The Self as a Nonlinear Dynamical Structure-Process

 

 

Helena Knyazeva

 

 

 

 

Abstract

 

The models of nonlinear dynamics and self-organization of complex systems are applied to understand the emergent patterns of individual thinking and behavior. A number of notions from the modern theory of complexity, such as poising at the edge of chaos, operational closure and self-production, autopoiesis, the existence of a multitude of possible discrete states and the existential of choice in the points of bifurcation, the slow, iterative going out to the automodel stage of development and the autocatalytic, avalanche-like growth of a new property, facilitate our comprehension of internal complexity of individual self. The self is considered as a nonlinear dynamical structure-process which has a certain spatial configuration and temporal depth. Such a view of the human mind and behavior coincides with the modern dynamical approach in cognitive science (F.Varela, T. van Gelder, A. Clark, and others). Cognition is embodied: the perceptual and mental processes are bound up with the “architecture” of the human body. Cognitive and creative activity is an enactive process: a man cognizes the world but at the same time the very process of cognition forms and changes him. Human life (and therefore human cognition) is an autopoietic activity because it directed to the search of elements that are missed, it longs for completing integral structures.

 

 

Key words

 

Blow-up regimes, complex systems, dynamical approach in cognitive science, embodied mind, nonlinear dynamics, self-organization, situated cognition, synergetics.

 

 

1. Transdisciplinarity of the Synergetic Models

 

The modern theory of self-organization of complex systems, also called synergetics, has its hard core in mathematical modeling and computer simulation of evolutionary processes in complex systems of nature. But models elaborated within the theory increasingly demonstrate their usefulness in analyzing human behavior and cognitive activities. The theory is transdisciplinary by its nature. Transdisciplinary research is characterized by the transfer of cognitive schemata from one disciplinary field to another as well as by the working out of joint research projects.

  Since the late sixties synergetics has been regarded by its founder H. Haken as a teaching of interaction (Haken, 1978). This is a transdisciplinary research field focused on the exploration of systems which are composed of several or many constituents and display new emergent macroscopic properties that are unexpected and nonderivable from the available state of elements. As regards human psychology, the complexity and mass character of interactions can be understood at least in double sense. On the one hand, the human body and brain consist of a multitude of cells, tissues, muscles, articulations of bones, neurons and neurons knots. On the other hand, the human body, brain and consciousness reveal highly complex and changeable behavior, they are multifunctional and multistable. As a matter of fact, the processes of self-organization of sensory and motor, perceptual and mental activities are processes of reduction of many degrees of freedom to a few or even to one degree of freedom, to a few or even to a certain independent variable – the so-called order parameters or an order parameter. The order parameters define key properties of a system on the level of the system as a whole.      

  Synergetics steps over boundaries between different scientific disciplines, including the boundaries between natural sciences and the humanities. The theory tries to construct certain bridges between inanimate and animate nature, between the quasi-purposes of systems behavior in inanimate nature and human rationality, between the birth of something new in nature, the so-called “creativity of nature” and the creative abilities of a human being. Similar patterns of evolution and of the structure formation are being studied in both domains. On the one hand, some features of living beings show themselves sometimes already in self-organizing systems of inanimate nature, and on the other hand, certain properties of inanimate nature can be found in living creatures, some of properties of life are already pre-given, pre-formed in the “dead nature”, in the general laws of evolution of the universe. Synergetics thus reveals common geometries of behavior at different levels of organization.

  There are already some attempts to apply the synergetic models of complex systems behavior to comprehend the human brain and its diverse activities, first of all the visual perception and pattern recognition (Haken and Stadler 1990; Haken 1996a, 1997) as well as to understand some phenomena of human cultural and social activities (Haken 1996b). In recent works (Knyazeva 1998; Knyazeva and Haken 1999), some essential principles of the synergetic outlook on the human cognitive and creative activities are expounded. 

