In this paper the concepts of the chaos theory: bifurcation and amplification, nonlinearity, negative and positive feedback,
and attractors are used to explain the creation and operation of two different schools. Polish and Canadian scenarios are compared.
As ones creation was chaotic the other's was seren and calm. The process of creation of Polish School was dynamic and complex
under the influences of different types of attractors. It encountered "bifurcation points" that were leading to different futures.
It arose from a coupling of feedback springing from random individual activity. It was shown that when diverse individuals self-organize,
they were able to create high adaptable and resilient organization. High-leverage initiatives that could trigger a transition from one
attractor to another, the problem of "resistance" contra "new attractor", the challenge of maintaining stability and changes were illustrated.
The process of positive and negative feedback were broadly analyzed based on examples of Canadian School. The paper ends with discussion on
simplicity / complexity and the role of intermittency in lives of schools.
Introduction
Very often I feel as I live in chaos. At the moment when I find myself in a routine, I feel uncomfortable and I try to change something.
I feel great when I start something new and meet new people. At the University of Calgary I studied the nonlinear phenomena in plasma physics
and the theory of chaos. I tried to understand my personal and professional life based on this theory.
Chaos is about letting go, accepting limits,and celebrating magic and mystery. Chaos theory is actively being applied to everything from medicine to economics,
social dynamics, and theories about how organizations form and change. The creativity inherent in chaos suggests that actually living life requires something more
than only participation. It requires an aesthetic sense - a feeling for what fits, what is in harmony, what will grow and what will die. Making a pact with chaos
gives us the possibility of living not as a controllers of nature but as creative participators. Chaos theory shows us how apparently tiny and insignificant things
can end up playing a major role in the way things turn up. By paying attention to subtlety, we open ourselves to creative dimensions that make our lives deeper and
more harmonious [Briggs and Peat, 1998].
In this paper I have applied the chaos theory for analysis of creation and operation of two different schools. I have initiated both schools, but the process of creation and running them were
totally different.
1. River as a Chaotic System |
Systems that self-organize out of chaos survive only by staying open to constant flow through of energy and material. Vortices
in rivers and streams typically emerge out of the swirls of turbulence produced downstream from obstructions in a fast, deep current. Each vortex has a definite shape,
but is in reality composed of the material flowing through it. The idea of openess and the image of the vortex provide a good way to explore one of the most important of the many
paradoxes of chaos. In a vortex, a constantly flowing cell wall separates inside from outside. However, the wall itself is both inside and outside. The vortex suggests the paradox
that the individual is also the universal.
Turbulence arises because all the pieces of movement are connected to each other, any piece of the action depending on the other pieces, and the feedback between the pieces
producing still more pieces.
All concepts: bifurcation points, attractors, turbulence and feedback, will be used to explain the creation and operation of two schools.
2. Bifurcation and Amplification
At various times in our lives, we all experience moments of insight when we see or hear something that would be meaningless, nonsensical or trivial to someone else.
However, these moments create a significant change in our perception. They are like rocks in the river splitting flow and in the chaos theory we call them bifurcation points.
These moments of insight create an image that seems somehow important and becomes amplified in our minds. The image begins to couple our thoughts together
and some new context emerges[Briggs and Peat, 1990].
Polish Scenario of Creation School
Until 1989 in Poland only state - owned schools had existed, with the very small exception of the privately owned schools belonging to the church. After the change in political
situation in 1989, Poland has witnessed the emerging of private schools on all levels of education - from primary, through secondary, to the higher schools. There are two
types of the so-called non-public schools: private and social ones.
Taking advantage of this opportunity I decided to return to Poland an open a school.
The short article from a Polish newspaper, sent by my father about opportunities of openning private schools was a bifurcation point, which started all the action.
We moved back to Poland and I started to work on project. I contacted different people: my friends from Warsaw University, officials from Ministry of Education,
priests, parents of future students, teachers, and others. It was created a very strong network of people who started to be involved in this project.
From the chaos perspective, all activity in society and nature is a collective activity. Individuals are an indivisible part of whole. Chaos offers many insights into the
curious, paradoxical relationship between individual and group. Self-organized systems composed of individuals contain varying levels of complexity. Each level has evolved its own
"rules." Organization arises from coupling of feedback springing from random individual activity. Chaos shows that when diverse individuals self-organize, they
are able to create highly adaptable and resilient forms. As individuals - each with their own self-organized creativity - coupled together, some degree of freedom are
given up but other degrees are discovered. A new collective intelligence emerges [Morgan, 1996].
Roy Fairfield sees networking as a way of maintaining a low-level chaotic substrate so that - as in the brain - the chaos will from time to time give birth to an intellectual self-organizing
structure [Fairfield, 1977].
