Fitness Landscape and other landscapes. LO27257

From: AM de Lange (
Date: 09/21/01

Replying to LO27222 --

Dear Organlearners,

Greetings to all of you.

I did not intend a Part 2 on energy and entropy landscapes. But I got
several questions in private on what would happen to such landscapes when
successive cycles (steps) are attempted as one cycle. In other words, what
would happen if participants are ignorant to the increase in complexity by
steps ("Steigerung"=staggering).

Before we answer these questions, let us summarise quickly the
energy-entropy dynamics. Every system consists of many forms of energy
organised into such a manner that the system "has a character of its own".
Each form of energy can be represented as the product of an extensive
factor X and an intensive factor Y. Should the system be scaled up or down
in size, all the intensive factors stay the same while all the extensive
factors become scaled too. A difference in the value of an intensive
factor acts as an entropic force. A difference in the value of an
extensive factor acts as an entropic flux. New entropy is produced by
entropic force-flux pairs.

A cycle (step) in deep creativity consists of two phases. Please refer to
figure 2
< >
and figure 3
< >
of LO27222.

In the first digestive phase some property which emerged in a past cycle
grows to maturity. Each intensive factor of every form of energy stays
almost the same whereas the complementary extensive factor gradually
increases by feeding upon the environment. Consequently the free energy of
the system increases. Furthermore, the rate of entropy production /_\S
slows down so that the system swings towards (approaches) equilibrium and
order. This equilibrium (/_\S low) will appear on the free energy
landscape (figure 2) as the summit of a ridge while on the entropy
landscape (figure 3) as the bottom of a valley (see the shaded regions).

In the second bifurcative phase this matured property will drive the
emergence of a new property. The free energy gained is now used to
increase the rate of entropy production /_\S so that the system swings
away from equilibrium towards chaos. This chaos (/_\S high) will appear on
the free energy landscape (figure 2) as the bottom of a valley while on
the entropy landscape (figure 3) as the summit of a ridge (see the
unshaded regions). For this novel property to emerge, two (but seldom
more) existing mature properties have to be joined. Just before joining
happens, the system begins to experience a free energy barrier (figure 2)
or an entropy gully (figure 3).

It is here where the LRC (Law of Requisite Complexity) becomes most
crucial. If the complexity of the two "to be joined properties" is too
low, the system will be bounced back by the free energy barrier or shy
away from the entropy gully. The barrier has become too high or the gully
too deep to cross it. Should the system have used much free energy and
thus produced much entropy to cross the barrier (or gully), the system may
break down when bouncing against the ridge (or falling into the canyon).
Hence a destructive immergence into lower order happens rather than the
constructive emergence to a higher order as was intended. As a result of
this the name ordinate bifurcation (forking) applies.

When we try to leap several creative cycles rather to create (complexify)
them each step by step and let them mature, we lose the generative power
of the digestive phase along each step. It is as if the free energy
barriers of all the steps which we wish to leap become added together
because too many existing properties have to be joined. I have drawn three
free energy landscapes to explain what will happen. (We will later come to
figure 7.) Please Rick, archive them in your kind and efficient manner and
supply us with their URLs.

Figure 4
< >
Figure 5
< >
Figure 6
< >
Figure 7
< >

In figure 4 a free energy landscape is drawn for trying to take three
steps at once. Note how the free energy gained by the past digestive phase
is by far not enough to overcome the high free energy barrier. The summit
of the hill shaded to the left is far lower than the summit of the
barrier. The system will simply be bounced back by this free energy
barrier. Not even a catalyst will be able to reduce this free energy
barrier sufficiently.

In figure 5 a free energy landscape is again drawn for same three steps.
But now only the last two will be attempted at once after the first step
has been taken on its own. Note how the free energy barrier of the first
step taken on its own is much smaller than the free energy barrier of the
last two steps taken together. In other words, at the first barrier the
LRC may allow an emergence whereas at the second barrier it will prevent
any emergence. Compare figure 5 with figure 4. The free energy barrier
(fig 5) of the last two steps taken together is not as high as the free
energy barrier (fig 4) of all three steps taken together. Yet it is still
unsurmountable high so that the LRC will not allow a constructive

  Fig 5:

In figure 6 a free energy landscape is drawn for trying to take three
steps consecutively, each on its own. Note how the free energy barrier of
each step is manageable in terms of the free energy hill before it gained
by digestion. In other words, the LRC may allow an emergence at each of
these steps.

  Fig 6:

[For those more mathematical minded, Goethe's "Steigerung" and
Mandelbrot's fractals seem to be similar. Fractal patterns are produced by
repeating a rotation and then a translation of a geometrical matrix many
times. In "Steigerung" the emergence is like rotation and the digestion
like translation. The matrix operated upon here is the Onsager matrix
connecting the various entropic forces to the various entropic fluxes.]

In any information managed activity like teaching and advertising it is
very important not to suggest to the client by the very information to
take more than one step at a time. The client will simply not be able to
overcome the total free energy barrier of the barriers of all the steps
put together. In teaching this is reflected in the rule "teach from the
known to the unknown". Whatever has become known could only have become
known in a stepwise fashion. But few teachers know this and are able to
select the next single step in the unknown. Thus we have to add to the
rule "teach from the known to the unknown in manageable steps".

This stepwise or fractal evolution in concepts and activities are also
crucial in the two LO disciplines Personal Mastery (PM) and Team Learning
(TL). Any "organlearner" of a LO should bear in mind his/her own personal
free energy landscape as well as those of fellow learners. There is no
sense in skipping the steps of learning because the free energy barrier
will become too high to do so. Recognition of the LRC in PM and TL is
vital to the success of these disciplines.

