CIRCLET 1: SCIENCE OF COMPLEXITY AS A STEP INTO
MODEST RE-ENCHANTMENT
A Crazy Pendulum Swings into the
Mystery of Chaos
A new paradigm we are seeing emerge from insights of chaos theory requires
of us nothing less then a brand new start in the description of nature
- a start which will affect our metaphysics and our physics, our cosmology
as well as our logic.49
(William Doll)
Pendulums are strange creatures. They like to swing backward and forward,
to and fro, pro and con. In the idealized abstract mathematical universe,
their movement is always rhythmic and always repetitive. There is not
much mystery around a pendulum's linear and predictable behaviour. No
surprises. If you measure just two variables, angle and velocity, you
can easily calculate their trajectories at any given moment. In the real
settings, forces of friction usually bring unwanted complications, but
you can neglect them for your convenience, reducing, and as such, idealizing
a swinging pendulum into a simple, predictable, and calculable system.
The behaviour of a real pendulum remains rhythmic and periodic, even though
stubborn friction forces eventually slow it down. For instance, when placed
between two magnets, a pendulum rhythmically moves back and forward, to
and fro.
The picture changes dramatically when a pendulum is forced to move between
three magnets. In this case, a mystery comes into play and possibilities
for reducing a pendulum into a simple system become questionable. When
you push a pendulum only slightly, it swings repetitively and regularly,
periodically attending each set of two magnets. Under a stronger push,
however, the pendulum exhibits a strange behavior. Being perhaps offended
by such impolite action as a push and feeling perhaps completely out of
equilibrium, a pendulum seemingly loses its mind, starting to swing wildly
and chaotically between the three magnets. It moves without any apparent
rhythm or particular direction: the previously regular behavior of the
pendulum is now chaotic.
Under such conditions, do not even try to predict its trajectory of movement.
The trajectories of a chaotically swinging pendulum never repeat themselves.
However, seemingly chaotic behavior of a pendulum is not as random as
it seems to be. Pushed out of equilibrium, a pendulum swings into an intriguing
space where randomness and order shake their hands. As a symbol of interplay
between order and randomness, a strikingly beautiful and complex pattern
emerges out of the chaotic trajectories of a single point. It looks like
a butterfly with stretched wings. The existence of this pattern indicates
that trajectories of a single point are not repeatable and not predictable,
yet are restricted and bounded by a complex shape. Increasingly explored,
behaviors of other chaotic systems reveal various shapes of patterns,
but a chaotic butterfly remains a symbol of a cunning chaos that cannot
be understood as a simple and unpretentious disorder. This complex pattern,
the chaotic butterfly, resembles a mysterious mask. Is it simply a coincidence
or is it a hint that playful chaos likes to hide its true ordered nature?
The butterfly's metaphoric involvement in chaotic endeavors is not limited
to the shape of a complex pattern. A butterfly effect is a poetic metaphor
for the interesting property of chaotic systems to produce far-reaching,
widely varying, and unpredictable responses under small initial changes.
What could be more minor and innocent than the flap of a butterfly wing?
Chaotic systems, however, behave in such a manner as if a butterfly's
flap of a wing can generate storms, tornadoes, and hurricanes on distant
planets. Oh, butterfly, butterfly, these chaotic systems are quite strange,
aren't they? This is why their chaotic attractors are called strange.
What is an attractor? Writes Isabelle Stengers:
An attractor is a stationary state or regime toward which an evolution
described by the well-determined system of equations leads. Usually, an
attractor is stable: different sets of different initial conditions determine
evolution toward the same attractor (for example, a state of thermodynamic
equilibrium, the immobile state of a real pendulum, from which one has
not abstracted friction; or limited cycle). Once this attractor has been
reached, the system will no longer spontaneously depart from it, fluctuations
aside. Strange attractors, on the other hand, do not have this property
or stability. Two neighbouring initial conditions can generate very different
evolutions. The slightest perturbation can push the system from one regime
into a very different one. Instead of stabilizing into a predictable and
well-determined state, the system wanders between possibilities; in other
words, although governed by deterministic equations, it adopts an aleatory
behavior.50
A Chaotic Butterfly Flies into the Science of Complexity
The science of complexity was born when the study of chaos moved deeper
into real-world situations. What a surprise: chaotic properties are intrinsic
to natural phenomena.
