Dialectic. Cosmos and Society

Editor: Anthony E. Mansueto: President, Foundation for Social Progress and Profesor/Investigador, Departamento de Ciencias Sociales, Inslitulo de Ciencias Sociales y Administracion, Universidad Autonoma de Ciudad Juarez, Ciudad Juarez, Mexico

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Dialectic as a Means for Understanding

Nonlinear Science

Irina Dobronravova

Why study theories of the self-organization of complex systems? There is a tendency to represent nonlinear science as primarily a science of chaos. But while the results of nonlinear theories of chaos are very impressive, they do not exhaust the results of this promising area of scientific investigation. Furthermore, from the standpoint of an effort to establish a new unity among the natural sciences on the foundations of nonlinearity, theories of self-organization are far more important. I have in mind here the possibility of understanding the relative stability of dissipative structures as a dynamic stability, as the self-reproduction of self-organized systems. This allows us to see stability from an evolutionary point of view. And it is precisely the problem of stability which is the main problem in the unification of modem science, integrating "the physics of being" and "the physics of becoming," to use Prigogine's expression, by retheorizing the content of both classical and non-classical physics from a nonlinear point of view.

The contemporary revolution in the natural sciences is associated with the creation and development of two new scientific programs, which both involve the study of nonlinear processes of self-organization in complex systems: the research program of unitary gauge theories and the research program of synergetics. These two research programs have resulted in a new style of scientific thinking, which we call "nonlinear (Dobronravova 1990)," oriented towards the analysis of whole systems in the process of becoming. Among the defining characteristics of this new style of thought, we identify:

This new style of thinking is associated with formation of a new world picture, where the world is presented as a self-organizing entity, both when taken as a whole and on many levels of organization. It might seem at first sight that only unitary gauge theories bear on the existence of the world as a whole, because they help ground modern cosmological models. And it is true that most synergetic theories concern mainly macroscopic objects. I hope to show, however, that only the new synergetic understanding of the integrity of self-organized systems makes it possible to say something about the world as a whole. This is because synergetics —the theory of self-organization- has made variable existence in its becoming and transiency the subject of investigation, while nonclassical physics (of which unitary gauge theories form a part), like classical physics before it, is directed towards the search for the essence, and the universality of the laws of it discovers is interpreted as a manifestation of invariability of the essence sought for. Such a static theory cannot comprehend the universe as a self-organizing, and thus evolutionary totality. Synergetics makes this possible.

The extension of the object of mathematical natural science from conservative to dissipative systems, from linear to nonlinear dynamics, from equilibrium to strongly nonequilibrium situations, from stability regarded as invariability to dynamic stability, has, to be sure, changed our understanding of reality and universality and their relation to natural laws In so far as they focus on universal, in variant laws, classical and nonclassical physics—the physics of being— both treat reality as substance. Self-organization is not, however, a fully regular process. The "choice" by a system of one path of development over another at bifurcation points is not determined by law. This makes the destiny of a self-organized system irreversible. Thus, natural science acquires the features of historical science. Its object is no longer nature "as the being of things, so far it is determined by general law" (Kant in Prolegomena, paragraph 14 ), but also the becoming these things as well as the formation of the general laws which govern that process of becoming. These means that the stable existence of a system will have a different ground than those envisioned by the physics of being, a ground which cannot be reduced to the continuous action of linear laws which are invariant with respect to the direction time. From the very beginning the description of self-organized systems has aimed at the search for the conditions of their stability. Moreover, the discovery of several types of stable solutions for nonlinear equations means that the historic commitment to generalization, which has always characterized scientific method, can be retained. For all the unpredictability which characterizes the development of self-organizing systems, as they opt for various alternative paths of development, synergetics has discovered that mathematical modeling is possible and that we can arrive at some general theoretical principles. Even if these principles are interpreted rather modestly as just a set of typical ways to realize self-organization, their discovery shows that the specific features of a natural science oriented to the cognition of the general have been retained.

