Please have patience with me. I cannot do it any shorter without losing
most of you along the way. Furthermore, that which I now will write about,
has never been touched upon by anyone else.
The worst of it all, this is my second attempt. Our server was beginning
to fall over and I tried to save my work. The email program did not gave
the usual prompts, but simply said "Accepted". When I looked for the saved
copy, it was gone. Today somebody wrote to me in private, saying that he
does not always follow me (putting it mildly). He also mentioned Jan
Smuts. I then realised what had happened. I mentioned Jan Smuts in my
orginal uncompleted version. It was mailed rather than saved in the last
quivering moments of the server! I AM VERY SORRY FOR THE FIRST UNFINISHED,
UNCORRECTED VERSION. IT WAS NEVER INTENDED TO BE MAILED LIKE THAT. I
wonder what has rushed out of mind during the immense entropy production
while writing? (I only get the digests and that happens very slowly here
in South Africa.) I fear that the unconcealed workings of my mind might
have shocked some of you. This second version, unfortunately, will not
have by far as much fire as the first one. Is that not sad? Is it not also
the same with you?
[Host's Note: My apologies also to At and all subscribers. I do try to
catch such errors which sometimes are obvious and sometimes are not.
Each one of you, in some way or another, is involved with at least one
ORGANISATION. Chemistry students are also involved with chemical
organisations every day. One example is the geometrical organisation of
atoms to form a molecule with a definite structure. Knowledge of the
geometrical structure of a molecule is very important because the entire
chemical FUNCTION (reactivity) of the molecule depends on its STRUCTURE!
In order TO CREATE the geometrical structure of a molecule, the student
needs to HAVE SOME MINIMAL ORGANISATION TO WORK FROM. (No creation, even a
mental one, can happen in the void.) The periodic table, for example, can
be used as a minimal organisation, but it is very difficult to do so.
Therefore a step between the periodic table and the geometrical structure
has been created, namely the so-called Lewis structure (named after the
chemist G N Lewis, one of my intelectual heros). The Lewis structure uses
the periodic table as its minimal organisation while the geometrical
structure uses the Lewis structure as its minimal organisation.
Now what is the Lewis structure? It is the ORGANISATION (arrangement) of
the chemically reactive electrons in the molecule. Most students find it
easy to create the Lewis structures of simple molecules. But as soon as
the molecule gets COMPLEX, the students become confused. This confusion
tends to destroy even the little which they know.
One day, about 15 years ago while being troubled about the students and
the difficulties they experienced to CREATE Lewis structures, I wondered
whether it would not be possible to give them a better way to organise
their thoughts on Lewis structures by using the Second Law of
Thermodynamics. This law says that the entropy of the universe must
increase. This increase acts as the primordial cause for any CHANGE,
whether it be towards greater CHAOS or ORDER.
I tackled the problem with a new branch of quantum mechanics, called
dissipative quantum mechanics. It uses advanced mathematical tools (called
operators) to determine how the orbitals in a molecule evolve. This
mathematics was too advanced for most students. Thus I had to create a
simple model to capture the essence of it all. The result was COMMUTATION.
Commutation allows us to trace (map) the increase in the entropy of order
(being entropy) as a result of an emergence. The students found
commutation to be a simple, yet powerful tool with which to create complex
Lewis structures. It also showed them, for example, how the the creation
of entropy leads to the emergence of every possible type of bond in the
molecule. I was delighted because for the first time ever I had a
quanittative model to illustrate emergence in the chemical world.
Only afterwards I began to realise that commutation allows us to trace the
entropy of being (order) and thus the Second Law in any organisation and
not merely chemical organisation on a molecular level. Sometimes, when I
read a book on system thinking and figure out a methodology set out in it,
I realise how much of it could be said in terms of commutation. So what is
the definition of commutation?
Definition:- Commutation is the INTERACTIVE SHARING of any number of minor
complex organisations among any number of major complex organisations any
number of times which then results in the EMERGENCE of an even MORE COMLEX
hyper-organisation. Commutation may also be quantified by what I call the
Commutation Number (CN) which I will explain below. That is all to it! Is
that not minimal organisation to the bone?
