Essentiality - "associativity-monadicity" (wholeness) LO18276

Mnr AM de Lange (
Fri, 5 Jun 1998 16:54:05 GMT+2

[Host's Note: Welcome back, At, from your trip! Readers: At is continuing
here a series on his seven essentialities. ...Rick]

Dear Organlearners,

Before we get to business, a few reminders:

"becoming-being" (liveness)
"identitity-categoricity" (sureness)
"associativity-monadicity" (wholeness)
"connect-beget" (fruitfulness)
"quantity-limit" (spareness)
"quality-variety" (otherness)
"open-paradigm" (openness)


"Creating a Passion for Learning LO17474"
< >
(About the history of the discovery.of the essentialities.)

"Essentialities of creativity LO17576 -Introduction"

"Essentialities and self-learning LO17610"

Essentiality - "becoming-being" (liveness) LO17651

Essentiality - "identitity-categoricity" (sureness) LO17823


The first two essentialities in hand will help us to get deeper into
this third essentiality.

One of the shortest and most powerful definitions of holism is
"the whole is more than the sum of its parts".

We can symbolise this defintion by a mathematical expression:
1 + 1 = 3 (one more than two)

Some of you might immediately jump up and say that holism is a sham
because 1 + 1 = 2. Well, this happened when Jan Smuts formulated his
philosophy of holism. Darwinian evolution by selection was at its
height. Why this wierd holism rather than selection for evolution?

Most people took strong exception. Few would examine their own tacit
knowledge, recognising that he was onto "something" and then try to
articulate this "something" better than Smuts. Using our mathematical
example, few would articulate it as
1 + 1 "=" 3 (one more as two)
What is this mysterious becoming "=". Note that I have changed the
equality sign = with quotation marks into "=". Thus it does not
symbolise "equals" any more, but rather "becomes".

Should we now carefully think about holism, we will
discover that "=" has two facets:
(1) the sum of the parts
(2) is more than
Facet (1) is concerned with "wholeness". Facet (2) is concerned with
"emergence" (the birth of something new). We cannot separate
"wholeness" and "emergence" from each other. The "wholeness" is a
requirement for "emergence". This is what holism is about.

Although we cannot seperate "wholeness" from "emergence", we can
surely distinguish between the two. This is what the "identity"
of the essentiality sureness is about. But if we say that "emergence"
requires only "wholeness", then we establish an uncategorical
identity. In fact, the seven essentialities of creativity as a unique
category entails six other things (liveness, sureness, fruitfulness,
spareness, otherness and openness) which together with wholeness are
inseparable from emergence.

Let us see how the other six essentialities contribute together with
holism to emergence. Take merely one of them (say otherness) to get
the idea. For example, we may have the abscence of "otherness",
eventhough we may have "wholeness". This will not promote
constructive emergences, but will rather cause destructive
immergences. These immergences can be articulated as "the whole is
less than the sum of its parts".

In terms of our mathematical examples, it would be:
1 + 1 "=" 1 (one less than two).
(Note the abscence of otherness or diversity in the expression.)

Now what would be represented by this mysterious sign "=" ? Let
us summarise it:
1 + 1 "=" 3 (when both wholeness and otherness operate)
1 + 1 "=" 1 (when only wholeness and not otherness operate)
Well, do the words "forking" or "bifurcation" not articulate what we
tacitly had in mind? The "=" is something which has two or more
possible outcomes for the same input (1 +1).

Mathematicans will call this thing "=" which has two or more possible
outputs for the same input (1 + 1) a relation. In other words, the
bifurcation is a relation and not a function. Mathematicians make a
categorical distiction between relations and functions. A function
has one and only one output for the same input.

The algebraic addition 1 + 1 = 2 is a function. But how will the
bifurcation 1 + 1 "=" 3 ever become a function so that
1 + 1 "=" 2 and 1 + 1 "=" 1 are not also other possible outputs?
The answer lies in the seven essentialities. Should we see with our
inner eye how they all operate in the complexity of "=", then the
relation "=" becomes the function "=" with 3 (and not 2 or 1) as its

This sign "=" represents a very complex becoming. We will call it an
"ordinate bifurcation" to distinguish it form all other relations.
The "ordinate" means that its outcome have to do with a progression
into more order. In the rest of this contribution we will
concentrate mainly on wholeness.


I often read how people refer to David Bohm on wholeness, but seldom
see any reference to Jan Smuts, the "father" of holism. He was an
intellectual giant in more than one manner. He was an attorney by
profession, a farmer, a general of war, a botanist, a statesman and
a philosopher. He was awarded 27 honorary doctorate degrees and more
than 30 awards of the highest merit all over the world.