The ability of science to retain its main features, even when its objects and methods are changed, is rooted in the development of fundamentally new styles of thinking and the development of new categories of thought. These new categories play a vital heuristic role at certain stages of scientific development. Thus to comprehend the situation of bifurcation with its break in the functioning of laws, when a system is transiting from one relatively stable state to another in which it will obey new laws, the limited categorical forms effective for the physics of being are inadequate. Paired categories of necessity and randomness, possibility and actuality, cause and effect within the conception of probable causality enable us at best to comprehend randomness as a manifestation of necessity, retaining the prearrangement of the necessity which initially limits the realm of the possible. Within the framework of these categories one cannot pose a question of the emergence of new a necessity governed by new laws, of the role of randomness in this becoming, or of the grounds for the emergence of the possibility of such a becoming and of conditions of preservation of what has become.

Fortunately, the philosophical tradition does have resources which can help us solve this problem. Among the most important of these is the Hegelian dialectic, with its analysis of the process of form building. Categorical analysis of theoretical descriptions of self-organized systems has already demonstrated the usefulness of the dialectic in the understanding of self-organization (Dobronravova 1990: 98-116). Here I would like to make particular use of categories derived from Hegel's Science of Logic. While the first definitions of becoming are given in the "theory of being," it is the "theory of the essence," which forms the middle part of the work which I find most useful. This is because the categories of being and becoming describe systems in their immediacy, whereas the quality is self-organization is something which comes to the fore only after analysis -i.e. only after theoretical mediation Such phenomena as laser performance or a heart beating do not reveal their similarity as self-organizing processes to the naked eye as it were, but do so only through the lens of scientific theory Besides, the relations of necessity, which are interesting for us, are described by Hegel in his theory of the essence.

Before proceeding, I would like to explain the way in which 1 use philosophical categories to interpret scientific results. I treat the philosophical heritage not as a historian of philosophy, investigating the grounds of the appearance of one or the other philosophical idea, but rather as a philosopher of science, trying to find in the history of philosophy the means to understand the current situation in science. I doing this, I draw freely on M. Mamardashwily's notion of philosophical inventions -ideas which, once developed, may be freely used by others as the basis for the development still other ideas (Mamardashwily, 1990, 94-95). I thus use one such philosophic invention, Hegel's dialectic, to help us understand recent developments in nonlinear science. More precisely, I will use certain parts of Hegel's "Science of Logic" as an instrument for theorizing the concept of "self-organization. " Given the powerful prejudice against Hegel among philosophers of science, I need to stress that 1 am not embracing Hegel's larger idealism or his attitude towards nature, but simply using some of his ideas, which he elaborated specifically as logical means for understanding becoming and the evolution of new totalities. The advantage of his approach is that it permits us regard a whole from the inside and thus to comprehend it in the process of its own becoming and self-reproduction. I would also like to stress here that my use of Hegel does not entail a critique of or a departure from scientific rationality. The basic character of scientific rationality has remained unchanged: the same reasoning and discursiveness, no special logics. That is, the phenomenon of becoming which is comprehended in the Hegelian dialectic is mathematically described by nonlinear dynamics and bifurcation theory, supplemented, where necessary, by probability descriptions.

The new whole which emerges as a result of self-organization may be generally described as a coherent structure. The problem just how a new structure emerges may be properly formulated as a problem of finding the ground of the becoming in the conditions of its realization, rather than the problem of a result obtained due to a certain cause. Categorical analysis of theories of self-organization has demonstrated (Dobronravova 1990:98-116) that medium nonlinearity should be regarded as the ground for the emergence of new coherent structures New wholes form due to the transition to ordered motion of medium elements whose motion prior to this transition was chaotic and noncorrelated. Until the problem can be described in linear equations (e.g. chemical kinetics equations), fluctuations (deviations from the average values which provide a solution for linear equation) may be neglected, because they are extinguished by the chaotic motion of the medium elements. However, at the critical control parameter value near the non-equilibrium phase transition, when medium nonlinearity becomes crucial, solutions to the nonlinear equations describing the system generally have two (or more) values. This phenomenon is called bifurcation. Here fluctuation is no longer a deviation from the average (which does not exist). Rather, the system makes a random choice between two equally probable solutions. It is the fluctuation, which "selects" one of two solutions of equations possible at a certain critical parameter value (condition), that can be understood as the cause, whose action is the formation of a coherent structure, i.e. the choice by the system of a certain evolutionary pathway. Hence the situation, where the choice may be both possible and random, is prior to the formation of the cause.