  Thus, the aim of this paper is to consider how the modern theory of self-organization of complex systems may contribute to comprehending the nature of individual self from the point of view of the modern theory of self-organization and complexity and to exploring emergent patterns of human mind and behavior when using the main principles of the synergetic holism, the building of a complex evolutionary whole from parts. The theory of synergetics doesn’t strive for recipes for productive creative activities, rational behavior and effective management under conditions of uncertainty and instability of environment, but rather attempts to reveal some synergetic mechanisms which might form the basis of the human cognitive and behavioral activities.

 

           

2. A New Evolutionary Holism:

Philosophical Consequences of the Theory of Complexity

 

  What is evolutionary whole? The main principle of holism that “the whole is more that the sum of its parts” may be traced back to ancient philosophical studies. One of the earliest formulations of the principle may be found in Taoism, in philosophy of Lao Tsu. However, a complete and profound sense of the principle has been revealed only by such theories, as gestalt-psychology, systems theory, and synergetics.

  The method of analyzing from the whole to the parts is quite unusual for the classical science. The latter moves in the course of analysis mostly from separate parts to a whole. From the synergetic point of view, it is order and control parameters that determine the behavior of the parts (subsystems) of complex systems. They allow us to enormously reduce the complexity of description of a system under consideration.

  The classical principle of superposition is not valid in the complex nonlinear world which we live in: the sum of partial solutions is not here a solution of equation. The whole is not equal to the sum of its parts. Generally speaking, it is neither more nor less than the sum of parts. It is qualitatively different in comparison to parts which are integrated in it.

 

  Circular causality. Parts of a complex system determine its dynamical properties, the order parameters. The order parameters in turn determine, or even “enslave”, the behavior of parts. The phenomenon is called by H. Haken circular causality (Haken 1996a, p.43). An emerging evolutionary whole alters its parts. The co-evolution of different structure formations means the transformation of all subsystems by mechanisms of system coordination and correlation between them. Besides, when altering parts, the whole can awaken some new unusual and still unprecedented properties of a part or several parts, it can call it/them into an uncommon being.

 

  Nonlinear synthesis of parts into a whole. Tempo-worlds. The complexity of a structure is connected with the coherence in behavior of its elements (substructures). This coherence is the concordance of the tempos of “life” of its substructures, something which is a result of diffusion and/or of dissipative processes that are a macroscopic manifestation of chaos. In order to construct a complex organization, it is necessary to coherently unify substructures within it and to synchronize the tempos of their evolution. As a result of the unification, structures fall into one tempo-world, i.e. they acquire one and the same moment of peaking, start to co-exist in one and the same tempo-world (Kurdyumov 1990; Knyazeva and Kurdyumov 2001).

  To create a complex structure it is necessary to know how to unify structures “of different ages”, i.e. structures of different stages of evolution and having different rates (tempos) of evolution. It is necessary to know how to include the elements of “memory”, the biological memory, DNA, or the memory of culture, cultural traditions. Inasmuch as the structure-attractors which characterize the developed, steady evolutionary stages of structures in a nonlinear world are described by the invariant-group solutions, the spatial and temporal properties of structure-processes turn to be tightly bound. The dynamics of development of a complex structure needs a coordinated (with one and the same moment of peaking) development of substructures of “different ages” within it, this leads generally to the breakdown of spatial symmetry. The insertion of “memory” (of elements of the past) signifies the symmetry breakdown in space.

  Different but not arbitrary structures can be unified. The degree of connection of structures which are to be integrated and the stages of their development are not arbitrary as well. There are various but not arbitrary ways of unification of structures into integral ones. There is a restricted set of integration ways, ways of construction of a complex evolutionary whole.

  The selectivity (the quantum character) of ways of integration of parts into a whole is connected with the imposed requirement of existence in one and the same tempo-world, i.e. of development of all parts with one and the same moment of peaking. This is the physical basis of quantification when integrating complex evolutionary structures. If joinable structures have even slightly different from each other moments of peaking, then, near the moment of peaking (the singularity), they will become incompatible in intensity.  

