali zation of an instrument of expansion (Cha<;c-Dunn & Hall 1997: 78 -82) .The dominant core states arc institutionally inflexible because of the sunk costs of commitment to institutional forn1s which arc the ba<;is of their core position.Peripheral area<; arc also locked into the existing institutional structures both by their poverty and by tics to the core, but some scmipcriphcral societies arc in a position where it is possible to make structural innovations and to implement them.The ncgaiivc paih~ opcraic as a sci of ( icmponuy) safciy valves.relieving popttlaiion pressure.
[Page <xl] J()t1111t1 l 1){ W()rl<l-Systent~ Re~ean:h A posiiivc feedback loop icml~ io cx.pamhmiil ii hiis a limii.One ofihc simplcsi way of rcprcscniingswili alimii is as a ncgaiivc feedback loop.Chase D(tnn and Hall rcprcscni ihc processes ofhicrarchy fonnaiion and inicnsifkaiion as o.;nnccicd ioncgaii,-c feedback loops involving popttlaiion pressure.circttmscripiion and conflici.The process ofcircrumscripiion was o:,nccivcd by Carncim (1970) io acm(tni for ihc fonnaiion of pri~iinc siaics.Popttlaiion pres,urc play, akcyrnlc.parilybccim~ coercive conirnl is difficrttli io accomplish if a dominaicd popnlaiion can move away.Chasc-D(tnn and Hall ,ttggcs i ihai ihc da,nre of ihc S;'> icm and iis hiiiing limiis ( demographic.ecological and its ability to handle internal and external conflict) arc central to other transformations of world-systems, as well as to state formation.It is the circumscription of the core powers benefiting from a given mode of appropriation that opens opportunities for semiperipheral innovation.
I cannot pursue this analysis further here, except to make one remark about the mutual reinforcement of hierarchy and intensification in relation to circumscription.We have suggested that hierarchy and intensification are not only mutually reinforcing, but that each of them constitutes a self-reinforcing process of accumulation/domination with intrinsic limits.The accumulation of capital and increase of productivity is analogous to Monopoly; the accumulation of power and domination to Risk.But of course, the economy docs not always polarize as in Monopoly; and conflict within the political state system docs not always end in world empire.If there arc intrinsic tendencies of such feedback loops to do so, this raises the question what counteracts those intrinsic tendencies.A central insight of world-systems theory is that it is the linkage of the two processes; a central issue of the circumscription model in the case of the circumscription of a world economy, is the breakdown of that linkage.
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Dialectical Theory
Traditionally, Marxists have dealt with the problems posed by evolutionary chang e, complex systems and system transformation by using concept s of the dialectic.However, the consolidation of a world-view and analytic strategy in opposition to mainstr eam liberal social and political thought sedimented a considerable amount of ideological baggage onto conceptions of dialectics.Even if we exclude the dialectics within classical Western philosophy, "dialectic" refers to a number of different kinds of analysis done by figures such as Hegel, Marx, Engels, Lenin, Loquacious, Stalin, Mao Zedong, Gramsci, Adorno, Habcrmas, and Bhaskar.It is doubtful that any single schema could welldescribe the key features of all of them.
We saw that Marx identified "dialectic" with the view that everything is changing and finite --nothing lasts forever.Engels characterized substantive dialectic as a process, "the great basic thought that the world is not to be comprehended as a complex of readymade things, but as a complex of processes, in which the things apparently stable, no less than their mind images in our heads, the concepts, go through an uninterrupt ed change of coming into being and passing away, in which in spite of all seeming accidcntality and of all temporary retrogression, a progressive development asserts itself in the end ... 11 (Engels 1888).

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It is possible to distinguish two broad branches of dialectics that are complementary and interrelated: epistemological (concerned with the transformation of concepts) and ontological or substantive (concerned with objective transformations of "things," Knapp & Spector, 1991).They are interrelated partly because the development of concepts and theories can be understood a..:; a natural social process or practice.Cultural categories build on each other and develop by a process similar to cumulative causation and positive feedback..As a theory of knowledge, dialectics often refers to a circular or nonfoundational epistemology (Rockmore, 1986), ba..:;cd on a feedback model of practice.Herc, we lay a..:;idc conceptual and epistemological a..:;pccts of dialectics to focus on substantive processes.
Traditionally, Marxists have approached substantive dialectics in terms of a family of concepts derived from Hegel, including negation, contradiction, dircmption, limit and sublation.Such concepts have a natural affinity with positive feedback dynamics.While neither Hegel nor Marx were "system..:; theorist..:;," Hegel had an acute sense of the ways in which cultural, political, social and historical arrangements and process es were often selfrcinforcing.He also recognized that such processes tended to p roducc accumulation and polarization and to hit limits, so that they become self-destroying by the same dynamics which had been self-reinforcing.Marx admired and develop ed these idea..:; , and later Marxists have applied them in a host of ways.
More generally, Marxists have approached substantive dialectics a..:; a focus on process.Anything whatever is changing; it is not only what it is but also what it is becoming.Anything whatever is finite; it will not la..:;t forever; it allows a "historical section" which traces its origin and self-maintenance to its demise.