The real-world chaotic systems, just as abstract mathematical chaotic
ones, evolve toward strange attractors, managing to survive in the world
of chaotic butterflies, in this intriguing space in-between. This space
is twilight, where day and night kiss each other; it is an ambiguous maybe
that escapes the certainties of yes or no. This space is the creative
and risky edge of chaos, where order and randomness co-exist. Imagine
whirlpools and vortexes that suddenly appear and disappear in the running
river. They maintain structured shapes within a never-stopping chaotic
flow of water, following therefore the rule of the chaotic butterfly,
which is bounded randomness. Real-world manifestations of abstract chaotic
systems are called complex systems. Indeed, you need to be sophisticated
and complex to manage survival on the edge of chaos, to maintain structure
within randomness, to preserve permanence within constant flux. Naturally,
it makes you unstable, sensitive to even slight changes in conditions,
and dependent on numerous variables.
Complexity is a staggering number of critical dependencies
and interactions among the huge number of important variables.51
It is not so easy to depend on everything, you know. Under such stressful
conditions you are entitled to exhibit nonlinear and unpredictable behavior.
As is increasingly understood, an unstable attitude is natural to the
majority of world phenomena. "The macroscopic world abounds with
complex processes and systems. Religious rites and ephemeral emotions,
musical musings and muddy meadows, global stock market crashes and wet
Sunday afternoons. This complexity is intrinsic to nature."52
In recent years, weather forecasting, fluid mechanics, chemistry, astrophysics,
economy, population biology, and brain research provide abundant data
for exploring unpredictable, dynamic, chaotic behavior. Models for chaotically
behaving systems are based on nonlinear equations with multiple, complex,
and often unexpected solutions. Solving nonlinear equations became possible
only recently with the development of a powerful computer technology.
This is not surprising since millions of numbers are entered into nonlinear
equations describing a complex problem.
If complexity is intrinsic to nature, this means that mechanistic science
simply missed a point by creating an idealized scientific world, while
collapsing all complex natural phenomena into simple predictable systems
and eliminating all but a few variables within experimental designs. Simplicity
was the motto and seduction of reductionist science, but the real world
turned out to be more unpredictable, more chaotic, and more complex than
we imagined while residing in a mechanistic universe. Intricate markings
on a butterfly's wings, shapes of snowflakes, rhythms of our hearts, the
collaboration of nerve cells within our brains, turbulently running top
water, the functioning of our body, the dynamics of ecosystems, complex
societies, swirling galaxies, and all-embracing Cosmos; there is no shortage
of ever-increasing complexity in our ever-evolving world. But how can
it happen?
The Magic of Self-Organization
Imagine the experiment.53
The liquid in a container is placed between cold and hot plates. When
the temperature gradient between plates is small, nothing observable happens.
The system is quite uniform, symmetrical, and stable. The system liquid
in the container is in the state near equilibrium. When the temperature
gradient is increased, the system moves further and further from equilibrium,
finally reaching so-called bifurcation point where thermal convection
suddenly shapes into a striking organized pattern of hexagonal cells.
These cells are formed through the synchronized movement of millions of
particles. A new order of organization jumps spontaneously into existence.
Such a process illustrates an amazing correlation between a huge number
of particles. "Everything happens as if each volume element was watching
the behavior of its neighbors and was taking it into account, so as to
play its own role adequately and to participate in the overall pattern."54
Enchanted by phenomena of spontaneous self-organization, the Nobel Laureate
chemist Illia Prigogine developed the theory of dissipative structures.55
He noticed that a new order of self-organization emerges only when the
system is open56 and exists in a far from equilibrium state, where matter
and energy flow as a boiling mountain river. The faster the river flows,
the further the complex system shifts from the equilibrium. At a bifurcation
point, the system reaches instability and spontaneously transforms itself
into a new structure with increased complexity.57
There is always an element of the unpredictable in the dynamic realm of
bifurcation points. When reaching this point, the system chooses the chaotic
attractor to be drawn to, deciding on what path to take among several
possibilities. The choice cannot be exactly predicted, as it actualizes
within the complex interplay of the history of the system, multiple histories
of related systems, and environmental conditions. Recognizing the inherent
unpredictability of chaotic behavior enables us to break a circle of sufficient
reason, since it constituted the ideal of a complete definition, which
lets nothing escape.
