To International Journal of Modern Social Sciences, 2017, 6(1): 22-33
International Journal of Modern Social Sciences
ISSN: 2169-9917
Florida, USA
Journal homepage: www.ModernScientificPress.com/Journals/IJMSS.aspx
Article
Social Dynamics, Social Hydrodynamics and Description of
Social Progress and Various Crises
Yi-Fang Chang
Department of Physics, Yunnan University, Kunming, 650091, China
Email: [email protected]; [email protected]
Article history: Received 21 October 2016, Revised 27 January 2017, Accepted 27 January 2017,
Published 31 January 2017.
Abstract: First, we discuss social field and social dynamics. Next, we research
systematically the social hydrodynamics as example of nonlinear whole sociology, which is
a macroscopic and whole description on sociology. This may include various social flows
and patterns, and is related with the social geography. An important result of
hydrodynamics is to form waves, and social waves may form various social tides.
Moreover, we discuss social justice and various defects as social crises. The social
hydrodynamics and corresponding waves and tides may describe positive social progress
and various negative social crises from mathematical and physical mechanism and methods.
Keywords: social hydrodynamics, social dynamics, wave, tide, defect, progress, crisis.
1. Introduction
It is known that defects may be described by Monte Carlo statistical method, molecular
dynamics, Schrödinger equation, density functional theory and energy minimum, etc. We discussed
generally the four variables and the eight aspects in social physics, and searched social
thermodynamics and the five fundamental laws of social complex systems, and proposed the nonlinear
whole sociology and its four basic laws (Chang 2013b).
Certain statistical aspects of social systems are described by appropriately defined quantities
named social potentials. Based on thermodynamic potentials and formalism, Stepanic, et al. (2000)
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
23
presented an approach to a quantitative description of social systems. Based on the synergetics, we
proposed the social synergetics and the four basic theorems. From the synergetic equations, we
obtained the equations on the rule of law, and proved mathematically that a society of the rule of law
cannot lack any aspect for three types of the legislation, the administration and the judicature. Further,
from synergetics we obtained the Lorenz model, which is a visualized two-party mechanism as a type
of stable structure in democracy. A developed direction of society is the combination from
macroscopic to microscopic order, from an actual capable handling to an ideal pursuance (Chang
2013a).
Based on the sameness for men or any elements in the social systems, we researched the social
thermodynamics, and possible entropy decrease in social sciences. Using the similar formulas of the
preference relation and the utility function, we proposed the confidence relations and the
corresponding influence functions that represent various interacting strengths of different families,
cliques and systems of organization. This produces a multiply connected topological economics.
Further, we discussed the binary periods of the political economy by the complex function and the
elliptic functions (Chang 2013c).
In this paper we research systematically the social hydrodynamics as example of nonlinear
whole sociology, which may form various social waves and tides, and describe positive social progress
and various negative social crises from mathematical and physical mechanism and methods.
2. Social Field and Social Dynamics
Lewin (1951) discussed field theory in social science. Wilkinson (1970) proposed the
community as a social field. Helbing (1994) developed a mathematical model for behavioral changes
under the influence of a social field. Levitt and Schiller (2004) researched the conceptualizing
simultaneity as a transnational social field perspective on society. Rawolle (2005) studied the crossfield effects and temporary social fields of Australian knowledge economy policies.
Social field in social sciences investigates social systems by mathematical and physical methods,
and is an important part of social physics. It may define distributions, and propose potential, force,
energy and entropy, etc., and determine field equations, and make qualitative analysis, and found
models. We discussed generally the social kinetic energy K, and the social potential energy U, and the
social force F (Chang 2013b). Religion and evil belief all are various potentials and forces. Band
energy corresponds to the social intelligentsia, etc.
Usual social equations should be nonlinear, which corresponds to the nonlinear whole sociology
(Chang 2013b). They may be the system dynamics. Synergetics equations are generally nonlinear
(Haken 1977, 1983; Weidlich et al. 1983), for example,
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
dX
 I  RX  CX 3 .
dt
24
(1)
It is first type of Appel equations. Let w(t )  eRX and   C  w2 dX , so X  w(t )Y ( ) , then
dY
 Y 3  ( A / Cw3 ) .
d
(2)
Based on Chinese traditional philosophy and culture, a series of equations may correspond to
Sky-Earth-Man, and we proposed the promotion-restraint sustainable developed pattern on the FiveElements (Fig. 1), which include social (S) progress (democracy, justice, stabilization), economical
development (F), science-technology (K), education-civilization (J) and environment-resource (H)
(Chang 2015b,c).
Fig. 1. Promotion-Restraint Developed Pattern on the Five-Elements
In Fig. 1, a solid line represents a promotion relation, and a dotted line represents a restraint
relation. In graph theory the promotion and restraint relations are just a graph isomorphic to its
complement (Diestel 2000).
The equations of both patterns are the simplest linear:
dX i
 ai X i  bi X j  ci X k ,
dt
(3)
here i=1,2,3 or i=1,2,..5, and + and – are promotion and restraint relations, respectively. Further, they
should be nonlinear:
dX i
 ai X i (1  bi X j  ci X k ) .
dt
(4)
3. Social Hydrodynamics as Example of Nonlinear Whole Sociology
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
25
Society includes various states, but they cannot usually be gas states. Solid states possess bigger
defects, and which diffuse easily, in particular, a pyramid structure. Modern society and persons are
more analogy with liquid, therefore, we may apply the social hydrodynamics (Chang 2013c).
Eyerman and Jamison (1991) researched social movements as a cognitive approach. Clifford
(1997) searched routes. Cohen (1997) discussed global diasporas. Shields (1997) proposed flow as a
new paradigm. Bauman (2000) researched liquid modernity, in which power relates velocity,
weightless, long distance, and globalization. Urry (2000, 2002) proposed the mobile sociology, and
discussed mobility and proximity.
Using the nonlinear equations of hydrodynamics we researched the formulations of the binary
and multiple centers in various social systems (Chang 2013c). Further, everyone possesses fate and
luck. General relativity shows that matter and movement determine the space-time of everyone. This as
a universal physical representation of causality is a great contribution to modern social science,
therefore, we proposed the social extensive general relativity, which may describe some evolutional
orbits of life and society (Chang 2014b).
In this article we research systematically the social hydrodynamics, which is a macroscopic and
whole description on sociology. It may include matter flows, energy flows, information flows, biologic
flows, virus flows, and money flows, commodity flows, brand flows, culture flows, music flows, even
global fluid, terrorism and its growth, etc. Religion fluid will change distribution of belief in some
regions, for instance, Islam in Europe.
In social hydrodynamics some keys are velocity, tension, viscosity, resistance, and pathway,
space-time. It may form turbulence, chaos, emergence, etc., and produce various social movements,
social regulations and social order. Papastergiadis (2000) researched the turbulence of migration.
Global Sea and global fluids produce globalization, shrinking world, global village and panhumanity
(Frankling et al. 2000).
In various social fields, gradient of the scalar field  is a vector field:
 
