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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?"

St. Petersburg: Aletheia, 2002. by Helena N. Knyazeva and Sergei P. Kurdyumov

Опубликовано в: Философия и синергетика


Main concepts and models of the modern theory of self-organization of complex systems, called also synergetics, are generalized and formulated in the book as principles of a synergetic world view. They are under discussion in the context of philosophical studies of holism, teleology, evolutionism as well as of gestalt-psychology; they are compared with some images from the history of human culture. The original and unfamiliar (to the Western readers) research results of the Moscow synergetic school which has its center at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences are expounded in the book. The heuristic value of the synergetic models of evolution and self-organization of complex systems in epistemology and cognitive psychology, education and teaching, futures studies, social management activities and systems of global security is shown in the book.

Complicated and paradoxical concepts of synergetics (structure-attractors, bifurcations, blow-up regimes, non-stationary dissipative structures of self-organization, fractals, non-linearity) are translated into an intelligible language and vividly illustrated by materials and examples from various fields of knowledge, starting with the laser thermonuclear fusion and concluding with mysterious phenomena of human psychology and creativity. The style of writing is close to that of popular-science literature. That’s why the book might be of interest and is quite comprehensible for students and specialists in the humanities.

It is shown that the development of synergetics entails deep changes in the conceptual net through which we comprehend the world. It means a radical shift of paradigm, a conceptual transition from being to becoming, from stability to sustainability, from images of order to chaos generating new ordered evolving structures, from self-maintaining systems to fast evolution through a nonlinear positive feedback, from evolution to co-evolution, reciprocal evolution of different complex systems. The new synergetic way of thinking is evolutionary, nonlinear and holistic. This is a modern stage of development within the traditions of cybernetics and system-structural analysis. However, many elements of the latter have undergone important changes since their appearance.

Synergetics is a multi-faceted phenomenon in modern science. It has a number of different dimensions. First of all, synergetics is a certain field of science, i.e. science of complexity, nonlinearity and chaos. Synergetics moves up to a meta-scientific level of research. Synergetics cannot be reduced to a certain concrete scientific discipline, be it physics, chemistry or biology. It concentrates the attention on common features of self-organization, structure formation and complex behavior of systems regardless of concrete nature of these systems. That is why it is rather natural to consider synergetics in aphilosophical dimension, i.e. to draw some philosophical consequences from the laws of evolution and self-organization discovered by synergetics. The epistemological dimension of synergetics constitutes the synergetics of cognition, the application of evolutionary nonlinear, synergetic models to the understanding of human cognitive and creative processes. It is an approach within the frames of evolutionary epistemology.

Synergetics has a socio-practical dimension. It means that synergetics enters into the studies of the constructive principles of co-evolution and self-organization of the complex socionatural, socioeconomic and geopolitical structures and the employment of the knowledge in practical activities. It includes the principles of sustainable development of social systems and the ways of constructing a world commonwealth. Synergetics can facilitate our reasonable orientation in the complex and unstable social world which is full of threats of various catastrophes. Synergetics can provides us with new methods of cognition and prediction of the course of historical processes as well as of the understanding of causes of evolutionary crises, the reliability of forecasts and the principal limits of predictability in ecology, sociology, economy, geopolicy. One may speak about a futuristic dimension of synergetics. The methodology of nonlinear synthesis based on the scientific principles of self-organization and co-evolution of the complex structures of the world might be used as methodological basis for projecting various paths of mankind into the future.

Some common patterns of the complex systems behavior are revealed in synergetics. The most essential elements of the synergetic world view which are set forth in the book are as follows:

1. the constructive role of chaos in evolution, the connection of chaos on a micro-level with evolution of structures on a macro-level. Chaos and fluctuations on a micro-level play the essential role in determining the actual trends, or “aims”, of processes at a macro-level. Chaos manifests itself as a “force”, as a mechanism underlying an exit to one of several evolutionary structure-attractors. The macro-organization evolves from chaos on micro-level. Dissipative processes, being the macroscopic revelation of micro-chaos, act in the same way as a sculptor who chisels and shapes a statue from a block of marble. Besides this, chaos serves as a basis for integration of relatively simple evolutionary structures into more complex ones. It is a mechanism of coordinating their tempos of evolution. Chaos, fluctuations on micro-level, is also a way of evolutionary switching, allowing a periodical transition from one evolutionary regime to another one;