In The End of Certainty: Time, Chaos, and New Laws of Nature, Prigogine
says that acceptance of unpredictability in science means acceptance of
a new kind of knowledge that overcomes the prejudice of determinism and
leads us to novelty.
Confession
as a highly improbable
open
complex
self-organizing
system
I confess
that I have absolutely no clue
how in the world I manage to maintain
my highly ordered physical structure
at the edge of chaos
A truly fascinating aspect of the self-organization phenomenon is interrelatedness
of parts in the system. For instance, spontaneous emergence of complex
and structured patterns in water under the gradient of temperatures requires
billions of particles to communicate. If particles were randomly moving
mindless balls, how then could they act so collaboratively? How would
they know how? As Prigogine notes, self-organization leads to coherence,
to effects that encompass billions and billions of particles. Figuratively
speaking, matter at equilibrium, with no arrow of time, is blind, but
with the arrow of time, it begins to see.58
The ability of inanimate matter to see sounds like re-enchantment to
me. For so many years I taught science which portrayed matter as inherently
passive and ultimately blind. Self-organization occurs everywhere, from
the very small to the very large, from atoms organizing themselves into
molecules, to galaxies gathering into clusters. It is happening through
total interrelatedness of everything: "trees with climates, people
with the environment, societies with each other. We no longer stand alone.
Nothing does."59
This new understanding is re-enchanting.
Re-Enchanting Dimensions of the
Science of Complexity
The science of complexity is still very young, but it already offers
an astonishing "opportunity to stand back and consider the global
interactions of fundamental units: atoms, elementary particles, genes
- to create a synthesis that crosses the border of scientific disciplines,
to see a grand vision of nature."60
This new grand vision
re-enchants the world.
Indeed, the realization that our reality is irreducibly complex, self-organizing,
often unpredictable, and intricately interrelated is re-enchantment. Retrieved
from an abstract mechanistic spell of simplicity, determinism, and reductionism,
the real world of oceans, ecosystems, exploding stars, swirling galaxies,
human brains, bacteria, economies, and atoms gradually emerges today as
a beautiful butterfly. It emerges along with all its pulsations, nonlinearity,
messiness, fuzziness, turbulence, irregularity, novelty, surprise, adaptation,
multiple choices, instability, nonpredictability, irreversibility, and
creativity. This world until now "slipped through the meshes of the
scientific method."61
This new vision re-enchants the human approach to Nature from domination
and control to respect, cooperation, and dialogue. Science of complexity
develops systemic thinking, the increasing awareness of the total interconnectedness
of all systems in the world. This awareness brings forth questions of
moral responsibility for actions and of the price to be paid for simplistic
and abusive treatment of Nature. Thinking about the risks of human-made
chaotic complexities and about the consequences of creating new, polluting
and destroying butterflies is definitely re-enchantment.62
Swinging away from the mechanistic world, the pendulum of our vision
of reality enters the edge of chaos, the magic land of the possible and
the unexpected, the twilight zone of interplay between flux and permanence,
randomness and structure, chance and necessity, fluctuations and deterministic
laws, stillness and motion, time arrested and time passing, being and
becoming.
