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"Куда идет мир? Каково будущее науки? Как "объять необъятное", получая образование - высшее, среднее, начальное? Как преодолеть "пропасть двух культур" - естественнонаучной и гуманитарной? Как создать и вырастить научную школу? Какова структура нашего познания? Как управлять риском? Можно ли с единой точки зрения взглянуть на проблемы математики и экономики, физики и психологии, компьютерных наук и географии, техники и философии?"

Irina N. Trofimova


Table 2 shows two different scenarios for the next stage of development. The condition for this stage is simple, universal and unavoidable: the change in environment. Under one scenario (A) we satisfy the system’s wish to have the highest compatibility between agents — very small differences between them within the clusters and small differences between clusters. The population has high homogeneity, everything «flies with the same speed», and everybody «speaks the same language». Is this not a dream of any young manager, teacher or politician?

Suppose we have a perturbation of this system arising from its from environment. This happens all the time in natural systems. Such a perturbation, i.e. an impact of some factors or elements causing a deviation from the established phase space, requires the system to respond with certain configurational traits, which in previous conditions were not required or were not popular.

Condition of development Stage of development Popul.Size Socia-bility Diver-sity Compa-tibility
Density and sociability increase. 0. Wondering, gathering as separate elements or unstable small groups Low Higher Low Low
Diversity increase as adaptation 1. Establishing unstable connections with low compatibility. Higher Same Higher Low
Access to distant elements 2. Sociability (and so population) increase, compatibility increase and clustering High High Higher Higher within the population

Optimization of structure of connections 3. Finding and holding the most compatible elements. High High Lower High within the population
«Renormalization» and «structuring» 4. Decrease of degrees of diversity, which are not used in the system and stabilizing the most compatible connections. Associa-tion of «small worlds» clusters Lower Same High within the cluster, low within the population
Environmental request for a change, low diversity 5A. Decomposition and death due to involvement of elements in other systems. Decompo-sition Low Lower High within the population
Environmental request for a change, high diversity 5B. Remodeling of structure of connections Ensemble architecture Higher High within the cluster, low within the population

Table 2. «Death of rigid» scenario (includes stage 5A) and «Survival of an ensemble» scenario (includes stage 5B).

Elements continue doing what they were doing. There are no miracles here: they continue calculating their differences and searching for the most compatible arrangements. A perturbation by definition causes a deviation in the configuration of some agents in some segment of the population. These deviant agents try to find compatible partners, but nobody prefers to establish a connection with them because of the resulting differences between their configuration and the rest of population. Thus, in totalitarian systems any ill agents as well as any novelty will die if the perturbation were is not very significant.

If we have a significant perturbation, it requires an adjustment of the structure of connections to the configurational change resulting from this perturbation. What does a system with limited diversity and strong ties between agents do in such a situation? It starts to decompose very quickly and dies. The elements can not longer find compatible members within this system due to the change in their configuration and start to participate in the clusters of the other systems.

Scenario 5B also has a population (association) of «small worlds» with the diversity within these world-groups probably lower than that within the population. The diversity of the population in this scenario still remains high. This means that the links between these «small worlds» are weak, and these world-groups are not super-stable .Also, from time to time their members could establish connections with some average-compatible agent, and a member of another small world could temporarily occupy the vacant space. This is an «ensemble» architecture of the population, when diversity is not only allowed, but is required both between the clusters and within the clusters.

These two scenarios show again the conditional benefits of unification and diversity. Unification, which happens under high sociability conditions and regression to means is beneficial for the functioning of a system under unperturbed conditions. The diversity of the connections, and imperfections in compatibility, create the set of just «good enough» connections, producing an ensemble of diverse elements, ready to establish connections with even more diverse elements. The diversity of an ensemble is its life saver, as it makes it more adaptive to a change of environment. The most stable, rigid and non-adaptive natural systems are those which have little diversity of elements, and the most unstable, but the most adaptive systems have a high diversity of agents.

4. Conclusions

We discussed that:
� Sociability is the major factor affecting clustering behaviour in a diverse population;
� Diversity and compatibility have ways to control sociability, and sociability has ways to control the diversity;
� Diversity, compatibility and sociability could be considered as global factors affecting the development of a system, as its interaction within the developmental stages defines the specific of these stages;
� Diversity of agents and an ensemble architecture of connections are beneficial for the survival of a natural system functioning in a changing environment, while unification is beneficial in stable conditions;
� Establishment of interactions between agents of a population on the basis of compatibility of their configurations is associated with a first order phase transition (in clustering behaviour), common in physical systems;
� Stickiness of agents decreases the possibility of a 1st order phase transition, but leads to a second order phase transition, common for biological systems.
� Compatibility of interests in making a connection makes a phase transition from a population of small clusters to an all-unified population smooth. Absence of compatibility makes this transition sharp.
� Artificial holding of a connection instead of compatibility condition delays the phase transition in size of population and sociability conditions, but then makes the phase transition very sharp.

6. Acknowledgments — The author is very grateful to Dr. William Sulis for his constructive editing and useful recommendations, which led to the final revision of this paper.

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