The application of Hegel's doctrines to bifurcation analysis thus allows us to understand that with the nonlinearity of medium as the ground, as the control parameter approaches its critical value, a system confronts objectively different isomeric and equally probable possibilities. The "choice" of a particular path of development is determined by fluctuation, and is thus a random choice. But any chosen solution appears to be necessary: it is determined by a real state of the system prior to phase transition. Thus, the randomness is an addition to the necessity. All possible paths of development have their own grounds and their own conditions of realization, and besides, the fluctuation value and the very situation of choice have objective grounds. As Hegel put it, "real necessity contains chance (Hegel 1974: 180) " This characteristic gives a profound description of the situation of self-organization, where the system is subjected to macroscopic laws between the bifurcations. In the vicinity of a bifurcation, a random choice returns the system to the way of necessity.

It is necessary to emphasize that fluctuation as a cause of order is far from being a "small cause of big effects". In a phase transition fluctuations are not small: they have not only a large amplitude, but also a long range (Prigogine 1985. 150). "There is no content in the action other than in the cause" (Hegel 1975: 146). A new coherent structure represents a large-scale fluctuation which shows the behavior of an integral macroscopic whole despite the short-range nature of the interaction between the medium elements, which cannot be compared in scale with the fully developed fluctuation. In some cases we are dealing with one fluctuation which, developing faster than the others, according to the "slaving" principle (G.Haken) "captures" the whole system, giving coherence to the action of its elements. In other cases many fluctuations appear simultaneously, and among these fluctuations a coherence is established which is supported by external conditions.

As it was mentioned above, among the conditions of self-organization a special place is occupied by the conditions which provide for the stability of newly formed coherent structures --i.e. for new wholes. The physics of being concerned itself with age-old systems the stability of which was grounded in laws which function uninterruptedly. But if the subject of natural science is to involve the formation of systems along with the laws which regulates their existence, then we need to understand the conditions under which these systems become stable in the first place.

In discussing the determination of form-building in the light of Hegel's dialectic, we considered the form building of the whole. This is important from a methodological standpoint, since the interrelation between the whole and the parts in the investigation of the becoming of the whole is opposite to the reductionistic principle, which regards the parts as something separate from the system and their inter-relationships as eternally stable. Indeed, from a dialectical viewpoint, a whole forms its constituents in the process of becoming. This categorical attitude enables us to adequately comprehend the action of the "slaving principle" - one of the fundamental principles of synergetics. This principle illustrates the situation within a process of self-organization wherein the most rapidly developing fluctuation "captures" the entire space of the initial medium, forming its constituents from the medium elements. Slower processes have no time to develop. Thus, at autowave formation synchronizing effects are observed: medium elements perform the oscillations with a frequency imposed by the most rapid source (i.e. in cardiac contractions rhythm is established). The same submission principle acts during the formation of thermal structures in plasma, of turbulences in the flow of liquid, of periodical vibrations in chemical reactions and so on. In all such cases, though the interactions between the medium elements are of a short range nature, instability may lead to the emergence of a long-range order due to which the system functions as a whole.

If, however, self-organization is understood as the becoming of a new whole, the problem of the stability of this new whole is replaced by the problem of its possible self- reproduction.

Self-organization can lead to the formation of wholes with different degrees of stability. Thus, coherent structures with limited stability, which are opened into the future stream of becoming (e.g. thermal structures in plasma), are formed by a certain arrangement of the elements of the medium. Here a permanent exchange with the medium takes place and, in the long run, the properties of the nonlinear medium appear to be crucial (determination by the ground, the system "forgets" the initial conditions of its formation). However, the stability of such systems is limited, since there is no way in which this new whole can reproduce itself within the medium.

Such a possibility is realized by stationary coherent structures in open systems - i e. dissipative structures. For them too the form is determined first of all by the ground of their existence - that is, the properties of the nonlinear medium. But external conditions also enter into the determination of their form: the dimension and the geometrical form of the initial system.

