# The Dynamics of Human Society Evolution

Ram C. Poudel and Jon G. McGowan, rcpouel@ioe.edu.np, jgmcgowa@ecs.umass.edu

## Introduction

Is the phenomenon of man different fundamentally from that of inanimate nature? Indeed there are some differences, however, there may not be a fine line separating animate from the inanimate at the fundamental level. Here, we summarize an article [1] about the evolution of human society that builds a case based on the foundation of classical mechanics and Niels Bohr’s Atomic Theory. New energy, identical in the form of that defined through the classical field theories, may be at play for the evolution of human society. The large-scale social collective and societies might be effectively understood from the perspective of energy flow; energetics in general.

Some argue that Bohr gave biologists a new conceptual tool. But many aspects of his Atomic Theory are still being integrated into human knowledge. About three-quarters of a century ago, Bohr wondered whether there exist unexplored aspects of epistemology in the analysis of natural phenomena. The dynamics of human society seems an obvious phenomenon for the authors to examine. This is why one of us proposed a new theory on the epistemology of Atomic Theory. The social field theory may also shed light on a better understanding of the dynamics of human society on the basis of physical experience. The theory helps define social force, social energy and the Hamiltonian of an individual in a society. The theory, however, may run counter to the flatland physics of an isolated system. Human society, after all, is an open and evolving system that may be understood better using thermodynamic principles.

The social dynamics may be understood better in terms of kinetics expressed in terms of the Hamiltonian of an individual in society. Kinetics considers movement in tandem with the underlying forces or the source term in general. What is the source term in social dynamics? According to Bertrand Russell, it is power: “The fundamental concept in social science is Power, in the same sense in which Energy is the fundamental concept in physics.” This observation is in accordance with one of the fundamental thermodynamics equations governing an open system – the rate of change of energy (E) is equal to power (P), or dE/dt = P. Human being/society is an open system in which matter, energy, entropy, and information flow in and out of the system’s boundaries. We expand the thermodynamic equations in order to develop provisional “equations of motion for social systems” in the way Wolfgang Weidlich [2] has long sought for. Obviously, the equations we have developed for the social system are based on kinetics. The equations are energetic descriptions of the social system that takes into account the power dynamics in the hierarchical society.

There are quite a bit of open-ended problems in social dynamics including the one ‘How Did Cooperative Behavior Evolve?’ [3] A monolithic culture, be it either natural science or social science, finds such questions elusive. If we follow the suggestions of Anthony J. Leggett, a 2003 Noble Laureate in Physics, it becomes important first to distinguish various levels of the problems we encounter in any disciplines. As is the case with condensed matter physics, [4] the open problems in social science may also be classified into the following three categories:

i) Hamiltonian known and tractable
ii) Hamiltonian partially known but intractable
iii) Hamiltonian not even known.

We placed social dynamics in one of the last two categories depending on the lens we choose to wear. Economic science registers money as the proxy for the Hamiltonian of an individual in society. For many of us with a background in the natural science, the arguments economic science make do not seem to provide enough direct evidence but economic science has supplied us with many interesting problems to solve that go beyond its boundaries. ‘It is not the load that breaks it down, it the way you carry it’ says Lou Holtz. Economic science may be carrying the dynamic load of human society the wrong way, it may need to be adjusted. Physicists are joining hands in the form of Econophysics; many engineers [5, 6] are also joining the fray. We offer Thermodynamics 2.0. Thermodynamics 2.0 is about bisociation [7] of thermodynamics with other academic disciplines such as physics, chemistry, biology, economics and many more. In a nutshell, Thermodynamics 2.0 is all about the coevolution of sciences - identifying and connecting dots of scientific revolutions in natural and social sciences.

Likewise with Leggett, the last categories (iii) are in many ways the most fascinating to us. We proposed an analogy between Niels Bohr’s Atomic Theory and human society- the phenomenon of poverty to be precise. The social field theory may not yet have experimental rigor though it adheres to most of our observations of societies in the East and West. The theory leads to the Hamiltonian $\left({H}\right)$ of an individual in the society.

The classical field theories define the potential energy of an object within the field of other objects that shares the same properties such as mass or charge or (di)pole strength. A force is a gradient of the potential energy. Many phenomena in nature can be interpreted in terms of four fundamental forces: electromagnetic, gravity, strong and weak nuclear forces. Are the myriad phenomena in nature governed by just these four fundamental forces? Many of us assume such a notion to be true. These forces were uncovered in order to explain various phenomena in natural science, and thus do not provide enough clues to explain social dynamics. We think a new type of force exists, especially among social beings. Earlier, we have made a case for the social field theory through a generalization of the classical field theories.

There is an inherent challenge to extend classical mechanics into the social system. This challenge led curious minds like Alfred J. Lotka to rely on energetics to understand evolution. In energetics, Lotka saw a physical principle competent enough to extend our systematic knowledge to natural selection. This is unfinished business; something that has yet to take off the ground. We go around this challenge in order to combine classical mechanics with Atomic Theory in order to come up with the equation for the evolution of human society. This is an effort to apply concepts arising from thermodynamics to areas outside of classical thermodynamics.

