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systemityThe principle of domain structure of natural self-organizing systems is easy to explain. It was first proposed almost a hundred year ago by a French physicist Pierre-Ernest Weiss in relation to the structure of ferromagnetics. The idea that any natural self-organizing system has a domain structure is much more difficult to demonstrate on real objects, and the details of a domain structure, the shape and size of domains, as well as other specific features of a given domain organization cannot be determined a priori even when complete information on all of the attributes of individual components of a system is available. Natural self-organizing systems are inherently and highly anisotropic - from the standpoint of understanding anisotropy as the antonym of isotropy, i.e. not just the changing of a system’s properties depending on the direction, but a radical restructuring in all the directions depending on the vector of an impact.
At present, the most fully studied domain structures are those of crystals and amorphous metal alloys – ferromagnetics, piezoelectrics, segnetoelectrics, pyroelectrics, etc. – due to their important role in development of modern technologies. These materials have anisotropic crystal grids that consist of simpler subgrids. Upon specific external impacts, domain structures of such systems undergo transformations accompanied by certain effects that can be measured and interpreted from the standpoint of physical laws. According to a theory that was developed over 70 years ago by Landau and Lifshitz for ferromagnetics, domain structures of such condensed media are conditioned by the principle of minimum energy in a body as a result of competition of contributions by individual domains. It is well known, for instance, that the stability of soap lather consisting of an incomputable amount of microscopically small soap bubbles that are in contact with each other is tremendously higher than the stability of one soap bubble with the same surface area as the total surface of soap lather. This is because the total internal energy of soap lather is by far lower than the internal energy of one bubble with the same surface area. The internal energy of soap lather is low due to interaction between the domain walls of the microbubbles, and the resultant of that interaction in the 3D-space appears to be minimal.
A decade after Weiss’ idea of domain structure of ferromagnetics, a German physicist Heinrich Barkhausen demonstrated that upon gradual and smooth changing of the magnetic field strength, magnetization and demagnetization of a ferromagnetic change stepwise and unevenly. This effect could be explained only through an assumption that magnetization and demagnetization affect entire domains, and not only individual atoms. That explanation seemed to provide a convincing proof of Weiss’ idea. Further, the progress in microscopy techniques had created a capability to directly demonstrate the domain structure of various condensed media, which however does not apply to most of natural systems.
Domain structure of some systems can be explained from the standpoint of human experience. For example, in the simplest form of self-organizing social system such as nuclear family, interaction between the parents is characterized by a number of factors – verbal, psychological, physical, organizational, and many others – that create a certain borderline between the spheres of parent-to-parent relations and parents-to-children relations. The same kind of invisible and non-measurable but clearly perceivable intra-family borders exists between the domains of communication between brother and sister, mother and daughter, mother and son, father and son, father and daughter. There are also borders that separate three-member groups of communication within a family. In communication with the extended family members, or with neighbors, etc. a nuclear family represents a single domain. However, each member of a nuclear family has his/her own outside contacts (at a workplace, school, etc) in which other family members are not involved or of which they may be even unaware. This is because any human as a product of human development, with a unique personal experience and specific internal impetuses, represents an individual domain.
Personal domain properties greatly vary depending on psychological and physical characters of an individual. This concept can be perfectly illustrated by Carl Jung’s typology as well as Aushra Augustinavichiute’s classification of psychotypes, known as socionics, which was developed based on Jung’s works and Freud's theory of the concious and subconscious (Augustinavichiute’s scientific works were not published during the Soviet regime). Socionics maintains that there are eight different information elements, and that human psyche uses eight psychological functions to process information. Different socionic types of personality have different coordination between the psychological functions, which results in different ways of perceiving, processing, and producing information, thus producing different thinking patterns, values, and behavior. These studies provide a convincing demonstration that personality domain structures greatly differ in different psychotypes. One can assume that a system borders between partial contacts are a counterpart of a system of domain walls. What those walls look like and how and in what dimensions they can be measured, etc. are not principal questions. What is by far more important is the formulation of the problem, which should call for development of fundamentally new methods of investigation, as well as the understanding that any attempt to study natural systems without taking into account their domain organization is not only unproductive but plainly senseless.