Deportation from the static and unchangeable reality toward the dynamic
realm of the edge of chaos introduces creativity as an inherent quality
of Nature. Prigogine writes that understanding of human creativity and
innovation as the amplification of laws of nature already present in physics
and chemistry bridges nature and culture. Discovering irreversibility,
instability, turbulence, risks, bifurcations, and creativity within the
very processes of births or deaths of galaxies and stars is definitely
re-enchantment because it is this instability of trajectories, these bifurcations
together with the bifurcations and creative risks in our lives, that are
today a source of inspiration to us.63
At this note, while drawing inspiration from a newborn blue star and
recognizing that my own creativity is a part of the universal creativity,
I will imagine into existence elements of science education that take
steps into re-enchanting dimensions of the science of complexity.
in a dramatic moment
when the unimagined is imagined
a sudden breath of possibility
stops us mid-step
we breath-dance
unexpected journey-landscapes into being
and in the space-moment of dance
recognize absence
embodied in our choreography-geography
on the edge of chaos
and are momentarily awed.64
In the meantime, I will make myself a cup of coffee and look around, admiring
all complexities of life...
The Chaotic Attract/or/iveness
of the Self-Organizing Curriculum and Pedagogy
If postmodern pedagogy is to emerge,
I predict it will center around the concept of self-organization.65
Multiple contributors to the book Learning
as Self-Organization, edited by Karl Pribram and Joseph King, stated
that the very nature of learning is the process of self-organization.66
As the flight of a chaotic butterfly goes from one pattern of organization
to another, learning occurs as a never-ending journey, from one newborn
meaning to another.
Learning as a non-linear flight of a chaotic butterfly seems to be a
reasonable metaphorical definition to me. It reconciles fluidity of information
and experiences with ever-evolving and ever-re-forming structured patterns
of knowing. According to the science of complexity, self-organizing processes
are deeply embedded in nature. If so, nonlinear self-organization appears
to provide a more natural basis for learning than artificial linear determinism.
Recently, various researchers attempted to conceptualize the dynamic and
nonlinear nature of learning and teaching on the basis of theory complexity,
advocating a self-organizing curriculum and pedagogy.67
Self-organization is related to:
dancing at the edge of chaos
perturbation
strange fractal chaotic attractors
adaptation
sensitivity to slight changes
ambiguity
nonlinearity
irreversibility
spontaneous emergence
ultimate interconnectedness
the whole more than the sum of parts
transformation open endedness
As Coveney & Highfield suggest, associative memories provide illustration
of self-organizing processes. Using the language of attractors, such associative
memories occur when the basin of attraction for a piece of music is shared
with one linked with a lover, perhaps caused by recollections of a passionate
embrace enjoyed on the dance floor. The attracting memory state contains
a representation of both song and lover.68 My thinking about self-organization
in education attracted certain memories, which, in turn, self-organized
themselves into a vivid picture.
Days of the Physical Science in an Elementary Schools Course
(A soap opera)
I am in the classroom. It is the last day and actually, the very last
moment of the course. I just wished my student teachers all the best and
now I am watching them leave the class in silence and disappointment,
without even the usual polite thank you or good-bye. It was three years
ago, but even today I cannot help but feel a tremendous guilt and pain.
Unfortunately, within the self-organizing progression, my course ended
up in a genuinely random state. A new, higher order did not emerge out
of this chaos.
This is the trick, write Rea and Ambrose. Applying the theory of complexity
to the classroom system you have to be able to create a responsively complex
system that balances and evolves at the edge of chaos, in the space between
permissively chaotic and strictly ordered systems.69
The challenge is to dance on the illusive rope, without shifting into
extremes.
The continuum: chaos, the edge of chaos (complexity), and order can be
compared to gaseous, liquid, and solid states of matter, respectively.
According to Rea and Ambrose, knowledge from the perspective of complexity
is perceived as creative fluidity of understanding versus chaotic spontaneous
interest or ordered accumulation of facts and skills. Complex curriculum
is co-planned, interdisciplinary, multidimensional versus chaotic, unplanned
or versus ordered, preplanned. Motivation is achieved through serious
fun versus chaotic fun and games or versus ordered serious work. Management
style is participatory versus chaotic permissive and ordered authoritarian.70
Davis and Sumara believe that the self-organizing teaching style is neither
totally teacher nor student-oriented but rather is an interactive style
that encourages students to converse with each other and the teacher.