  Thus, the synthesis of relatively simple evolutionary structures in an entire complex structure occurs by the establishment of a common tempo of evolution in all unified parts (fragments, simple structures). The intensity of processes in various fragments of the complex structure can be diverse. The fact of integration signifies that structures becoming parts of a whole acquire a common rate development.

 

  The role of topology of integration. An integrated complex structure arises only if there is a certain degree of overlapping of simple structures. There must be a certain topology, “architecture” of overlapping. A constructive “sense of proportion ” must be observed. If the area of overlapping is not sufficient, then the structures will develop independently, they wont feel each other, and they will live in different tempo-worlds. But if the overlapping is too wide, then the structures will flow together very fast, they will straight away “degenerate” in one rapidly developing structure.

  The factor of unification of parts into a whole structure is chaos, dissipation, fluctuations or their analogue. Chaos plays a constructive role not only in the moments of choosing a further evolutionary path, but also in the processes of assembling a complex evolutionary whole. Chaos leads to the establishment of coherence of development in all parts (substructures). Chaos serves as a “glue” that binds parts into a united whole.

  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.

 

  Non-linearity of development and the emergent properties of systems. Emergent properties of entities are connected with the non-linearity of development of systems in the world. The concept of non-linearity a profound philosophical sense. The content of this concept may be elucidated by a few more intelligible notions, namely: a) the notion of multiplicity of evolutionary pathways, the availability of alternative pathways of evolution (it is well worth to underline here the fact that a large number of evolutionary pathways is characteristic even for one and the same invariable complex system); b) the notion of choice between these alternative pathways of evolution; c) the notion of tempo of evolution, i.e. the speed of evolutionary processes in a complex system; d) the notion of irreversibility of evolution.

  Complex systems are organized in a hierarchical way. A part itself can be a whole that consists in turn of smaller parts on an underlying level of world organization. A part (for instance, an individual) can be more complex than a whole (for instance, society) if its non-linearity is stronger than that of the whole. The stronger non-linearity means that a structural entity on this level of organization possesses a more complex spectrum of forms as well as of possible pathways and regimes of development.

 

 

3. Blow-up Regimes and the Discrete Spectra of Evolutionary Structures

 

  Two other consequences of synergetics that are important for our comprehension of the complexity of individual self are peculiarities of the blow-up regimes and the notion of discrete spectra of structure-attractors of evolution.       

  Synergetics discovers laws and conditions for very fast, avalanche-like processes, blow-up regimes. These are processes when some characteristic parameters (temperature, energy, information etc.) grow infinitely during a finite period of time.

 

Q(t)  ¥ , when t ®  tf

 

where tf is the blow-up time or time of peaking. Of course, infinite growth is impossible in real systems of the world. But the rapid growth of the characteristic values in several orders, sometimes even in several times, allows us to observe a number of astonishing effects which have been predicted by the theory of blow-up regimes (Achromeeva et al. 1989; Samarskii et al. 1995. Blow-up regimes are being studied now in more than sixty different mathematical problems, starting from plasma physics (laser thermonuclear synthesis) and concluding with neurophysiology (the modeling of signal propagation along neural nets) and epidemiology (spreading of infections). There are possibly similar blow-up regimes in human psychology.

  The mechanism of such a super-rapid growth is a volumetric nonlinear positive feedback. There is a self-influence in every local area of a complex system. A local change of conditions of the system has an influence on the work of nonlinear source in this place. Therefore, this feedback signifies an accelerated self-stimulating increase of the intensity of processes all over the space of the system.

  Blow-up regimes show an amazing peculiarity. The course of development has two essentially different stage of development, namely: a prolonged meta-stable stage, when all characteristics of processes increase extremely slowly and insignificantly, and a stage of asymptotic instability near the moment of peaking, when a threat of stochastic decay of a complex structure appears.