The portrait of an atom that Bohr’s theory presents resembles certain characteristics of our own solar system. Nature doesn’t differentiate sciences, but we do for good and bad reasons. In this theoretical approach, based on energetics, we argue that human society evolves following the laws of energy along with underlying forms and structures that human ingenuity develops and sustains over time.

## Social Field Theory

There are many types of field theories in social science. None of these theories are in the language of energy. The social field theory that we summarize here was born out of an effort to understand the link between energy access and poverty dynamics. We have formalized it based on Bohr’s theory of the H-atom, which connects classical and quantum mechanics in a way many engineering students may find easy to understand.

The social field is characterized in terms of Social Strength (S), Individual Strength (I) and social distance (r). The variables S and I have a bearing on the pole strength in a magnetic field. The social distance is the relation of social entities to other entities measuring the degree of their contact or isolation. We define the Trust Vector (${\Gamma }$) as being reciprocal to social distance, i.e. r x ${\Gamma }$ = 1. The two hypotheses of the social field theory are:

1. Social Field is a quasi-conservative field, defined as a field for which total energy is a monotonic function of time.
2. Energy levels in the social field are quantized in similar notions to how they are in established models of an atom, for example Bohr's theory of the hydrogen atom and Schrödinger’s equation.

To some of us trained in a monolithic culture, the idea of a social field could easily be a “The Blind Man and the Elephant.” One of the internal reviewers wrote: “I don’t believe a single variable can be an adequate measure of the “social strength” of an individual, nor do I believe that “social distance” can be described by a single variable.” We understand the frustration of the reviewer. However, social strength (S) is an n-dimensional variable, and so is the social distance (r) or the trust vector (${\Gamma }$). The social field is a non-inertial field characterized in terms of energy. We define the non-inertial field as the field for which terms like acceleration keeps evolving. Human societies evolve in steps as some anthropologists have made the case for [8]. These steps may well be conceived by the energy levels following HP02.

The total energy of an individual is composed of two forms of energy, Potential Energy (PE) ${-}{S}{I}{\Gamma }$, and Kinetic Energy (KE) = ½ ${S}{I}{\Gamma }$. The same expression of kinetic energy can also be derived based on the Virial theorem. In the social field, we equate the potential energy to capabilities ${{C}}_{{2}}$, and kinetic energy to capital ${{C}}_{{1}}{,}$ of an individual. The total energy in the social field is the Hamiltonian of an individual, ${H}{=}{H}\left({{C}}_{{1}}{,}{{C}}_{{2}}{,}{t}\right)$. Entropy in the social field turns out to be $\stackrel{{\mathrm{´}}}{{I}}{l}{o}{g}\left({S}{I}\right)$. The social field is a non-inertial field that autonomously evolves with time. HP02 provides a structure for the hierarchical social field.

This theory may provide an additional clue about the operations of ‘animate agencies’ with reference to the Second Law of Thermodynamics along the line of reasoning proposed by Prigogine for an open system.

## Equation of Motion

Equations of motion (EOM) describe the time evolution of the state of a system. In fact, the equation we propose for the social field is a power equation, power P = Force (F) x velocity (v), where power is defined as the rate of change of energy. The change of energy is expressed in terms of the total derivative of the Hamiltonian ${H}{=}{H}\left({{C}}_{{1}}{,}{{C}}_{{2}}{,}{t}\right)$ in the framework of the Navier-Stokes equations. The EOM for an individual in the social field turns out to be,

$\frac{{\partial }{H}}{{\partial }{t}}{+}\frac{{\partial }{H}}{{\partial }{{C}}_{{1}}}\frac{{d}{{C}}_{{1}}}{{d}{t}}{+}\frac{{\partial }{H}}{{\partial }{{C}}_{{2}}}\frac{{d}{{C}}_{{2}}}{{d}{t}}$ = $\left({{F}}_{{e}{n}}{+}{{F}}_{{e}{x}}\right)\frac{{1}}{{{\Gamma }}^{{2}}}\frac{{d}{\Gamma }}{{d}{t}}{±}\stackrel{{\mathrm{´}}}{{Q}}$. (1)

In Eq. (1), $\stackrel{{\mathrm{´}}}{{Q}}$ includes both the generation and dissipation terms. The Hamiltonian of a society can be aggregated in terms of the probability distribution function Hs. Hence for society, EOM will be

$\frac{{\partial }}{{\partial }{\mathbit{t}}}{{\mathbit{H}}}_{{\mathbit{s}}}\left({\mathbit{n}}{,}{\mathbit{t}}\right){=}{-}{\sum }_{\begin{array}{c}{\mathbit{i}}{=}{1,2}\\ {\mathbit{n}}\end{array}}\frac{{\partial }{{\mathbit{H}}}_{{\mathbit{s}}}\left({\mathbit{n}}{,}{\mathbit{t}}\right)}{{\partial }{{\mathbit{C}}}_{{\mathbit{i}}}}\stackrel{{\mathrm{´}}}{{{\mathbit{C}}}_{{\mathbit{i}}}}{+}\left({{\mathbit{F}}}_{{\mathbit{s}}}\left({\mathbit{n}}{,}{\mathbit{t}}\right){+}{{\mathbit{F}}}_{{\mathbit{b}}}\left({\mathbit{n}}{,}{\mathbit{t}}\right)\right)\stackrel{{\mathrm{´}}}{{{\mathbit{r}}}_{{\mathbit{n}}}}{±}{\stackrel{{\mathrm{´}}}{{\mathbit{Q}}}}_{{\mathbit{s}}}$ (2)

