We study the isoperimetric problem for the radially symmetric measures. Applying the spherical symmetrization procedure and variational arguments we reduce this problem to a one-dimensional ODE of the second order. Solving numerically this ODE we get an empirical description of isoperimetric regions of the planar radially symmetric exponential power laws. We also prove some isoperimetric inequalities for the log-convex measures. It is shown, in particular, that the symmetric balls of large size are isoperimetric sets for strictly log-convex and radially symmetric measures. In addition, we establish some comparison results for general log-convex measures.
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. This is more or less identical with the working of the collective learning mechanism. 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, suggesting the presence within the biosphere of a certain analogue of the collective learning mechanism. We discuss how such positive feedback mechanisms can be modelled mathematically.
The call to “know thyself” is neither a matter of presence and absence to self, nor the necessary or unnecessary possibility or impossibility of self-knowledge ‒ rather it is a problem. And the oracle gives a sign of this problem, i.e., it implies that which is ne-ither spoken nor concealed. But then, if implication is the problem of the sign, it is because it suspends the very possibility of self-knowledge, and of the self.
The state is usually considered to be a centralized and specialized coercive institution for governing a society. Contrariwise, our approach stems from the presumption that the state should be studied as a type of society for which this institution is adequate. This leads to the necessity of paying special attention to the coming to the fore of the non-kin relations in state society. Political centralization cannot be regarded as a feature specific to the state, as it is applicable to many non-state forms of societies. In the meantime, the feature typical only for the state is specialization resulting in administrators’ professionalization, that is, in the formation of bureaucracy which is related directly to the non-kin social ties coming into prominence. As for the right to coerce, it is a dependent variable: the legitimate violence in states is exercised through and by bureaucrats who operate within bureaucratic institutions.
В истории восприятия интеллектуального наследия Оригена русскими богословами и философами последних столетий выделяются несколько ключевых моментов и несколько ключевых фигур. Это, прежде всего, Григорий Сковорода (1722–1794), Владимир Соловьёв (1853–1900), Сергей Булгаков (1871–1944), Николай Бердяев (1874–1948) и Георгий Флоровский (1893–1979). Значимость этих авторов для нашего исследования определяется сочетанием трёх обстоятельств: (1) ключевой ролью названных мыслителей в эволюции русской богословской и философской мысли и (2) тем фактом, что их собственная интеллектуальная эволюция, а также (3) восприятие их идей современниками и/или более поздними исследователями осуществлялись в тесной связи с проблемой Оригена. Таким образом, процесс восприятия интеллектуального наследия Оригена в России оказался в существенной степени обусловлен теми спорами, которые велись и ведутся вокруг ключевых представителей так называемой «русской религиозной философии».
The formation of the Afroeurasian world-system was one of the crucial points of social evolution, starting from which the social evolution rate and effectiveness increased dramatically. In the present article we analyze processes and scales of global integration in historical perspective, starting with the Agrarian Revolution. We connect the main phases of historical globalization with the processes of the development of the Afroeurasian world-system. In the framework of the Afroeurasian world-system the integration began a few thousand years BCE. In this world-system the continental and supracontinental links became rather developed long before the Great Geographic Discoveries and thus, they could quite be denoted as global (albeit in a somehow limited sense). As some researchers are still inclined to underestimate the scale of those links in the pre-Industrial era, it appears necessary to provide additional empirical support for our statement. It also turns necessary to apply a special methodology (which necessitated the use of the world-system approach). We analyze some versions of periodization of globalization history. We also propose our own periodization of globalization history using as its basis the growing scale of intersocietal links as an indicator of the level of globalization development.
The article deals with the problem of normative evaluation of war and mass violence. The doctrines of Realism, Pacifism, Militarism, Realism and Just War are the most widely used theoretical and normative tools of this evaluation and normative practice. The latest developments have brought the Just War theory to the fore. The peak of popularity of the Just War Theory may prove, nevertheless, to be its swan's song. The recent theoretical findings as well as the political applications of this ethical theory in Kosovo and Iraq, have proved to be somewhat less then adequate, to say the least. Theoretically it hovers uneasily in between Militarism and Pacifism, pragmatically it may work as a smoke screen for the most hideous forms of agression and an instrument of the wide scale information war. The author of this article is holding that we must not put aside the idea of the morally constrained war, it may be modified. The result of this modification may be entitled Necessary War doctrine. The necessary war differs significantly from the just war, it is closer to pacifism and less prone to theoretical critisism. The foundations of this doctrine has been laid by Russian philosopher Ivan Ilyin.