CHAOS THEORY AND SYSTEMIC DYNAMICS IN EDUCATIONS
Professor Djordje Nadrljanski, PhD
University of Split
Mila Nadrljanski, PhD - docent
University of Split
Marko Tomašević, PhD
University of Split
Apstract
Chaos theory ought to be comprehended as very important for social dynamical field. It gives a new, a little bit twisted perspective to the notion of complexity and holistic reflection. The analysing of nonlinear system conduct is like walking through labyrinth whose walls are moving with every step (in other words, playing a game changes it). The systems precomplex for traditional mathematics can be studied with simple laws, e.g. fractal geometry and fuzzy logic. Complexity laws hang on hierarchial scale (scalar, self – resemblance) and they are not caused by the conduct of constituing parts. It is less probably that one can explain conduct of parts studying entirety conduct.
Key words: Chaos theory, Education, Systemic dynamics
1
New time understanding comes to the comprehension that time is not really defined by clock, but by rhythm and iterations. Four sorts of attractors define the nature of patterns:
· Dotted attractor (attracted or rejected by certain activity)
· Cyclical attractor (organised among one or many activities)
· Torus attractor (organised complexity that repeats)
· Strange attractor (unpredictable complex patterns appear through certain time).
When chaos theory is used in social context, four contractors, observed from perspective, can be explained with the next:
· Dotted attractors (dichotomy/one-way direction) present behaviour of social beings in search for their natural instincts fear, love hatred, desire for division or self-interest.
· Cyclical attractors (dialectic/self-preserved) would refer onto the principle of multidimensionality, search for openly opposite but complementary tendencies: stability and change, safety and freedom, and even differention and integration. Cyclical or periodical emphasis from one orientation to another, is the result of suboptimism.
· Torus attractors (equally final/negatively-entropical/aim searchers) reflect behaviour of socially cultural systems with choice of outcomes and means; unpredictable patterns come out of stylistic aptitudes of appropriate factors.
Education is being performed more in surroundings of constant changes and uncertainties. Fact development of new technologies, changeability of structures and conditions, information accessibility, are only some of factors that intensify changes in educational surroundings that becomes more complex and dynamic. Faster reaction of education system on changes is claimed, time together with information becomes key factor for successfulness. In order to react on changes quickly and efficiently, education system must be able to foresee what will happen next year, and the very fact that education is being performed in changeable surroundings, makes it yet more difficult, and even makes it impossible.
Ten years ago it was relatively easy to predict what would happen if education was led on the right track, desired results would be realised. Meanwhile, it is today in doubt and more difficult to be done. Exactly here appears the need for redefining traditional concepts of controlling and inventing new ones. To this effect nowadays in the world are more being used the knowledge and achievements of deterministic chaos theory, the science although relatively young one, gives high and original contribution. Chaos theory had originated and has developed at first in natural sciences, just in the field of physics and meteorology, and after that is being applied in biology, chemistry, medicine and during the last 10-12 years more and more goes through researches of organisation and education. It is a multidisciplinary science that changes the way of observing and comprehending the world, discovers new legalities and universal behaviours that cross limits of various scientific fields. As the systems studied by chaos theory are unpredictable and seemingly chaotic, in other words act as it is impossible to find order in them, one of central concepts is the strengthening of total conduct of the system, instead of the strengthening of the precise state.
The basis feature of chaotic systems is fine sensitivity in starting conditions where quite little input change may cause great changes in output value. It is known in literature entitled ”Butterfly’s effect“ and it may be expressed already by undoubtedly known words “The butterfly in China flies up from a flower, and next week the sky in Split becomes overcast.“ There are two substantial elements in deterministic chaos; attractors and fractals. Attractors present an area in field of results toward which system dynamics is directed. Attractors enable transforming seemingly unexpected data into noticeable data, i.e. they present results model of system conduct. Their size and form depend on key parameters and dynamics to which system is by such parameters directed. Key parameter is any factor influencing system conduct. The most famous attractor is Loren’s attractor presented in the picture number 1.
Picture 1. Loren’s attractor
Another important element is fractal, which is defined as irregular geometrical form. Fractals are significant for chaos theory, because the very conduct of chaotic systems is founded on fractal geometry, which one, in contrast to the traditional Euclid’s geometry, deals with the description of irregular forms in nature, which ones are more numerous than regular and linear forms.
Significant fractal characteristic is its self-resemblance, that indicates that fractal will look, almost, even completely identically, no matter in what size or proportion it is observed, as it can be seen in the picture 2, where is presented the fractal form of snowdrop, than fractal dimension which is not integer, but fraction.
Picture 2. Fractal appearance
Fractals are used for organizational structure forming, so in literature are already being cited new forms of organization called fractal organization, which is one of substantial forms of education adjustment to changes in surroundings. Often is raised the question of significance of chaos theory for self-education, and how at all the theory, whose origins are based on physical systems, can be applied on education. The chaos theory in fact raises the question of traditional ways of understanding and education control. According to such concept education is a system that requires unyielding check up. Meanwhile, it is a part of mechanistic and deterministic view on the world which was in power up to the beginning of the 20th century, when begin doubts in determinism, so then appear new theories and knowledge, and among them as well chaos theory.
