Replying to LO28792 --
Andrew Campbell < ACampnona@aol.com > writes:
>Elizabeth is about somewhere between two and three
>years old, she has hair like the wheat in the fields and
>eyes like sky. Elizabeth watched me come and go as I
>have watched the flowers in her garden come and go.
>I am now a kind of 'strange attractor' for her, as her
>'flowers' were for me.
>The late Donella H Meadows wrote a paper in 1997 it
>was as a result of an outburst at a meeting concerned
>with growth, limits to growth and finding the leverage
>points (Jay Forrester was her teacher/mentor). She was
>in her own terms 'simmering' (filling up in entropy production;-)
>again in her own words she realised that all these 'informed
>and educated' ( read clever) people were leveraging the
>wrong places, so she stormed up to a flip chart and
>reeled of almost spontaneously in reverse order of priority
>the leverage points as she saw it for a more sustainable
>world wellbeing and wellbecoming.
>I would never have found her essay unless I has typed
>into the google.com search engine -
>I don't think there are cheap tickets to system change.
>You have to work at it, whether that means rigorously
>analyzing a system or rigorously casting off paradigms.
>In the end, it seems that leverage has less to do with
>pushing levers than it does with disciplined thinking
>combined with strategically, profoundly, madly letting go. "
>Copyright: Donella H. Meadows
>In the entire article I cannot see the word "child"...
>At, what is a 'strange attractor'?
Greetings dear Andrew,
There are several "strange attractors" in a kindergarten. But I will come
back to them later.
What is the opposite of a "strange attractor"? Is it a "familiar repulsor"
or is this too opposite? I think we have to consider a "familiar
attractor". It is a certain state which a system will reach no matter how
many times and from what initial conditions the process gets repeated.
Here is an example -- a tensioned guitar string vibrating side to side and
eventually coming to rest in the linear position. Here is another one -- a
teaspoon of sugar in glass of water dissolves and disperses evenly through
In both cases free energy had been used up to produce entropy. In both
cases a state had been reach in which the entropy is a maximum and the
free energy a minimum. In both cases air the microscopic particles (air
molecules for string and sugar molecules for solution) have more chaos in
their motion at the end state. It seems as if order has dissipated into
At the end of the 19th century Ludwig Boltzmann began to use the concept
of chaos to explain why "entropy production" resulted in such decisive
behaviours. But in 1903 Henri Poincaré wrote in his 1903 book "Science and
Method" the opposite:
>"If that enabled us to predict the succeeding situation with
>the same approximation, that is all we require, and we
>should say that the phenomenon had been predicted, that
>it is governed by laws. But it is not always so; it may
>happen that small differences in the initial conditions
>produce very great ones in the final phenomena. A small
>error in the former will produce an enormous error in the
>latter. Prediction becomes impossible, and we have the
In 1938 Norbert Wiener, the father of cybernetics, took one step further
by writing the mathematical paper "The Homogeneous Chaos". In 1963 another
step was taken by E.N.Lorenz in his paper "Deterministic nonperiodic
flow". He described a system of equations, intended to model weather
patterns, displaying a butterfly-like effect, each time ending up in a
different strange attractor. What Poincare had foreseen, he had
demonstrated. In 1975 Li & Yorke published their paper "Period Three
Implies Chaos", indicating that unpredictable orbits get manifested by way
of bifurcations in phase space. In 1984 "Order out of Chaos" by Ilya
Prigogine and Stengers appeared and in 1987 James Gleick's "Chaos: Making
a New Science" saw the light. Chaos, strange attractors and butterflies
became part of the new dialogue.
It is a pity that nobody saw any significance in the following. Let us
take the two examples above. When a piano is played close to the guitar
string, it will begin to vibrate at certain harmonic tones. When a glass
with a solution of sugar is left so that water evaporates from it, sugar
crystals will eventually begin to form. In other words, order does not
always dissipate into chaos. Chaos may also dissipate into order.
In these two examples, the guitar string beginning to resonate or the
sugar solution beginning to crystalise, the outcome is easily predictable.