As for the possibility that other external factors may affect the process of self-organization, it should be taken into account that even a weak effect upon the nonlinear system in the vicinity of bifurcation may determine its destiny, while much stronger effects out of the vicinity of bifurcation cannot disturb the stability of the dissipative structure. To the conditions of this stability I. Prigogine assigns the remoteness from equilibrium and the openness of the system which provides for a local decrease in entropy connected with dissipative structure formation and maintenance of this state related to a higher level of organization. The flux of energy and matter passing through the system provides for the export of excess entropy to the medium. Apart from this, the dimension of the system is important because "the stabilization of dissipative structures requires a great number of degrees of freedom" (Prigogine 1985: 156- 157), though in the vicinity of bifurcation the law of large numbers is violated. The connection between the internal and external for dissipative structures as well as for open nonstationary integrities remains very close, and the boundary between them is conditional. All the elements of the medium in this area become "internal" for dissipative structure performing certain functions within its constituents. The elements however are not secured with these constituents. They can perform different functions moving from one constituent to another (e.g. ascending and descending convection fluxes which form the walls of Benard cells and their central part). Besides, under external parameter changes (temperature, system dimensions, etc. ) the same elements form different structures.

An entirely different degree of segregation between the internal and the external is found in systems whose degree of stability is such that we can understand them only by reference to the category of totality. Hegel defines totality in this way: "a separate circle as a totality in itself breaks through its elements' limit and grounds a wider sphere..." (Hegel 1974: 48). By totalities I mean those self-organized systems which have such a level of self-reproducing stability that they may serve as elements for the systems with higher levels of self-organization. They are the structural units of the matter: nuclei, atoms, molecules, and living organisms(l).

The categorical differentiation of integrity, whole, and totality helps us avoid the confusion of different types of self-organized systems. It also helps us to comprehend that the degree of integrity of living organisms, though they do form dissipative structure hierarchies, is much higher than in usually investigated dissipative structures including those which perform certain functions in the organism as a whole. The stable integrity of living organisms is comparable only with the quantum integrity of the structural units of matter.(1)

Analyzing the stability of nucleus, atom, and molecule as a dynamic stability -i.e. a constant reproducibility of form- allows these traditional subjects of the physics of being to be regarded from the inside, as totalities in the Hegelian sense (Hegel 1974: 48). From the point of view of physics this means taking into consideration the openness of these systems with respect to the physical vacuum of those fields whose quanta are the system's elements. This openness is associated with a constant virtual energy exchange with the vacuum which is manifested in experimentally observed effects such as Lamb's shift. Such exchange cannot be identified as a dissipation in a literal sense (electrons lose no energy), but metaphorically it is possible to refer to "virtual dissipation". The study of nuclei, atoms, and molecules as dynamically stable self-organized structures, virtually opened with respect to physical vacuum, makes it possible to situate the content of the nonclassical physics of being in the context of the evolutionary ideas of the nonlinear worldview.

During the becoming of a totality a transition from the internal into the external and back occurred, i.e. self-organization took place. However, these processes could occur only under conditions different from the conditions of stability of the objects under study: at different energies, at different stages of development. Here the self-reproduction of the whole also takes place, but it is determined, as if by law, by the stable object structure which has become a form. The stability of the totality itself, its ability to survive in the course of evolution, showed the conformity of the form to the inner content of stable objects as well as to the conditions of their formation.

Having undergone a "natural selection", the totality demonstrated the necessity of its own existence, i.e. its reality. Thus, we recognize the "absolute anxiety of becoming" (Hegel), which is a necessary initial point of development, though it is only one of the points. We also recognize the irreversibility of development which, with the account of dialectics of randomness and necessity in the process of becoming, assumes the stable reality of the object which became a dynamically stable entity and may serve as an elemental ground for further complexity. If I. Prigogine is proceeding from "being to becoming," making a notable step from being to understanding its genetic grounds, we should not forget about the way from becoming to being, about the importance of the theoretical reproduction of evolutionary irreversibility and about the understanding of the grounds for the origin and existence of dynamically stable objects as necessary stages on this path.