A family as a solid structure that has a domain organization lies in the basis of a state that is also a domain wherein domain walls are represented not only by the state borders but also by numerous other factors of separation from adjacent domains, i.e. neighboring states. In the same way as a magnetic field applied to a ferromagnetic can change the shape of domains and configuration of domain walls, the political system of a state can influence the internal domains of the state. It is obvious how differently the democracy and totalitarianism influence the domain organization. Democracy, being conducive to personal freedom, makes the domain structure of the society more flexible, dynamic, self-organizing, and – as a result – more predictable. Totalitarianism is aimed at making the society ultimately controllable (and thus predictable) through purposeful social administration (including religious dogmatism in the forms that are compatible with a given society), at the establishment of unnatural rules of formation of the domain system and – through selective and precision terror – at the weakening of the intra- and inter-domain interactions and making the domain walls more rigid. Totalitarianism’s ultimate, although unattainable, goal is to destroy the domain structure of a society by making all of its components as much identical as possible. A totalitarian power instinctively realizes that a civil society is based on individuals, and therefore it tries to transform them into indistinguishable clones that are unable to form a domain-structure social system.
It is well known from numerous historical examples that a domain-type social structure has high stability at the lower hierarchical levels, quickly recovers from any kind of pressure, and is itself capable of influencing the more complex forms of social domain structure. The domain character of a social structure manifests itself, for instance, in the rise of separatism despite the globalization processes that in principle should have had an opposite effect. In the same way, behavior of ethnic diasporas in the developed European countries is contrary to the linear logic. The dynamics of changes in the religious sphere, especially within the past half a century, is, too, an interesting subject of analysis from the standpoint of the domain structure of human society. These examples certainly demonstrate that the structure and function of a system is not governed by the laws of arithmetics.
There are many similar examples from other areas, such as culture, politics, economy, meteorology, biogeocenosis, ethnography, linguistics (for instance, the existence of unique phonemes or shibboleth words that are hard to pronounce by non-native speakers can certainly be considered as a natural way of formation of one of the dimensions of a domain wall). However, tackling the problem of the domain structure of natural self-organizing systems at a purely speculative level would most probably provide nothing more than another term in a series of overused terms such as “system” (as a synonym of a multitude of components with a certain degree of similarity), “synergetics” (as a synonym of progressive interaction), “dissipation”, and the like that are widely used nowadays for adding a scientific flavor to any kind of speculative statements. The idea of domain structure of any natural self-organizing system is too nontrivial to be limited to the philosophical level of analysis, as the most highly scientific speculations on the matter of the “black box” will be washed against its walls. This is clearly seen on the example of the “general systems theory” by Ludwig von Bertalanffy which is based on a misconception, to wit, on the assumption of obviousness of what is by no means obvious. This false assumption was exactly what made the theory astonishingly popular in scientific and even more so in pseudoscientific circles, as it is never easy to accept the fact that all the baggage of educated knowledge appears useless for the purpose of analysis of behavior of natural self-organizing systems. Only exact scientific approaches can inspire strong interest in a fundamental revision of the existing views on the problem of analysis of natural self-organizing systems. The principle of universality of the domain structure of systems is one of the most important positions which alone can fundamentally reform the conventional views on the problem.
The hypothesis that the domain structure is a universal character of any natural self-organizing system stems from simple logic. (It is noteworthy that the principle of holism “The whole is more than the sum of its parts” directly follows from the hypothesis of the domain structure of systems.) The key peculiarity of a domain system is the disparate nature of adjacent domains, i.e. each individual domain has certain factors of alienation from the adjacent domains. Had any domain been surrounded by domains with identical internal structure, they all would merge into one larger domain. If all of the domains of a system were similar, the system could not have a domain structure. However, there are no natural self-organizing systems that would consist of identical components with identical interrelations.
Based on a commonly accepted view on a ‘system’ as a totality of components that form a structural-functional entity that is self-emergent, it is clear that any system needs a mechanism of protection from dissipation in a high-dimensional space in which its components exist. That kind of protection can only be provided by a domain wall that is impervious to penetration of random objects from the outer environment which are not relevant to the system’s functions. The earlier mentioned Barkhausen effect that demonstrates an uneven stepwise process of magnetization and demagnetization upon a gradual and smooth changing of magnetic field strength, as well as many other experiments indicate that the orientation of magnetic moments is not the only and, apparently, not a primary factor determining the formation of a system’s domain structure.
