Complexity is understood differently in anthropology and the complexity studies. I discuss the two principles of socio-political organization, particularly, the phenomenon of homoarchy as a counterpart to that of heterarchy. Respectively to heterarchy - "... the relation of elements to one another when they are unranked or when they possess the potential for being ranked in a number of different ways," homoarchy is "the relation of elements to one another when they are rigidly ranked one way only, and thus possess no (or limited) potential for being unranked or ranked in another or a number of different ways at least without cardinal reshaping of the whole socio-political order." For anthropology, it is wrong to postulate that either heterarchy or homoarchy presupposes a higher level of complexity, while for the complexity students the heterarchic model is more complex than homoarchic: It is not less sustained but has a higher degree of non-equilibrium.
Introduction: The essence of the problem
By the present, the complexity studies have firmly established themselves as a highly prospective field of research that embraces actually the whole variety of the living and still nature phenomena. This definitely means that the social scientists, among others, should be sensitive and responsive to the theories elaborated within the complexity studies in order to enrich their purely social-scientific approaches with the achievements of this broader discipline. This seems especially important for anthropologists and archaeologists, as far as just for them the notion of complexity is as central and as crucially significant as it is for the complexity studies students. At the same time, what ought to be comprehended clearly at the very outset, is a meaningful difference in the understanding of the phenomenon of complexity and, hence, in the contents of the respective term, between the social scientists and complexity students. In the social sciences (anthropology including archaeology) complexity is routinely, from the 19th century evolutionists (Claessen, 2000: 15) on, understood as structural, for the rise of which different socio-economic, political, ideological, ecological and other factors or their sets are regarded as responsible, depending on particular researchers' approaches (see: Wenke, 1999: 331-385; Denton, 2004; Sassaman, 2004: 231-236). Thus, the more components, that is "levels of socio-political integration", towering each other a culture embraces, the more complex the culture is, disregarding the way the levels (the structural components of the whole) are interrelated, and this approach differs from the one employed in the complexity studies - as sustained non-equilibrium. So, in the social sciences "[definitions of complexity begin with a connotation that is as applicable to mechanical or biological systems as it is to societies: complexity is a relative measure of the number of parts in a system and number of interrelationships among those parts" (Sassaman, 2004: 231; original emphasis). A very recent clear application of this approach in anthropology and archaeology is provided by Henry Wright who further "canonizes" it by using as the background for codifying data for the "Atlas of Chiefdoms and Early States": "Total complexity... is the product of specializations of local units, local exchange, and administrative complexity" - "the sum of administrative segments and decisionmaking" levels that tower each other (2006: 3).
This approach is recognized as valid not only with respect to separate societies but to their agglomerations either: For example, a world system is regarded as a complex entity, above all, because it comprises of a considerable number of constituent societies interrelated hierarchically, i.e., divided into core and peripheral. For the majority of social scientists bothered with the problem of societal complexity at all the socio-cultural history, in its worldwide dimension, is the history of constant unidirectional growth of complexity from simple to middle-range to complex and eventually to contemporary supercomplex societies and their aggregates accompanied by the respective growth of stability understood as the societies' ability to cope with the prospect of their fission: "Change in the direction of increasing complexity goes on because more complex organization permits greater internal stability in the system" (Scott, 1989: 6). …