The traditional distinctions between teachers and students, different
disciplines, classrooms and community are blurred and fluid.71 Stadler,
Vetter, Haynes, and Kruse propose that self-organizing curriculum and
pedagogy should allow students to learn nonlinearly and to find their
own self-organizing rhythms.72
I thought I understood this all and when designing
and instructing my course Physical Science in Elementary Schools,
I celebrated the concept of self-organization. But after the first year
of my teaching this course, I watched my students leave in disappointment
and I knew what was wrong. All my good intentions to create a self-organizing
and therefore dynamic, creative, interactive, open-ended, fluid, nonlinear,
and cross-disciplinary course never self-organized themselves into a higher
order. The chaotic butterfly never emerged from the randomness. The chaotic
classroom tends to be out of control, write Rea and Ambrose.73
That is exactly what happened.
In their anonymous evaluations, students commented that the course was
too confusing, too strange, and too disorganized. It embraced too much
other stuff and too little real science. They invited me to come down
to earth. They advised me to read the IRP and to follow it closely. They
could not afford to be fancy. They needed to survive in the harsh surroundings
of a real school. They needed to adjust to the existing instead of thinking
about the possible...
CONFUSION
we are choosing and we are chosen
but it is not always in harmony
and if not,
the entire world looses
its harmonious image
black seems to be white
white seems to be black
all complicated things
seem so simple
and all simple things
are impossibly complicated
the beauty around me
is unbearably unattractive
the order of things
is absolutely chaotic
and I am so very cold
under the hot sun of summer74
As an illustration of nonlinearity in the process of thinking, this forgotten
poem that I wrote several years ago suddenly popped up. This poem does
not seem to have educational relevance; however, confusion can be understood
as something that pushes a system (me!) out of equilibrium. Such a state,
recalling the theory of dissipative structures, is the necessary condition
for self-organization. In this light, confusion, perturbation, disturbance
are an essential part of the self-organizing process.
Writes Doll:
One requirement is perturbation. A system self-organizes only when there
is a perturbation, problem, or disturbance when the system is unsettled
and needs to resettle, to continue functioning. As Piaget says the unsettlement
(disequilibrium) provides the driving force. However, as we well know
from lived experience, not every perturbation leads to the sort of chaos
that takes us not to a new or more complex level of order but to an abyss
of destruction. The history of our present century has shown us the real
potential of this possibility.75
Under what conditions then does perturbation become a positive factor
in the self-organization process? As Doll notes, there is little literature
related to this issue and there is nothing in the educational field. He
speculates that multiple perspectives and an atmosphere of exploration
are a must in order for perturbation to have a positive effect. Perturbation
will trigger self-organization only when the environment is rich enough
and open enough to multiple uses, interpretations, and perspectives to
come into play.76
Under what conditions does confusion or perturbation become a positive
rather than a destructive factor? My own thoughts in regard to this issue
self-organized themselves around strange chaotic attractors. I believe
that my poor success during the first year of teaching the science education
course resulted from an undeveloped, undefined, malfunctioning, and unattractive
chaotic attractor. Perturbation in the form of my invitation to re-enchant
our thinking about ourselves, the world, and teaching science did not
lead to the desirable transformation. The course was cross-disciplinary
and multidimensional in its approaches to teaching science, but unfortunately
it never became more than the collection and interplay of bits and pieces
of ideas.
In the light of this understanding, the self-organizing curriculum and
pedagogy has to be attract/or/ive; otherwise, self-organization simply
will not occur. In the mechanistic, ordered classroom, there are point
attractors in the form of rigid plans and prescribed outcomes. It is expected
that students will! Life is easier when the certainty of point attractors
protects you. Strange chaotic attractors however, have multiple dimensions
and are subject to influences of the butterfly effect, and as such, to
small perturbations. The trick is to invent an attractor that would be
strange enough to attract and to cause transformation in students, but
not so strange it turns them away.
During my second and third years of teaching the same science education
course, I attempted to create such a chaotic butterfly, using a vision
emerging from new science as a chaotic attractor for re-enchanting ideas.