One way to become senstive to the insights of a person, is to read a
biography on that person. A person's intellectual emergences are part
of that person's whole life of experiences. By reading a person's
biography, we can prepare ourselves better to understand the depth of
that person's insights.

A very fine book on Jan Smuts is
Jan Smuts - An illustrated biography.
by Trewhella Cameron. Human&Rousseau, Cape Town, 1994.

Smuts' famous book "Holism and Evolution" was eventually published in
1926. But the main drafts of this manuscript was already completed in
1911 at an age of 31! The manuscript then had the title "An Inquiry
into the Whole". In that manuscript Smuts explained the evolutionary
process as "an unfolding of inner potentialities, a movement from the
external to the internal". In it he has articulated many of the
concepts which thinkers on evolution such as Maturana, Kauffman
or Prigogine recently have done.

What happened to his 1911 manuscript? People strongly disagreed on
its contents. Even a close friend of Smuts, Wolfstenholme, advised
him not to rush into publication of the book. The idea of the "whole"
as a "universal manifesting force" was too distant from their own
ideas. Eventhough he carefully argued the differences between the
"whole" as a "universal manifesting force" and the fundamental forces
of the universe such as gravitation and electro-magnetism, people
were not ready to understand the meaning of what he wrote about. The
book finally became published 15 years later in 1926 after some

This is how he described the whole in 1911:
* "What then is the Whole?... (it) includes whatever is, the entire
* universe, material and immaterial, whether considered as an
* outward visible system, filled with motionas and energies, or as
* containing the infinite phenomena of life and mind; The Whole
* contains the totality of being or experience, both actual or
* possible; inshort, whatever is, either to the inner or outer
* experience of man. Whatever objects, material or immaterial, form
* the subject matters of the various sciences from physics to
* psychology, fall within the Whole. although as we shall see they
* do not exhaust the meaning of the Whole .... If we had the mental
* vision, our objective would be to penetrate to that concept of
* the whole, which is no mere aggregation, or sum total or compound
* of its parts, but which is itself one and indivisable, a real
* vitalic organic unity of which the multiplicities of the universe
* are not the constituent parts, but aspects, phenomena or
* manifestations."

General Jan Smuts' political opponent for many decades was general
JBM Herzog. These two men had so much in common. They fought side by
side in the first devastating war of this century (Anglo-Boer war of
1899-1902). During this war 27 000 woman and children of my people
died in British concentration camps. The death of these people made
an everkasting people on both. Two finer gentlemen were there not.
They had immense respect for each other. Yet, they never could fathom
each other. Why?

Whereas Smuts was extremely sensitive to wholeness, Herzog was
extremely sensitive to sureness. The one's sensitivity was a
stumbling block to the other's sensitivity! (We will again take up
this theme right at the end.)


Think of the many "isms" we have read or heard about:
capitalism, holism, communism, socialism, pragmatism, idealism,
positivism, existentialism, nihilism, rationalism, spiritualism,....
They all have one thing in common. Each of them looks at reality from
a specific point of view. Each of them favours exclusive thinking
rather than inclusive thinking. Thus each of them has some stain
of "apartheid".

Why then has the name "holism" the suffix "ism"? Why did Smuts
himself created the name "holism". Is it not an oxymoron, a shot in
the foot? Well, every "ism" is unique. Holism is unique in the sense
that it looks at the whole from the viewpoint of the whole. But
having the seven essentialities now available after so many years, we
see that if we look at the whole from only the whole, we are again
thinking exclusively. We should look at the whole from every possible

Let us take the essentiality "becoming-being" (liveness) as example.
We should look at the whole from its beings, but also from its
becomings. Should we favour being, we will think of the whole and
its parts as being (structure). We will relegate becoming to a
subordinate role. This is called ontological thinking. On the other
hand, should we favour becoming as many post-modernists now do, we
will think of the whole and its parts as becoming (process),
relegating being (structure) to a subordinate role.

We can employ each of the other five essentialities to uncover new
facets of the whole. Due to lack of space I will not do it. But we
must also not forget the use of the seminal name
"associativity-monadicity" to uncover facets of "wholeness" (the
nominal name). We have to think of the whole as one (this is where
the "monadicity" comes in) and also of the whole as many (this is
where "associativity" comes in).

Is it not possible to fall into the trap of "essentialism" by
thinking exclusively in terms of the seven essentialities? Yes. That
is why we have to think of the seven essentialities as pertaining
merely to the form (syntaxis, mechanics, feminity) of creativity. We
also have to think in terms of the content (semantics, dynamics,
masculinity) of creativity. It is then when many uncommon concepts
such as "energy protection", "entroppy production", "free energy",
chaos, order and bifurcations comes to light.