  Structures develop very slowly during rather long period of time. They are meta-stable. To put it differently, blow-up regimes have a prolonged quasi-stationary stage. Further, when structures have grown sufficiently and have overcome a threshold of the slow growth, these structures become to develop super rapidly in a blow-up regime. Near a moment of peaking, i.e. at the stage of infinite increase of characteristic quantities, complex localized structures become unstable and may fall apart under the influence of small fluctuations. The natural stochastic, probabilistic, "radio-active" decay of nonstationary complex structures near the blow-up point is, therefore, a consequence of instability of organization of such structures towards chaotic fluctuations at a microlevel.

  The evolution of complex structures undergoes an alternation of various regimes of process development. There cannot be sharp growth of a structure without a threat of its fall and destruction. There are some universal laws which govern these rhythms. They are peculiar to living beings as well as to complex structures in inanimate nature. There are 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. Depending on a result of interplay between two opposite factors in a given system - the action of nonlinear feedback (a volumetric nonlinear source) and the dissipative, scattering processes, - three different evolutionary regimes can be established in a corresponding complex nonlinear system.

  How did the pivotal synergetic idea of spectra of evolutionary structure-attractors arise? The scholars of the Keldysh Institute of Applied Mathematics and the Institute of Mathematical Modeling (the Russian Academy of Sciences) managed to discover mechanisms of localization, structure formation in open nonlinear media (in complex systems). In relatively simple mathematical and computational models, a result of fundamental importance has been obtained: a continuous open nonlinear medium potentially contains in itself different kinds of localization processes (different kinds of structures). A medium is a united source that acts as a carrier of different forms of future organization, as a field of different evolutionary paths (Kurdyumov 1990; Samarskii et al. 1995).

  Structure (or organization) is not interpreted here in a stationary sense. It is a process localized in certain regions of a continuous open nonlinear medium. The process has a certain geometry and is capable of developing, of reconstructing and moving in the medium. In other words, the structure is a spot of organization wandering inside the medium. An open nonlinear medium (system) covers itself by organization spots.

  An internal mechanism of structure generation and evolution (reconstruction, integration and disintegration) is a competition, or an interplay, between two opposite factors in a medium. One of them is the factor which dissipates, scatters about inhomogeneities in the medium; it can be of various nature: diffusion, dispersion, hydrodynamics, etc. For example, it can be diffusion of neutrons, or diffusion (dissemination) of knowledge, or diffusion (spreading) of infectious diseases. The other factor is a nonlinear source that can be also of different kinds. The source (of energy, information or infection) creates inhomogeneities in the continuous medium. It can be an active medium in the nuclear reactor which generates an avalanche flow of neutrons, or it can be a source of knowledge or infectious diseases.

  There are no arbitrary structures that can be self-maintained in a given complex nonlinear system. Only structures in accordance with the inner evolutionary trends of the system can arise. And nothing else but select meta-stable structures can be constructed in the system. This is a kind of evolutionary law of prohibition (Knyazeva and Haken 2000). This idea of discrete spectrum of evolutionary structure-attractors leads to some more concrete consequences:

 

1.       There are a number of types of possible structure-attractors, i.e. evolutionary pathways, even for a relatively simple open nonlinear medium (system). A whole “zoo” of structures of self-organization, that is a set of rather exotic structures, can be contained even in a relatively simple medium. This is even more true of such complex systems as the human brain and consciousness or human society.

 

2.       The number of possible structures can be very big, but it is limited. The spectrum is by no means continuous one. Only a definite set of evolutionary pathways is “allowed” by the nature of a given complex system itself. The spectra of possible, “allowed” structures correspond to sets of the eigenfunctions of the nonlinear equations describing the evolutionary processes in the complex system. The sets of eigenfunctions of the corresponding nonlinear equations are mathematical representations of spectra of evolutionary structure-attractors.