This was different from the year one, when I did not stress enough that
all my ideas are inspired by new science itself.
Anonymous evaluations of the course from these two years indicated that
the chaotic butterfly is not born yet, but a hint of its silhouette is
gradually emerging from the midst of playful chaos. I hope the higher
order of my understanding will eventually emerge as I approach the bifurcation
point through the amplifying feedback loops of my readings, research,
conversations, teaching and living experiences, thinking, dreaming, imagining,
and reflections...
Your re-enchanted approach to physical science has inspired my teaching.
The interdisciplinary connections to our emotional connections plus experiences
in the physical world make science" something real. Thank you for
helping me to learn to see, appreciate, understand, and feel able to incorporate
this approach into my teaching.
I enjoyed your class much, especially close to the end. I sometimes felt
frustrated because directions of lessons were unclear. Try introducing
concepts plus ideas plus explaining the purpose of activities at the beginning.
This will help your students understand where you are going. Your knowledge
of science is so competent. Don't be so nervous!
Great approaches to teaching science. Need some transitions from standard
science to (re) enchanted science.
I have enjoyed this class. The instructor presents science in an unorthodox
plus exciting manner, which stresses student participation. I would have
preferred more concrete examples/step by step.
Even those who were attracted and transformed by my course, repeatedly
and consistently suggested more organization and more step-by-step directions.
Balancing at the edge of chaos is a tricky and risky task!
Days of the Physical Science in Elementary Schools Course:
Science of
Complexity in Elementary Schools?
(A soap opera)
What can poor mortals say about clouds?
While people describe them, they vanish.77
(John Muir)
If you drink a soup Monday,
it will rain on your wedding day.78
(An example of a butterfly effect suggested by a third-grader)
…then we asked them to imagine clouds and to describe them continued
Holly, reflecting on her team's field teaching assignment in the elementary
school. One little boy literally choked me. During the whole lesson he
was unnoticeable, quiet, and insecure. This imagery exercise completely
transformed him. He described changing shapes of the clouds so vividly
and so poetically. I simply could not believe something like that came
from the third-grader.
The topic of the team's lesson was weather. If you limit your lesson
to hands-on activities, you will have an interesting conventional science
lesson. However, teaching re-enchanted science requires a flight of fantasy.
Connecting the topic of the science lesson with weather folklore and imagery
exercises was definitely a re-enchanting idea:
Lightning never strikes in the same place twice. Is it true or false?
A ring around the sun or moon, brings rain or snow upon you soon. Have
you ever noticed that?
Red sky at night, sailors delight, red sky in morning, sailors take warning.
This saying is taken from the Bible. The sky becomes red at sunrise and
sunset when sunrays shine through cirrus clouds. Cirrus clouds are an
indicator of the approach of a warm front. Since most of our weather moves
from west to east, clouds in the west are the first sign of an oncoming
warm front probably arriving in 24 to 36 hours.
-Why just probably, but not for certain?
-Because the weather is never completely predictable! Too many different
conditions influence it. A butterfly effect!
A butterfly effect through the eyes of third-graders:
Raining and pouring it's most likely to be boring.
If you balance a spoon, there will be a typhoon.
If dogs are drooling it's a clear day in the morning.
Observing or imagining running clouds and then describing their intricate,
ever changing shapes; connecting human complex endeavors with natural
complexities through folklore; emphasizing the inherent unpredictability
of weather; and even discussing a butterfly effect - this lesson seemed
to be in touch with the very essence of the science of complexity. Was
it too complex for elementary kids? There are infinite dimensions for
research within a fractal chaotic attractor of questions: When and how
can we start to introduce the concepts of complexity? At what level and
through what scientific activities could young children grasp this phenomenon?
In the meantime, take your class to the river or creek and observe whirlpools
and vortices spontaneously emerging and disappearing in the running water.
Allow the students to admire (scientifically) the intricate beauty of
a butterfly, the complex shape of a snowflake, or the amazing interconnectedness
of ecosystems and social systems. Demonstrate the chemical clock as an
example of the spontaneous emergence of order or conduct an experiment
with a layer of water between hot and cold plates.
