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European Journal of Applied Sciences – Vol. 12, No. 5
Publication Date: October 25, 2024
DOI:10.14738/aivp.125.17556.
Cui, W., Li, R., & Pan, L. (2024). Toward a Unified Theory for Complex Systems. European Journal of Applied Sciences, Vol - 12(5).
69-103.
Services for Science and Education – United Kingdom
Toward a Unified Theory for Complex Systems
Weicheng Cui
Research Center for Industries of the Future,
Westlake University, Hangzhou, 310030, Zhejiang, China
Rong Li
Key Laboratory of Coastal Environment and
Resources of Zhejiang Province, School of Engineering,
Westlake University, Hangzhou, 310030, Zhejiang, China
Lingli Pan
Key Laboratory of Coastal Environment and
Resources of Zhejiang Province, School of Engineering,
Westlake University, Hangzhou, 310030, Zhejiang, China
ABSTRACT
The system serves as a general model for addressing various encountered issues,
with the complexity of systems we handle increasing steadily. From the 2021 map
of complexity sciences, 67 distinct theories or sub-disciplines can be counted,
leading to the difficulty in selecting an appropriate theory for a particular
problem. This paper aims to establish an axiomatic framework for a unified theory
for complex systems, spanning from micro to macro scales and encompassing
entities from non-living to living objects. The unification was carried out from
fundamental concepts, fundamental assumptions and mathematical languages.
The original contributions in this unified system theory include: (1) moving away
from a revolution against classical mechanics and embracing its generalization,
(2) offering a dualist approach to the mind-body problem instead of the monist
solution of the past, and (3) introducing an active force for living objects in living
state. The efficacy of this unified theory is illustrated through multiple practical
applications.
Keywords: Complex system, unified theory, axiomatic framework, mind-body duality,
active force, co-existence of a pair of conflicting concepts.
INTRODUCTION
A system is a group of interacting or interrelated entities that form a unified whole. A system
is delineated by its spatial and temporal boundaries, surrounded and influenced by its
environment, described by its structure and purpose and expressed in its functioning [1]. A
schematic representation of a general system is shown in Fig.1b. However, the definition of
complex systems has been highly debated in the past and a significant consensus is (1)
composed of many elements; (2) displaying emergent phenomena; (3) exhibiting nonlinear
behaviour [2].
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European Journal of Applied Sciences (EJAS) Vol. 12, Issue 5, October-2024
Fig.1 (a) A system with its four spaces. (b). An illustration of the concept of a system.
System is a very general model for modelling any problems we encounter [1] and nowadays
the systems we can handle become more and more complex. We can treat the whole earth as a
system and study the sustainability issue of human beings on the earth using complex system
theory [3-4] which may be the most concerned issue for most of human beings. Due to the
philosophical conflicts existed among classical mechanics, quantum mechanics and relativity
theory, the theories used to handle complex systems are very diverse, see 2021 MAP of
complexity sciences [5]. They are the mixtures of these three fundamental theories for
complex systems. From this map, one can count at least 67 different theories or sub- disciplines. For any practical problem we encounter, one can find that many different theories
from this MAP are supposed to be valid for handling this problem but if one does try different
theories, the results from these theories will be very different. In such a situation, one
certainly wonders which theory should be trusted. So, developing a unified theory for
complex systems is an ideal situation for solving this wonder. The purpose of this paper is to
present our pursuit in this direction. The so-called “unified” means a theory that covers the
scale from micro to macro and includes the objects from non-living to living. Generally
speaking, the question one can have is either philosophical or scientific. For scientific
questions, one can show whether the solution is correct or not, but for philosophical
questions, it is hard to prove whether the solution is correct or not, so it is just a selection
problem [6]. Different selections of axioms or postulates can build different theories and that
is the main reason for the diversity of complexity sciences. For important philosophical
questions involved in the process of constructing the system model, we will present different
selections by others and explain why we make a certain selection. Furthermore, another
reason for the diversity is the change in the definitions of many fundamental concepts related
to the system theory. Some of them are clarified in our unified theory, and these include
universe, world, time, space, matter, mass, ether, mind, energy, field, heat, work, information,
probability and life. Our main idea is to give up the revolution perspective used in quantum
mechanics and relativity theory and generalize the ideas in classical mechanics to handle
complex systems. The generalization is mainly to use the dualist answer to the mind-body
System
World
Universe
Environment
(a) Four spaces are needed in a system model:
universe, world, environment and system
(b) A general system consists of non- living and living objects and their
environment which must be confined to
the scope of the world
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Cui, W., Li, R., & Pan, L. (2024). Toward a Unified Theory for Complex Systems. European Journal of Applied Sciences, Vol - 12(5). 69-103.
URL: http://dx.doi.org/10.14738/aivp.125.17556
problem rather than the monist solution used in the past, and for a living object, an active
force is introduced in the living state due to the mind-body-environment interaction.
The paper is structured as follows. In section 2, the general description of a complex system is
given. Section 3 discusses and clarifies some fundamental concepts involved in describing
complex systems. In section 4, the axiomatic framework for a unified theory for complex
systems is presented. In section 5, some demonstrations are given to illustrate how the
unified theory is used to solve those problems which are claimed to be unable to be solved by
classical mechanics. This demonstrates the potential ability of this new theory as a unified
theory for complex systems. The last section makes a summary and some important
conclusions are drawn.
GENERAL DESCRIPTION OF A COMPLEX SYSTEM
For the simplicity of demonstration purpose, we simplify all the visible objects contained in
the system and environment we study as the material particles of mass, i.e. we ignore the
volume of the objects for the time being. These particles can be divided into two types: living
particles, which have self-moving abilities, and non-living particles, which do not have the
self-moving ability. The non-living particle is just a special case of a living particle when it is
dead. So, in the following, we first treat all particles as living particles.
The description of a general complex system can be derived from a generalization of the
formulation by J. C. C. McKinsey, A. C. Sugar and P. Suppes [7]. It is shown in Fig.2 as a
schematic representation. We call this generalized McKinsey-Sugar-Suppes (MSS) system of
classical particle mechanics as a representative complex system.
Fig.2 A schematic representation of complex particle systems
A complex system has seven primitive notions: S, E, T, m, s, Fp, and Fa. S and E are sets of
numbers of particles in the system and environment respectively, T is the set of real numbers
for time, m is a real-valued unary function defined on S and E, s and Fa are vector-valued
functions defined on the Cartesian product S T, and Fp is a vector-valued function defined on
the Cartesian product S E T. Intuitively, S corresponds to the set of particles in the system,
E corresponds to the set of particles in the environment and T is to be physically interpreted
as a set of real numbers measuring elapsed times (in terms of some unit of time, and
o x
y
E
P