Since a functioning system by necessity consists of various components with spontaneous interactions, maintaining of long-range order in the system, i.e. orderliness that is the consistent throughout the entire multi-dimensional space of the functioning system, is impossible, especially in conditions of continuous response to external impact. In studies of condensed media, certain experimental physical approaches are available that allow an assessment of the proportion between near-range and long-range orders – for example, an assessment of the width of Bragg peaks in X-ray photographs. However, none of the direct physical analysis methods are usable in investigations of natural self-organizing systems. Therefore, structural-functional principles that underlie the formation of domain organization can be considered only in very general terms, and such considerations can be meaningful only if they come along with experimental methods of their verification.
In very general terms, it can be assumed that the purpose of domain organization of a system is to ensure a high near-range order without increasing a long-range order as the maintenance of a high long-range order requires higher expenditure of organizational, operational, and energy resources. Indeed, to create a system that is totally organized in terms of a near-range order and totally excludes the necessity of a long-range order, it is sufficient to have just two variants of near-range order organization. Such a system differs from an amorphous substance by having domain walls that prevent a disturbance of the near-range order. Inside each of the two kinds of domains, the properties of components may be completely averaged, i.e. be in the state of an ultimate equilibrium; however, the system itself, even though represented by just two kinds of domains, may have an extremely complex organization, and its complexity will be inconceivably increasing upon even a very slight increase of the number of variants of the near-range order. This is the paradox of a system: while the entropy of an entire domain system may be very low, the entropy in any small area of the system will be ultimately high. In a crystalline substance, a domain system can emerge even based on automorphous groups that are formed due to defects of the crystalline grid, whereas in real natural self-organizing systems the diversity of domain organization may be idefinitely high.
Thus, it follows from the above discourse that any natural self-organizing system represents a mosaic of equilibrium communities (or ‘equicoms’ as a shortened form) each of which is maximally averaged in terms of the parameters of their constituent elements.This thesis can be illustrated by the following example. There is no clear answer to the question of why populations of individual continents did not get ethnically randomized even though there were no significant obstacles for migration. Population communities that eventually got transformed into individual states had been undergoing the averaging under the influence of specific conditions of the habitat, as well as climatic and many other factors. The averaging led to formation of domains. Due to various reasons, the formation of states based on those domains was not always determined by the averaging factor, which resulted in both separatism and unification of states. While in international relations, individual states act as individual systems, within an individual state there is a complex domain structure that includes domains that are coaxially functioning in different dimensions – such as social, political, territorial, professional, etc. Therefore, for any human-being, even if that human-being acts as a part of a self-organizing system and is directly or indirectly connected with it, the understanding of the mechanism of the system functioning is hardly achievable through logical analysis because the evolution of logical analysis has developed outside of the system.
The subject of this analysis also concerns such an important aspect as formation of psycho-social domains in the global structure of the world population. This topic is of interest both from the standpoint of the advantages provided by the concept of domain organization of a self-organizing system and the use of reductorials (the use of self-organizing system’s components with their inherent attributes) for imitation of behavior of complex systems, as well as the advantages of the use of hierarchical grouping in the development of methods of analysis of complex systems. There are many attributes of psycho-social spheres of functioning of populations of individual states as well as of the world as as a united system of the human population. Those attributes can be listed in the order of their dominance, i.e percentage of population involved in the respective spheres, e.g. (1) financial status; (2) health; (3) age; (4) religion; (5) race; (6) gender, including sexual orientation; (7) nationality; and many others. These spheres constitute predominantly coaxially positioned domains of the psycho-social system, and the domain structure of each individual is unique. As is apparent, each of the above-listed factors is functioning in the form of a dichotomy that leads to formation of domain structures that are separated from each other by a domain wall, e.g. (1) wealthy – poor; (2) healthy – disabled; (3) parents – children; (4) religious – atheists; as well as: a specific religious doctrine – all other religious doctrines; (5) a specific race – all other races; (6) men – women; (7) native-born citizens – immigrants; etc. The above-listed dichotomies are the most profound, although there are many other factors that influence the behavior of the system as a whole. In certain situations, less significant dichotomies, such as, for instance, driver – pedestrian, employed – unemployed, smoker – nonsmoker, drinker – nondrinker, etc. may enter into synergetic relations with other dichotomies, causing unpredictable effects.
Since all of these factors are concurrently functioning in the psycho-social system, it is impossible to mentally visualize how such a complex poly-domain system is functioning, and – even more so – to develop methods of direct analysis of that kind of systems. The use of reductorials for imitation of behavior of such systems has undeniable advantages over a hypothetical possibility of direct analysis and – through the capability of selection of parameters – creates new approaches in such a complex science as conflictology.
