If a complex structure is organized from more simple structures in a right topological way (if there are a certain degree of interaction of substructures and a certain symmetry of architecture of an originating united structure), an exit to a new, higher level of hierarchical organization occurs, i.e. a step towards a super-organization is taken. Thereby the rate of development of structures which are integrated into a complex one is being picked up. The rapidly developing structures �pull to themselves� by the tempo of life the slowly developing structures. If an evolutionary whole is rightly organized, the whole begins to develop at a rapid pace which is higher than there was a pace of the most rapid developing structure before the unification.
The path of unity and of integration of different parts into entire structures is not steady, permanent and monodirectoral. The evolutionary ascent towards more are more complex forms and structures passes through a number of cycles of decay and integration, of disruption from the whole and inclusion in it, the braking of the processes and their acceleration.
From the theory of self-organization it follows that any open systems with strong nonlinearity are most likely to pulse. They have natural cycles of development: the stages of differentiation of parts alternate with the stages of their integration, scattering alternates with rapprochement, the weakening of bonds changes into their strengthening. The world seems to go towards a universal unity, a superorganism. But it moves forward not monotonously but through certain fluctuations and pulsation. The stages of decay, even if partial, are followed by stages of more and more powerful unifications of structures. This modern scientific notion of complexity reminds us of the eastern images of �rhythms of life� that are peculiar to our world, first of all, of the Chinese symbol Yin-Yang.
The cycles of increase and decrease of the intensity of processes, of decay and unifications of parts indicate regularity of nonlinear processes; the cycles are determined by the very nature of nonlinear processes. Any complex structures at the moment of maximum of accretion, or at the culmination of development (at the moment of peaking of processes), are subjected to the inner instability with respect to small perturbations, they are under the threat of decay.
The history of mankind testifies that the world empires increased in size and became stronger to the maximum extent and in the end they came asunder, sometimes disappeared completely without leaving a trace. But if the beginning of decay of some geopolitical system is observed, it is reasonable, from the synergetic point of view, to put a question: is the nonlinearity of the system sufficient to turn the evolutionary processes back, to switch them to another regime of the renewal of bonds, the attenuation of processes in the central domain and their stirring at the periphery of the structure? If the nonlinearity isn’t sufficient, then the former intensive processes may simply be extinguished and come to naught.
Thus, the fundamental principle of behavior of complex nonlinear systems is the periodical alternation of stages of evolution and involution, the unrolling and the rolling, the explosion of activity, the increase of intensity of processes and their fading, weakening, the converging to the center, the integration and the disintegration, at least the partial decay. There are profound analogies here to the historical testimonies of the downfall of civilizations and the break-up of great world empires, to the cycles of N.D.Kondratieff, the oscillatory regimes of J.K.Galbraith, the ethnogenetic rhythms of L.N.Gumilioff.
At the initial stage of formation of a complex structure, its right topological organization is of great importance. When the process of integration occurs, the structures aren’t simply put together, they don’t simply become parts of the whole in an unaltered, undistorted form. They become somehow transformed ; they form strata on each other and intersect, and at the same time some of their parts fall out. As the physicists say in such a case, there exists an overlapping with the energy loss. This signifies that the unification leads to the economy of energy, to the diminution of material expenses and human efforts.
The topologically proper organization of structures in an entire evolutionary structure results in an approach to the moment of peaking, the moment of maximum development. The whole develops faster than its integral parts. It is more profitable to develop together, since the joint, co-evolutionary development is connected with a saving of material (in particular, energetic), spiritual and other resources. Every new way of the topologically proper integration of structures, the appearance of successive layers (with bigger exponent of nonlinearity) of hierarchical organization picks up speed of development of the whole as well as its integral parts. Therefore, the evolutionary path to the building of more and more complex organizations of structures in the world is to a certain extent pre-determined. We should lend our ears to Eliot’s advice: �We must be still and still moving / Into another intensity / For a further union, a deeper communication� (Eliot, 2000, p.260).