Let us rename 'minor complex organisation' to TRON, 'major complex
organisation' to KERNEL and 'hyper complex organisation' to HYPERORG in
order to have shorter names. Let us see how the CN (commutation number) is
If one kernel and one tron commutes, then CN=1x1=1. We say that a
monokernel, monotron hyperorg has emerged. If one kernel and each of three
trons commute with it, then CN=1x3=3. We say that a monokernel, tritron
hyperorg has emerged. For numbers greater than three, we may also use the
general suffix poly-. Thus, when one kernel and each of seven (hepta-)
trons commute with it, CN=1x7=7 while a monokernel polytron hyperorg has
If two kernels both commute with one tron, then CN=2x1=2. We say that a
dikernel, monotron hyperorg has emerged. If two kernels both commute with
three trons, then CN=2x3=6.
If each of five kernels commute with one tron, then CN=5x1=5. We say that
a polykernal, monotron hyperorg has emerged. If each of five kernels
commute with each of six electrons, then CN=5x6=30. A polykernel,
polytronic hyperorg has emerged.
So far nothing exciting has happened. The arithmatic is also elementary.
Let us then see what happens when two hyperorgs themselves begin to
commute so that an even more complex hyperorg emerges. Let us keep it very
Assume that monokernel hyperorg A, having 5 trons, commutes with hyperorg
B, having 7 trons, as follows: hyperorg A allows 2 of its trons to commute
also with the kernel of B and hyperorg B allows 3 of its trons to commute
also with the kernel of A. The 5-2=3 trons in hypeorg A which are "shared"
only with the kernel in A are called UNSHARED trons. The 2 trons in A
which are shared with the kernels of both A and B are called shared trons.
In other words, hyperorg B has 7-3=4 unshared trons and 3 shared trons.
Let us now calculate the commutation number CN resulting from
this new commutation:
* CN = (1x3 + 2x2) + (4x1 + 2x3) = 17.
The numbers in the first pair of brackets refer to hyperorg A
and the numbers in the last pair of brackets to B.
* Let us find the sum of the CN of the hyperorgs before they
began to commute.
CN = (1x5) + (1x7) = 12
* Compare the two CNs:
When two separate hyperorgs A and B in a system begin to commute,
the CN of the system INCREASES (from 12 to 17 in the example)
while a more complex hyperorg EMERGE. In other words, this result
trace exctly what the Second Law says: the emergence of a more
complex creation is the result of the increase in entropy,
specifically the entropy manifested as order of being.
* We may also formulate the comparison of the two CNs as follows.
When a hyperorg AB emerge from two commuting hyperorgs A and B,
the CN OF THE COMMUTING HYPERORG IS MORE THAN THE SUM OF THE CNs
OF THE UNCOMMUTING PARTS. Compare this with the definition of
holism: the whole is more than the the sum of the parts. In
other words, commutation quantifies almost what holism says.
Are you getting excited? Take it slowly because there is more to come.
Let is think of this very forum/list for LOs which Rick is caring for.
Each member of it is a creation - a hyperorg. The forum itself is a
creation - a hyperorg. Let us trace the role of commutation when this list
itself becomes a LO!
Every person is a hyperorg. Think of the physical/material part of that
person as the kernel and of every distinct thought (tacit or articulated)
in the mind of that person as a tron. All the trons which that person HAS
SELF CREATED, commute with that person's kernel (neural system and rest of
the body). Thus the person (hyperorg) has a very high CN, say CN(A). This
is the case when A has not yet commuted with B. Thus al the trons of A are
unshared. The same applies to person B with CN(B). Thus the total CN
before any learning/dialogue/commutation between A and B takes place, is
Assume a dialogue begins between persons A and B. In other words, allow
commutation between hyperorgs A and B . Let A make one tron available so
that it can also commuted with B. For example, the tron might be: "I, Jack
Smith, enjoy learning organisations". The commutation happens as soon as
the kernel of B finds the tron of A attractive, i.e. reacts positively to
it. For example, "My, what an interesting person you are". Thus A has
CN(A)-1 unshared trons, B has CN(B) unshared trons and there is 1 shared
tron. Consequently the commutation number increases to
(CN(A)-1)x1+1x2+CN(B)x1 = CN(A)+CN(B)+1. This is an increase of 1.