It is also possible to fall into the trap of "creativism". Please
make a distiction between "creativism" and "creationism". The term
"creationism" was first used by Darwin to lable those who took strong
position against evolution in terms of the Bible, especially the book
Genesis. I do not now want to go into this issue.

Yes. It is possible to fall in the trap of "creativism", trying to
view everything in terms of creativity.Thus we must even extend
creativity into at least two directions XXX and YYY so that this new
"association" (XXX, creativity and YYY) affords yet another way to
look at the whole! Here it depends on the unique wholeness of every
person what XXX and YYY will be. For me and my experiences,
XXX=entropy and YYY=learning.


Associativity is an important aspect of wholeness. What do we mean by
associativity? In accounts on "human rights" the phrase "freedom of
association" is often used. We mean by it the unrestricted
possibility of forming and exploring any network of relationships.
But often we are quick to pass judgement on the morality of such
associations, thinking in terms of the oxymoron "unholy whole". The
word "holy" ("halig" in old English) means "whole" so that "unholy
whole" means "unwhole whole".

Such judgements happen when we do not understand that morality
concerns the constructive outcome of all seven essentialities and not
merely wholeness. Thus we impair wholeness to prevent the emergence
of a whole by the qualification "unholy", perceiving the result as an
immoral association. However, wholeness cannot be understood in terms
of wholeness alone - all seven essentialities are needed. When using
less than all seven essentialties in our judgements, we act much more
immoral than the immorality which we wish to judge.

When we set up associations, we should use all seven essentialities
to guide us. Consider, for example the essentiality "quality-variety"
(otherness). Are we prepared to associate with people having motoric
or mental handicaps? Are we prepared to associate with people from
different social, racial, cultural or religious backgrounds? Are we
prepared to associate with people considered as the misfits of
society? Are we prepared to associate ourselves with other living
species, animals and plants?

Why should we be prepared to form such associations? Well, if we have
any definite emergence in mind, then such associations become most
important, i.e essential.


The axiom of associativity is basic to every branch of mathematics. .
The articulation of this axiom is deceptively simple:
(X * Y) * Z = X * (Y * Z)
where * is any mathematical operation (becoming) such as addition +
and multiplication x. The brackets in (X * Y) * Z mean that first we
have to associate beings X and Y with becoming * before we associate
the result with Z. The equality sign says that there is ONE
underlying, ordered network of beings (X, Y and Z) and becomings (*),
namely X * Y * Z, which makes both (X * Y) * Z and X * (Y * Z)

The Y in the associative pattern X * Y * Z is the intermediate
member. It can be combined with either X or Z before it can be
combined with the remainder of the association. Thus it plays the
role of a commutor or "umlomo" (the Zulu word for a "mouthpiece").
The more complex an association becomes, the more important the role
of the commutor or "umlomo" becomes. Let me illustrate it.

Our first example is from physics. The unprecedented success
of physics is primarily due to its measurements. Copernicus
postulated the heliocentric theory. But nobody was interested - only
a few copies of his book were sold. One copy got into the hands of
Keppler. He began to make very precise measurements on the
movements of the planets. Galilei used them to conclude that the
heliocentric theory made much more sense than the geocentric theory
of Aristoteles. Whereas the theory proposed by Copernicus made little
impact, exactly the same theory proposed by Galilei, but now
sustained by measurements, rocked the very foundations of the church.

All physico-chemical measurements can be symbolised by the following
object * measuring-device * observer
The actual measurement concerns the association
(object * measuring-device) * observer
The observer allows the measuring device to interact with the object
free from the observer's intervention. But after a measurement has
been obtained, the observer interpret the measuring device and the
observation (quantity) as an extension of his own sensory organs.
Thus the interpretation conserns the association
object * (measuring-device * observer)

Let us take our second example from chemistry. Chemistry is about the
making or braking of bonds between atoms. The basic pattern is the
nucleus * bond-electron * nucleus
The ability of the bond electron to commute with both nuclei
(nucleusA * bond-electron) * nucleusB
nucleusA * (bond-electron * nucleusB)
results in the emergence of the molecule. Thus the bond electrons
again act as "umlomos", but now in a quite different manner than the
first example.

We can continue with this line of thinking into even the most complex
phenomena incorporating human culture. For example, a major aspect
of the role of teachers, facilitators and managers is to act as a
commutator or "umlomo". For example, in the case of a teacher we have
the association
reality * teacher * learner.
To be able to teach the teacher needs the experience
(reality * teacher) * learner
But the actual teaching is the association
reality * (teacher * learner)
The ultimate goal of teaching is to gradually replace the teacher
with as diverse collection of "umlomos" as possible, selected by the
learner as each situation requires. Thus the success of teaching is
to obtain the association
reality * umlomo * learner


The word "monad" was first used by Leibniz more than three hundred
years ago to stress the oneness of a logically conceived individual.
I use the word "monadicity" to refer to this "oneness" facet of
"wholeness". Jan Smuts himself used the word "whole". Amost fifty
years later, probably through Arthur Koestler, the word "holon" came
into use. Although the word "holon" itself sounds nice, it is rough
on the ears to make a predicate out of this noun, for example
"holonicity". The closest known word to monadicity is "unity". Please
do not confuse monadicity with monadology.