8 NOT ONLY THE DESIRABLE BUT ALSO ATTAINABLE FUTURES
It is important to understand that we are not external observers, but participants of the historical adventure (see: Loye, 1999). We are within the trends of social development. We should not remain passive. We have no right simply to expect what will happen, but should become creators of the desirable futures. Dennis Gabor said that �the future cannot be predicted, but it can be created�. This research attitude makes a peculiar sense in synergetics. If we manage to discover spectra of evolutionary aims of complex systems, spectra of structure-attractors of their evolution (it is already done for the simplest natural systems, and nowadays the Russian scholars construct models of economic development of certain regions in Russia under the conditions of instability and economic crisis from these methodological positions /Kapitza et al. 1997/), then the role of humans and their responsibility in choosing the most favorable scenario of development rarely increase.
From the standpoint of synergetics, the changing of emphasis in approaching global problems is required: not arm-twisting and power policy but the search of ways of co-evolution of complex social and geopolitical systems in the world. The pursuit of policy by power methods is too dangerous in the modern complex and nonlinearly developing world, where even random bugs in the branching informational and computer nets can bring to a world catastrophe. The more complex a system is, the more functions it performs, the more unstable it is. Therefore, the understanding of forms of common life of heterogeneous structures which are situated on different levels of development and of the paths of their sustainable co-evolutionary development becomes a constructive alternative of today’s policy.
Synergetics shows how it is possible to multiply reduce the required time and the necessary efforts and to generate by means of a resonant influence the desirable and � what is no less important � feasible structures in a given complex system, i.e. certain structures from a discrete spectrum of potentially possible structure-attractors. Besides, it demonstrates how it is possible to achieve the proper and persistent unification of relatively simple evolutionary structures into more complex entities and to accelerate in that way the tempo of their evolution.
The world we live in is nonlinear and open. The world is creative. An unexpected and often charming new appears in it. Synergetics reveals laws underlying the emergent phenomena. The future is multiple and uncertain in our nonlinear world. As one sometimes expresses it now, it is a fuzzy future. The nonlinear world often gives surprises to us. In such a world, the probability of fulfillment of even improbable events increases. That is why our hope for a bright future could be connected not only with our deliberate choice of actions which conform to the inner trends of complex organizations, but also with a lucky chance to attain unattainable. Let us work together to accomplish the unfeasible. Let us hope that even the hopeless can come true.
We all somehow or other think of the future, because we wish to spend there a large or ever larger part of our life. Although we all are interested in our own destiny, not many of us professionally occupy ourselves with futures studies. For the latter, synergetics can be used as a non-traditional and constructive methodological basis.
Synergetics is an optimistic attempt to cope with nonlinear situations and to make use of the methods of effective nonlinear management of complex systems in the states of instability. This is the way of attainment of a desirable and at the same time a realizable future, the future that is coordinated with the own properties of complex systems. The world belong to those who give it the greatest hope.
Acknowledgments:
The research presented in this paper is supported in 1999-2002 by the Russian Foundation of Basic Research (grant # 00-06-80011 for H.Knyazeva, grant # 99-01-01091 for S.P.Kurdyumov as well as grant # 01-06-80204 for both of them) as well as by the Russian Humanitarian Foundation (grant # 99-03-19696 for S.P.Kurdyumov).
References:
Akhromeeva, T.S., Kurdyumov, S.P., Malinetskii, G.G. and Samarskii, A.A., 1989, Nonstationary Dissipative Structures and Diffusion-Induced Chaos in Nonlinear Media, Physical Reports, 176, 186-372.
Barrow, J.D. and Tipler, F.J., 1987, The Anthropic Cosmological Principle, Clarendon Press, Oxford.
Belavin, V.A., Knyazeva, H.N., Kurdyumov S.P., 1997, Blow-up and Laws of Co-evolution of Complex Systems, Phystech Journal, 3 (1), 107-113.
Belavin, V.A., Kurdyumov S.P., 2000, Blow-up regimes in Demographic Systems. The Scenario of Strengthening of Nonlinearity, Computational Mathematics and Mathematical Physics, 40 (2), 238-251.