2. the non-unequivocal purposefulness, the elements of pre-determination on the field of multiple evolutionary paths. The future states of complex systems escape our control and prediction. The future is open, not unequivocal. But at the same time, there is a definite spectrum of “aims” of development available in any given open nonlinear medium. If we choose an arbitrary path of evolution, we have to be aware that this particular path may not be feasible in a given medium. Only a definite set of evolutionary pathways are open, only certain kinds of structures can emerge. These discrete spectra of evolutionary structure-attractors look much like spectra of purposes of evolution. There is, so to speak, “a tacit knowledge” on the part of medium itself. The spectra are determined exclusively by the inner properties of open nonlinear systems. The future turns out to be open in form of spectra of pre-determined possibilities;

3. the laws of very fast, avalanche-like processes, blow-up regimes in complex systems. Synergetics investigates conditions for self-organization far from equilibrium and reveals laws of very fast, avalanche-like growth when meta-stable localized complicated structures may emerge. Such a process of nonlinear, self-stimulating growth takes place all over the space of a complex system (medium), i.e. in every local area of it;

4. the existence of changing rhythms and regimes of evolutionary processes, the nonlinear dynamics of the course of evolutionary processes. There are some cyclical changes of state: upsurge – slump – stagnation – upsurge – slump etc. Only obeying these “life rhythms”, or oscillatory modes, can complex systems maintain their integrity and develop dynamically. The mechanism of the “self-movement”, auto-oscillation, reminds one of the oriental images – the image of Yin-Yang. According to the synergetic models stated in the book, changing of the two different, complementary regimes, HS- and LS-modes with peaking, takes place in open systems with strong nonlinearity. HS-mode is a mode of “infinitely running out wave” when there is no localization, all structures, heterogeneities are being washed away. LS-mode with peaking is a mode of “converging wave of burning”, a mode of localization and intensive growth of processes in a more and more narrow area near the maximum;

5. the patterns of constructing complex totalities from simpler elements (or subsystems), that is the elaboration of a kind of a new evolutionary holism. A complex structure is an integration of structures of “different ages”, that is: structures at the different stages of evolutionary development. The integration of relatively simple structures into a complex one occurs by the establishment of a common tempo of development in all unified parts (fragments, simple structures). Structures of “different ages” start to co-exist in one and the same tempo-world;

6. the ways of nonlinear management of complex systems, the possibility of affecting complex systems, and catalyzing their development towards still higher levels of organization, through small-scale, but resonant, intervention. From synergetics, we learn how it is possible to multiply reduce time and efforts needed to generate, by a resonant influence, desired and, what is no less important, feasible complex structures. Synergetics gives proof of the following thesis: in order to control efficiently complicated systems (media), a right topological configuration, an “architecture” of driving mechanism is important, not the intensity of an influence. Weak, but organized in a right topological way – so called resonant, – influences upon complex systems are extremely effective. The art of soft management consists in the ways of self-management and of self-control of complex systems.

One of specific features of the book is its interdisciplinary character. It determines an eventual circle of readers. The book can be of interest for a) natural scientists who want to comprehend the foundations of modern interdisciplinary research fields, their philosophical aspects, b) philosophers who have intentions to link their investigations with recent developments in natural sciences, to fill their philosophical constructions with some concrete contents, c) intellectuals who are concerned with movement of the modern culture and art, because a wide scope of the cultural materials is being used in the book, some parallels between the scientific synergetic notions and the cultural images are being made; d) students who wish to get a survey view of the modern scientific knowledge development, to overcome hard disciplinary boundaries, to make a general acquaintance with the heuristic synergetic models of complex behavior as well as with a new nonlinear synergetic world view.


Chapter 1. Synergetics from the Historical Retrospective Point of View.

Precursors of Synergetics in Science
Chapter 2. Synergetics as a new Paradigm.