Probably the most important manifestation of the two facets
"associativity" and "monadicity" of "wholeness" is the dogma of
the "triune godhead" of most christian churches - one God with three
different personalities: Father, Son and Holy Spirit. But as
Augustinus had noted, it is not unique. For example, think of one
plant with three distictive parts: roots, stem and leaves.

When the parts of a whole are innumerous and diverse, we easily
forget this monadicity (unity) of wholeness. Here is way to prevent
it. Ask a question on your favourite topic in a subject which you
know well. Allow yourself the minimum of data to answer the question.
Use the answer to this question as additional data for a nwe
question. Ask a second question using this new data and the first
data. Answer this second question. Use its answer to generate the
third question. See how many questions you can link into one giant
network question. See if you can cover the whole subject with such a
network question. This will certainly test your holistic view on the

The monadicity (unity) of wholeness operates on many levels. When
considering an individual human, the highest level of monadicity is
that between body and soul. On the lower level of, say, the body, the
monadicity is affected by the skeletal, neural, hematological (blood)
and epidermal (skin) systems. These four systems cover the entire
body in contrast to the other organs which make use of them as
commuters to associate with the rest of the body.

But humans have also higher levels of monadicity than the individual.
Failing to realise this leads to individualism. There is also the
social dimension of monadidity levels. The family is at a lower level
than a community which itself is at a lower level than the nation.

It is important to understand that a higher level of monadicity
cannot undo a lower level of monadicity or vice versa.without
seriously impairing wholeness. It is because the hierarchy of
monadicty levels has associativity. It is the task of the
intermediate levels to bond (commute) the lower and higher levels in
any such an association.

For example, people often find it difficult to visualise a "learning
organisation" in terms of a "learning individual". It is because they
contrast these two, rather than viewing "systems thinking"
(intermediate level) to bond "learning individuals" (the lower
level) into a "learning organisation" (the higher level of
monadicity). This is made clear by Senge when he considers "systems
thinking" as the fifth discipline for learning organisations.
Unfortunately, often there is is little monadicity (unity) in "system
thinking" or "personal mastery" so that the learning organisation
will fail to emerge.


The more wholeness is impaired, the less we will have constructive
creativity (emergences and digestions) and the more we will have
destructive creativity (immergences and indigestions). Any viewpoint
which impairs wholeness is fragmentaristic.

Fragmentarism leads to destructive creativity just like
demarcationism (the opposite of sureness). By comparing the lives of
Smuts and Herzog, an unprecedented drama of the struggle between the
two essentialities, wholeness (Smuts) and sureness (Herzog), unfolds.
Each one contributed immensely to South Africa's emergence,
unprecedented in the history of Africa.

However, this woeful struggle between them (rather than a fruitful
inclusion) also caused the breeding ground for the ideology of
"apartheid". Unfortunately, both generals discovered it too late
(Herzog just before WWII and Smuts four years after WWII).
Fragmentarism and demarcationism became the key elements of
"apartheid". Let us be forwarned not to set the seven essentialities
against each other, nor to use the little we know about one or more
of them for destructive purposes. The result can be devastating as
South Africans are now discovering after 50 years of "apartheid".

This is what Smuts had to say after his political defeat in 1948 when
he found out that the ignorance in the minds and arrogance in the
hearts of humans can become almost as strong as the "universal
manifesting force" of the whole:

* "I am now an old man, after fifty years hard labour for the
* advance of South Africa. If there is blame for the present
* future, let it be mine, as no doubt the heavy punishment will be.
* I can take it."

By these words Smuts leads us to our real problem. Those who
endeavour for constructive creativity, are more than willing to
accept resposibility for destructive events. But those who employ
destructive creativity to ensure their own future, seldom accept
responsibility for their deeds. (Just think about India, Pakistan and
nuclear bombs.)

The above is manifested day after day in the present hearnings of the
Truth and Reconsiliation Commision on apartheid. But even the TRC is
failing more and more because of the power of destructive creativity
- the deliberate impairing of the seven essentialities of creativity.

When will we ever learn that there are two roads like the double
helix of DNA? The one is narrow, non-linear, upwards and sparsely
populated. and leads to heaven The other one is wide, smooth,
downwards and over populated and leads to hell. It is easy to go from
the narrow to the wide road - just act as if nothing is essential.

Best wishes


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

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