Blow-up Regimes. Evolution of the Idea. The Laws of Co-evolution of Complex Structures, 1999, Nauka Publishers, Moscow (in Russian)
Dimova, S., Kaschiev, M., Koleva, M., Vasileva D., 1998, Numerical Analysis of Radially Nonsymmetrical Blow-up Solutions of a Nonlinear Parabolic Problem, Journal of Computational and Applied Mathematics, 97, 81-97.
Eliot, T.S., 2000, Selected Verse, Raduga Publishers, Moscow.
Galaktionov, V.A., 1999, Dynamical Systems of Inequalities and Nonlinear Parabolic Equations, Commun. in Partial Differential Equations, 24 (11 & 12), 2191-2236.
Haken, H., 1978, Synergetics, Springer, Berlin.
Haken, H. and Knyazeva, H., 2000, Arbitrariness in Nature: Synergetics and Evolutionary Laws of Prohibition, Journal for General Philosophy of Sciences, 31 (1), 57-73.
Hideg, E., 2000, New Paradigms for Studies of Futures, the paper presented at the Methodology Seminar in Futures Studies �The Quest for the Futures�, June 13-15 2000, Turku (Finland) (to appear in the Proceedings).
Kapitza, S.P., 1995, Population Dynamics and the Future of the World, Proceedings of the 44th Pugwash conference on science and world affaires. Towards a war-free world, World Scientific, Singapore.
Kapitza, S.P., 1998, Population Growth, Sustainable Development and Environment, World Culture Report, Culture, Creativity and Markets, UNESCO, Paris.
Kapitza S.P., Kurdyumov, S.P. and Malinetskii, G.G., 1997, Synergetics and Prognoses of the Future, Nauka Publishers, Moscow (in Russian).
Knyazeva, H., 1999a, Synergetics and the Images of Future, Futures, 31 (3/4), 281-290.
Knyazeva, H., 1999b, The Synergetic Principles of Nonlinear Thinking, World Futures, 54 ( 2),163-181.
Knyazeva, E.N. and Kurdyumov, S.P., 1994, Evolution and Self-organization Laws in Complex Systems, Nauka Publishers, Moscow (in Russian).
Knyazeva, E.N. and Kurdyumov, S.P., 1997, The Anthropic Principle in Synergetics, Voprosy Filosofii, Moscow, N 3, 62-79 (in Russian)
Kurdyumov, S.P., Malinetskii, G.G., and Potapov, A.B., 1995, Nonstationary Structures, Dynamic Chaos, and Cellular Automata, International Journal of Fluid Mechanics Research, 22 (5-6), 75-133.
Laszlo, E., 1991, The Age of Bifurcation, Gordon and Breach, New York.
Laszlo, E., 1996, The Systems View of the World. Hampton Press, Cresskill (NJ).
Loye, D.(Ed.), 1999, The Evolutionary Outrider: The Impact of the Human Agent on Evolution, Praeger, Westport (CT).
Mainzer, K. (Ed.), 1999, Komplexe Systeme und Nichtlineare Dynamik in Natur und Gesellschaft. Komplexitätsforschung in Deutschland auf dem Weg ins nächste Jahrhundert, Springer, Heidelberg.
Morin, E., 1990, Introduction à la pensée complexe, ESF éditeur, Paris.
Morin, E., 1999, Seven Complex Lessons in Education for the Future, UNESCO, Paris.
Nováky, E., 2000, Methodological Renewal in Futures Studies, the paper presented at the Methodology Seminar in Futures Studies �The Quest for the Futures�, June 13-15 2000, Turku (Finland) (to appear in the Proceedings).
Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P. and Mikhailov, A.P., 1995, Blow-up in Problems for Quasilinear Parabolic Equations, Walter de Gruyter, Berlin.
Zmitrenko, N.V., and Kurdyumov S.P., 1992, Time Reversion of Processes in Dissipative Systems, Modern Physics Letters B, 6 (1), 49-54.