Replying to LO27670 --
Dear Organlearners,
Debbie Bendick" <dbendick@mmcable.com> writes:
>I am beginning to explore the notion of "nested
>relationships" in learning organizations. I am
>approaching the topic from the perspective of
>common ed administration. I am interested in the
>impact / role of principal-teacher relationships, ie
teacher-teacher, teacher-student, teacher-parent, etc.
Greetings Debbie,
I am glad that you have asked the question.
I wonder how many fellow learners thought that the phrase "nested
relationships" is yet another dedicated term recently created for the
discussion of learning organisations.
It is not. It is a phrase which I have encountered in many subjects of
academy over more than forty years. I heard it the first time in
Mathematics 1 at university in a course on set theory some forty years
ago. The various set operations are intended to uncover nested
relationships. Your "principal-teacher relationships, ie teacher-teacher,
teacher-student, teacher-parent, ..." can be modelled by such set
operations.
After university, as a researcher in soil science, I encountered it again
in a study on erosion. Erosion happens in soils wherever their nested
relationships get broken. Similarly, when nested relationships in a
community broke down, its spirituality gets eroded.
After so many diverse encounters this phrase now let me think of four
concepts. They are information, knowledge, complexity and creativity.
Allow me to tell why. Also allow me to tell it in a certain manner. Jan
Smuts defined holism for the Oxford Dictionary as "the whole is more than
the sum of its parts". In other words, when parts get nested by
relationships into a whole, something emerge which all the parts without
these relationships would not have. I will now use holism as the framework
to present the nested relationships between information, knowledge,
complexity and creativity. Thereby I hope that for each of you fellow
learners something will emerge from the whole of this essay of which all
the parts together do not have.
I will once again ask Rick to place the following image with five
figures in the archives. Please Rick, supply us with its URL.
[Host's Note: Certainly! The URL for At's graphic is below. ..Rick]
http://www.learning-org.com/graphics/LO27686_Nested.gif
Each of the five figures consists of information rather than knowledge.
Personal knowledge are required to make sense out of the information in
each figure. As for complexity, none of these figures is particularly
complex. Each can be created by a simple program like Paintbrush so that
exceptional creativity is not required. So let us delve into the
information of each figure to explore what knowledge, complexity and
creativity have to do with them.
In figure 1 you will see some letters as if they express the word
"gemeenskap". But they have been separated with a purpose as
"ge-meen-skap".
The letter "g" sounds like the guttural consonant "ch" in "loch". The
short "e" sounds like the vowel "I" in "fit". The "g" and "e" are nested
in what is known as the syllable "ge". The next three sounds "m", "ee" and
"n" are nested in the syllable "meen". The long "ee" sound is between that
of "men" and "mean". The last four sounds "s", "k", "a" and "p" are
nested in the syllable "skap". Its "a" is pronounced like in "what". Did
you hear these sounds in your head? Then the letters are not phonological
INFORMATION (data) any more, but have become phonological KNOWLEDGE.
Whereas letters indicate sounds, a nest (syllable) of them indicates a
form of meaning (morpheme). The syllable "ge-" is a prefix which indicates
a completed act. The syllable "meen" is the root which indicates the same
as the English verb "mean"= "aim for the common". The syllable "-skap" is
a suffix equivalent to the English "-ship". (Old English
"sciepen"=create.) It indicates that the root act has been dealt with
creatively. Did you modify mentally the "meen"with the "ge-" and "-skap"?
Then the syllables are not morphemic INFORMATION any more, but have become
morphemic KNOWLEDGE.
As a result of these nested modifications several meanings emerge for the
word "gemeenskap" in my mother tongue Afrikaans. The English equivalents
for them are communication, community, communion, connection and
intercourse. Which one will it actually be? The nesting of the word
"gemeenskap" with other words in a sentence will determine which meaning
applies. Hence the word would be meaningless or vague to any fellow
learner who does not have some KNOWLEDGE of Afrikaans vocabulary and the
construction of sentences in Afrikaans.
I could have used any one of thousands of Afrikaans words as illustration.
I could have selected from dozens of morphemic modifications (prefixes and
suffixes) to illustrate the power of Afrikaans for letting new meanings
emerge. Otherwise I could have used English which has its own way for
making new words. I could also have used another language. Thinking of all
these possibilities brings me under the impression of the COMPLEXITY of
language.
