2010 5 5 General Systems Theory Jeffrey Forrest

8/13/2019 2010 5 5 General Systems Theory Jeffrey Forrest

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Brief Intro to General SystemsTheory 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 itsorganization, the customary investigation of individualparts and processes cannot provide a complete

explanation of the phenomenon of life. This investigationgives us no information about the coordination of partsand processes. Thus the chief task of biology must be todiscover the laws of biological systems (at all levels oforganization). We believe that the attempts to find afoundation at this theoretical level point at fundamental

changes in the world picture. This view, considered as amethod of investigation, we call organismic biologyand, as an attempt at an explanation, the system theoryof the organism.


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From this statement and seemingly

unsolvable problems in practice, such asprediction of zero-probability disastrous

weather conditions,

we see the concept of systems wasformally introduced.

As tested in the past 90 some years, this

concept has been widely accepted by theentire spectrum of science and technology


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Some of historical milestones:

1948, Norbert Wieners paper: Cybernetics or Controland Communication in the Animal and the Machine.

1954, Ludwig von Bertalanffy, Anatol Rapoport, RalphW. Gerard, Kenneth Boulding establish Society for the

Advancement of General Systems Theory, in 1956renamed to Society for General Systems Research.

1955, W. Ross Ashbys work: Introduction to Cybernetics

1968, Ludwig von Bertalanffys 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 becomesa 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 inindividual 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 beviewed as a genuine two-dimensional

science. With the added advantage of the

second dimensionthe systems science,we (Lin, 2009; 2010) can show some

important impacts of this second

dimension on the first dimensionthe

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 whatthey are supposed to do.


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Zadeh (1962): important problems insystems science:

Systems characteristics, systemsclassifications, systems identification,signal representation, signal classification,systems analysis, systems synthesis,systems control and programming,systems optimization, learning andadaptation, systems liability, stability, and

controllability.Main task of systems science: general

properties of systems without consideringtheir physical specifics


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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)

Aristotles whole is greater than the sum of

its parts

In modern times, new contents added to theancient 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 isdistinguished 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 foreveryone to think about systems, tomanipulate abstract systems, and to

implement conclusions about generalsystems to specific structures ororganizations.


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Why:

Modern science, the 1st dimension, mostlymakes use of numbers, quantities, andparametric dimensions on the intuitive

background of Euclidean spaces, such asCartesian coordinate systems.

Because of this reason, modern science hasbrought forward its greatness.

Here the common language: concept ofnumbers and its abstractionquantities

the common intuition: Euclidean spaces.


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Intuition for general/abstract systems

In 1990s, it is shown

1.Nonlinear evolution models = singularityproblems of mathematical blown-ups of

uneven formal evolutions2. Nonlinear evolution models describe

mutual reactions of uneven structures of

materialsThat 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

Beckers Rotten Kid Theorem(1974) If a familyhas a head who cares about all other membersso much that he transfers his resources to themautomatically, then any redistribution of theheads income among members of thehousehold would not affect the consumption ofany member, as long as the head continues tocontribute to all. Additionally, other members are

also motivated to maximize the family incomeand consumption, even if their welfare dependson their own consumption alone.


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Theorem (Lin & Forrest, 2008) Beckers Rotten

Kid Theorem holds true, if and only if the

distribution of the benevolent heads resourcesis 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 thefollowing publications and references there:

Lin, Y. (1999). General Systems Theory: AMathematical Approach. New York: Kluwer

Academic and Plenum Publishers.

Lin, Y. (2008). Systemic Yoyos: Some Impacts ofthe Second Dimension. New York: AuerbachPublications, an imprint of Taylor and Francis.

Lin, Y., and OuYang, S. C. (2010). Irregularitiesand Prediction of Major Disasters. New York:

Auerbach Publications, an imprint of Taylor and

Francis.


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Thank You

Documents

2010 5 5 General Systems Theory Jeffrey Forrest