Mathematical Modeling of New Quality Emergence

Quantitative Models of Emergence in Light of Mathematical Theory of Human Systems

Part 1: Mathematical Modeling of New Quality Emergence from Interactions of Qualitatively Different Phenomena by the Method of State Equations



By Pavel Barseghyan, PhD

Texas and Armenia




Public life is a stream of different quantitative and qualitative emergencies that are the result of people’s actions and activities.

In turn, arbitrary actions and activities of humans can be adequately represented by mathematical models in the form of equations of state.

The equation of state of an arbitrary action or activity combines the various resources needed for people’s lives and activities, people’s knowledge and skills, and the results of their activities.

The results of people’s actions and activities contain a variety of quantitative and qualitativ emergences that have different nature and scale.

In the first part of the article, is considered the mathematical model of the emergance of qualitatively new phenomena as a result of the interaction and integration of various qualitative phenomena.

The following parts of the article will discuss the mathematical models of nonlinear and probabilistic nature of the emergence phenomenon.


In recent decades, the quantitative science of human life and activity has been making unprecedented progress for the simple reason that highly developed societies and mankind in general are increasingly in need of it.

The reason for this is the steep rise of the complexity of human civilization, where the management of public life encounters unprecedented difficulties and challenges of a critical nature, which solutions are no longer effective through traditional means of experience and intuition and often lead to catastrophic and large-scale errors.

The solution to the issue is modern expert systems based on an adequate quantitative description of public processes, which can help critical decision makers in avoiding catastrophic errors with severe consequences.

The core of such expert systems should be the quantitative theory of the activity of humans and human systems.

This theory and the mathematical models underlying it are substantially promoted by the fact that neighboring fields such as theoretical physics, mathematical control theory, mathematical economics, mathematical biology, systems theory, organizational science, etc. have accumulated huge experience in the development of quantitative methods, which can serve as a methodological basis for the creation of serious quantitative science on human behavior and activity.

One of the central problems of quantitative science of human life and activity is the emergence problem, which has been the focus of the leading scientific forces for last decades [1, 2, 3, 4].

The experience of the quantitative sciences mentioned above has shown that the most efficient solutions of the problems related to complex processes and phenomena usually rely on the mathematical description of the fundamental nature of those processes and phenomena.

This means that such a complex phenomenon as emergence, as well as many other human activity related phenomena, can be qualitatively explained and quantitatively described only within the framework of the mathematical theory of human activity of the fundamental nature.

Classification of the emergence phenomenon in terms of mathematical modeling

For mathematical modeling of a fundamental nature, it is also necessary to classify the phenomenon of the emergence of new qualities from different angles.

In this sense, emergence, as a phenomenon, can be linear and non-linear. In addition, the emergence phenomenon can be considered within the framework of the deterministic approach, that is, at the level of average values of the parameters and within the framework of the probabilistic approach, that is, at the level of distribution functions of random variables characterizing the emergence phenomenon.

Further, according to another classification, the emergence can be weak and strong, a circumstance that is presented in more detail in the scientific literature [2, 4].

If we look at the emergence classification from the perspective that they are the result of human activity, then similar to human activity emergence also can be homogeneous or heterogeneous [6].

Emergence, like any other phenomenon related to people’s lives and activities, can be independent of the time factor, that is to say, time invariant and time dependent.


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How to cite this paper: Barseghyan, P. (2020). Quantitative Models of Emergence in Light of Mathematical Theory of Human Systems – Part 1: Mathematical Modeling of New Quality Emergence from Interactions of Qualitatively Different Phenomena by the Method of State Equations; PM World Journal, Vol. IX, Issue III, March. Available online at https://pmworldlibrary.net/wp-content/uploads/2020/03/pmwj91-Mar2020-Barsegyan-Quantitative-Models-of-Emergence-part1.pdf



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 terbpl@gmail.com