Obviously, the process of nesting relationships does not stop here. I can
nest the word "ge-meen-skap" with other words into a sentence. I can nest
that sentence with other sentences in a paragraph to communicate an idea.
I can nest this paragraph with others in an entire chapter to create a
context for this idea. I can nest these chapters in a book to explore the
nesting of many ideas. Without CREATIVITY it will not be possible for me
to write such a book.
Without CREATIVITY it will not be possible for me to relate the concept
"nested relationship" within "nested relationships". Let us see how it is
done.
The example "gemeenskap" might give the impression that "nested
relationships" is merely a linguistic phenomenon. To counteract this
impression, please look at figure 2. Here we have the symbol C occurring
two times, the symbol H occurring four times and the symbol O occurring
two times. What on earth do these data represent? If you look at figure 2
from left to right, the first data "C", "H", "H" and "H" are nested in a
cluster "CHHH" (indicated by a circle which is not part of the data). The
second "C" and one "O" are nested in a cluster "CO". The last "O" and last
"H" are nested in a cluster "OH". Do you by now understand what this
external (it is on the screen!) INFORMATION represents? No? Then it is
because you do not have the inner KNOWLEDGE to make sense of it. It is not
your fault. It is merely you still have to learn what this information
means. Let us get an indication what this knowledge might involve.
The symbols C, H or O represent a carbon, hydrogen or oxygen atom. The
nest "CHHH" is called technically an alkyl group. The nest "CO" is called
a carbonyl group. The nest "OH"is called a hydroxyl group. Whenever a
carbonyl group "CO" and a hydroxyl group "OH" are next to each other, they
get nested together as "COOH" which is called the carboxylic group. It is
an important reactive group in organic chemistry. The alkyl group "CHHH"
and the carboxylic group "COOH" are nested in the organic molecule
"CH3CO2H". What is it? Acetic acid -- etanoic acid (to use the systemic
name). A dilution of it in water is called vinegar!
I hope that by now you have a clearer comprehension of the difference
between information and knowledge. The "CH3CO2H" constitutes information.
But knowledge involves acts such like creating a 3D image of the
molecule's shape in the mind, associating it with vinegar, using it to
give food an acid taste and preserving canned foods with it. Do you know
that there are some two million other organic compounds which we could
have used as examples to illustrate "nested relationships"? Does this not
hint to complexity? Do you know that most of these compounds have been
synthesised in laboratories, even those compounds which have been produced
by nature itself? Does this not hint to human creativity?
Language and chemistry. Is that enough to convince you that "nested
relationships" is not the possession of a particular subject of academy?
Not yet? Then please look at figure 3. It is fragment of a musical score.
It is two bars of Beethoven's piano sonata op 101. This sonata had a
curious spell over many later composers like Liszt, Mendelssohn, Schumann
and Wagner. Its seamless lyricism made them speak of this sonata as having
infinite melodies.
The top five rows indicate what the right hand should do with notes of
higher pitch. The bottom five rows indicate what the left hand should do
with notes of lower pitch. The right hand begins by pressing down 2 notes
(drawn above each other), thereafter 1, 2, 2, 1, 2 to complete the first
bar. In other words, by pressing 2 notes down, they are nested together to
give a harmonious sound. There is also a nesting for rhythm (beat). In the
first bar the first three harmonious groups are nested together and then
the last three groups as another nest. In the second bar again the first
three groups are nested together while the forth group forms a nest on its
own. The curve above indicates that the four nests | 3 3 | 3 1....| have
to be taken together as one nest before a rest is taken. The last note in
the second bar belong to a new cluster of nests. We will not go into the
much different effect which the nests in the left hand have.
We might say that what made Beethoven the greatest composer ever, is his
astounding ability to created nested relationships in every aspect of
music like harmony, rhythm, melody and texture. The fantastic outcome of
it all is to let untold feelings emerge when listening to that music
performed. All the lines, dots and other symbols in figure 3 concern
information. But letting the eyes move from left to right so as to convert
them into music "heard in the mind" (called sight reading) concerns
knowledge. Working through all of at least Beethoven's 33 sonatas makes us
aware of complexity. All of this have been made possible by Beethoven's
unique creativity.
