Elements of the Mathematical Theory of Human Systems Part 4

Quantitative interpretation of the victory, defeat and concessions of human systems by the method of state equations



By Pavel Barseghyan, PhD

Yerevan, Armenia and

Plano, Texas, USA



The mathematical theory of human systems has many applications in the fields of analysis, synthesis and optimization of confrontations and conflicts between the groups of people of different scales.

The clash between human systems arises from a conflict of interest, be it the usual conflict of interests in people’s daily lives or a serious clash of interests in international relations, or a clash of civilizations.

The purpose of the article is to show that the problems of quantitative description and analysis of conflicts between human systems can be reduced to the method of state equations.

According to this method, the activities of each party to the conflict can be represented by the equation of state, on the basis of which the benefits and losses obtained from the activities of the parties are evaluated.

In the case of significant differences between the benefits and losses of the conflicting parties, the balance of power between them can be violated, which can lead to non-equilibrium phenomena such as the victory of one of the parties.

In the work on the basis of quantitative assessments of the benefits and losses of the conflicting parties, quantitative interpretations of the victories and defeats of people are also given.

The methods discussed in the article may have many practical applications, including the analysis of different types of competition between human systems, as well as assessments and predictions of the results of the conflict between countries and their various blocs and alliances.

Key words: Human systems, mathematical theory, state equations, systems theory, equilibrium, non-equilibrium, benefits, change management, losses, victory, defeat, concessions, conflicts.


For mathematical modeling and simulation of confrontations and conflicts between human systems, it is necessary to have an adequate quantitative description of their activities and relations among themselves.

The mathematical theory of human systems, the axis of which is a quantitative description of the actions and activities of people by means of the equations of state, is also suitable for studying and managing confrontations and conflicts between different groups of people.

In different cases, the conflicting parties may be negotiators in business and diplomacy or participants in a scientific debate whose opinions differ on the issues under discussion, or the equation of state may partially describe the relationship between the client and the seller, or between the customer and vendor, etc.

In addition, in the context of the further effective penetration of quantitative methods into the sphere of human systems management, the symbiosis of the possibilities of behavioral models of people’s life based on the equations of state [1] and the basic propositions of systems theory is very important [2, 3].

Such symbiosis allows, along with traditional qualitative methods of studying human systems, to create new scientific methods for analyzing, synthesizing and optimizing the behavior and activities of people on the basis of quantitative approaches of a fundamental nature.

The essence of quantitative methods of analyzing the behavior and activities of people, based on the equations of the state of human systems, is as follows.

Each human system can be quantitatively described by an equation of state that incorporates the needed resources for people’s activities, their knowledge, skills and tools used by them and the results of their activities.

In this sense, the purpose of quantitative analysis of the behavior and activity of human systems is to evaluate and predict the results of their activities in the form of gain and losses based on the equation of state and the characteristic data of the system (the number and motivation of people, the effectiveness of their activities and tools used, etc.).

In the case of confrontation and conflicts of human systems, the problem of analyzing their behavior and activities is to assess the results of their clash in the form of victory (or gain) and defeat (or loss), having the data of the conflicting parties.

The problem of the synthesis of human systems is that by having the desired results of its behavior and activity, by inverse calculation on the basis of the equations of state, find those values of the system parameters that can provide the given desired result.

In the case of confrontation and conflicts between human systems, the problem of synthesis in planning the behavior and activity of one of the parties is to use the method of state equations to find those values of the system parameters with which it will be possible to defeat the potential enemy or, at least, not to be defeated by him.

Since any synthesis problem has a lot of solutions, the goal of optimal synthesis or optimization of systems is to choose from this set of solutions those that are more preferable in terms of price, quality, risk and feasibility.

The method of the equations of state has a deterministic character and describes the problem of analysis, synthesis and optimization at the level of average values of the parameters of human systems.

But, as is known, mathematical modeling of systems at the level of mean values of parameters can be considered as a first approximation, which does not always lead to comprehensively grounded solutions to problems [4].

From this point of view, for a more detailed consideration of the problem, the parameters in the equations of state of human systems can be divided into three groups:


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About the Author

Pavel Barseghyan
, PhD

Yerevan, Armenia
Plano, Texas, USA


Dr. Pavel Barseghyan
is a consultant in the field of quantitative project management, project data mining and organizational science. Has over 45 years’ experience in academia, the electronics industry, the EDA industry and Project Management Research and tools development. During the period of 1999-2010 he was the Vice President of Research for Numetrics Management Systems. Prior to joining Numetrics, Dr. Barseghyan worked as an R&D manager at Infinite Technology Corp. in Texas. He was also a founder and the president of an EDA start-up company, DAN Technologies, Ltd. that focused on high-level chip design planning and RTL structural floor planning technologies. Before joining ITC, Dr. Barseghyan was head of the Electronic Design and CAD department at the State Engineering University of Armenia, focusing on development of the Theory of Massively Interconnected Systems and its applications to electronic design. During the period of 1975-1990, he was also a member of the University Educational Policy Commission for Electronic Design and CAD Direction in the Higher Education Ministry of the former USSR. Earlier in his career he was a senior researcher in Yerevan Research and Development Institute of Mathematical Machines (Armenia). He is an author of nine monographs and textbooks and more than 100 scientific articles in the area of quantitative project management, mathematical theory of human work, electronic design and EDA methodologies, and tools development. More than 10 Ph.D. degrees have been awarded under his supervision. Dr. Barseghyan holds an MS in Electrical Engineering (1967) and Ph.D. (1972) and Doctor of Technical Sciences (1990) in Computer Engineering from Yerevan Polytechnic Institute (Armenia). Pavel’s publications can be found here: http://www.scribd.com/pbarseghyan and here: http://pavelbarseghyan.wordpress.com/. Pavel can be contacted at [email protected]

To view works by Dr. Barseghyan previously published in the PM World Journal, visit his author showcase in the PM World Library at https://pmworldlibrary.net/authors/dr-pavel-barseghyan/