Genesis of equifinality and multifinality of open systems

Gribkov Andrei Armovich ORCID: 0000-0002-9734-105X Doctor of Technical Science Senior Researcher, Scientific and Production Complex "Technological Center" 124498, Russia, Moscow, Zelenograd, Shokin Square, 1, building 7 andarmo@yandex.ru Other publications by this author

Introduction

The practice of studying the evolution of open systems, regardless of the subject area under study and the level of complexity of these systems, demonstrates the widespread properties of equifinality ^{[1, p. 79]} and multifinality ^{[2, p. 60]}.

Equifinality (Latin aequus — equal, proportional, finalis — finite) is a dynamic property of a system that carries out movement (transition) in various ways from different initial states to the same final state. At the same time, the differences in the initial states can be significant.

Multifinality (Latin multum — many, finalis — finite) is a dynamic property of a system with minor changes in initial conditions to achieve fundamentally different final states. At the same time, the number of these final states is limited and usually small. Instead of the term "multifinality", the term "polyphinality" is sometimes used (other-Greek: — a lot), which has the same meaning.

According to another definition, multifinality is the ability (property) of systems identical in origin and structural composition to achieve different end states. According to the author, such a definition is inaccurate, since the term "identical" has both the meaning of "similar, similar" and "identical". In the first case, the proposed alternative definition of multifinality has the same meaning as the main one. In the second case, it does not correspond to reality.

At first glance, the properties of equifinality and multifinality are opposite, but in reality this is not the case. These properties of open systems have a common origin. The purpose of this study is to disclose it.

Examples of equifinality and multifinality

Before proceeding to determine the genesis and significance of the equifinality and multifinality properties of systems, let's consider practical examples of their implementation. Such consideration will allow us to form a preliminary idea of the prevalence of these properties of systems, spheres and conditions of manifestation, as well as their possible causes.

Equifinality is characteristic of systems of various natures – physical, chemical, biological, economic, social, etc.

An example of physical systems demonstrating the equifinality property are spherical (spherical) or material structures close to them in shape: atomic nuclei, liquid droplets (in the absence of gravity), planets, stars, globular star clusters, elliptical galaxies (type E0), globular clusters of galaxies, etc. Another example of equifinal physical systems are formed from solutions or melts of different materials, crystals of a simple shape (47 forms in total), the symmetry in which is determined by seven syngonies (groups of types of symmetry) – cubic, hexagonal, tetragonal, trigonal, rhombic, monocline and triclinic ^{[3, pp. 27-41]}.

The equifinality property of biological systems is widespread. Summarizing his research in the field of self-organization and evolution of biological macromolecules, M. Eigen writes: "Each individual system resulting from mutations and selection is unpredictable with respect to its structure; nevertheless, the inevitable result is always the process of evolution... optimizing the process of evolution is in principle inevitable, although the choice of a particular path is not deterministic ..." ^{[4, p. 207]}. The observed parallelism in the evolution of different species is also of interest. It reveals a certain structural commonality in systems with similar functions formed on different evolutionary trajectories ^[5]. As a result, the general constitution, shape and structure of parts and organs of animals and plants are similar or even similar, i.e. they have isomorphism.  

The property of equifinality is widespread in various economic systems of various levels – starting with organizational design and ending with state economic policy and the development of the world economy. At the enterprise level, equifinality is understood as an opportunity to achieve strategic goals by various means ^[6]. The presence of equifinality significantly expands the reliability of strategic planning of enterprises. Innovative activity of enterprises assumes the preservation of equifinality in the process of mastering new types of products or improving its quality. Equifinality in this case is considered as a condition for the effectiveness of business process management ^[7]. Within the framework of the state economic policy, the requirement of the equifinality of competition policy is formulated ^{[8, p. 29]}, i.e. the policy of preventing anti-competitive agreements and abuse of dominant position, as well as combating unfair competition. The development of the world economy and civilization as a whole also demonstrates the property of equifinality. As practice shows, socio-economic development can have only a few basic variants (combinations) of development ^[9].

The property of multifinality, as well as the property of equifinality, is common at all levels of being, in all subject areas. At the same time, the property of multifinality most often becomes the subject of research in the field of psychology and sociology. This is due to the maximum sensitivity of systems associated with human consciousness (individual and social) to the variability of their defining parameters.