Conflicts that emerge in specific countries and in the world as a whole are often developing according to a common scenario. In that scenario, the most unpredictable and logically inexplainable phase is a transition from propaganda of specific ideological positions to generalization of that ideology in the public. This process which is well known in the world history, including the examples of explosive growth of populations supporting the ideas of communism, fascism, Islamic fundamentalism, etc., can be thoroughly explained by specific historical factors, can be illustrated by statistical data and fit into sociological laws, or can be defined as mass psychosis occurring in accordance with the laws of ochlocracy, but it cannot be timely and scientifically predicted during its most important and explosive phase of building up of a generalization which culminates in the transition from an initial idea – which may be as naïve and absurd as, for instance, the ideas of the worldwide caliphate or the worldwide victory of the proletarian revolution – to the level of a state policy. The truth of the matter is that any human being has a certain extent of resentment. A resentment (not to be confused with anger as it is a different feeling) can subconsciously emerge in most diverse areas of the psycho-social sphere, including areas that at first glance may seem insignificant. As the psycho-social sphere represents a system of a very complex domain structure, a resentment generalization process occurs in such a way that – regardless of the human will and logic – all of the same-sign dichotomies join into one domain structure that is separated by a domain wall from the domain structures that include the opposite-sign dichotomies.
My intent was to point out that the most complex natural self-organizing systems can be analyzed based on the principle of universality of the domain structure of systems. In particular, even at the level of simple formulation of the above-stated positions, it is clear what the social institutions in democratic states have been doing and what more can be done (not at the intuitive level, but at the level of scientifically-founded solutions) in order to protect their societies from psycho-social generalization of ideas that pose a danger to society. For instance, legalization of same-sex marriage is more of a factor of prevention of generalization than a factor of homosexual propaganda. State care for disabled individuals, the principles of political correctness, affirmative action, and many other policies and initiatives designed to support various social minorities, are also important strategic measures for maintaining stability in individual societies and in the world.
A succession of the emergence of worldwide epidemics of communism, fascism, Islamic fundamentalism, and terrorism is historically connected with certain stages in the development of the global civilization, in particular, with the processes of globalization and development of information technologies. For instance, the unprecedented extensiveness of spreading of the communism epidemic as well as an equally extensive spread of opposition to the communist ideology are directly related to the fact that financial well-being is the dominant sphere of the psycho-social system which involves the largest part of the world population. At first glance, the above-said may seem self-evident, especially when viewed in retrospect. However, it should be noted that the above-discussed hypothetical model coupled with the methods provided by this invention creates a capability of timely prediction based on accurate quantitative analysis.
The concept of domain structure of natural self-organizing systems leads to revision of some of the well-established positions of the chaos theory. Even when there is an ideal order inside each of a system’s individual domains, the domain system as a whole shows a chaos that is resistive to systematic analysis. Chaos is a part of the nature of a domain structure, as each domain is different from an adjacent domain, and the domain distribution topography, by its nature, is extremely labile. One of the basic postulates of the chaos theory is the notion of sensitive dependence on initial conditions – an effect that was first described in 1890 by a French mathematician J. Hadamard . Due to its immanent lability, any natural system reacts to any negligibly small impact by generating a disproportionately strong response that involves re-organization of the entire system of domains. This is what underlies the sensitive dependence on initial conditions.
In order to prove the idea of universality of the domain structure of natural self-organizing systems, one needs universal criteria of a domain-type organization. The following four criteria appeared sufficient for verification of the experimental results disclosed in this work and were found to provide an actual picture of the domain structure of systems.
1. Any domain has alienation factors to protect itself from integration with adjacent domains.
2. Any domain represents a completely closed system in a space of dimensions of the domain’s attribute.
3. The topography of a domain structure is governed by laws that are incomprehensible to the human mind and incompatible with the human logic.
4. A system’s lability reaction to small disturbances is disproportionately strong from the standpoint of the human logic.
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Re: Notes from magnetic expert ;-)
Date: 2012-05-14 11:39 pm (UTC)http://arxiv.org/ftp/arxiv/papers/0803/0803.0034.pdf
http://arxiv.org/ftp/arxiv/papers/0805/0805.0455.pdf
http://arxiv.org/ftp/arxiv/papers/0806/0806.1355.pdf