Kauffman79 describes sand piles as an example of self-organizing systems:
an avalanche on the pile of sand provides a paradigm for how complexity
can emerge. Take the class to the beach or playground and let children
to play with sand piles. When a sand pile grows, its slope becomes steeper.
When it reaches the so-called critical threshold, or far-from-equilibrium
state, adding more sand causes surface grains to slide off, leaving the
slope unchanged. Regardless of whether the pile starts out too steep or
too shallow, it always ends up at this critical state, where sand piles
self-organize themselves into a certain structure.
Even traditional experiments, such as growing crystals or watching something
rust, can speak on behalf of complexity. In chemical reactions, the products
are qualitatively different than the sum of reagents. Rust is more than
just combined oxygen and iron; it has its own new qualities. This is also
true for human societies, as well as for the dynamic and evolving universe
as a whole, which is more than sum of parts. Tell your students an emerging
universal story written by the new science of complexity.
I envision a complex science curriculum as a slime mold, which is a favorite
Prigogine's example of self-organization. The slime mold is something
between a collection of single cells and an organism. When there is enough
food, separated cells act as solitary wanderers, completely ignoring each
other. However, when food disappears, the state far-from-equilibrium is
reached. Under stressful circumstances, cells notice each other and organize
themselves into a single organism, a multi-celled slug, with a head and
a tail.
Just as a slime mold self-assembles from separate cells into a whole organism,
complex science curriculum self-organizes itself through interacting with
other subjects. Since the science of complexity reveals the interconnectedness
of all systems and variables, the science curriculum consequently must
be cross-disciplinary, diverse, and extend into the communities and natural
world. In this light, field trips, museums, community and ecological projects,
and other informal activities have great value for the self-organizing
science curriculum.
You can extend the walls of your classroom by getting out into the world
or by bringing the world into the classroom through the dramatic play.
Imagine you are visiting a harbour.
The moment, like a harbour at low tide, sea-smells or curricular opportunities
for exploration. Why has the local fish processing plant has been closed?
What happened to the vanished schools of cod? What life lives beneath
the sea? What impact does human construction have on the ecology and economies
of a bay? What new animal surfaces in the rebirthing of technology and
biology? Within whose science, economics, employment, environment, context,
experience does this moment happen?80
Stop, invites Lynn Fels: "Understand that curriculum does not and
cannot exist apart of the world." Become, I would add. Start looking
at the world through the re-enchanting filter of complexity! Admire unpredictability,
interconnectedness, dynamism, self-organization, and the novelty in Nature.
Appreciate her ability to dance at the edge of chaos and remember that
human creativity is an extension of Nature's creativity.
Do we dance curriculum into
being on the edge of chaos?81
The Weakness of Complex Systemic Re-Enchantment
Listen, if someone lights up the stars, this means, someone needs it!
(Russian poet, Vladimir Mayakovski)
in the classroom-complex system
the teacher-complex system
teaches children-complex systems
about complex systems
The child as a self-organizing system: The
case against instruction as we know it.82 This is the title of the recent
article on educational applications of complexity. It is like a gift for
me because it illustrates perfectly my statement regarding the weakness
of complexity's re-enchanting power. Under mechanistic education the child
is a unit, an it, an object for manipulation. Under the complex education,
the child is a self-organizing dissipative system.
I wish to express my solidarity with the poet
from the film Mindwalk who became tired of perceiving himself as
a system. I am not flattered myself to be referred to as a system, even
if I am a chaotic, complex, dissipative, interconnected, self-regulating,
and self-organizing one. I see a resemblance between mechanistic objects
and complex systems because there is something mechanistic in the word
system. For me, systems can be open or isolated, adiabatic or isothermal,
simple or complex, but in no way can I imagine feeling systems, crying
systems, laughing systems... In other words, systems and life do not seem
to make a comfortable match. I cannot imagine the system that is I, or
we, or she, or he. The system is it.
There is the question: What if a child is not a system, but the World?
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