We have to prepare all documents for creation of society, for accreditation, hire teachers and administrative staff, prepare
entrance examinations, enroll students. We needed everything: location (building), furniture, equipment, books, blackboards,
and so on. We roared like a river in the spring. In the language of chaos theory, we created a complex system that was under
influence of different types of attractors. It encountered "bifurcation points" that were leading to different futures. In this case
the bifurcation points were the meetings of different groups of people. At these meetings different groups made decisions about
the future steps of the school. Members of Society of Friends of School Ark prepared all documents for registration of society and
getting an accreditation of the school. Parents of future students decided to prepare building for the school. They were responsible
for renovation and decoration of the building. The future teachers were responsible for choosing curricula and books and preparation
outlines for courses. Administrative staff decided to buy the furniture and equipment for school.
In chaos theory, at bifurcation points such as these meetings the energy within the system could self-organize through unpredictable leaps
into different system states. Bifurcation points and associated "attractors"always exist as latent potentials within any complex nonlinear system.
They signal potentials for self-organization and the evolution of new form. However, the path of system evolution is completely
unpredictable, because, given the complexity and nonlinearity, seemingly insignificant changes can fold to create large effects [Morgan, 1996].
The building for the school was in complete disarray, and it was expected that a construction company would need to be hired for renovation.
This project seemed to need at least half a year to finish. However, the energy and enthusiasm of most parents of future students changed the destiny
of the building completely. They were able organize themseves in teams and unexpectedly within two manths the job was done.
Like river, we found a way to be creative with what was available. From May to September 1990 we created our school: 140 students, 10 teachers,
principal and viceprincipal, secretary, and accountant. The process of creation was very chaotic, but we were able to create a complex and stable organization
like the vortex in the river.
Canadian Scenario of Creation School
In 1992 I came back to Calgary and decided to open a private international senior school. The process of creation was much less chaotic. I already
had good experience in creating schools. This time I prepared all documents for registration of non-profit company, accreditation from Alberta Education
by myself. I found the location, bought furniture, equipment and books. It took me half year of hard work. In June 1993 I got
an accreditation and I coud register the first students. The process of creation of this school reminds me of the serene and calm river.
3. Small Change Create Large Effects
A major implication of the chaos-complexity perspective, is that small but critical changes at critical times can trigger
major transforming effects.
By developing this idea, it follows that any person wishing to change the context in which they are operating should
search for "doable" high-leverage initiatives that can trigger a transition from one attractor to another.
Chaos theory also gives clear indications of where they should look for these initiatives. As will be recalled,
the tensions between competing attractors generate "bifurcation points" leading to different paths of future development.
Most often these manifest themselves as paradoxes or tensions between the status quo and alternative future states
[Briggs and Peat, 1996].
For example, in Polish scenario, the drive toward the openning of non-public schools may generate all kinds of oppositions from the status quo.
For example, government officials or some teachers may feel that non-public schools will lead to "poorer quality of teaching," "business approach to schools,"
"less control," and "loss of powetr." Normally these fears and concerns will generate actions seeking to reinforce
the current situation. The chaos manager must recognize these "forks in the road" and create a context supporting the
new line of development by finding interventions that transcend the paradoxes or make them irrelevant.
4. Negative and Positive Feedback
In chaotic system, everything is connected, through negative and positive feedback. "Negative feedback" is the type that keeps things in check.
"Positive feedback" pushes systems to explode or spiral out of control. Feedback is the instrument of new life. One of the most important discoveries
in chaos theory has been that positive feedback can cause complex, even chaotic behavior concealed inside orderly system
to unfold, and that negative feedback can grow inside an otherwise chaotic system, suddenly organizing it and making it stable.
The theory of chaos and complexity encourage us to understand how change unfolds through circular patterns of interaction.
This requires that we think about changes in terms of loops rather than lines. Processes of negative feedback, where change
in a variable initiate counteracting forces leading to changes in the opposite direction, are important in accounting for
the stability of systems. Processes characterized by positive feedback, where more leads to more and less to less, are
important in accounting for ascalating patterns of system change. Together, these feedback mechanisms can explain why systems
gain or preserve a given form and how this form can be elaborated and transformed over time [Maruyama, 1982].
To illustrate this process, I give an example from our international school in Calgary. One year, our teacher for English 30
was very lenient. She attracted a lot of new students for the night class. This was positive feedback. The provincial exams have
shown that the differences between school mark and exams were more than 30% on average. We had trouble with Alberta Education Ministry.
We have to change the approach to awarding grades and the prerequisite for this class. as a result, negative feedback loops are
created and the students flow pattern became organized and stable.
The complex and chaotic systems which means most of the systems we encounter in nature an in society, cannot accurately be predicted
or exclusively controlled. Chaos tells us that each one of us has an unrecognized but enormous influence on the feedback loops.