An aggregated multi-body equation in the social field leads to an implicit multivariate Fokker-Planck equation. We propose Eq. (2) as a stopgap to knowledge about “equations of motion for social systems” Wolfgang Weidlich [2] claimed this to be non-existent in the literature. Lotka-Volterra type of equation can be derived from it when some additional assumptions are made [1]. One of the field theorists in sociology, Pierre Bourdieu has implied three major forms of capital. Accordingly, we propose to contract the n-dimensional social field to R3. These three reduced dimensions are i) economic ii) cultural and iii) social. This contracted description may provide logical reasoning to interpret the trends in social capital [9] in many societies.

It may be inappropriate to talk about social dynamics without linking it to money, a concept of paramount significance to economic science. The energetics framework conceives of money in accordance with original insights of Howard Odum: money flows in circles, but energy flows through a system and ultimately comes out in a degraded form.

The article presents how classical mechanics and quantum mechanics (especially Atomic Theory) may complement each other in order to explain some phenomenon that is not understood well in terms of physical principles. Obviously, these are half-backed ideas still awaiting criticisms from scientific communities. As Bohr argued, complementarity also has a place in social sciences. Ernst Mayr offered another example of complementary perspectives in biology. He emphasized two broad types of causation in biology: ultimate (i.e., evolutionary) and proximate (i.e., physiological). In the words of Bohr, both types of explanations have their uses, but not necessarily for addressing the same questions. Here, classical mechanics meets with quantum mechanics in order to make some more sense of social dynamics and the evolution of human society within the framework of energetics.

In the same manner by which Bohr defended his case, we would like to invoke the precedence: “The test of any theory is not whether it contradicts preconceived philosophical notions, but only whether it contradicts the experimental fact.” Our natural science instincts, obviously, leads us to aspire being rigorous about testing the theory with more available facts. Unfortunately, there is not much high-quality data on how societies are related to one another. Hence, it is difficult to draw quantitative conclusions. The best things we can do at this stage is to wait curiously to see which working alternatives to the ideas of human society evolution are in tune with the observations of many conscious minds in the 21st century.

We end this summary with Philippe Nozieres’ quote ‘‘only simple qualitative arguments can reveal the underlying physics”. Some might see it as a light in the qualitative argument that social field theory brings forth. While others may easily consider it a misplaced analogy. Many of us are filled with preconceptions about the world around us; we are not exceptions either. Nonetheless, if a true opinion accompanied by reason is knowledge, this transgression by a duo of engineers may contribute to an essential advance in human knowledge, especially about the evolution of human society and the integration of the sciences. We are all spectators and actors in an evolving human society. Together we can understand ‘The Elephant’ better!

## Acknowledgements

We benefited from the input of participants at multiple conferences. We would also like to mention Energy for Capabilities Development Partnership, and Complex Systems Group at Worcester Polytechnic Institute (WPI) in Worcester, MA.

## References

[1] R. C. Poudel and J. G. McGowan, "The Dynamics of Human Society Evolution: An Energetics Approach," arXiv.org, 8 April 2019.

[2] W. Weidlich, "Sociodynamics - A Systematic Approach to Mathematical Modelling in the Social Sciences," Nonlinear Phenomena in Complex Systems, pp. 479 - 487, 2002.

[3] E. Pennisi, "How Did Cooperative Behavior Evolve?," Science, vol. 309, no. 5731, p. 93, 2005.

[4] A. J. Leggett, "Reflections on the past, present and future of condensed matter physics," Science Bulletin, vol. 63, p. 1019–1022, 2018.

[5] A. Bejan and S. Lorente, "Constructal law of design and evolution: Physics, biology, technology, and society," Journal of Applied Physics, vol. 113, no. 151301, 2013.

[6] A. Annila, "Natural thermodynamics," Physica A: Statistical Mechanics and its Applications, vol. 444, pp. 843-852, 2016.

[7] A. Koestler, The Act of Creation, New York: Macmillan, 1964.

[8] T. E. Currie, S. J. Greenhill, R. D. Gray, T. Hasegawa and R. Mace, "Rise and fall of political complexity in island South-East Asia and the Pacific.," Nature, vol. 467, no. 7317, p. 801, 2010.

[9] R. D. Putnam, Bowling Alone: The Collapse and Revival of American Community, Touchstone Books by Simon & Schuster, 2001.

These contributions have not been peer-refereed. They represent solely the view(s) of the author(s) and not necessarily the view of APS.