 

 

3.       The spectra of evolutionary structure-attractors are determined exclusively by the own properties of a corresponding complex system (open nonlinear medium). They are its inner potentials, so to speak, a “tacit knowledge” of the system itself.

 

4.       The discrete sets evolutionary paths into the future presuppose ways of a special soft, or nonlinear, management. The art of soft management consists in the ways of self-management and the self-control of complex systems. It is a management by “clever” and appropriate, so called resonant, influences. Some human actions are doomed to be unsuccessful. They fail if they are not in line with the inner trends of development of complex systems.

 

 

5.       Some possible changes of inner properties of complex systems can lead to a transformation of spectra of evolutionary structure-attractors, sets of possible paths into the future.

 

  The problem of obtaining accurate spectra of evolutionary structure-attractors of complex systems has been solved so far only in particular cases. Hence, we are faced with a vast area to explore. In fact, it is a “super-problem”, close to that of W. Heisenberg in nuclear physics, when nonlinear equations are required to describe a medium which as a self-organizing system would yield stable states in form of the spectrum of elementary particles.

  It seems that synergetics can initiate more complex research problems to be studied by psychologists and philosophers. For example, a task of determining a spectrum of human emotional states or a spectrum of psychological types of personality.

  Six basic emotional states of a human being, namely pleasure (joy), sadness, anger, fear, surprise, disgust, have been distinguished by psychologists. These are, of course, a kind of pure, idealized emotional states, but real human emotions can be qualified as inclined to this or that of basic states. Highly correlated external and internal symptoms such as facial expressions, heart beats, blood pressure and so on determine these various emotional states of humans. It’s worthwhile to study the states as behavioral patterns with respect to their control and order parameters. The central question will be to cast the concepts into a scientific form that includes procedures for quantifying them. An enormous amount of research work lies ahead for behavior and psychological science in the light of the modern theory of self-organization and complexity.

 

 

4. The Individual Self: A Self-organizing Complexity

 

Structures of self-organization are not hard blocks from which the observed well-ordered universe is built. They are rather metastable localized processes that are able to become permanently transformed, to enter into the cooperative interaction with other processes and to form thereby larger entities or, on the contrary, to come apart and sometimes to completely disappear in the general chaotic background of the universe. The observed well-ordered world is the world where structures-processes of self-organization live their own life. If we consider a human being, his cognitive abilities and practical intentions, the construction of his personality, the hierarchical layers of his consciousness-subconsciousness, the historical strata of his memory, all these formations can be understood as structure-processes of self-organization. Many synergetic notions, such as self-organization and poising at the edge of chaos, operational closeness and self-production, autopoiesis, a multitude of possible discrete states and the existential choice in the moments of bifurcation, the slow, iterative going out to the automodel stage of development and the autocatalytic, avalanche-like growth of a new property, are in use for a better understanding of the internal complexity of individual self.

 

  Poising at the Edge of Chaos. Nature is wise in constructing complex structure formations, but these structures are rather fragile. They are poised “at the edge of chaos” in such a way that even the best little step in the direction of improvement of their organization can initiate the process of their rapid spontaneous decay. Such properties of self-organizing systems are studied in the theory of self-organized criticality (Bak 1997).

  Availability of chaotic elements, i.e. a relative irregularity is often a sign of human health, both corporal and spiritual, a sign of stability of personal structure. For example, only a strong aperiodicity in heartbeat means a sickly state – arrhythmia, whereas some small chaotic fluctuations in heartbeat are quite normal; they are a result of especially internal rather than external factors. A line of demarcation between the health and an illness, between life-giving and basilisk chaos is rather polysemantic and mobile. The question is: what portion of chaos must a human carry in himself in order to be healthy?