Language, music, chemistry! Not enough? Then please look at figure 4 which
involves statistics. Assume that eight variables X1, X2, ..., X8 influence
the outcome of a property Y, each one to a different extend. In
multi-variable regression analysis the task is to determine how much each
variable X influences the outcome Y. Each of X1, X2, ..., X8 represents
its own nest of data so that X1, X2, ..., X8 together represent the
information. Determining the amounts by which each influence the outcome Y
(self a nest of data) requires knowledge of fitting by "least squares".
In simple things we may still get away with regression analysis. But, for
example, in genetics where different genes have emerged during different
epochs in the evolution of a species we cannot assume that, say, eight
genes X1, X2, ..., X8 influence a property Y of a species simultaneously.
Thus Sewall Wright, a most original thinker in genetics, expanded
regression analysis into a complex procedure called path analysis. Only a
few knowledgeable persons can do path analysis and interpret the results
correctly. With path analysis it is possible to group the variables into
nests and the nests into a hierarchy. In figure 4 the variables X2, X7 and
X8 form the shallowest nest whereas the variables X4 and X5 form the
deepest nest. This points to complexity. Wright's accomplishments points
to creativity of the highest order.
What about some biology? One of the central tasks to biology is to arrange
living specimens into a systematical order. All specimens looking very
much the same are nested together in a box (taxon) called the species.
Species closely related to each other are nested in a taxon called the
genus. All genera closely related to each other are nested in a taxon
called the family. From families we move to ever increasing nested
relationships like the order, class, phylum and kingdom. The two best
known kingdoms are the plantae and the animalia.
All the preserved specimens in a herbarium or museum constitute its
taxonomical information. Classifying any of its specimens correctly
requires knowledge. Thinking of the millions of specimens preserved in the
thousands of herbariums and museums all over the world indicates an
overwhelming complexity. The modification of the classification order to
accommodate consistently a newly iscovered species often requires stunning
creativity.
I can go on and on by giving examples in subjects like mathematics,
physics, geology, geography, economy, politics and theology to name some.
Even "non-standard subjects" like holism and autopoiesis have nested
relationships indicated by phrases like "wholes of wholes" and
"coordination of coordinations". I will be surprised if there is a subject
in academy which cannot offer us even one example of nested relationships.
Hence I hope that you fellow learners will not be surprised again that
whenever you deal with nested relationships, you also will have to deal
with information, knowledge, complexity and creativity.
The WHAT of nested relationships is one thing while their WHY is another
thing. WHY does the universe present us with such a dazzling diversity of
nested relationships? It all is the result of what I prefer to call the
"one-to-many-mapping" of LEP (Law of Entropy Production). We may also call
it the "factual ordering of deep evolution".With "factual ordering" I mean
all the facts presented in an ordered manner. With "deep evolution" I mean
all kinds of evolution like that of the elements, the galaxies, the
chemical compounds, geological minerals, living organisms, human
languages, nations, educations, economies and even religions.
Mathematicians prefer to call any "one-to-many-mapping" by the technical
term "relation". This they distinguish from any "many-to-one-mapping"
which they will call a "function". This term relation is closely connected
to the concept of "nested relationships" as we will soon see. Think of
something such as "nested functionships" and perhaps you will intuitively
feel that we ought to focus on "nested relationships".
The "factual ordering of deep evolution" can be represented by a network
of "one-to-many-mappings". Figure 5 depicts graphically two consecutive
"one-to-many-mappings". The first one is a "one-to-four-mapping" while its
bottom outcome gives rise to the second "one-to-three-mapping". But why do
we have such a "factual ordering of deep evolution"? This where all the
various theories proposed for evolution come in. Here we may think of
Darwin's natural selection, Smut's holism, Maturana's autopoiesis and
Prigogine's irreversible self-organisation.
The more we nest different kinds of evolution together, the more complex
the theory has to be to reflect this nest of evolutions. Should we focus
on the "factual ordering of deep evolution" itself, then the complex
theory will became very close to the TOE (Theory Of Everything), if not
actually TOE itself. Should we bear only one of the 7Es (seven
essentialities of creativity) in mind, then we cannot help but to think of
this TOE. For example, consider wholeness. Wholeness means that we cannot
fragment anything else from whatever whole we want to work with. That
whole may be a nest of wholes, but it will self always be in a nest with
other wholes. Whatever direction we move into, wholes-within-whole or
whole-within-wholes, it is seemingly an endless network of nests related
to each other.
