Guidance in LO with metaphors LO14365

Mnr AM de Lange (
Tue, 15 Jul 1997 14:48:56 GMT+2

This is a long contribution because of its complexity. It boils down to
this: by using a metaphor/parable of a higher level of complexity we can
say much less, requiring the listener to fill in the details. Hence we
promote the non-linearity of whatever we wish to talk about.

Please skip the rest if the above says enough.

Why are metaphors important in learning and hence in the guiding
of Learning Organisations?

Learning is basically a non-linear process. Now what is a non- linear
process? Let us symbolise any process as p(a) where "a" represents the
input which is transformed by the process "p" to an output "p(a)". Now
consider two expressions. The first expression is p(a + b) which says
"first make a whole of the inputs a and b and then let the process p act
on this holon as as input to produce one output". The second expression is
p(a) + p(b) which says "first let the process p act on each of inputs a
and b and then make a whole from the outputs together".

We could also have used a "-" sign rather than a "+" sign in
these two expressions. Whereas the "+" sign concerns a "bringing
together or synthesis" the "-" sign will concern a "taking apart
or analysis". In other words, by using both these two signs
we should actually think of structural complexity. Thus the
two expressions will have to be written as p(a +/- b) and
p(a) +/- p(b). Hence p(a +/- b) means "first change the
complexity and then let the process p act on the result"
while p(a) +/- p(b) means "first let the process p act on each
of the parts and then change the complexity".

With these two expression we can now formulate the difference
between a linear and non-linear process.
* The process p is linear when p(a +/- b) = p(a) +/- p(b).
* The process p is non-linear when p(a + b) <> p(a) + p(b).
In other words, the first equation says it is immaterial in a
linear process at which stage parts are added together or
divided from each other. The final output will remain
indifferently to any act changing complexity (analysis or
synthesis) whatever stage this act is introduced. The second
equation says that the stage at which a complexity act is
introduced into a non-linear process is vitally important to its
final output. A non-linear process is thus very sensitive to
complexity. Why? Because a non-linear process itself modifies

We are now in a position to formulate a basic property of a LO.
We first formulate a LO as the process "LO" which transforms any
input "a" into the output "LO(a)". Hence:
LO(a +/- b) <> LO(a) +/- LO(b)
In other words, a LO is very sensitive to the introduction of any
complexity act +/- during any stage of its development. This is
so because the LO itself modifies complexity. How? Through the
process of learning which itself modifies complexity. In my
forth-coming book (Entropy, Creativity and Learning: how to
manage chaos, order and complexity in nature and culture) this
modification of complexity by learning will be explained in
great detail.

Now what has this all to do with metaphors? I am sure that
despite all the mathematics above, many of you are still not
sure what a non-linear process is. Let me explain it then by
means of a metaphor. Consider the growth process g of a single
kernel of wheat into a mature plant g( ) with several stalks of
wheat. Let g(N) represent the growth in a poor soil enriched
only with a nitrogen fertiliser. Likewise, let g(P) represent
the growth in the same poor soil enriched only with a phosphate
fertiliser, let g(K) represent the growth in the same poor soil
enriched only with a potassium fertiliser, etc.

Now consider the expression g(N) + g(P) + g(K) + .... It means
that we wait for the crop to mature only after which we mix the
harvest together to get nutrinionally balanced wheat. On the
other hand, the expression g(N + P + K + ...) means that we
first enrich the poor soil in all the nutrients and then wait for
the crop to mature into a nutritionally balanced wheat harvest.

Any wheat farmer will tell you that
g(N) + g(P) + g(K) + .... <> g(N + P + K + ...)
The left part of the equation will produce a poor harvest, low
in quality and quantity. A farmer will never divide a land
into a number of parts, give the one part only nitrogen, the
next part only phosphate, another part only potassium, etc. A
farmer will bring the whole land up to standard. This is the
story which the right part of the equation tells us: it will
produce a superior harvest.

Note that I have used "farming" as a metaphor for a non-linear
process. Why? Because farming is basically itself a non-linear
process. This was one of my discoveries during 1968-71 when I
worked as a soil scientist in an agricultural research
insititute. In those days the terms "non-linear systems" and
"complex adaptive systems" had not yet emerged in science.
However, I became convinced that a soil had to be treated as a
reactive, complex whole in order to make the most out of it.
Unfortunately, what appeared as sensible to me in those times
appeared to my colleagues as madness.