You can use your own imagination too see how figures 4-6 in the free
energy landscape will appear in the entropy landscape. When trying to skip
several steps, the gully in an entropy ridge will become a canyon while a
canyon will become a rift. The person will experience how the ridge of
chaos becomes the edge chaos for which no safe crossing is possible.

Why cannot people of 3rd world countries catch up with people of st world
countries? Why cannot people living in the slums of a city catch up with
people living in the rich suburbs? Why cannot the workers understand what
the manager wants them to do? Why cannot the board of directors steer the
company safely through times requiring a paradigm shift? There are many
possible causes. In my opinion, the most important among them is the free
energy barrier in each cycle of deep creativity. Lumping cycles together
as one cycle produces a free energy barrier too high ever to cross.

Even our systems of law (jurisprudence) often do not take this free energy
barrier into account. A person who had been bounced back by it may have
caused a destructive immergence punishable by law. Before the barrier can
be crossed, the person then gets bounced back by another barrier which may
also lead to a crime. Every free energy barrier of these crimes adds
together in an unsurmountable high barrier of free energy. When the law
then catches up with these criminals they are put behind bars and fences.
Are these bars and fences not often a metaphor which signifies the
unsurmountable free energy barriers in the spirituality of these

Here in Pretoria alone thousands of children go to school without having
had food for breakfast. How can they overcome the free energy barriers in
the body and especially the brain at school without the digestion of food?
It is foolish to try and teach a child about to faint with hunger.

But what about the mental digestions and bifurcations of pupils and
students? Curricula over stuffed with topics as well as the practice of
rote learning trying to cope with this deluge result in too many too high
mental free energy barriers to overcome. Thus the educational system is
characterised at all levels by low performers and dropouts. It is caused
by an ignorance to the LRC or assuming that the student will find through
rote learning a way of side stepping the LRC. All this happens between
four walls called the class room or lecture hall. Are these four walls not
often a metaphor which signifies the unsurmountable free energy barriers
in the spirituality of these failing learners?

A major problem when communicating with people who are at various levels
of complexity is at which level of complexity the communication should be
addressed to. If the address is to some high level, each of the major
steps presented consists of many minor steps jumped. Those from the lower
levels will experience a very high free energy barrier like in figure 4.
If the address is to some lower level, each of the minor steps have to
presented too. The effect is that free energy landscape becomes expanded
like in figure 6. This will make the presentation boring to those from the
high levels who have already covered the landscape.

Some solution to this problem is to make use of stories acting as
metaphors and parables. Present an intermediate step which matches the
average audience, although it may be boring for those high up and too
difficult for those low down. Make a few suggestions to keep the minds of
those higher up busy. Then tell a story to illustrate the step. Those from
the higher levels will try to understand how the story is applicable to
the suggested challenges. Those from the intermediate levels will try to
understand how the matching step figures in the story. Those from the
lower levels will use the story trying to understand what the too complex
matching step is about. The story acts like a catalyst in lowering the
free energy barrier of it and thus reducing the time to cross it.

The solution is not perfect because the more diverse the levels of
complexity to be addressed, the better the story has to be to keep all
levels busy. Select the story carefully because those from higher levels
need to be challenged, those from intermediate levels need to be kept
interested and those of the lower levels need to be helped by catalysis.
Sometimes a carefully selected joke will work where a story cannot. What
the joke does, is to make the audience aware of their tacit knowledge on
that creativity which they will need to deal with the step.

Also try to avoid heating up the temperament of the audience with
emotional talk and body language. Although they may become enthralled by
such an address, it will also flatten their entropy landscape. The
resulting loss in features will disorientate them from what the future
actually requires. Hence they may do things which were not implied by the
address. This heating mode of address by some leaders became more frequent
during the last decade of apartheid, resulting in irresponsible behaviours
of some followers as were disclosed before the TRC (Truth and
Reconciliation Commission). The strange confession of these followers from
both sides was that they did not realise how disorientated they became.
This confession was often considered to be a lie.

Is one of the striking differences between an OO (Ordinary Organisation)
and a LO not that the free energy landscape of a LO is much better
formed? How? It is said that the "living organism" serves as a much better
metaphor for the LO than the "artificial machine". Two of the biomophisms
(patterns common to all forms of life) is that organisms
(1) have hereditary molecules (DNA and RNA)
(2) hereditary molecules are replicated during cell division.

The DNA molecule (chromosome) looks like a long ladder (with many
thousands of steps) twisted into a helix. When the DNA molecule is
replicated, the enzyme (catalyst) DNA-polymerase cuts each step of the
ladder in half. They are not cut all at once, but one by one in sequence.
The reason is that the enzyme has to complete each half side of the ladder
by adding the basic units (nucleotide bases, glucose and phosphates) to
the other half. Thus two ladders are created. Should these units be added
all at once, the free energy barrier would be immensely high, figure 4 not
even a match to it. However, the enzyme adds them unit by unit so that the
free energy landscape looks like figure 6, but now with thousands of steps
in it. See figure 7. The effect of cutting the steps (nucleotide base
pairs) one by one so that the units can be replicated stepwise, is that
the chromosome splits in an inverted Y fashion.

  Fig 7:

A cluster of steps in the ladder act as a gene. All the genes together of
the entire DNA (divided into a few dozen of molecules called chromosomes)
is called the genome of the organism. Some genes are active while the
majority are inactive. The active genes are responsible for the physical
characteristics of the organism so that we will recognise it as a snake or
a bird. What "genes" (memes) will we activate so as to give character to
our LO? Do we want it to become a "snake" or a "bird", a warrier or a

How about assembling the "DNA of love" as our calling for this millennium?

With care and best wishes


At de Lange <> 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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