Elements of the Mathematical Theory of Human Systems Part 2

Structural Mathematical Models of the Life of Humans Based on the Method of State Equations


By Pavel Barseghyan, PhD

Yerevan, Armenia and

Plano, Texas, USA



Quantitative representation of the structure of the life and activity of humans is one of the central problems of the mathematical theory of Human systems.

The fact that human activity consists of separate actions allows us to build a mathematical theory of Human systems on the basis of quantitative models of people’s actions.

The first step in constructing such a theory is a structural representation of human activity in the form of mixed networks of the sequences of actions that make up the content of the people’s life process.

This approach allows us by using the equation of state of human actions to develop a quantitative description of Human systems of arbitrary complexity in the form of a system of state equations.

The second part of the paper is devoted to the structural representation of human life and activity as a set of flows of people’s biological and social actions.

At the heart of the mathematical model of human life and activity lies the fundamental statement that the biological and social aspects of human life are conditioned by each other and constitute a single whole.

Introduction: Problems of practical applications of the mathematical theory of human systems

Quantitative description of the behavior and activities of people and human systems from single conceptual positions is crucial for organizational science, which, in turn, can have a variety of economic, political, geopolitical and other applications.

The point is that the present state of organizational science, with its fragmented and segmental methods, needs the development of such scientific theories and mathematical models that, by virtue of their generality, can consider the quantitative description of the lives of people in different political, economic, social, business, religious , moral and other conditions, as particular applications of the same scientific approach [1].

To develop such a scientific approach, first of all, it is necessary to search for and find in the various organizational forms of people’s lives such common features or such a commonality on the basis of which it would be possible to build some universal theory of human systems.

From the point of view of quantitative description, the obvious commonality of the various organizational forms of people’s association under study is that they are all systems for which the main provisions of the general theory of systems are applicable.

In addition, these organizational forms of uniting people have another specific commonality, namely, that they are all human systems with characteristic internal laws of a biological and social nature, at the center of which are the psychology and behavior of people with their various manifestations.

In short, all organizational forms of uniting people, as well as different societies, be they totalitarian, authoritarian or based on democratic principles, basically are based on the same human psychology, which simply has different manifestations under different conditions.

Continuing the search for commonalities in the behavior and activities of people, we can see that they all consist of individual actions of people, each of which have a magnitude and size, the complexity of implementation, and for their implementation are required effort, time, knowledge and skills of people [ 2].

This means that in order to develop a universal mathematical theory of human behavior and activity, it is first necessary to develop a quantitative theory of individual actions of people of a universal nature as a first step in this direction.

The second step towards developing a mathematical theory of human activity is the development of quantitative methods of transition from describing people’s actions to describing their activities.

To develop a mathematical theory of people’s activities on the basis of a quantitative description of their actions, the structural representation of people’s activities in the form of various combinations of flows and successive chains of their actions is of great importance.


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Editor’s note: Part one of this paper was published in the December 2017 edition of the PM World Journal.  Read that and other papers by Dr. Barseghyan by visiting his author showcase in the PM World Library at https://pmworldlibrary.net/authors/dr-pavel-barseghyan/

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/

Dr. Barseghyan can be contacted at [email protected]