An important implication of chaos-complexity perspectives rests in the idea that the fundamental role of managers is to shape
and cretae "context" in which appropriate forms of self-organization can occur. Managers have to become skilled in helping to shape the parameters
that can define an appropriate context, while allowing the details to unfold within this frame. In this way, they can help to shape emergent processes
of self-organization, while avoiding the trap of imposing too much control. The focus on attractor patterns thus creates a powerful
perspective for the management of stability and the management of change, suggesting that transformational change ultimately
involves the creation of "new contexts" that can break the hold of dominant attractor patterns in favor of new ones [Morgan, 1996].
To illustrate the challenge of mainating stability, I would like to show a case of my internationl school. The challenge is
to create a relatively stable space within which teachers are able to perform their job. The context is bombarded by all kinds
of random influences: students are coming from different countries, from different educational systems, with different ages (from 10 to 50 or more years old),
with knowledge of English on different levels, unexpected changes of staff, unexpected group of visitors, difficulties in bringing
students to Canada (difficulties with getting student visas). The challenge is to hold such situation under the influence of a strong
attractor pattern that minimizes distrupting influences, so that the teachers can teach effectively. In other situations where the
dominant attractor pattern is sustaining an undesirable state, the challenge will be to open the door to instability, or even to create the instability
that will help a new pattern of behavior emerge. Consider the hiring of inflexible teachers who are not able to cope with changing
number of students in class through semester, with different levels of their ability. They will try to impose traditional methods
of teaching which make students unhappy and unsatisfied. To break the power of the established attractor we will have to find ways
of creating a new context. One strategy may be to transform the mindsets of teachers by showing the realities. Another way may be
to change the teachers.
It is important to note that the manager acting on the insights of chaos and complexity theory cannot be in control of the change. He or she
cannot define the precise form that the new attractor pattern will take. The important point is that the manager helps to create
the conditions under which the new context can emerge. To the extent that the system remains locked into the old context, no
significant change is possible.
As chaos writer Jeffrey Goldstein has noted, much of the literature on organizational change has focused on the problem of "resistance,"
instead of focusing on how new "attractors" can "pull" the latent energies of a system to a point where they can organize into a new form.
Resistance arises when the forces of an established attractor are more powerful than those of a new or emergent one. The challenge
is to shift the balance. New context can also be created by engaging in new actions that help to push the system into a new state.
Experiments, changes in the staff of teachers and administrators, new programs, and numerous other events, actions, and experiences
can themselves embody powerful messages that catalyze other changes in the context as the system adjusts itself to the new reality.
The generation of new understanding and new actions, in whatever order they evolve, are the keys to contextual change [Goldstein, 1994].
Positive Feedback
Magorah Maruyama has developed the loop analysis, showing how positive feedback accounts for the differentiation of
complex systems.
For example, one student was attracted to our international school. He registered for the full time program. Other students followed,
they asked about other programs like TOEFL preparation courses or computer courses. Because of their interest we started to offer more courses,
hence more students enrolled. Adult students asked about academic programs funded by government. We prepared the proposals and soon the programs were
offered. A group of adult students signed up. Parents asked for tutoring of mathematics and science. A tutoring center was created. Students and teachers
were asking for ESL books, a bookstore was opened.
In the process, the empty space has been transformed by series of positive feedback loops that amplify the effects of the initial differentiation.
Maruyama argues that this kind of process explains the evolution of both nature and society, processes of positive feedback
producing changes that are quite out of proportion with the initial "kick" or incident that activates them. As in the case of the "butterfly effect,"
small changes can produce large effects. Initial kicks of high probability (e.g. preparation of school (location and formalities)) can escalate to
produce deviations that have a very low probability (e.g. that a particular student or group of students will enroll).
Accidental events and connections in social life, given favorable circumstances, initiate open-ended processes of self-organization in which positive
and negative feedback interact to produce changing patterns that may at some point assume relatively stable forms [Maruyama, 1982].
Peter Senge shows that many systems tend to be inherently unstable because of delayed feedback and response between
elements, which leads people to underplay or exaggerate their behaviors. Other systems may constantly hit constraints that
prevent full development. And yet in other systems, positive feedback loops may be escalating and driving a system into a destructive
state. It is found in the dynamics of many social and corporate welfare systems and in the way individuals and organizations plunder
long-term benefits for short-term gains. Solutions depend on the development of shared understanding of the problem, and an ability
to reframe system dynamics so that short-term individual interest and long-term sustainability and development become more
balanced and integrated. The complexity of most social systems is such that the analysis can rarely be complete because
the problem or focus with which one starts often ends up being part of a larger problem requiring a broader focus.