For example, in psychopathology, multifinality manifests itself in the form of the possibility of developing a variety of mental disorders under the influence of any one etiological factor. In family psychology, multifinality is studied in the context of the multiplicity of consequences of family breakdown for a child, depending on gender, age and other characteristics ^{[10, pp. 90-91]}.

The socio-economic development of individual industries, countries and the world as a whole within limited time intervals is characterized by a significant dependence on factors that, from the point of view of epistemology, are random and do not relate to the essential features of the object of knowledge (industry, country or world). For example, wars in the continuation of human history were provoked by the competition of royal families, accidental and non-accidental deaths of leaders and other factors that are not determined and do not determine the historical process. However, a minor event that happened at the right time and in the right place turned out to be decisive, initiating a change in the direction of development. The role of "randomness" in the historical process has not been fully understood until now and is often disputed ^[11]. Nevertheless, the subject of dispute is the degree of influence of chance on the historical process, but not the fact of the presence of such influence.

It is quite difficult to trace the implementation of multifinality in the development of biological systems: biological species do not keep records of their changes. However, biological systems exhibit a special form of multifinality – polymorphism. Polymorphism (from Greek: - diverse) is the ability of some organisms to exist in states with different internal structures or in different external forms during their life cycle. For example, in insects polymorphism can be sexual, caste, ecological and seasonal ^{[12, pp. 144-148]}.

Polymorphism is inherent not only in biological, but also in chemical and physical systems. In chemistry, polymorphism is the ability of one substance to form different structures of crystal cells ^[13]. At the same time, the change in the system parameters for the transition to a different crystal cell structure may be insignificant (for example, a change in temperature or pressure by fractions of percent).

Chemical elements can have several isotopes, and the molecules formed from them can have several allotropic modifications. The existence of isotopes and allotropic modifications of molecules are examples of the implementation of polymorphism and multifinality in physics and in physical chemistry.

In plants and animals, along with polymorphism, multifinality can also be realized in the form of metamorphosis ^{[12, pp. 111-125]}, in which a deep transformation of the structure of the organism (or its individual organs) occurs in the process of individual development. The most famous example of metamorphosis is the transformation of a caterpillar into a butterfly.

Genesis of equifinality and multifinality

The process of system development is a change in its composition, structure, shape and connections, i.e. transformations, the quantitative description of which has a discrete character. In some cases, the description will be carried out by means of binary calculus (dichotomy – there is a property or there is no property), in other cases – by means of natural numbers (an integer number of elements, connections, levels, etc.).

A system defined by quasi—continuous (Latin quasi - allegedly, almost, as if; continuous, or having an extremely small step of discreteness) quantitative parameter values for some given initial state, changing, determines its new composition, structure, shape and connections by means of a discrete description (with a large step or even within binary relations). As a result, there is a transformation of quasi-continuous quantitative values at the input into discrete ones at the output.

In some cases, such a transformation can neutralize significant quantitative variations of input values, as if "rounding" them to the same discrete value at the output. This is a case of equifinality. In other cases, a slight change in the input values is sufficient for "rounding" to occur to another, larger or smaller discrete value at the output. This is a case of multifinality. We write "rounding" in quotation marks because in reality there is no rounding of numerical values, but the transition of the system from one form (structure, composition, etc.) to another, despite the fact that the forms are determined by discrete quantitative parameters.

Within the framework of epistemology, the transformation discussed above is reliably described as the transition of quantitative (gradual, quasi–continuous) changes into qualitative (discrete - binary or natural (integer) changes associated with changes in structures, forms and connections). 

In reality, these qualitative changes, even being discrete in nature, nevertheless, should be able to generate a huge variety of forms. Even for not the most complex systems, the number of potentially possible forms is extremely large. However, in practice, such an increase in the number of options does not occur due to the limited variety of forms implemented in nature.

The observed limitation of the diversity of forms is a phenomenon of isomorphism – the repeatability of forms and relationships in systems at different levels of the organization of matter, in various subject areas. The phenomenon of isomorphism is a "catalyst" for the properties of equifinality and multifinality, giving them a ubiquitous character. Otherwise, these properties would still manifest themselves in individual cases, but would not have such a significant impact on the processes of development of systems at all levels – from physical to social and spiritual. Isomorphism, which determines a radical decrease in the diversity of forms realized in nature, "increases the distance" between the possible results of development. This creates conditions for the manifestation of the property of both equifinality and multifinality.

So, it can be stated that the properties of equifinality and multifinality are a consequence of the transformation of quasi-continuous quantitative changes into discrete qualitative forms, as well as the limited diversity of these forms due to isomorphism.