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This clearly wa..:; the central idea that Marx a..:;cribed to biological evolution, as remark ed above .It is because any thing is interconn ected with everything els e that it is a..:; it is; and so these interrelations can be defined a..:; part of its essential being.And this inclusiv e or systemic conception of the thing to be explained leads to the centrality of the concept of contradictions a..:; the ba..:;is of an explanation of developmental dynamics and developmental possibilities (Knapp & Spector, 1991).Thus, Marxist treatm ents usually cmpha..:;izc interconnection, holism, transfo rmation, finiteness, accumulation, polarization, limits and contradiction.
This essay has stressed that there is an affinity between these aspects of dialectic and the dynamics of complex systems, particularly systems of positive feedback.Not all analyses of positive feedback arc dialectical; not all dialectical analyses concern positive feedbacks; but most systems of positive feedback arc highly likely to display dialectical properties.
Systems of positive feedback are simple and arguably pervasive.One example of this process is an accumulation loop (Monopoly) in which control of economic resources leads to further resources.Another is the process of domination (Risk) in which control of power or coercive resources generates further power.Both processes arc recursive and must ordinarily be analyzed as holistic systems, and both tend to be unstable and path dependent and to generate inequalities.The tendency to generate inequalities is one reason that the concepts of contradiction and conflict arc apt; the fact that their expansion tends to bring them into collision with limits (such as ecological carrying capacity) is another.

Journa I of World-Systems Research
Thus, I would agree with the enigmatic opening sentence of Ekhardt's essay, "A Dialectical Evolutionary Theory of Civilizations, Empires and Wars." A "dialectical evolutionary theory" tries to relate the concepts of civilization, empire, and war to one another in such a way that their interaction results in positive feedback loops leading them ever upward and onward in a spiraling motion, unless and until it leads them in the opposite direction by way of negative feedback loops which reverse the direction of the spiral."(Eckhardt, 1995:75) As a matter oftcnninology, a vicious cycle or downward spiral is usually also term ed a "positive feedback loop," since it is a same-sign causal loop.In any case, Eckhardt postpones discussion of it to later publications.His analysis uses time series data on civilizations (measured by Krocbcr's geniuses), empires (measur ed by Taagcpcra's territorial size), and wars (battles) to argue that variations in these over time arc highly intercorrelated and to show an ( exponential) increase in these variables over thre e millennia.This is certainly consistent with a self-reinforcing, autocatalytic process of accumulation and domination.
There are some limitations of Eckhardt's model specifications and historical data.
Correlations and factor analyses arc weak evidence of causal conn ections, sinc e it is notorious that variables often tend to move together over tim e even when ther e arc no causal connection among them.Moreover, when the data arc historical mentions (of, say, battles), there is the further problem that historians' mentions of anything -rats, clouds or sexual peccadillo es -arc often a function of the gross volume of historical analysis focused upon a period or a group .

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Moreover, Eckhardt's analysis is only dialectical in a limited sense.No qualitative changes are posited over the entire three millennia, but merely an invariant correlation of civilizations, empires and wars.It would appear that the relevant question is wheth er or not the social dynamic ha.., changed.Nevertheless, the virtue of Eckhardt's analysis is that it links the concepts of dialectics and positive feedback.
From the standpoint adopted here, there arc three main implications of the sclfrcinforcing processes plausibly involved in this transformation : • The dynamics of development also generate inequality within and betwe en the political units.• Development tends to collide with external and internal limits.
• At the limit of expansion, positive feedback loops arc transformed from a beneficent cycle of development to a vicious cycle of collaps e.
Self-reinforcing processes arc powerful analytical tools in accounting for long term social developments and their possible branches.If groups with one kind of resource arc in a strong position to acquire other resources, the result is a dynamic that generates accumulation, inequality and polarization.Moreover, the same dynamic that generates expansion insures that limits to that expansion produce an inherently unstable situation, and collapse or contraction.