Let B now reply by making 3 trons available of which A finds only two
attractive enough to share. Thus B now has 3-1=2 shared trons and CN(B)-2
unshared trons while A still has CN(A)-1 unshared and 1 shared tron. Thus
the commution number increases to (CN(A)-1)x1+(1+2)x2+(CN(B)-2)x1 =
CN(A)+CN(B)+3. Meanwhile, what has emerged? A more complex hyperorg
emerged called by the names mutual understanding, caring, friendship, etc.
Thanks to Peter Senge, we can use the generical name LEARNING ORGANISATION
to refer to these names collectively.
We can make a very important generalisation. Think of a person who makes
one unshared thought (tron) available and it commutes with N bodies
(kernels) in a LO. (The LO obviously contains more than N members - do you
still remeMber the EXCITING thread Inner circle -> Outer circle?)
Consequently the CN of the LO will increase with N. If, however, the
person makes so much thoughts (trons) available that M of them each
commutes with N bodies (kernels), the CN of the LO will increase rapidly
with MxN. From this we may conclude the more complex the commutation in a
LO becomes, the more the CN of the LO has to increase. As has been said
before, this increase in the CN traces the increase in entropy which is
required by the Second Law of thermodynamics.
One word of caution. Do not confuse commutation with communication.
Commutation is a much more general and less predicated concept thaN
communication. Commutation happens in the nuleus of an atom between the
protons and neutrons (check your nuclear physics). It happens in a
molecule between the kernels (check your molecular chemistry). It happens
between my succulent plants and the environment which I lovingly provide
for them in my nursery. It happens in the desert when I and a Sun person
(Bushman) meet each other and begin a dailogue. It happens when I and a
student learn together - the student about the learning material and I
about entropy, creativity and learning. It even happens in my church on
the level of spirituality.
On the other hand, vilification, rudeness, arrogance, ignorance. etc., are
all negative activities which indicate that a thought (tron) made avaiable
for commutation (interactive sharing), has not been commuted. Thus the
tron remains unshared. In other words, the CN does not increase. In fact,
these negative activities may even break already shared trons loose. For
every such a break the CN decreases with 1. Does this means that the
Second Law becomes invalid? No, what happens, is that only a certain kind
of entropy (entropy manifested as order of being) decreases. Since the
total entropy has to increase, the other kind of entropy (manifested as
chaos of becoming) will have to INCREASE MUCH FASTER than the decrease in
entropy of order. In other words, negative and destructive feelings causes
immergEnces, make the organisation more chaotic and hence decreases its
The fact that the CN traces not the total entropy, but only that part of
it which is manifested as order of being, has its advantages and
disadvantages. One of its advantages is that it quantifies the law which I
call the Law of Inverse Lusts. This law says that the positive lusts (to
learn, to honour, to care, to understand, to love) are inverse to the
negative lusts (to vilify, to denigrate, to ignore, to hate). In other
words, when the lusts of the one type increases, lusts of the other type
have to decrease. This is exactly what the bible says: sweet and bitter
water cannot come out of the same fountain. This can now also be
quantified by the commutation number. If the positive lusts increase, the
CN increases, but if the negative lusts increases, the CN decreases.
Sherri Malouf, do you understand this law better now?
Yesterday, the wife of a friend of mine phoned me. She asked me, very
embarassing to both of us, whether I have seen anything going on between
him and a certain other woman. I replied that I have not seen or heard of
anything between them and that it is the truth. She said she do not know
whether she should believe me or not because I sounded as if I know
something. She also said that my friend does not want to continue with
their marriage. I felt very sad because he is my friend, she is a fine
lady, the break-up of any marriage troubles me and I know the Law of
Inverse Lusts. A few months ago I became aware that in my friend the
positive lusts were decreasing while the negative lusts were increasing.
His wife is right, I knew something, but how could I explain to her that
my knowledge came through the Law of Inverse lusts?
Have you commuted with the trons above - trons which have commuted for
many years with only my kernel?
At de Lange
Gold Fields Computer Centre for Education
University of Pretoria
Pretoria, South Africa
"Mnr AM de Lange" <AMDELANGE@gold.up.ac.za>
Learning-org -- An Internet Dialog on Learning Organizations For info: <firstname.lastname@example.org> -or- <http://world.std.com/~lo/>