Michael Tokarev, Corporation AXIS Ltd, St.Petersburg, Russia

PhD

Email: Michael_tok@mail.ru

On the definition of

General Systems Theory

Abstract: Definition, classification of systems and system paradoxes. How we can solve systemic paradoxes.

Keywords: Systems, System Engineering, General System Theory, System Paradoxes

Introduction

Known classic of General Systems Theory V.N. Sadowski [3, 51-56] analyzes dozens of existing Systems' definitions. Other authors add new definitions, but a single, universally accepted Systems definition still does not exist. Why this happens, what matters in definitions do not have the answers yet, how "General Systems Theory" metascience and particularistic science relate, the paradoxes of general systems theory will be discussed in this article. These issues arise of the analysis of existing definitions and their research by V.N. Sadowski in the book "Foundations of General Systems Theory." [3] From our point of view as long as it is the best and most comprehensive study to date of the existing state of things in terms of the General System Theory (GST). The purpose of this paper is to formulate the most pressing issues in the context of system definitions and offer their solutions.

Existing definitions and issues arising from them. Entropy

The most common definition of systems is formulated as "a combination of elements," or even as "any object is a system." Many authors have presented the formal definitions of an aggregation of two multitudes: elements and relationships [1, 10-21], [4, 45-52].

Our task is not to refute or criticize existing definitions. We're just going to try to formulate questions to the definitions and try to find answers to those for which it is possible within this article.

In the analysis of any definition there is the first important question, the answer to which is connected to all systems definitions and classifications. This question will be worded as follows: "Does a system really exist?" Not many researchers ask this question, but those who are wondering, as a rule, respond to it positively. It seems to us that the question can’t be answered at all. Why? Let's think constructively.

Were there Systems before the mankind? If we answer in the affirmative (systems have always existed), what is the point in trying to determine them? They already exist, someone created them, and therefore defined? Somewhere we can find a description of these systems, because the system does not exist without its description.

With artificial systems everything is clear in such context. At their creation of people creates also their description. And what about those systems, which include both elements: those existed prior humans and artificial elements? Obviously, prior to mankind, to be exact, even to the end of XIX century, no one knew what the system in the modern sense were, did not describe them. So, we can only speak of the objects or entities existence, but not the system.

It seems to us that the answer to this fundamental question must be sought in the following. A man created the concept of a system. He "adjusts" the existing reality to his concept. In fact we find the objects, try to assign them the system properties (which we have invented ourselves) and state that systems exist. It's fine if scientists understand that examine just a model, not the system. The researchers come to paradoxical conclusions: for example, the type (genus, family) of animals - is also a system. Obviously, from the point of view of nature of it is not so, because the concept of genus, species, family also came up with people. Certainly, nature was not busy with splitting all living beings into the genera and species. In fact, these systems are completely virtual. Otherwise we'll have to admit a creator, who invented not only flora and fauna, but also classified them.

Thus, if we wave away the non-scientific idea of a universal creator, we are forced to admit that the system did not exist before humans and does not exist now. Here we see the fundamental paradox of the system science: everybody talks about a non-existing, and not only talks, but also uses in their practice and research. Of course, aside from all of this there are artificial systems that people originally created as such. But in this case, and the conceptual apparatus is immediately objective. In particular, if we build a car as a system of interacting elements that has to deliver goods from point A to point B, we define the system on the basis of interacting elements, goals and functions.

Thus, solving this major issue, we split at least (and fundamentally) natural and artificial systems, knowing that the latter are systems a priori. The mixed systems (which the person creates itself, using as some elements natural objects, for example a mountain slope at movement of the slalomist) also can be carried to systems as we can thoroughly describe them.

Now we consider natural systems (which exist only in our minds).