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There arc at lca..,t two bodies of analysis that such a theory can mobilize and integrat e.The first is the burgeoning analysis of the dynamics of complex non-linear systems .Th e second is the older body of diale ctical historical and political analyses.The idealism and obscurantism of many of Hegel's constructions is well known.But whatever else he wa..,, Hegel wa.., an erudit e historian and systematic thinker who wa.., extremely sensitive to self-reinforcing processes of accumulation and to their tendenc y to produce polarization and conflict.His cultural, political and historical analyses have been extended, since then, by Marxist think ers.Rcca..,t in systems terms, even torturous forms of argument from the Philosophy o.lH istory, which arc utterly inadequate a.., theory, arc immensel y intere sting theoretically a.., outcomes to be explained.For example, the great overall structure of that work pictures a "world spirit" that undergoes a discontinuous development with geographical displac ements.After a rhythmic development in one area, such a.., Persia, the "world spirit" takes a flying leap to another, such a.., Greec e. W c arc only now in a position to theoretically grasp and empirically analyze the kinds of discontinuit y and geographical displacement to which such Hegelian dialectical analyses drew attention.

Conclusion
It ha.., been remarked that all theories of history (and hence all macro-dynamic models) boil down to a circle or a line .Evolutionary theories produce lines in the form of directional secular trends.Cyclical theories generate circles, which include the degenerate circle of a point (i.e .arguments that human nature is everywhere the same) and the snow storm of postmodcrnism (i.e.arguments that all patterns and macro-theori es arc merely subjective forms of ideological domination) .Dialectical theorie s arc often viewed a.., combining cycles and trends -a cycle leading to an advance and a recapitulation at a higher level -producing a kind of spiral.

Journal of World-Systems Research
This essay has argued that a common and pervasive form of dynami c system -the positive feedback loop -produces many of the characteristics of dialectical systems.Classical dialectics produced a somewhat portentous apparatus of concepts for analyzing change, such as diremption, contradiction, negation, sublation and limit.Cont emporary systems dynamics and analyses of non-linear systems, provide useful tools for analyzing social transformations, and produce systems with discontinuou s dynamics that are easily described in terms of dialectical categories.They generate systems that often accomplish accumulation by a dynamic that necessaril y creates polarization ("diremption'), and whose historical trajectory may be both forked ("bifurcation") and repeat at a hi gher level of prior developments.The concepts oflimit and contradiction give the essential dynamics of such systems.The marriage of the richness of the traditional concepts of dialectic s with the quantitative techniques of contemporary dynamic systems analysis is a promising way to address many contemporary theoretical problem s.

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Page 88] Journal of World-Systems Research c) Cha..,c-Dunn and Hall: A third example of a systemic model of social transformation is the iterative model ofworld-systc1rn transformation developed by Cha..,c-Dunn & Hall

[
Page 89]Journa I of World-Systems ResearchThe core of Cha<;c-Dunn and Hall's model of political circumscription is the positive feedback.loop connecting hierarchy formation and intensific ation.Hierarc hy form ation refers to "increa<;c s in socially struc tured inequalities within or among soci eti es (e.g.cla<;s formation, state formation, or empir e formation)" (Cha<;c Dunn & Hall 1997: 101-3), and intensificati on refe rs to "techno logical innovat ions and the adoption of intensifi ed production practic es" (ibid.).Hierarchy an d intensification arc formulated abstractly, to apply to different modes of accum ulation in different epochs.1n Marxist terms, they arc analogous to the relations and the forces of production.Cha<;c-Dunn and Hall (1997: 102)   suggest that similar dynamics repeat themselves (iterate) in the tran sformati ons of "modes of accumulation."Several a<;pccts of the model highlight the characteristics of positive feedback.models of accumu lation and domin ation.nnd powcrfol inicr~iion bciwccn hicrruclly fonnaiion nnd inicnsifkniion, aml • ihc grcai posiiivc loop involving i~ oilier six.variables ( ignoring ihc five ncgaii,-c paihs.
and which generates a "dilemma" between a value commitment to an open society and the dynamic of unequal life chances and segregation generated by cumulative causation .A similar functionalism deformed his developmental economics.