Dialogue with I.Prigogine

2.1. The Creation Fire

2.2. The Curtailment of the Complex:

the Notion of Structure-Attractors of Evolution

2.3. The Image of an Open Medium

2.4. Philosophical Sense of the Concept of ‘Nonlinearity’

2.5. Blow-up Processes

2.6. Development through Instability

2.7. Wandering over a Field of Evolutionary Ways

2.8. Does the Modem Science Lose its Materialistic Character?

2.9. Once again about Reductionism

2.10. A New Image of Determinism


Chapter 3. The Synergetic Extension of the Anthropic Principle

3.1. Synergetics as a Science of Complexity

3.2. The Anthropic Principle in Synergetics

3.2.1. A Narrow Evolutionary Corridor in the Complexity

3.2.2. Reduction of Complexity

3.2.3. Justification of the Model. Competition of Two Factors in a Nonlinear System

3.2.4. The Problem of Reconstruction of an Attractor

3.2.5. The Method of AAS (Approximate Auto-model Solutions)

3.2.6. A New Type of Strange Attractors

3.2.7. A Spectrum of Structure-Attractors Exists Close by the S-Regime

3.3. The Complexity: the Whole and the Aim

3.4. On the Way Towards Synergetics with Human Face

3.5. Models of Synergetics, Development of Humankind, Demographic Crises

3.5.1. The Hyperbolic Character of the World Population Growth

3.5.2. The Inner Stability of the Law of Growth

3.5.3. The Asymptotic Instability. Demographic Crises.

The Modern Danger of a Super-catastrophe.

3.5.4. Periods in Human History. The Shortening of the Period

3.5.5. Oscillations in Space. Nets of Cities. Christaller’s Lattices

3.5.6. The Media of Information. The Possibility of Strengthening of Nonlinearity

3.5.7. Some Expectations and Forecasts


Chapter 4. Synergetics in the Context of Culture

4.1. Synergetic Ideas and Images of Human Culture

4.1.1. Attractors. The Aims of Evolution

4.1.2. Bifurcations. Branchings. Choice

4.1.3. Fractals. Self-similarity of Processes on the Different Levels.


4.1.4. The Vortex Begetting

4.2. Synergetics at the Crossroads of the Eastern and the Western Cultures.

Synergetics and the East

4.2.1. Everything in Everything

4.2.2. The Potential and the Unrevealed

4.2.3. The Yin-Yang Rhythms. Eternal Recurrence

4.2.4. The Idea of Connection between Tempoworlds

4.2.5. The Creative Role of Chance

4.2.6. How Is the Shortest Path Possible?

4.2.7. The Idea of Resonance. Bonds of the Echo Type

4.3. Synergetics and the Traditions of the West

4.3.1. Plato’s Perfect Bodies of Nature

4.3.2. The Cosmic Vortexes of Descartes

4.3.3. Monadology of Leibniz

4.3.4. The Image of Becoming in Chaos Described by Nietzsche

4.3.5. The Creative Evolution According to Bergson

4.3.6. The Modi of Time by Heidegger


Chapter 5. The Main Principles of Synergetic Worldview

5.1. New Notion of Chaos

5.2. New Teleology

5.3. New Holism

5.3.1. The Integration of Structures through the Establishment

of a Common Tempo of Development

5.3.2. How is the Acceleration of Tempo of Development Possible? . 91

5.3.3. Symmetry and Asymmetry

5.3.4. The Past and the Future are ‘Impressed’ on an Architecture

of a Structure

5.3.5. ‘Self-rising to the Surface’ of Memory Structures

5.3.6. A Meeting of Different Tempoworlds

5.4. New Principles of Management

5.4.1. The Application of the New Methodology to the World

of Physical Processes

5.4.2. Its Application to the Human and Social World.

Constructive Principles of the Complex Systems Co-evolution

In the Search of Parameters of Order.

Super-rapid Development of Processes in Social Systems

The Field of Evolutionary Paths in Social Systems

Problems of Co-evolution of a Human and Nature

Determination of Evolutionary Processes from the Future

Role of Chaos in Social Development

When Can a Personality Influence the Course of History?