i.
i 1 xi
n
grad    
(5)
For example, income of people is the scalar field, whose gradient may describe difference of total
citizens. If gradient of stable circumstance and society is too big, stability of these systems will be
destroyed. Gradient of the tensor field A of n order is a tensor field of n+1 order:
gradA  A  {
Aij
}.
xk
(6)

Divergence of the vector field A is a scalar field. It may describe loss of capital, etc. Divergence
of the tensor field A of n order is a tensor field of n-1 order:
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33

 A
divA    A  { ij } .
xi
26
(7)

Rotation of the vector field A is still a vector field.
Further, they may be various social tensor fields, spinor fields, twistor fields and superposition
of many fields.
The equation of continuity is:

   ( v )  0 ,
t
(8)
here  is the social fluid density. We discussed the social thermodynamics and its five fundamental
laws (Chang 2013c), in which the extensive energy includes person, money, resources, land, time, etc.,

but they may change, for example, information, etc. There is   v  0 for constant  . Liquid may be



rotation or irrotation. Irrotational flow is   v  0 . Liquid equation with source is   v  divv   .
Very big natality of some nations forms the sources of person flow.
For entropy the equation of continuity is:
 ( s )
   ( sv )  0 ,
t
(9)
here sv is the social entropy flux density. If self-organized and other ordering structures appear, their
entropy will be smaller, whose necessary condition of entropy decrease in isolated system is existence
of internal interactions (Chang 1997, 2005, 2012). Further, we proposed quantitatively a universal
entropy theory on evolution of any natural and social systems (Chang 2014a).
Euler’s equation is:
dV V 1
1

  | V |2 V    F  p .
dt
t 2

(10)
The nonlinear hydrodynamic equation with viscous fluid is the Navier-Stokes equation (Chang,
2007, 2013b):

dV
V
e

 [
 (V)V ]  F  V  B  gradp  V  graddivV . (11)
dt
t
c
3
Hydrodynamics introduces the velocity potential function  ( x, y ) and the flow function  ( x, y ) ,
in which the complex potential is:
w( z )   ( x, y )  i ( x, y ) .
(12)
Here z=x+iy. The complex velocity is dw / dz  u  iv .
Hydrodynamics may form various flow modes, in which some basic modes are: 1) Beeline
uniform flow w( z)  Vei z . 2) Plane source (sink) flow w(z)=mlnz. 3) Point eddy flow
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
27
w( z )  (i / 2 ) ln z . 4) Plane dipole flow w(z)=-(m/z). 5) Turbulence. 6) Lorenz model. 7) Various
chaotic flows, etc. They may combine various singular points and qualitative analysis theory.
The residue theorem is:

l
n
f ( z )dz  2i  Re sf (bi ) ,
(13)
i 1
here bi are various residues of singular points in a loop region. Their meanings are probably that these
points in this loop correspond to most problems, for example, war and peace, development, etc.
An important result of hydrodynamics is to form waves, which may develop billow and tsunami,
etc. Wave velocity is c   /    / k . Both velocities of shallow water wave and deep-water wave are
different. Shallow water wave agrees with soliton equation (Scott, et al. 1973). Shock wave has the
continuous tangential velocity at the surface of discontinuity, which is a type of soliton.
Giddens (1984) proposed the duality of structure. We proposed the social individual-wave
duality, and researched the social topology and the social strain field, and searched the pattern
dynamics and the damage mechanics in sociology. From this mechanism the crisis of society may be
described mathematically by the qualitative analysis method, and discussed some social phenomenon
and war crisis (Chang 2015a).
Social waves and social movements may form various social tides. Its base is social statistics,
and nonlinearity. The quasi-periodic waves correspond to the quasi-periodic economic conjunctures.
Social turbulence is a type of social chaos. It may form energy-containing eddy and dissipation eddy.
When the Reynolds number is enough large, flow forms fully developed turbulence, which is
characterized by the presence of an extremely irregular disordered variation of the velocity with time at
each point (Landau, et al. 1987).
In social sciences various flows may usually be plane problems, for example, money, persons,
refugee, etc. If they are developed to three-dimensions, so refugee and persons with ability, etc., will
classify and delaminate, in particular, for network and information.
In social hydrodynamics, when various fluids form different patterns, we discuss the social
geography. For example, much flows are collected, and form city, it is an attractor and basin. Peers,
magnates, dignitaries, and high science-technology form peaks in different regions. It may describe
equalitarianism, despotism, oligarch, etc.
Further, social hydrodynamics may develop to social magnetohydrodynamics, and social general
relativity (Chang 2014b), etc.
Lefebvre (1991) proposed the production of space. Zohar and Marshall (1994) applied quantum
physics, and proposed the quantum society. Mol and Law (1994) discussed regions, networks and
fluids, in which there is wave-particle duality, and may apply to city, and develop to global wave and
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
28
particle, and globally networks and fluids (Urry 2003). Various networks correspond to the social
topology (Chang 2015a). Globalization as the new structure with autopoiesis (Luhmann 1990), autoreproduced, self-making is a self-organization system. It should be a process with entropy decrease
(Chang 2013c).
4. Social Progress and Various Social Crises
The social hydrodynamics and corresponding waves and tides may describe positive social
progress. We should increase velocity of positive energy, and research to form the origin of various
tides of new science-technology, of democracy and peace, and form the equal network society, so that
promote social progress and developments. According to third law (economic growth mode transition
and new developed period law) of the nonlinear theory of economic growth (Chang 2013b), further
development of social economy must exploits new merchandise and market, and adjust output
configuration, and reform technique, and train personnel, so that boost up the immanence ability of
social development and the international competitiveness. The society should reform continuously to
achieve a higher seedtime, i.e., search new economic growth point for microeconomics.
Based on the basic social laws on energy and entropy, we discussed some social sustainable
developed patterns: 1) The nonlinear limit and cycle pattern of three elements; 2) the synergetic pattern
on society-economy-environment developed together; 3) the promotion-restraint pattern on FiveElements. Their basis is lower entropy, even entropy decrease (Chang 2015b).
From this we should construct the stable social structure. We discussed various stable social
structures of different levels. Chinese history shows a statistical rule, and forms a super-stable
structure. The basis of the modern stable and harmonious society is equality. The comparison and
combination at all times and in all over the world will redound to build a perfect society (Chang
2016b).
Contrarily, based on the mathematical and physical mechanism and methods of social
hydrodynamics, they may also describe various negative social crises. We should avoid and check the
sources of various social crises, and decrease diffusion velocity of crises, and reduce the height of
shock waves. Positive ways are increase flow flux, and negative ways are increase viscosity and
resistance, even build breakwater.
Social hydrodynamics passes through nonlinear mechanism to derive social chaos, which
obtains social storm, for example, the Drastic Change of the East European Countries, Arab Spring,
many waves on freedom-democracy, network, information society, and so on. Russel, et al. (1980),
discussed three-wave coupled equations, whose fractal dimension D=2.32. Baker (1993) discussed
chaos, order, sociological theory, and attractors as centriphery. Stewart (2001) searched complexity
