Elements of the Mathematical Theory of Human Systems

Part 6: Human Life as a Project (The differential equation of human life)



Pavel Barseghyan, PhD

Texas and Armenia



One of the main trends in modern methods of social management are the attempts to consider social life as a process of implementing large and small projects.

From this point of view, human life and the whole civilization can also be viewed as projects of various scales that have a beginning, a course of life and its end.

If we consider the life of different scale of human systems from the point of view of the dynamics of their abilities and skills, we can easily notice that these abilities grow from the birth of a person or from the appearance of larger human systems, at some age or after some time they reach a maximum. and then follows their decline, aging, and the end of life or activity.

This paper is devoted to mathematical modeling of the entire human life cycle using static and dynamic approaches for this purpose.

Key words: mathematical model of human life, differential equation of human life, logistic function, dynamics of human abilities, institutional model of human systems, quantitative modeling of the human aging process.

Introduction: Human life as a project

The rapid development of methods and approaches to planning and implementing projects gradually creates a convenient environment for further generalizations of model representations of projects that can be used to promote quantitative methods in other areas of human activity [1].

In particular, we are talking about the fact that over time the number of attempts to consider the life of society as a process of implementing various types of projects increases.

These trends, in turn, create a favorable environment and a clear platform for the further development of methods in project management.

In addition, there are a number of fundamental ideas and approaches through which it is possible within the framework of the same methodology to consider not only the key problems of quantitative description of projects, but also many issues related to public life, which still do not have adequate quantitative solutions.

The idea of such a fundamental nature is the process of implementing projects and various manifestations of social life as a process of growth and accumulation, combined with the development of appropriate quantitative methods and models.

In particular, a similar idea was implemented in [2], where the project implementation process is considered as a growth process using logistic differential equations.

Typically, the methodologies used for project management assume that people’s performance remains unchanged during project implementation.

This statement is acceptable only for those projects that have a relatively short duration, during which the productivity of people does not change significantly.

But if we are talking about long-term projects, or other long-term actions and activities of people, the statement about the constancy of their performance no longer corresponds to reality, which, in turn, causes incorrect estimates and decisions.

Such a long-term project can be considered the life of a person also, during which his/her abilities, which in a particular case can be identified with his/her productivity in a normal working process, are subject to significant changes with age.

This means that in order to view society’s life as a set of parallel projects, it is first necessary to be able to do the same at the human level, since the person is a cell and unit of social life.

Having as a platform a quantitative model of human life from birth to the end of life, one can proceed to more complex cases of the dynamic representation of the coexistence of people and the life of society as a whole.

Since the basis of human activity are the abilities and possibilities of people, then human life should be viewed as a unity of the processes of growth of his abilities, and then their decline after a certain age.

To achieve this goal, namely, to describe the process of human life from birth to its end, it is necessary to have a flexible mathematical model that can adequately describe the slow growth of a person’s abilities and skills after birth, their rapid growth during the period of maturity and peaking at a young age and then presenting their decrease due to aging.

The mathematical model of human life must be so flexible that it can also reflect such phenomena as early maturation and late maturation of a person, as well as various rates of aging.

But on the other hand, consideration of these and many other circumstances can lead to insurmountable and unnecessary mathematical difficulties in building a comprehensive quantitative model of the growth and then the decline of human abilities and skills.

Therefore, in the mathematical modeling of such complex phenomena, it is advisable to follow the principle of the gradual complication of the model under development.

This means that at the first stage it is necessary to limit ourselves to building a simple structural model of the phenomenon being studied, provided that the developed model will adequately reflect at least the qualitative aspects of the problem.

Based on these considerations, we consider the dynamics of human capabilities depending on age as a single process, without breaking them into separate components.


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How to cite this paper: Barseghyan, P. (2019). Elements of the Mathematical Theory of Human Systems – Part 6: Human Life as a Project (The differential equation of human life); PM World Journal, Vol. VIII, Issue II (February). Available online at https://pmworldjournal.net/wp-content/uploads/2019/02/pmwj79-Feb2019-Barseghyan-the-differential-equation-of-human-life-featured-paper.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 [email protected]