Let us think more closely what a metaphor is. It derives from
the Greek prefix 'meta-' which means 'between' or 'over' and the
Greek word 'phero' which means 'carry'.

A metaphor is a manner of speaking in which one phenomenon
is likened to another as if it is the other. A parable is a
short story weaved around a metaphor. A succesful metaphor or
parable requires very little explanation. In fact, they are used
to explain rather than to be explained. If the metaphor (or
parable) itself has to be explained, then it should rather
be called a simile (or an allegory). For example, "Sherri is a
lioness" is a metaphor whereas "The ability of Sherri to solve a
problem is like a lioness hunting for her prey" is a simile.
(Note the phrase "is like a" which seldom occur in a metaphor.)
Thus "Sherri is a lioness who, hungered by a problem, stalks the
solution until she has caught and devoured it" is a parable.
Unfortunately for Sherri, tradition requires that a parable has
to have a religious or moral lesson. But my example of "farming"
above shows that we can free ourselves from the consriction of

In other words, coming back to the etymology of the word, a
metaphor carries ('phero') a message by getting laid over
('meta-') the phenomenon or standing between ('meta-') the
phenomenon and its observer. Thus it is of utmost importance to
select a metaphor which does not distort or fade the original
phenomenon. Consequently, in metaphoric words, a metaphor is
the beautiful dress which a lady wears - looking at the dress
makes you wish to know her better.

Let us once again investigate the reason why we should use
metaphors in guiding the members of an organisation how to
transform it into a LO. We will now discuss this reason with
respect to language. Language, like artistry, rationality and
spirituality, is one of the higher order emergents of
creativity. This means that the functioning of a higher order
emergent depends on creativity as its founding base. But there
is also a back action. The higher order emergents act as the
fuel which creativity needs dyanmically. It is the linguistic,
artistic, rational and spiritual desires of a person which
drives the creativity of that person. This is what makes the
person to create spontaneously. Let is now observer the back
action of language on creativity.

The first written language was Egyptian hieroglyphs. These
hieroglyphs are ortographically very complex. Some of them
represents phonemes (vowels and consonants) like our written
European languages do. Others represents syllables like the
written Arabian languages do. Others represents words or even
sentences like the east Asian languages do.

It is often said that our analytical and atomical way of
thinking originated with Rene Descartes. However, I think that
this way of thinking appears spontaneously whenever people get
used to writing their language in a PHONETICAL ortography. This
is what happened in Europe after the invention of the Guthenberg
press. It also happened in ancient Greece after using papirus
extensively to carry script. However, it happened far less when
the ortography was syllabic (middle east) or ideographic (far

Thus we tend to favourite communication styles which have to
cope with an atomistic and analytic way of thinking. We also
experience other communication styles as alien and usually
cannot employ them spontaneously. Just as we carefully construct
our words in terms of their phonemes, we construct our concepts
in terms of simple, defined words. We continue with this
process until we even carefully construct our systems in terms
of our unique concepts. However, should we along this process of
linguistic complexifixation l( ) pay too much attention to part
a of the system before we pay too much attention to part b,
thereafter part c, etc, we will arrive at the linear description
l(a) + l(b) + l(c) + ... . Clearly, since
l(a) + l(b) + l(c) + ... <> l(a + b + c + ...),
we have to find the non-linear description l(a + b + c + ...).
This is obtained by using the metaphor/parable - saying much
less by making use of a higher level of complexity.

We are about to enter a new epoch in human history in which we
have to deal with complexity in a bold and powerful manner. We
have to perceive essences beyond their intimidating detail. One
way is to establish isomorphisms or adjunctions between the
essences of a well experienced phenomenon and the essences of
the complex thing we wish to perceive. This is why metaphors and
parables will become very important in our communications.

Would it not be exciting if we begin a thread in which we
identify metaphots/parables which could be used to explain
various facets of a LO? Or is the concept of a LO not so complex
as to require the use of metaphors/parables? I do not think so.
Sometimes exciting threads develop on this forum. Have you ever
noticed how many of them actucally began with a metaphor or

Best wishes


At de Lange Gold Fields Computer Centre for Education University of Pretoria Pretoria, South Africa email:

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