A Path of Acceleration of Evolution

Laws of Integration of Complex Social Structures

Pulsative Rhythm of the Accent to Unity

The Possibility of Transformation of the Field of Paths of Evolution


Chapter 6. On The Way Towards Synergetics of Cognition

6.1. ‘Babylon Tower’ of Knowledge

6.2. Criticism of the Traditional Linear View

6.3. Is Synergetics Applicable to the Analysis of Cognitive Processes?

6.4. Three Arguments in Defense of Synergetics of Cognition

6.5. Nonlinear View of Cognitive Evolution

6.6. The Embodied Mind: The Prospects of Application of the Models of Nonlinear Dynamics in Cognitive Science


Chapter 7. The Mental Ferment of the Creators. Synergetic View

of ‘Cognitive Robinzonian Activities’

7.1. Scenarios of the Creative Thinking

7.2. The Emergent Appearance of a New or its Latent

Predetermination? The Attractors of the Creative Thinking

7.3. Self-organization as a Mechanism of the Creative Thinking

7.3.1. Holism in the Creative Work

7.3.2. The Art of Selection

7.3.3. Self-completing

7.3.4. A Cascade of the Talent Crystallization

7.3.5. The Phenomenon of Resonance

7.4. Beyond the Mental: the Path of the Creative Intuition and the Yoga Path

7.4.1. To Erase the Old Tracks

7.4.2. The Consciousness as a Treasure-house

7.4.3. The Tighting into a point

7.4.4. An Hierarchy of the Consciousness

The Connection of Tempoworlds

7.4.5. The Rhythms of the Creative Activities

7.4.6. Human Being as a Device. A Resonance

7.4.7. A Danger of Splitting of the Consciousness

7.4.8. A Topology of the Soul


Chapter 8. The Adventures of the Collective Mind.

The Historical Development of Science and Culture from the Synergetic Point of View

8.1. Alternative and Diverse Evolutionary Ways

of Scientific Knowledge

8.2. Unevenness of Tempo of Scientific Progress.

An Oscillatory Regime

8.3. Impossibilities of the Getting Rid of the Prejudices in Science.

Misconceptions of the Collective Mind

8.4. The Nature of Innovations

8.4.1. The New as a Forgotten Old

8.4.2. The New as an Intersection of Scientific Traditions

8.4.3. The New as a ‘Mutation’ of Cultural Relay-races

8.5. The Phenomenon of Inertia of the Paradigmatic Consciousness

8.6. Conditions of ‘Survival’ of the New in Science

8.6.1. How Can the Searching Spirit Express ‘der Zeitgeist’

(the ‘Spirit of Time’)?

8.6.2. The Phenomenon of the Simultaneous Scientific Discoveries.

The Ideas are Looking for People

8.6.3. Ecology of Knowledge. The Individual ‘Building into Culture’


Chapter 9. Synergetics of Education

9.1. Why Does Synergetics Have a Special Significance for Education?

9.1.1. Interdisciplinarity of Synergetics

9.1.2. The Synthetic Function of Synergetics

9.1.3. Synergetics as a Strategy of Research

9.1.4. The connection of Synergetics with the Future

9.1.5. Synergetics as a Method and Contents of Education

9.2. The Synergetic Methods of Education

9.2.1. Self-Education

9.2.2. Nonlinear Dialogue

9.2.3. Awakening Education

9.2.4. Education as an Adaptive Modification

9.2.5. Education as a Phase Transition

9.2.6. Gestalt-education

9.3. Return to the Visual Thinking


Chapter 10. Synergetics and the Futures Studies

10.1. Thinking Oriented towards Foreseeing the Future

10.2. Global Problems and Global Opportunities

10.3. Changes in� Attitudes of Research

10.4. Alternative and Attainable Future. A Spectrum of Pathways into the Future

10.5. Horizons of Future. Limits of Predictability

10.6. Future is already here. One has only to learn to see it

10.7. The Art of Soft Management

10.5. To Attain Unattainable. Hopes for Better Future



Appendix I.
Belavin, V.A., Kapitza, S.P., and Kurdyumov, S.P. The Mathematical Model of Global Demographic Processes with Regard for Spatial Distribution.

Appendix II.
Knyazeva E.N. Complex Systems and Nonlinear Dynamics in Nature and in Society.
Notes on the 1st Annual Conference of the German Society for Complex Systems and Nonlinear Dynamics (October 1997)

Appendix III.
Synergetics: Thirty-years-old Child and his Father. Interview with Prof. H.Haken. Conducted by H.Knyazeva.