In an apparently chaotic universe, chaotic patterns all around us, from weather and nature down to the man-made stock market, our own personalities, arrhythmic hearts, population growth, and dripping faucets, it seems that randomness reigns.
Not so! Many apparently random events can be represented by a simple computation which, when iterated, produce complex results. A formula which is constantly repeated can produce models of trees, or weather systems, and if the values from each stage feeds back into the next stage, chaos is produced. When the repetition is done on different scales, self similarity appears. Therefore chaos can be called oxymoronic, synonyms being
- regular irregularities,
- deterministic disorder,
- stable chaos,
- ordered freedom.
All these are paradoxical, but exist at the heart of nature. Our equations should be the result of the behaviour of systems and consonant with epistemology.
Most natural processes are chaotic systems,as well as many man made ones.
The sea is a chaotic system determined by a certain number of inputs like the phase of the moon, land masses, wind etc. A general pattern can be predicted, but such a complex system is hard to predict in detail.
The stock markets appear to be random and unpredictable, but the human decisions which drive this are conscious of the complexities and dependancies.
In developing dynamic systems, there is an envelope of possibilities in which haphazardness is contained, and these systems are exquisitely sensitive to initial conditions, circumstances and relationships. This results in exponential growing consequences which are unpredictable, and it is interesting to note that the path all this will follow is determined by infinitesimal bits of information fed into the system.
Meteorologist Edward Lorenz found that exponential development, with a starting number of two, is startingly different from when the starting value is 2.000001!
Where classical science stops, chaos begins. For as long as mankind has been enquiring into the the laws of nature, we have been aware of our ignorance about turbulence in the atmosphere as well in the sea or the wind, and the path of lightnings. Oscillations of the function of the brain and heart, fluctuations in wildlife populations, variation in the songs of birds, structure of the galactic nebulae, and clustering of stars can also be added to the list.
Economists showed the same patterns occurring in old data.
Physiologists found that if the human heart did not have the ability to develop chaotic patterns we would not be able to survive: when flight has to take place, the heart must have the ability to swing out of a normal rhythm into a chaotic one in a second, in order to supply the increased demand of blood to the muscles, and afterwards return to an orderly pattern again.
Educational systems are no exception to the rule. Lampert* writes in the Harvard Educational Review: “ When I consider the conflicts that arise in the classroom, I see tensions between individual students or confrontations between myself and a particular group.
I cannot see my goals as a neat dichotomy and my job as making clear choices. My aims for any particular student are tangled with my aims for each of the others in the class. I am responsible for choosing a course of action in circumstances where choice leads to further conflict.”
Both teacher and students add to uncertainty in the classroom. The teacher is an agent of chaos in the classroom, and every decision leads to an infinite number of possible new class scenarios. Of all the people in the room, the teacher is the most chaotic element because the teacher makes the decisions that drive many of the of the reactions of the other agents in the room.
How does thinking about chaos help teachers? Look at the way chaos theorists view uncertainty.
You can’t ever be certain as to results, so do what you think, based on your education and experience when designing something.
Buchmann* wrote,”Teaching and learning require decision, not helpless hesitation. Decisive action may give the appearance of certitude.This is what deceives novice teachers into thinking that their experienced colleagues are sure of their subjects, students and efficacy.”
As long as uncertainty and chaos are awaited with acceptance and calmness, confidence is a good approach to chaos.
The good news about chaos is that it is natural, and a key component of the universe. Chaos may cause uncertainty but it also creates the opportunities that create hope, change and diversification. Teachers need to prepare for chaos and accept uncertainty as a natural condition.
Nobody can control all the chaos we have around us every day, but we can make impacts on the small slice of the universe we reside in.
- Floden, R.E. and Buchmann, M(1993)Detachment and concern: Conversations in the Philosophy of teaching and teacher education. N.Y:Teachers College Press.
- Lampert,M(1985). “How do teachers manage to teach?:Perspectives on dilemmas in practice.” Harvard Educational Review(55): 178-94.