Considering equifinality and multifinality, we attributed them by default to the properties of open systems. An open system is a system that is in constant interaction with its suprasystem. The author's research has shown that all real systems are open (except the Universe), dissipative and exist due to the excessive reaction of their suprasystems to their activity ^[14]. At the same time, the development of the system (structure formation) is a process of local decrease of entropy against the background of its general (at the level of the suprasystem) increase ^[15].

Within the framework of epistemology or science, it is possible to represent a system as closed (isolated), the stability of which is already provided within the framework of a suprasystem. At the same time, sustainability processes and mechanisms are excluded from consideration. Such a representation may be adequate for static systems that ensure their stability (i.e., the constancy of parameters) in changing external conditions, but for developing (in general, changing) systems, it produces contradictions in the description and therefore is not applicable.

Multifinality and multiplicativity

Along with the real property of the multifinality of open systems, there are cases of imaginary multifinality in the practice of cognition, which is based on uncertainty in determining "minor changes in initial conditions". For many systems, the state of which is determined as a result of the complex action of many factors (a set of parameters), the state of stability is realized not as a balance of counter-directional actions on the system, but on the basis of maintaining a non-equilibrium state. Such stability is characteristic of "living" (biological, social, economic) and other evolving systems, including chemical and physical ones. The existence of such systems is regulated by the principle of stable disequilibrium ^{[16, p. 32]} and the concept of dynamic kinetic stability ^[17,18]. To preserve such systems, disequilibrium ("life") must be preserved in them, and achieving equilibrium means the cessation of the existence of the system (i.e., its "death").

Extremely simplifying the processes actually occurring in such systems, the disequilibrium in them can be identified with a certain difference in the values of the system parameters. In the logic of such an understanding of disequilibrium, "minor changes in the initial conditions" can lead to almost unlimited variability (relative values) of the output parameters of the changing system. The slightest changes in the input parameters can lead to changes in the output thousands and millions of times, or even to a change in their direction (if this parameter is vector).

The sensitivity of the output parameters of the system to variations in input parameters can be enhanced even more due to the implementation of positive feedback mechanisms in it, in which a change in the output signal of the system leads to such a change in the input signal that contributes to a further deviation of the output signal from the initial value.

The property of increased sensitivity to variations in input parameters, which is demonstrated by systems with unequal stability, including those with positive feedback mechanisms, we will call multiplicativity (Latin multiplicare — multiply, multiply, increase). Naturally, this property manifests itself, for example, in biological systems (for example, hypersensitivity of allergy sufferers). In engineering, this property is used in the construction of ultra-sensitive measuring devices.

Externally, multiplicativity is similar to multifinality. However, its genesis has nothing to do with multifinality. One of the obvious discrepancies of the properties under consideration is the absence of a certain set of possible outcomes in the case of multiplicativity. As a result of the implementation of this property, quasi-continuous quantitative values at the input are translated into quasi-continuous quantitative values at the output.

In some subject areas, it is not possible to draw a line between multiplicativity and multifinality. One of such problematic areas is meteorology. As is known, systems of equations relating atmospheric parameters, dynamic parameters of air mass movement, and other factors affecting the weather, in many cases do not have stable solutions. A slight change in the input data is enough to radically change the results of forecasting. There is no doubt that in this case there are both nonequilibrium processes and self-excitation corresponding to multiplicativity (associated with positive feedback, for example, the greenhouse effect), and discretization of outcomes corresponding to multifinality (precipitation will fall or will not fall, there will be rain, snow or hail, etc.).

Conclusions

The research results presented in the article can be summarized in the form of the following main conclusions:

1. The properties of equifinality and multifinality are widespread in all subject areas, at all levels of the organization: in physical, chemical, biological, economic, social, etc. open systems

2. The properties of equifinality and multifinality are a consequence of the transformation of quasi-continuous quantitative changes into discrete qualitative forms, as well as the limited diversity of these forms due to isomorphism.

3. Along with the real property of the multifinality of open systems in the practice of cognition, there are cases of multiplicativity - a property that looks like multifinality, but has a completely different genesis. The multiplicativity property is manifested in systems with unequal stability, including those with positive feedback mechanisms.

4. In some systems, for example, meteorological mathematical models, the properties of multiplicativity and multifinality are manifested simultaneously and cannot be unambiguously distinguished.

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