Perhaps the most curious (but also least understood) contender for a
theory to reflect upon the "factual ordering of deep evolution" upon, is
LEP. LEP is the cause of irreversibility, the fact that time proceeds
forward. Calculating entropy increases based on measurements is so complex
that few can actually do it. Consequently few are able to follow both the
movie of "entropy production" and the movie of "deep evolution" to search
for any connections. Let us assume that these calculations have been done
for the two consecutive "one-to-many-mappings" in figure 5. Let us plot
all these increases on a graph (entropy vs time) and position that graph
under the diagram of the "one-to-many-mappings".
Notice on the graph the regions for a slow rise of entropy (valleys close
to equilibrium) or for a fast rise of entropy (ridges close to chaos). As
soon as a "one-to-many-mapping" happens, there is also a fast increase in
entropy, i.e. the entropy production is high. Chaos is increasing and when
the system is about to break apart, the one of the old order becomes the
many of the new order. Thereafter each of the many of the new order has to
mature. During this maturing, the increase in entropy slows down. But
whenever one of the new order has become mature itself, the
"one-to-many-mapping" may happen again.
The rhythm (...-slow-fast-slow-fast-...) is the necessary condition for
"one-to-many-mapping", but not the sufficiency condition. The sufficiency
condition is even more complex than the necessary condition. It requires
an advancement in each of the 7Es (liveness, sureness, wholeness,
fruitfulness, spareness, otherness, openness). If merely one of the 7Es is
too immature, the "one-to-many- mapping" will still happen, but now each
of the newer "many"s will be less complex than the original "one". The
system will actually break apart. Complexer nests will break into simpler
nests with a resulting loss in relationships between the nests. Nested
relationships will degenrate into a myth.
Debbie, you write:
>I am interested in the impact / role of
>principal-teacher relationships and how other
>relationships might evolve from or mirror the
>principal-teacher relationships, ie teacher-teacher,
>teacher-student, teacher-parent, etc. I'd like to do
>a case study in a school with demonstrated success
>to explore this idea.
Were it not for the fact that you used the word "evolve", I would have not
painted such a rich picture on "nested relationships" for you and fellow
learners. I think that should we want to understand any evolution at all,
we must bear in mind its context or entire surroundings. It is the same
with the concept "nested relationships". It has been evolving while our
minds are dealing with information, knowledge, complexity and creativity.
It is one of the ways how we mentally bring them all together.
"Principal-teacher relationships" are not just there. They have to evolve.
Thus they need an environment favourable for their evolution. This
enviroment is provided when the school becomes a LO. Schools are schools,
but they are seldom LOs. Sometimes a class of pupils in a school may
become a LO. I have had the wonderful experience of two classes having
emerged into a LO. That was some 20 years before Senge's book on LOs
appeared.
Debbie, I think that you are very brave to explore the "principal-teacher
relationships". It is one of the many kinds of possible "leader-follower
relationships". It is a relationship very dear to me because I have had
personal experience how one principal can lift a school into the highest
echelon of excellence while the next one can force it into the lowest
within a few years. The people who benefit or suffer most are the pupils,
those who cannot be held responsible for such nested relationships except
for learning about them.
I think that you will also have to study some books on leadership. You may
also have a look at a series of essays which I have completed recently for
our LO-dialogue under the subject "Leadership and constructive
creativity". The way in which I presented these essays, namely with
"one-to-many-mapping" as the central theme, might have been too esoteric
for many a fellow learner. However, I am glad that I did it in that way
because it now fits in nicely with this essay on "nested relationships".
Lastly, I cannot stress enough that the "nested relationships" you are
interested in, are not a static picture, but a dynamic movie. You will
surely learn through "a case study in a school with demonstrated success",
but the danger is that you will see the end result (picture) rather than
also the process (movie) leading to it. If you can find a school of which
"increasing success have been demonstrated", then you will have so much
more to learn. Thus you might search for a school operating somewhat like
a Learning Organisation, if not actually operating as one.
Unfortunately, such schools are very rare in modern times because of the
rote learning which is dished out to pupils. Hence another clue which you
may bear in mind in searching for that elusive school is to look for a
school in which a very high premium is placed on authentic (creative)
learning. Unfortunately, few principals have knowledge of and passion
(guts) for authentic learning like Socrates, Jesus or Pestalozzi once had.
How I wish that society would once again place a high premium on
principals with teachership rather than a politically correct bureaucrat.
Lastly, I wish you all success with your highly original venture.
With care and best wishes
--At de Lange <amdelange@gold.up.ac.za> 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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