  Chaos is a natural randomizer, i.e. a random-signal generator in nature. Chaos makes our organs more flexible and more suited for a changeable environment. A complex organization emerges and maintains itself at the edge of chaos. “The edge of chaos is a dynamic, fluid transition zone exiting between two extremes: predictable order and unpredictable chaos¼ All of life evolves to the edge of chaos, where it remains flexibly poised in a critical state of readiness¼ Only between extremes, at the edge of chaos, can psychological balance be achieved. At the edge of chaos, we are best equipped psychologically to deal with erratic and unpredictable events in life”(Marks-Tarlow 1999, p. 322-323).     

  The more stereotyped human behavior is, the more suspicions of a pathology there are. Whereas a psychologically healthy man conforms to the patterns of behavior depending on social roles he plays at the present moment, a man with a mental disease pursues – to a considerable or lesser degree – only one object (idée fixe), his behavior is – to a great extent – repeatable, iterative, liable to cyclic attractors. His behavior doesn’t have due flexibility and isn’t sensitive to an unsteady environment.   

 

  To be chaotic means to be creative. Chaotic cognition. The human creative activity is in need of special stages or permanently existing layers of subconscious random, chaotic movements of mind. To be productive, cognition should have periods when it plunges into chaos. Nowadays some specific methods of chaotic cognition are under development. Such methods allow thinkers to explore new possibilities and to make maximum use of moments of intensive inspired work when the increase of new knowledge occurs. Creative thinking is divergent thinking. The pathway of creativity consists in giving oneself over to chaos in order to take possession of it. That is to resign oneself to control of chaos when at the same time seizing the opportunity to create a refined structure.

  Every human has a shady side which lies not only in his psychological weaknesses and shortcomings but also harbors a demonic dynamics. This monstrous, explosive, non-organized energy that cuts its way though layers of subconsciousness is similar to avalanche-like natural processes, the so-called blow-up regimes, studied in synergetics, in which new, so far unwitnessed structures of self-organization arise. A “wandering look” of mind – this is an image that might rather precisely express the basis of human creativity. The mind should be decentralized, defocused; it should move freely between vectors of directional activity. The “wandering over the field of possible pathways of development”, the chaotic movement of creative mind leads every now and then to coming out to one of structure-attractors. Thereby, a vector of creative activity, leading to a break-through into a new, is determined. The field of possibilities is put to the test and sounded out. As a result, one of latent structures is materialized; the crystallization of new knowledge occurs.    

  Thus, chaos is necessary in order to allow a cognitive system to go out to a structure-attractor, its own trend of development and to initiate the process of its self-organization. As a matter of fact, it was known long ago and was expressed in allegorical, poetical forms, such as, for example, in one of aphorisms of Nietzsche: “Man muß noch Chaos in sich haben, um einen tanzenden Stern gebären zu können” (Nietzsche 1955, S.284).

  According to the synergetic model of H. Haken (order parameters, slaving principle, circular causality), as a result of creative activity or creative teaching, new order parameters of behavior of a human as a complex nonlinear system spring up. The system “swings” over all accessible degrees of freedom, and after that new macroscopic structures of knowledge or of experience appear. Creativity is a factor of success, because it implicitly relies on chaos as a way of self-renewal. To undertake something means to change oneself permanently and to find vectors of further development. 

 

   Individual landscapes of personality. Every personality is autonomous and all-sufficient. If we apply a term from the theory of autopoiesis elaborated by H. Maturana and F.Varela, we may say that a personality is operationally closed, i.e. a man derives his strength and intentions of his activity from himself, makes his own plans, actualizes himself, devotes himself to the world. The Russian academician P. L. Kapitza once noted that “the main sign of talent consists in the fact that a man knows what he wants”. At the same time the self is a polylayer and many-dimensional formation which is dissolved in situations, actualized in different social and family roles, distributed in a topological way. The self has its own space of life which borders are fragile and mobile. An individual landscape of personality is built into a landscape of his family as well as of the corresponding social group, nation, and noospheric reason.