Application of the category of totality to the most stable self-organized systems suggests the need to consider one more aspect of this category of Hegel's dialectics. The totality of a separate circle, which "breaks through the limit of its elements and grounds the wider sphere" (Hegel 1974: 48) is more than the property of a given circle. The totality of every circle is possible as a moment of the whole. Not in vain the category of totality was used by Hegel in phenomenological description to characterize the world of phenomena. (Hegel 1974: 135). Indeed, the integrity of nuclei, atoms, molecules, and living organisms cannot be described as a totality without bearing in mind that they fit into the totality of the world, since the common destiny of its development determined both their elemental composition and the kind of interaction which takes place within them, as well as the permanent connection with the physical vacuum which gave rise to these elements. The category of totality thus necessarily raises the question of the universe.

But what if, as some trends in modem cosmology suggest, the "universe" which we perceive is just one of many "swelling universes" (Linde 1984) that emerge as fluctuations of the primary vacuum which is natural under the conditions of primordial chaos. How would this affect our thinking about totalities?

From the point of view of unitary gauge theories the formation of a set of elementary particles and their interactions are treated as a result of spontaneous initial symmetry breaking under phase transitions carried out within the period of decreasing temperature in the expanding space of the universe. (Weinberg S.: 1981). Synergetics allows us to understand the emergence of the universe as a process of self-organization (Prigogine and Nicolis 1990: 317-326). This leaves open the possibility of other random choices under symmetry breaking and of the existence of the other worlds, respectively.

The problem of the plurality of the worlds is not new in the history of philosophy, but the questions put forward in modem cosmology (How does the matter emerge from nothing? What was prior to the beginning of time?, etc.) with their paradoxical form touch the limits of comprehension of specific scientific statements. Since the limits of meaning in human thought are given by its categorical structure, the correct formulation and solution of such limit problem⁸ of knowledge requires that we clearly identify the content of both scientific and philosophical categories and that we specify just how they relate to each other. In this case we are dealing with the category of "matter" in its relation with the category of the "world" and the cosmological notion of the observed universe. Clarification of the relationship between these ideas should give us the philosophical foundations we need for the construction of a scientific picture of the world on the basis of new cosmological theories.

One attempt to comprehend the content of these categories has been made by Ukrainian philosophers S.B. Krymsky and V.I, Kuznetsov (Krymsky and Kuznetsov 1984). They suggest that complete realization of the potential latent in matter should be identified not with the "world," but with the Universum. The notion "world" which is related to the cosmological universe observed is just peculiar state of the matter with hindered peculiarities.

Defining the content of the notion of the "world", the authors of the above paper identify a number of characteristics associated with this notion in the philosophic tradition. Among these they include the integrity of the world as unity in diversity, and monadicity of the world whose borderline of peculiarity goes through every object which is the bearer of this specific form of material existence determined by the system of laws that function within this world order. All these and the other attributive characteristics of the category of the "world" are appropriately specified in the modem physical picture of the world. Thus, the harmony of the world order is realized via the principles of symmetry which determine the possible types of laws of physics. The type of local symmetry breaking determines the meaning of physical constants and the peculiar elementary composition of all the objects in the given world, etc.

This approach to understanding the basis for the existence of the various elementary particles changes the status of the laws which determine the origin of these particles by associating them with the specific destiny of the specific world, making them no longer universal but rather specific to a particular world. The problem of universality however remains unsolved. The description of our world as one of many possible variants in a complex evolutionary process makes it possible to discuss other variants. There may be an anti-world e.g., where quarks cannot be transformed into leptons, and antibarions would prevail over barions, unlike in our world, where at the moment of the initial symmetry breaking between the strong and electroweak interactions the number of particles exceeded the number of antiparticlcs.

This is the way to solve the problem of the existence of anti-worlds with respect to modem physical picture of the world. This problem was posed within the framework of the quantum-field theories ideas of an earlier worldview: the particles could be born in vacuum only in combination with their antiparticles, so the existence of an anti-world was presumed to be parallel to the existence of our world. The concept of the world as a self-organized whole interprets the origin of the world rather than anti-world as a random irreversible choice in the process of world formation and explains the absence of a real anti-world parallel to the world while retaining the idea of the possibility of its existence in the Universum.