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
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theories, social theory and social complexity. In Iraq and Syria many forces converge to arouse that
war becomes chaos and turbulence.
Castells (1996, 1997, 1998) discussed the information age, and analyzed network and web of life,
in which networks of power lead to networks of resistance, and produce the power-resistance attractor.
Beck (1992,1998) proposed risk society and world risk society. Jessop (2000) discussed the
crisis of the national spatio-temporal fix and the tendential ecological dominance of globalizing
capitalism. Davis (2000) discussed crises of cities. Law, et al. (2000) pointed out, perfection of some
systems not only is impossible, and it will become strong inducement of self-frustration of systems.
Contrarily, at times some unstable or imperfect systems may turn into “safety” factors due to internal
complex relations (Urry 2003). So are often some social stability and crises, external stability is
probably very unstable.
It is well-known that chaos produces the butterfly effect. For example,
An egg aroused a smoking,
A smoking aroused a visitation,
A visitation led a prince abortion,
A prince abortion brought a dynastic disillusion.
Crises dynamics and their equations, one side may expand, and all chaos expands, and
dimensions are increase, areas are extended. Another side they may tend to disappear. Further, these
theories may develop to social evolutionary equations. They may be Landau-Hopf way, Ruelle-Takens
way, at ring surface the quasi-periodic bifurcations of movement, double-periods to chaos way, and
Pomean-Manneville intermittent chaos way (Haken 1983), etc.
Various solutions of these equations may be: (1). Stable solutions, and correspond to stable
society. (2). Periodic and quasi-periodic solutions, which may be periodic change or super-stability
(Chang 2016b). (3). Chaos solutions with microscopic not-rules and macroscopic rules. (4). Complete
random.
5. Description of Defects and Social Justice
We propose that social crises are various defects, which include point defects, linear defects,
planar defects and volume defects, etc. Defects and dislocation may be microscopic and macroscopic
descriptions. In Chinese traditional morality it corresponds to self-cultivating (cultivate individual
moral character), family-regulating (run the family unison), state-ordering (manage the nation in
order), and the land great governed (peace will prevail throughout the universe) from small to big.
Fick’s first law of diffusion is:
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
J  D
dc
.
dx
30
(14)
J is flux of diffusion matter.
Fick’s second law of diffusion is:
dc
d 2c
D 2 .
dx
dx
(15)
Einstein-Smolucchowski diffusion equation is (Tilley 2008):
 x2  2Drt .
(16)
First D. Harvey (1973) proposed social justice and the city. Then Harvey (1996, 2005, 2013)
discussed justice, nature and the geography of difference. Further, Pirie (1983) proposed spatial justice.
Soja (2000, 2010) discussed spatial justice. He applied the trial ectics of being: space, history and
sociality. They form three-dimensions of justice. Urbanization arouses new spatial justice. Cities are
main regions of modern social crises, because cities show easily inequality in society (Piketty 2014),
for example, the back slums, and their defects diffuse easily, and bring an explosive revolution, for
example, the Arab Spring (Hass et al. 2013). Therefore, Harvey (2013) proposed rebel cities from the
right to the city to the urban revolution.
Crises classify the city crises, the ecological crises, belief crises, etc. Crises diffuse to originate
from some social potentials and forces. Social crises are mainly origin of inequality of fortune and
income dispensation. Reduced difference is decrease potential. But, if there is not potential, social
development will absent drive. Crises originate from mind, which is related with Buddhism (Chang
2015d) and psychology on happiness (Chang 2016a), etc.
Forst (2002) in Context of Justice: Political Philosophy beyond Liberalism and
Communitarianism proposed a new idea: right of justification is beyond Liberalism and
Communitarianism, whose philosophic foundation is moral right. Julien (2011) researched the silent
transformations. Honneth (2014) discussed freedom’s right as the social foundations of democratic life.
In 2014 Annual Conference of the “Philosophy and Social Sciences” in Prague L.Hohos proposed a
new civilization paradigm: transformation as an alternative to revolution.
Social progress and crises are related with revolutions (Goldstone 1982; Peceny 2007). When the
accumulated value of some variables once reaches to a certainty, revolution will happen possibly
(Paulson 2006).
Zhang Yi-Ping proposes the shipboard wave theory. In social fields any things like the regular
boats in time-river, they cannot but arose waves. Based on the rules and theory of wave, we may
forecast moving direction and velocity, and estimate their effects. It is a causality of social
hydrodynamics.
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Int. J. Modern Soc. Sci. 2017, 6(1): 22-33
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In a word, based on the principles and mechanism of the social hydrodynamics we may describe
positive social progress and various negative social crises by mathematical and physical methods.
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