  These notions are strikingly close to the ideas of Kurt Lewin (1890-1947) who was a disciple of the Berlin school of gestalt-psychology but developed later on his original research trend called by different names: “dynamical theory”, “topological psychology”, “vectorial psychology”, “field theory”. Lewin introduced a notion of “space of life” (“Lebensraum”). This is a personality together with his psychological environment in such a form how it exists for the personality. As a rule, the space of life is taken into consideration, if personal needs, motivation, mood, purposes, doubts and fears, ideals are analyzed.

  What is structure of the personal space of life? The concept of purpose as an ordering of forces in a dynamical field of personality plays here the central role. The space of life contains “the psychological past”, “the psychological present” and “the psychological future”, they are different dimensions of the available space of life (Lewin 1982, p. 68). Lewin introduced the principle of simultaneity (synchronism) and of simultaneous influence of the past and the future: any act of behavior and any possible change of the psychological field depend purely on the state of the field at the present moment.  The psychological past, present and future are parts of the psychological field in a certain point of time. Both the past (accumulated experience) and the future (expectations, desires, apprehensions and hopes) exert influence on forces regulating the today’s behavior of an individual.

  The space of life of personality is a certain field on which different forces, determinative tendencies, aspirations come into collision with each other. Thereby, the purpose is understood as a force field of psychological activities structured in a certain way; it is a disposition of forces in space. As a matter of fact, this is a certain dispersed purpose. The notion of vector finds a quite constructive use in topological psychology. Firstly, forces that are available in the psychological field can differ in magnitude. Secondly, one can perceive various directions of forces (of aspirations) within the psychological field. The very notion of direction makes sense only if one can distinguish different directions, as we might say from the synergetic point of view, different structure-attractors of psychological activities.

  Individual landscapes of personality are configurations of the inner (own) space and of environment of an acting and cognitive subject. These configurations are determined by a dispersed purpose, by a spectrum of structure-attractors of cognitive and creative activities.

  The cognitive activities are partly pre-determined by latent and overt attitudes and plans. The cognitive subject is permanently in a multistable state and takes a random walk about the field of possibilities. There is a zigzag path that every time actualizes only one possibility from an available spectrum of theirs. The individual landscape a whole series of purposes and paths that lead to them. One can form a picture of a certain space where all possible forms of trains of thought are already available in a concealed, latent way. When a new knowledge arises, a fan of possibilities rolls up into one possibility from a set of discrete states.

  Another specific feature of the individual landscape of personality is synchronism. The landscape involves possible pathways of future development as well as some traces of the past activities. Applying a term of Kurt Lewin, one may say that the landscape has a certain temporal depth. The synchronism of configurations of the human soul was a subject of investigation in the works of Karl Jung as well: “The soul is all that a human has already done and that he still has to do in the future”. The memory of the past is always at present, but it can exert influence on the course of life only before points of “bifurcation”, i.e. at the moment of decisive choice of one of possible courses of life. If the point of “bifurcation” is already passed, the choice is made, the human activities are determined by the future rather than by the past. In such a case, the activities are built from the future, in accordance with one of structure-attractors of development.   

           

  Instabilities. Cascades of Crystallization of Personality. The structure of the landscape of the individual self is not rigid. Change in the intrinsic characteristics of a personality leads to reconstructing the field of pathways of his movement into the future. The stages of child’s education as well as the further self-education condition periodic qualitative transformations of a spectrum of purposes of life (plans, expectations and hopes) and a spectrum of possibilities. The personality passes through periods of instabilities and crises, as a result crystallizations of personality (his knowledge, his talent, etc.) can take place. The long process of self-education and of permanent creative activity is connected with a whole series of “bifurcation”, cascades of crystallization of personality, several events of qualitative reconstruction of structure-attractors, non-linear phase transitions. The individual landscape is repeatedly rebuilt in a qualitative way. A person becomes times and again another one. A creator is created. As Paul Valéry once noted in his diaries, the attained exerts a backward influence on the creator. The work alters an author.    