Instead of thinking about problems mechanistically and trying to manipulate linear "causes" and "effects," it encourages
us to develop mind-sets and skills that focus on recognizing and changing patterns. It provides a methodology for analyzing
a system's "attractor patterns" and changing their trajectory. It provides further insights on how small changes can create
large effects. The newly formed organizations often have a flexible, searching, chaotic quality. In the case of a business, this
chaotic quality may allow it to burst successfully onto the commercial stage. However, after a time the organization falls prey
to the grip of the standard "good business" assumptions and begins to petrify. Eventually, competition, hierarchy, and power begin
to dominate the organization's activity. Negative feedback loops controlling the way things are done become reinforced, and
soon the organization's strange attractor is reduced to a limit cycle [Senge,1990].
This process happened in our polish school. There were so many negative feedbacks that from the chaotic system changed
to the rigid limit cycle. I was not able to continue to work in this environment.
Simple and Complex
Chaos reveals that what looks increadibly complicated may have a simple origin, while surface simplicity may conceal something
stunning complex. For example society is a relatively simple and stable form that emerges out of the complex dreams, desires,
and contributions of its members. A healthy society draws upon the energy and creativity of its members and at the same time provides
them with values, ethics, and a shared sense of meaning. Whenever interactions, iterations, and feedback are at work, simplicity
and complexity constantly transform into one another. The situation becomes particularly striking when the simplicity and complexity
alternates in what scientists call intermittency. Many societies give intermittency an explicit role. It usually goes
under the name of carnival or fiesta, an outburst of happy, creative chaos. Such burst of chaos allows the good order of society
to continue throughout the rest of the year. Such societies understand a simple but comlex truth that underlying the chaos of
carnival is the renewal of important feedback loops that hold society together [Briggs and Peat, 1998].
Similarly, in both schools, I found that small distractions in the school instruction routine like field trips, potluck
parties, teacher and students birthday parties, and thematical activities give a large burst of energy and improve relations in the school.
Sometimes chaos also bursts, uninvited, into our lives and can result in renewal or transformation. An irrational act, striking dream, or
unfortunate coincidence challenges the normal order of our lives by asking us to give more attention to its nuances and subtle
patterns [Briggs and Peat, 1998].
Chaos theory's answer is that complexity and simplicity are not so much inherent in objects themselves, but in the way things
interact with each other, and we, in turn, interact with them.
Conclusion
In this paper I analyzed the creation and operationof two different schools. As ones creation was chaotic the other's was seren and calm.
However the reverse is true for process of running of the two schools. The creation of the Polish School was very dynamic - chaotic. A lot
of people were involved (friends, officials from Ministry of Education, parents, teachers, priest, memebers of society). There were three
stages of creation and many bifurcation points. On the other hand the running of the school was not so chaotic. Registration of students
was once per year. Students were accepted to the school in grade nine and continue for four years. The students population
was monolithic and very rarely changed. All students took the same courses and were divided into eight classes of 20 students.
Teachers were hired for long periods of time. Introducing small changes, like new policy of hiring teachers, new curricula created a great
resistance. I was not able to fight, and only solution I saw was the move to the new environment.
In the Canadian School the process of creation was very straightforward, but it was able to to produce a very dynamic system.
We had a large and divergent flow of students. They arrived and started studying at a continuous basis. I prepared a very flexible program
for the students. For example, students with a weak knowledge of English could start high school part time while still learning English as
a second language full time. Other students, especially adult students, could take only necessary courses to continue their post-secondary
education. The school was very sensitive to the needs of students. For instance, new courses could be organized within a short time frame.
Hence there was great variety of choices for students, like ESL program, high school, academic apgrading program, independent study, study tour etc.
On regular basis the monotony of instruction was interupted with different activities, which enhance the school culture and community.
Reference
1. Briggs, John. (1992). Fractals, The Pattern of Chaos. A Touchstone Book.
2. Briggs, John and Peat, F. David. (1990). Turbulent Mirror. Harper & Row, Publishers, New York.
3. Briggs, John and Peat, F. David. (1998). Seven Life Lessons of Chaos, Timless Wisdom From The Science of Change. Harper
Collins Publishers.
4. Fairfield, Roy. (1977) Person-Centered Graduate Education. Buffalo: Prometheus.
5. Gardner, J.W. (1986). "The Tasks of Leadership." Leadership Papers No.2. Washington, D.C. Independent sector, March 1986.
6. Goldstein, J. (1994). The Unshackled Organizations. Portland, or: Productivity Press.
7. Maruyama, M, "The Second Cybernetics: Deviation Amplifying Mutual Casual Processes." American Scientist, 51: 164-179, 1963.
8. Maruyama, M. "Mindscapes, Management, Business Policy, and Public Policy." Academy of Management Review, 7: 612-619, 1982.
9. Morgan, Gareth. (1996). Images of Organization. Sage Publications.
10. Senge, Peter. (1990) The Fifth Discipline. New York: Doubleday.
Back to Top