In this way, in traditional manner comprehended, education is inert, slowly reacts on changes and it may badly be adapted to incentives coming from complex and chaotic surroundings. The very application of chaos theory to education would not remain on pure assumptions, there are cited education characteristics identified by chaos researchers and practitioners, and which are analogous to the ones in complex physical systems, what has enabled theory chaos application onto education. Those characteristics are:
1. Non – linearity
2. Non – predictability
3. Interdependency
4. Synergetic conduct
5. Autopoesis
6. Limits
7. Reversed connections
8. Self organisation
Chaos theory enables better understanding of operations of organisation. Applying its concepts education prepares itself for fast reaction in view of the changes in extern surroundings. Its signification reflects in the identification of key parameters directing system from one dynamic state into another, it takes care of unpredicted circumstances and supports assimilation of flexible strategies for unexpected events. It is considerably to emphasize that the modification of the education aims is beforehand foreseen, so it does not cause shocks and surprises. Substantial characteristics of management in chaotic conditions are early identification of events, fact answer with mix of strategy and acceptance of the uncertainty in which education takes place. Understanding of events dynamics enables consideration about actions and consequences coming from it.
During defining of management conception one ought to respect some rules substantial for chaotic systems, and they are as follows:
· Managers ought to give attention to communication at all levels in education
· Little changes can cause great effects in chaotic conditions
· Unforeseeable and unexpected characteristics can be expected in systems
Using positive feed-back, education receives information from surroundings about state in surroundings, so it sets up field of order by control over events or changes. Because of feature of educational surroundings, on account of faster adjustment, the very education must be changed, so there appears the need for strengthening of surroundings that learns.
Systemic dynamics
System conduct, especially the conduct of complex dynamic social and natural systems is already fifty years the object of research of the method known as System Dynamics. The method has developed in case of the need for better understanding and control of the system with feed-back, primarily of social systems, i.e. better understanding of changes in system and possibilities of influence on factors that cause changes through time and get to successfulness, in other words unsuccessfulness of certain system. The first systems studied with the help of systemic dynamics, were business systems, so the systemic dynamics was in the beginning considered as managerial discipline. The originator of that method was Jay Forrester. As a manager of various projects and member of management in different companies, he has observed that basical obstructions for company progress do not come from method or means of work, but from politics and decisions made by management on the basic of feed-back information. Feed-back information coming from environment and from system conduct. It is a cyclical process in which decision is result of change, and change again influences on decisions that will be made later. Decision that solves a certain problem in company is based on politics of that company, which then directs company toward success or failure.
· Systemic dynamics has a great part in understanding influences of various politics on system conduct because it enables creating computer models which simulate system conduct in view of the applied politics.
· On the basis of logical simulatory model of dynamical system, it is possible to put certain mathematical equitations and with their help to present arithmetically and graphically system movement in future.
The using of simulatory models in discovering consequences of conduct of certain system, has stimulated Forrester and his followers to research also other dynamic systems except business ones. Nowadays systemic dynamics applies in various fields as ecology, micro and macro economy, medicine, engineering, researches of social trends, education etc.
Short history of systemic dynamics
Systemic dynamics as a new methodology of modelling complex dynamic systems appeared in the middle of the fifties of the twentieth century, and is connected with the works of professor Joy Forrester from Massachusetts Institute of Technology. Forrester was then interceded with several projects connected with testing army equipment (supervisory mechanisms, flying simulators), so as a member of management observed that the problems with projects are not exclusively of engineering nature, but that they come from politics set by management itself. Forrester published the book „Industrial Dynamics“ in 1961. He had presented in it the basis of systemic dynamics and its use in solving business-management problems. A little later he observed that that method can be applied also in other fields, for example in system as town, so he presented in the book „Urban Dynamics“ how the strategy of town development can influence solving different problems. Forrester had been researching during last twenty years two fields:
· Forming economy model of U.S.A with the help of systemic dynamics and
· Applying systemic dynamics in school system (from kindergarten to faculty)
Basic notions of systemic dynamics
Systemic dynamics is a methodology that combines theory, philosophy and methods for analysis and management of conduct in complex systems with feed – back, such as business and other social systems. Feed – back supposes that an activity X results by activity Y which again influences upon X etc. It is erroneously to observe independently and linearly the connection between X and Y, as well between Y and X, but it is necessary to observe the whole system as a cyclic feed – back loop, so that system conduct could be predicted. The world around us is not linear, it is cyclical. Man lives in surroundings where a state leads to decision making that causes changes and brings to a new state on which basis he makes new decisions. It can be graphically presented by cyclic feed – back loop as it is in the picture 3.
Picture 3. Cyclic feedback loop
Systemic dynamics as methodology used for apprehension of system conduct supposes construction of simulatory model of dynamical system through the next steps:
· problem identification – defining of the point for system observation, defining system limit, aim of model, etc.
· system conceptualization – strengthening of elements and structure of system, diagram making, setting dynamical hypotheses that explain cause of problem,
· model formalisation – building computer simulatory model of system that presents essence of problem.
· analysis of model conduct – testing of model that ought to copy conduct of real system,
· evaluation and validation of model, as well testing of alternative problem solutions,
· model application
Systemic dynamics methodology
Systemic dynamics is based on System Thinking concept. Systemic thinking enables observing system structures, so that system conduct could be understood, but it does not imply building a simulatory model. Modelling of system structural enables system dynamics. System structure includes four hierarchical components.
· System limits – limits have to be defined so to include only those elements that cause certain system conduct
· Cyclic feed – back loop as basic system presentation – system conduct is defined by elements structure in closed loop; feed – back loop is responsible for changes in structure during course of time.
· Levels and rates – within system there are levels or states and rates or changes of state. Levels or states present quantity of an element, e. g. number of employees, and level of water in water tank, etc. feet or rates present unit of change of state (increasing or decreasing of level).