Thus we may speak of them as "familiar attractor" states. But when walking
in a flat desert on a hot day, one knows that sooner or later a "desert
devil" (mini tornado) will develop, but one does not know where and what
shapes it will take, except that it is a spiralling vortex of hot air and
dust. Such a "desert devil" is strong enough to sweep one off one's feet,
but not strong enough to lift one into the air. This "desert devil" then
is a strange "attractor". The very butterfly may be one self, setting air
in motion by one's walking. First one hears a "swish" when setting down a
foot and then suddenly a deep roar escalating into a howl accompanies the
formation of the "desert devil".
Mathematicans were able to simulate in their abstract math systems "order
out of chaos" having "strange attractors" long before Prigogine published
"Order out of Chaos". But what Prigogine did was to show that
dissipation=(the production of entropy using up free energy) is the
necessary condition to have such order out of chaos in material systems.
Once we have figured out the necessary conditions, it is time to figure
out the sufficiency condition. For me it involves the 7Es (seven
essentialities of creativity).
Since the eighties more and more thinkers of systems in which humans are
involved in some or other manner began to appreciate the chaos which
precedes the forming of a new order. Unfortunately, few seem to grasp the
necessity of dissipation in abstract systems just like in material
systems. They do not think of "free energy" and "entropy production" each
having both a material and an abstract dimension. Nevertheless, they are
keen on applying the "new science" to their own profession. See for
Andrew, a kindergarten is an excellent place to observe the formation of
"strange attractors". The kids are usually kept for an hour or so in
rooms, doing constructive work (like paint and paste) in a playful way.
Then they are allowed to go outside and do what they wish. They burst with
free energy through the doors, running around, laughing, teasing and
squirmishing. The chaos among them increases. Teachers have their hands
full trying to prevent anyone getting hurt. Then, suddenly, two or three
kids flock off to go and play in, say, the sandpit. The teachers begin to
smile because "they know tacitly" that the bifurcation point has been
reached. With ten minutes the majority of kids will play in the sand pit
and the rest in small groups at different other objects. The next day the
majority might prefer the "climb lattice" while performing tricks like
monkeys, or playing "house-house" while imitating adults with dolls and
boxes under the trees.
Here in the Discovery Centre the same sort of thing happens. Children of
various ages are usually transported by bus to the centre. In the bus
their free energy builds up to breaking point. They pour out of the bus
into the centre. Often the chaos which they create cannot be disciplined
fully by their teachers. Once they are set free among the apparatusses
they create chaos with various intensities. Kids from kinder gartens
create it most naturally. Children from primary schools do it less when
"disciplined", but more robustly when less "disciplined". Teenagers from
secondary schools do it even less when "disciplined", but almost
destructively when less "disciplined".
So what is this "discipline"? I think it is the training that "order from
chaos" is good while "chaos from order" is bad. Thus the swing from order
(the bus) to chaos (the first 30 minutes in the centre) and thus back to
order (after 30 minutes) is most natural to kids. In primary school
children the swing is either more dampened ("disciplined") or more robust
(less "disciplined"). In secondary school teenagers the swing is either
even more dampened or can almost get destructively out of hand.
The problem why "chaos from order" is considered to be bad is because
"chaos" is considered the dialectical opposite of "order". This happens
easily when both "chaos" and "order" are considered to be properties of a
system. But are they not perhaps properties of something in that system?
Think of the essentiality liveness ("becoming-being") in that system. Is
"chaos" not perhaps the "diversity of becoming" in that system while
"order" is the "diversity of being" in it? Is "becoming" and "being"
dialectical opposites or are they complementary duals? Is it thus not
perhaps that "chaos" and "order" are complementary duals?
I think that kinder garten teachers know best not to interfere too much
between the swing from "order" to "chaos" and back again. They handle
"order" and "chaos" best as complementary duals. After an hour in the
rooms, another hour on the play grounds, these kids are hungry and ready
afterwards to rest for for an hour. Schooling has the effect that the
older children become, the more they deal with "order" and "chaos" as
dialectical opposites -- and the less they play, eat and rest. When as
adults they find themselves within civil demonstrations, these dialectical
forces may erupt in violent clashes and destruction of property. In stead
of a "strange attractor" emerging, the bifurcation in the demonstration
immerges destructively into a "familiar repulsor" -- a state of demolition
which repulses the majority of citizins.
Andrew, would you not like life to be more like a kinder garten?
With care and best wishes
At de Lange <firstname.lastname@example.org> Snailmail: A M de Lange Gold Fields Computer Centre Faculty of Science - University of Pretoria Pretoria 0001 - Rep of South Africa
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