Usually, natural systems are classified as animate (living) and inanimate (non-living) ones. Analyzing these objects from the system point of view, we are compelled to be engaged in modeling, as we do not know enough about them, about the hierarchy of these systems, and possibly even the dimension in which they exist. For example, a stone lying in the mountains. Is it a system? From the point of view of the most general definition ("any object is a system") a stone is undoubtedly the system. From the point of view of the extension of the concept (for example, an observer or function), the stone can’t be considered a system,  until we started to study it and / or until it is comes into operation. Of course, we can think of the functions of internal heat, molecules and atoms inside it, the crystal structure, etc. But is it a system while it is lying, and it is not being studied? In that case, why bother to talk about such an object as a system? Only because of a common definition of the System itself?

No less obvious the application of the notion “system” to objects of fauna. Is a particular bird a system? From a biological point of view (only because it is more convenient to be studied by a  man) - of course. And from the point of view of other fauna? Possible – it is also a system. A bird feeds, feed others, in addition it gets a lot more besides input actions. We may say that here the interpretations of definitions of the hierarchy, morphology and interaction of elements, the micro and macro levels are performed. One point confuses us: the bird itself does not know it and, moreover, does not take any concerted action to be in the system. Just feeds, breeds and dies. From this point of view, it is like the inanimate nature, stone, which also does not "know" that it is the system.

There is only one answer to all these questions: a human called it a system. He himself invented system. And each person (the researcher), has its own system or to tell the model more precisely. In fact, this system is some kind of a model for our understanding of a particular entity. The model itself, in turn, is also a system. And when the researchers begins to study the model, he/she has to disengage himself/herself from the "system" (more precisely, from the subject). No researcher argues with this. Do we do with an object, which exists, not realizing that it a system?

The person giving the definition of the system, tries to simplify the study of all the systems to unify their properties, suggesting that in the future it may be possible by studying one (the one that he understands) system to project (extrapolate) the system properties on the other system he understands less. If this does not work directly, it makes changes to the definitions, complicating them by adding new elements and features. Such "fitting" of definitions for a research specific needs leads to the greater separation of new definitions from classical ones, and, as a consequence, to greater entropy in the system definitions themselves.

Discuss the entropy and the second law of thermodynamics, which, from our point of view, is applied indiscriminately to almost all known systems.

Interpretation of second law of thermodynamics is unambiguous: "Entropy of an isolated system may increase or remain unchanged. Reduction of entropy in an isolated system is impossible" [2, 77]. What do many systems researchers do? They apply the second law of thermodynamics and the concept of entropy itself to any of the studied systems. In this case,  few people pay attention to the paradox that, for example, self-organizing system does not increase the entropy inside themselves, but reduce, not desintegrate, but are being created, and organize themselves. This error has been long known to physicists and many other scientists. The concept of an isolated system in the definition of thermodynamics means no system interchange with the environment, not only by means of substance (closed system), but also by energy.

Another mistake made by researchers who follow the fashion - application of the laws of thermodynamics to any system, including ones of not physical, and certainly not of a thermodynamic nature. For example, how does a perfect system of geometric axioms relates to thermodynamics and how we can apply the principles of entropy change to it?

However, despite these considerations, all systems eventually die (entropy increases). Why? Is there a common cause of death of all the systems? And may the root cause of this common cause be the determination, which is man-made? Meaning that the man gives the definition of the system in which it ends its existence (and this definition may include this course latently, possible only in the context of the investigator).

Most researchers believe that the system is, by definition, hierarchical, that the system itself may enter into other systems as an element (subsystem), and each of the elements of the system is the system on its own level of consideration. However, if at the intuitive level, this can be imagined, at the level of universal definition systems this property may seem controversial. Why?

If we assume that the system as a term was invented by people (not nature and not the creator), then considering a particular system in a large number of cases, the researcher does not appeal to the macro or micro systems, even not assuming that there is a hierarchy. As an example, study the alphabet. With this study, it is possible to ignore the fact that a particular alphabet is a subset of all human alphabets. But at the micro level, in some context, we are absolutely not interested in each letter as a system (for example, lettering or placing them side by side in constructing words, etc.). One can argue that in this case a systematic approach does not apply. But in course of the alphabet model study we can look at it from the point of view of other system properties, in particular the main - integrity (agregation of letters has properties not possessed by each letter separately).