Thus, a state of matter different from the one characteristic of our world can become the subject of a physical theory, irrespective of whether matter actually exists in such a state in the actually existing world. The mode of its existence presupposes a relative stability as well as the possibility to grow more complex up to the level of life and intellect, or else the physical constants related to the other possible symmetries and their breaking will make the existence of this form of matter unstable and its constitution into a world impossible.

It would appear most reasonable to refer the universality of laws to their realization in the Universum. It should be emphasized however, that only our world is actually existent for us, and the other worlds are only theoretically possible (Krymsky and Kuznetsov 1984: 95-96). The metaphor "island universes" used by cosmologists unintentionally provokes the image of a certain enveloping space, which is fundamentally wrong, because space-time exists as the space-time of a given world only from the moment at which the gravitational interaction became separated from the other fundamental forces (supergravitation theory) (Freedman and New Van Hejsen 1979). Matter, therefore, can be understood properly only in the context of a particular world, defined by a particular pattern of symmetry breaking.

Within the framework of the nonlinear worldview, the problem of the universality of the most general physical principles can be formulated only with reference to the whole complex of possible worlds. We bear in mind the assumption that fundamentally different possibilities for the origin of worlds whose mode of existence might be based on symmetry principles other than those which dominate our own world can be offered at the expense of chaotic virtual oscillations of initial vacuum in cosmological scenario of "swelling universes". True vacuum, as a lower energy state of certain types of fields, carries with it definite symmetry principles, the value of physical constants, and possible variants in their breaking at world formation. Here the range of possibilities is already determined, and while a particular world is yet unchosen, we deal with the special instead of the general.

Now it is evident that in the modem scientific worldview, the problem of the world's being cannot but be regarded as the problem of its becoming and transiency. Retention of this being for a certain period of its transient existence can be understood heuristically proceeding from the experience of nonlinear natural science only as a dynamic stability determined by the coherence of it constituents.

REFERENCES

Dobronravova I.S. (1990) "Synergetics: Becoming of Nonlinear Thinking". Kiev: Lybid Press. (in Russian)

Freedman D., New Van Hejsen P. (1979) "Supergravitation and Unification of Physical Laws", UFN, vol. 128: 22-34.

Haken G. (1980) "Synergetics ", Russian translation - Moskow: Mir.

Hegel G.W.F. (1975) "Enzykolp—die der Philosophischen Wissenschaften", vol. 1. Berlin:

Academie-Verlag.

Hegel G.W.F. (1975) "Phenomenologie des Geistes". Berlin: Academie-Verlag. Hegel G.W.F. (1974) "Wissenschaft der Logik". Berlin: Academie-Verlag.

Krymsky S.B., Kuznetsov V.I. (1984) "Weltanschanung Categories in Modem Natural Sciences". Kiev: Naukova Dumka. (in Russian)

Linde A.A. (1984) "The Swelling Universe", UFN, 144: 177-214. (in Russian)

Mamardashwily M. (1990) "The Idea of Succession and Philosophical Tradition", in Mamardashwily M. "How I Understand Philosophy". Moscow: Progress Press, (in Russian)

Prigogine I. (1985) "From Being to Becoming". Russian translation - Moscow:Nauka Press. Sit'ko S.P., Andreev E.A., Dobronravova I.S. (1988) "The Whole as a Result of Self-Organization", Journal of Biological Physics, 16: 71. Veinberg S. (1981) "The First Three Minutes", Russian translation - Moscow: Alomizdat.

1. One of the reasons for creation of the quantum physics of the living was the discovery of characteristic eigen-frequencies in the mm-range electromagnetic radiation and the interpretation of this event as a correlation of living systems with the criterion of the stable integrity of quantum systems, i.e. the living was regarded as the next step following the molecular step on the quantum ladder. The existence of the alive as a dissipative structure hierarchy is considered to be a condition of such integrity. (Sitko S.P., Andreev E.A., Dobronravova I.S. 1988: 71).