Elements of the Mathematical Theory of Human Systems

Part 1: Assessment of the Results of Human Actions and Activities Based on the Method of State Equations


By Pavel Barseghyan, PhD

Yerevan, Armenia and

Plano, Texas, USA



Quantitative description of people’s behavior should become the core of organizational science and a reliable basis for making various kinds of decisions for the problems that arise during the life of human society.

Whatever the area of human activity these decisions are made the center of the whole process is a certain Human system. It can be an individual, a group of people, a team of developers, an organization, a country, the whole world, etc.

The state of the Human systems can be stable or unstable, equilibrium or non-equilibrium. In the equilibrium state, there is some balance between the system parameters (or variables), the reflection of which are the state equations of Human systems.

The combination of the equations of state with people’s goals and the extreme principles of their behavior makes it possible to derive functional relationships between the parameters of the Human systems under study by analytical means that are common in physics and other quantitative sciences.

The universal nature of the method of state equations of Human systems allows us to use  simple algebraic equations of state to adequately represent the behavior of vast variety of human activities, including the relations between the people, conflicts between them, international relations, and much more.

The heart of the mathematical theory of Human systems is the assessment of the results of human actions, because each action produces some result in the form of benefit or damage.

The first part of this paper is devoted to the assessment of the results of human actions and activities using the method of state equations of Human systems.

Introduction: The problems of constructing a quantitative theory of human systems

Traditional methods of managing people’s activities, based on their experience and intuition, often fail because of the complexity and scale of the problems being solved and the limited time frame for their implementation.

The main reason for these difficulties is the limited ability of people who are responsible for making complex decisions on managing large-scale projects, entire sectors of the economy, state affairs, conflict situations between countries, and so on.

Even a simple observation of the course of human history clearly demonstrates that when difficulties arise in realizing their goals, people come up with appropriate tools that facilitate their work and increase their efficiency.

At present, exactly such a situation has arisen in a number of areas of human activity, where miscalculations in making decisions have catastrophic consequences [1, 2].

Solving this problem requires the creation of tools of a new type, helping humans in making complex decisions and which will naturally be associated with computer technologies.

But the use of computer technologies in any field implies a clear and accurate description of the relevant processes and phenomena, which in our case is related to the description of human actions and activities and mathematical modeling of human behavior.

From here the fundamental need to create mathematical models of people’s actions and activities [3].

Since any human activity is a sequence of people’s actions, the first task of modeling their behavior and decision-making process is the creation of mathematical models of people’s actions.

Each action is the fulfillment of the next requirement of life by a person who, in order to achieve this goal, spends effort, time, knowledge and skills.

Besides, each action has its own mathematical equation, which reflects the balance or equilibrium between the requirements of life and the ability of man [3].

State equation of an arbitrary human action (or activity) is a consequence of the balance between the need to commit actions (or activity) by a person and his/her ability to bring them to completion

To ensure the normal life process of any human system, a balance or equilibrium is needed between the big and small problems that arise and accompany a person during the life process on the one hand and the ability of people to solve these problems on the other hand.


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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]