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Mathematical model of societal productive forces structural evolution is discussed, particularly with regard to evolution of social production of life. There are an a lyzed some methodological grounds and issues of mathematical modeling, like correlation between accuracy and complexity/simplicity of models. There are pre sented both concep tual model of social production of life (by V.Khmelko) and mathematical model developed according to the conceptual one.

This article offers an analysis and mathematical modeling of the influence of
one of the major factors of the World System macrodynamics throughout most
part of its history (since the 'urban revolution') – the factor of interaction of
civilizations with their barbarian periphery. The proposed mathematical model
is intended to describe possible influence of interaction between civilizational
core of the World System and its barbarian periphery on the formation
of the specific curve of the world urbanization dynamics. It simulates completion
of the phase transition, behavior of the system in the attraction basin and
beginning of the phase transition to the attraction basin of the new attractor
and is aimed to identify the role of the factor of interaction between the civilizational
core and barbarian periphery in the formation of attractor effect during
the completion of phase transition, that is for clarification of the reason
why there was observed not only slowdown of growth rates of the main indicators
of the World System development after completion of phase transitions
during its development, but also their falling with the subsequent temporary
stabilization near some equilibrium level. Achievements of modern barbarology,
including the understanding of complexity of the barbarian periphery itself
and its heterogeneity are considered. The basic principle of the proposed dynamic
model is that sizes, power and level of complexity in realization of external
policy functions in nomadic unions (empires) closely correspond to sizes,
power and level of political culture and activity of the core states with which
nomads constantly had to do (this point has been established in works of the
known experts in nomadic studies). Various alternatives are shown in the model,
when depending on power and size of one of the two components of the system 'civilization – barbarian periphery' studied by us, another one also
changes significantly as it has to respond to the challenge properly, or can
make less efforts feeling no threat or resistance. This principle is observed
throughout the long period of the history of the World System. It is shown that
interaction between the civilizational center and barbarian periphery really
can explain some characteristic features of the World System dynamics in the
4th millennium BCE – the 2nd millennium CE. The ways of further development
of the model are outlined.

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear,
second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically.

Demonstrates the value of mathematical modeling in social movement research, particularly for investigating collective action. Eight fundamental principles in generating & analyzing formal mathematical models are outlined & some strengths & weaknesses of mathematical modeling & simulation approaches are identified. Some specialized computer programs ideally suited to working with these models & simulations are reviewed. For the nonmathematically inclined, some principles are offered to guide the evaluation of formal models used in others' research. 1 Figure, 1 Appendix, 51 References. K. Hyatt Stewart

"'Who says what to whom, through what channel and with what effect?' - damit wollte Harold Lasswell 1948 das Feld der Kommunikationswissenschaft beschreiben. In die gleiche Richtung weist das mathematische Kommunikationsmodell von Shannon und Weaver: Sie wird bei ihnen zu einem Konzept der Nachrichtentechniker, die Medien als Kanäle verstehen und über Signalgebungen und technische Informationsbegriffe grübeln. So entsteht ein naturwissenschaftlich inspiriertes Kommunikationsmodell, das in der sozialwissenschaftlichen Kommunikationswissenschaft vorherrschend wird. Es hat auch deswegen soviel Akzeptanz gefunden, weil es für die quantitative Kommunikationsforschung gut verwendbar war. Sozialwissenschaftlich inspirierte Ansätze blieben demgegenüber randständig. - Sie konzipieren Kommunikation als soziales Handeln im Sinne Max Webers oder untersuchen sie wie die Cultural Studies von den jeweiligen Handlungskontexten her, schließen an Meads Vorstellungen von Interaktion als wechselseitige Interpretation von Symbolen oder an die Theorie kommunikativen Handelns von Habermas an. Der Vortrag analysiert Konsequenzen, die sich aus einer derartigen naturwissenschaftlichen Kommunikationsvorstellung ergeben: Sie ist kommunikator- statt rezipientenorientiert, tendiert zu technizistischen, isolierten Konzepten und dazu, die Frage nach dem Warum und Wozu zu übersehen sowie, die sozialen und kulturellen Kontexte mediatisierter Kommunikation einerseits und ihre Bedeutung für die Rekonstruktion der Kontexte andererseits zu ignorieren. Schließlich überbetont sie Inhalte und verdinglicht Kommunikation mit und mittels Medien als etwas eigenständiges, anstatt - gerade heute wichtig - verschiedene Formen von Kommunikation zu analysieren, die wie Fernsehen, Schreiben, Telefonieren oder Computerspielen alle von dem auch von Gesten begleiteten Face-to-face-Gespräch von Menschen miteinander abgeleitet sind. Von daher kann man sagen, dass ein derartiges naturwissenschaftliches Modell für manche Fragestellungen adäquat ist, dass sich aber eine sozialwissenschaftliche Kommunikationswissenschaft darauf nicht beschränken darf: das wird angesichts des Wandels der Medien gerade heute immer deutlicher." (Autorenreferat)

Following an overview of James Heckman's (2000) article on the state of econometrics to shed light on the role of statistics in political science, efforts to link theory & data in formal empirical research are scrutinized. The empirical content of formal models is described, using the example of political outcomes in a democracy to illustrate the simultaneous equations model. Why contemporary theorists see such a model as inadequate is addressed, along with how they are moving beyond them. In addition, why they view such empirical work as unsatisfactory is considered as well as how they are pursuing stronger theory-data links. However, benefits of inadequate models for structuring empirical work are noted. Attention turns to a series of thumbnail sketches of examples from microinstitutionalist theory & austere political theory with simultaneous equations modeling & structural estimation; examples come from US politics, comparative politics, international relations, & international political economy. Four standards guide a look at the substantive contributions of formal empirical work: (1) understanding political phenomena & solving empirical puzzles, (2) advancing rich theory & stimulating new theory, (3) rejecting theory, & (4) improving public policy. Advances in the study of voter turnout are seen to demonstrate the utility of formal empirical work. A call is made for more & improved research of this kind. 3 Figures. J. Zendejas