 

  Fractal Geometry of Human Behavior. The fractal pictures of human behavior are determined, in the first place, by some stable, reiterative, reproducible structures (patterns) of behavior and, in the second place, by self-similarity of these structures on different levels and on different scales of human activities. The fractal dynamics signifies either the structure of a strange, chaotic attractor that underlie the human behavior or self-organization of a complex structure in the vicinity of a critical point, “at the edge of chaos”.

  The landscape of individual self has a certain fractal depth. In other words, configurations of situations of life demonstrate a property of scale invariance. A creative man is creative in all kinds of activities, both in the large and in the small. He is creative on all levels of the scientific and practical activities, down to the everyday life. For example, he can develop his original methods of cooking – of the preparation of house-made veal cutlets. It is paradoxical that the creative, non-linear writing is connected with the creative, non-linear cooking. On all levels and in all fragments of the chain of his actions, one can discover his “handwriting”, his original style of creative activity. 

 

 

5. The Individual Mind: Embodiment, Situation, and Enactivation

 

  The synergetic approach to understanding the human mind and behavior coincides with the modern dynamical approach in cognitive science (F.Varela, R. Brooks, T. van Gelder, R. D. Beer, A. Clark and others) which is based on the applying the models of nonlinear mathematics and of the theory of complex adaptive systems. The dynamical approach is defined by three key words: embodied, situated and enactive cognition. What is sense of these new concepts?  

  Cognition is embodied: the perceptual and mental processes are bound up with the “architecture” of human body. F.Varela with his co-authors explains the term as follows: “By using the term embodied we mean to highlight two points: first, that cognition depends upon the kinds of experience that come from having a body with various sensorimotor capacities, and second, that these individual sensorimotor capacities are themselves embedded in a more encompassing biological, psychological, and cultural context”(Varela et al. 1991, p.172-173). The processes of perception and motor activity are indissolubly connected in the real processes of cognition. The mental processes are bound up not only with the emotionality of an individual but also with peculiarities of his corporal organization. Therefore, it is in a certain sense true that a human thinks using his body and not only his brain. It is said for a long time that there is a language of body that constitutes a basis of nonverbal communication. If there is the language of body, may be the thinking is not concentrated in the head but is poured over the whole body. 

  Cognition is situated:  a cognitive act expands into a situation that possesses certain topological properties. The relations of a cognitive subject with his environment are essential. From the standpoint, memory isn’t considered as something accumulated in a symbolic form in the head, it is rather spread over environment. The cognitive psychology becomes an ecological psychology.

  The third neologism is enactive cognition. It is introduced to lay emphasis on the active side of perception and thinking, of the human cognition in general. We learn, remember, and get to know something when we act. Cognition is an epistemic action: cognition occurs in action and through action. A human conceives the world but at the same time the very process of cognition forms and changes him, imparts configurations to his cognitive activity. A going man paves the way, but at the same time the way makes the going man; when the path is traversed, he becomes another man. And what is more, the cognizing subject not only cognizes the world but also constructs it, because if the world of a pigeon is colored in five colors, the bats perceive the world in ultra-violet rays and the world of humans is polychromatic, it is senseless to question the real color of the world. Thus, as Varela says, the world can be characterized not by attributes but only by potencies that can be enactivated in the cognitive activity. In such an enactive process of cognition, new emergent structures arise and develop, sometimes fall into decay or, on the contrary, become complicated and are completed. Human life (and therefore human cognition) is an autopoietic activity because it directed to the search of elements that are missed, it longs for completing integral structures.

 

 

Acknowledgements

 

The research is supported in 2001-03 by the Russian Foundation of the Humanities (# 01-03-00367a).

 

 

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For information on how to order Helena Knyazeva’s forthcoming book follow this link.

 

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