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Brief Intro to General Systems
Theory and Its Applications
Yi Lin
(aka Jeffrey Yi

Lin Forrest)
Department of Mathematics
Slippery Rock University
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1. Systems Movement
von Bertalanffy (1934) wrote:
Since the fundamental character of living things is its
organization, the customary investigation of individual
parts and processes cannot provide a complete
explanation of the phenomenon of life. This investigation
gives us no information about the coordination of parts
and processes. Thus the chief task of biology must be to
discover the laws of biological systems (at all levels of
organization). We believe that the attempts to find a
foundation at this theoretical level point at fundamental
changes in the world picture. This view, considered as a
method of investigation, we call “organismic biology”
and, as an attempt at an explanation, “the system theory
of the organism.”
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From this statement and seemingly
unsolvable problems in practice, such as
prediction of zero

probability disastrous
weather conditions,
we see the concept of systems was
formally introduced.
As tested in the past 90 some years, this
concept has been widely accepted by the
entire spectrum of science and technology
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Some of historical milestones:
1948, Norbert Wiener’s paper:
Cybernetics or Control
and Communication in the Animal and the Machine.
1954, Ludwig von Bertalanffy, Anatol Rapoport, Ralph
W. Gerard, Kenneth Boulding establish Society for the
Advancement of General Systems Theory, in 1956
renamed to Society for General Systems Research.
1955, W. Ross Ashby’s work:
Introduction to Cybernetics
1968, Ludwig von Bertalanffy’s work:
General System
theory: Foundations, Development, Applications
1988, the Society for General Systems Research is
renamed as International Society for Systems Sciences.
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Klir (2001):
Systems thinking focuses on those properties of
systems and associated problems that emanate
from the general notion of systemhood,
while the divisions of the classical science have
been done largely on properties of thinghood,
systems research naturally transcends all the
disciplines of the classical science and becomes
a force making the existing disciplinary
boundaries totally irrelevant and superficial.
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Cross

disciplinary feature of the systems research
implies
Researches of systems science can be applied
to virtually all disciplines of the classical
science;
Issues involving systemhood, studied in
individual specialization of the classical
science, can be studied comprehensively and
thoroughly; and
A unifying influence on the classical science
where a growing number of narrow disciplines
is created.
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So,
the classical and systems sciences can be
viewed as a genuine two

dimensional
science. With the added advantage of the
second dimension
–
the systems science,
we (Lin, 2009; 2010) can show some
important impacts of this second
dimension on the first dimension
–
the
classical science.
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2. Basic Concepts
Systems methodology:
Quastler (1965):
employs the concepts of a black
box and a white box to show research problems
(of the past) can be represented as white boxes,
and their environments as black boxes. The
objects of systems are classified into several
categories … Through a set of rules, policies,
and regulations, sensors and effectors do what
they are supposed to do.
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Zadeh (1962): important problems in
systems science:
Systems characteristics, systems
classifications, systems identification,
signal representation, signal classification,
systems analysis, systems synthesis,
systems control and programming,
systems optimization, learning and
adaptation, systems liability, stability, and
controllability.
Main task of systems science: general
properties of systems without considering
their physical specifics
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Zadeh’s viewpoint:
Systems science is an independent scientific
endeavor whose job is to develop an
abstract foundation with concepts and
frames in order to study various behaviors
of different kinds of systems.
Therefore, systems science should be
based on a theory of mathematical
structures of systems with the purpose of
studying the foundation of organizations
and systems structures.
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What is a system?
As all concepts in science, ideas / thinking
logic of systems have a long history.
Chinese traditional medicine (~5,000 years)
Aristotle’s “whole is greater than the sum of
its parts”
In modern times, new contents added to the
ancient systems thinking
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The methodology of studying systems as
wholes agrees with the development trend
of modern science,
Where:
divide the object of consideration into parts
as small as possible and studying all of the
individual parts,
seek interactions and connections between
phenomena, and to observe and
comprehend more and bigger pictures of
nature.
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Concept of system is difficult if not impossible
Klir (2001) defines a system as what is
distinguished as a system.
To establish a theory of general systems with
applicable results, Lin (1987) introduces the
following mathematical definition:
S = (M, R)
M: the set of objects of the system,
R a set of relations of the objects.
These relations in R make the system S appear.
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3. The Geometric Intuition
We need an extremely important tool:
A common language and intuition
which can be easily employed for
everyone to think about systems, to
manipulate abstract systems, and to
implement conclusions about general
systems to specific structures or
organizations.
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Why:
Modern science, the 1st dimension, mostly
makes use of numbers, quantities, and
parametric dimensions on the intuitive
background of Euclidean spaces, such as
Cartesian coordinate systems.
Because of this reason, modern science has
brought forward its greatness.
Here the common language: concept of
numbers and its abstraction
–
quantities
the common intuition: Euclidean spaces.
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Intuition for general/abstract systems
In 1990s, it is shown
1.Nonlinear evolution models = singularity
problems of mathematical blown

ups of
uneven formal evolutions
2. Nonlinear evolution models describe
mutual reactions of uneven structures of
materials
That is, nonlinearity is no longer a problem
of formal quantities.
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On blown

up theory, the concepts of black holes,
big bangs, and converging and diverging eddy
motions are coined together
(Wu and Lin, 2002)
:
Figure 1.1. Eddy motion model of a general system
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4. Application
:
The Rotten Kid Theorem
Becker’s Rotten Kid Theorem
(1974)
If a family
has a head who cares about all other members
so much that he transfers his resources to them
automatically, then any redistribution of the
head’s income among members of the
household would not affect the consumption of
any member, as long as the head continues to
contribute to all. Additionally, other members are
also motivated to maximize the family income
and consumption, even if their welfare depends
on their own consumption alone.
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Theorem
(Lin & Forrest, 2008)
Becker’s Rotten
Kid Theorem holds true, if and only if the
distribution of the benevolent head’s resources
is not in conflict with the consumption
preferences of any selfish member.
Figure 10.3. Interactions between benevolent head H and a selfish kid K
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Main references
All materials presented here can be found in the
following publications and references there:
Lin, Y. (1999). General Systems Theory: A
Mathematical Approach. New York: Kluwer
Academic and Plenum Publishers.
Lin, Y. (2008). Systemic Yoyos: Some Impacts of
the Second Dimension. New York: Auerbach
Publications, an imprint of Taylor and Francis.
Lin, Y., and OuYang, S. C. (2010). Irregularities
and Prediction of Major Disasters. New York:
Auerbach Publications, an imprint of Taylor and
Francis.
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