Perhaps we have no questions only to this particular property system - a property of integrity (the interaction of elements of the system leads to system properties / functions that each element separately unable to perform or “the object properties can’t be reduced to the sum of the properties of its constituent elements and non-deducibility of the last properties of the whole”

System paradoxes

The urgency of the questions is confirmed by systemic paradoxes in V.N. Sadowski works [3]. And in particular, the first paradox of hierarchy, which is the following: for a complete description of the element as a "system element" there must be a full description of the system that can’t be described fully until each element is described.

Therefore, the question of the legality of a systematic approach analysis of micro and macro-level systems remains not resolved.

Let's consider a simple example. A man, as a biological system, consists of elements (subsystems): circulatory, digestive system, musculoskeletal, respiratory, etc. If we try to describe the circulatory system, as a separate, outside of the body, we can miss important features of nutrients carried by the blood, oxygen, and various chemical elements necessary for metabolism, etc. For a complete description of the circulatory system, as part of the body, we need to have a complete description of the body (including the blood system). Thus, for the study of any element of a complex system, we have to build a model that is different from the object due to substantial simplification. Considering the provision of oxygen, we can abstract away from the digestive system, which significantly affects feedback and the circulatory system, wich in some cases may be affected so much that the work of the respiratory system will be blocked.

Even more interesting example is when a person studies a community of people, to which he /she belongs, and his/her decisions can affect the outcome of the system. In this case, self-knowledge is not just difficult, it is impossible.

On the other hand, if we consider a vehicle as the system, studing any of its units (subsystem) is simplified by the fact that creating a car we base its structure on system properties. However and in this example there can be functions, usually parasitic which the designer cannot guess before the car will be released in operation.

Here we agree with V.N. Sadowski: "The attempt to interpret paradoxes considered static, applied to the system knowledge, taken out of its development, inevitably leads to the conclusion that the system thinking is impossible." [3,245].

The solution of system paradoxes at research

Proceeding from the analysis of the definitions which has been carried out by V. N. Sadovsky [3, 98-101], we suggest dividing all systems into 2 categories:

1. The artificial systems including any elements, including natural. Here are no difficulties of the solution of paradox of hierarchy are present as the researcher at creation of system has its complete description. As an example we can use a building where prior to construction a person develops a project, schemes. Also, development of a management automated system, which includes infrastructure , regulations and human roles (not a physical person but only his functions within automated system).
2. Natural systems which do not involve people participation. When carrying out researches of such systems it is necessary to use instead of the term System the term Model. In that case the researcher bypasses paradox of Hierarchy by means of a complete description of model of system. The researcher turns object into artificial system like reflection in a mirror. As usual it occurs when modeling, the part of information on System is thus lost and/or it is considered insignificant.

Conclusions

Thus, when using the described way of classification of all objects (Systems in classical understanding), there is a possibility of a solution of the system paradox problem. It is obvious that the majority of researchers does so in practice. However, sticking to the definition of a system, they are compelled to generalize definitions of studied systems, to add to them properties which real systems probably don't have. And, thinking that they work with systems, not with models, can make the mistakes connected with rejection of insignificant system signs.

V. N. Sadovsky in [3,240-244] suggests solving contradictions through fixing of certain properties or system elements, considering systems in dynamics. However, actually these decisions lead to emergence of the same models described above.

Coming back to definition of the concept System it is necessary to remember that the system only then is that when it is possible to describe it. Otherwise, any restrictions or generalizations lead only to emergence of new definitions which aren't general, and define only a context of the specific researcher.

References

1. Mesarovic M.D., Yasuhiko Takahara General System Theory: mathematical foundations. System Research Center. Cleveland. Ohio. 1975
2. Осипов А.И., Уваров А.В. Энтропия и ее роль в науке. // Соросовский образовательный журнал, т.8, №1. 2004
3. Садовский В.Н. Основания общей теории систем. –М: Наука, 1974
4. Lars Skittner General System Theory. Ideas and Applications. World Scientific Publishing Co. 2001