Replying to LO24096 --
In LO24096 I asked you not to get frustrated by the "mathematical traffic"
in that contribution because I used it on purpose. Can my "madness" have
purpose? Is it not "madness" to ask you to focus on something which you
cannot focus on or do not want to focus on.
The purpose of the mathematics in that contribution was to make
you tacitly aware of a common pattern when various forms of
energy become transformed into other forms of energy. I used
as examples the following three forms of energy and formed
(lifted out) the "becoming pattern" for each:
* pneumatic energy (eq. tyre, respiratory subsystem)
[P(2) - P(1)] x /_\V > 0
P = pressure, V = volume
* electrical energy (eq ignition, neurological subsystem)
[E(2) - E(1)] x /_\Q > 0
E = electrical potential. Q = eletrical charge
* chemical energy (eq combustion, anabolic subsystem)
[M(2) - M(1)] x /_\N > 0
M = chemical potential, N = amount of compound
I used for each of these three forms of energy two examples, one taken
from the automobile as an inanimate system (technology) and one taken from
the human body as a living system (biology). By taking examples from both
technological and biological systems, I intended to make you tacitly aware
that we are working with a common pattern worthy for general Systems
Thinking. By using three different forms of energy in each system, I
intended to make you tacitly aware that this pattern is common to all
forms of energy. If I did not succeed to make you tacitly aware as I
intended, then you may blame me. But I will appreciate it much more should
you tell me why my intentions failed.
Although I tried to make you tacitly aware of this common pattern, I did
not try to articulate this pattern in that contribution. The reason is
simply that the stress brought about by bringing formal mathematics into
the picture may cause your mind to explode by immergence rather than
evolve by emergence. However, I have exposed you in LO23887, LO23921,
LO23954 and LO23986 to all the experiences which you will need to
formliase that common pattern which you are now tacitly aware of. So let
us do it!
What then is the form common to all these patterns? To find the andswer,
we will consider all these patterns as content and find the deeper form in
Look at the symbolic expressions above. The following parts, one
from each, correspond. They are:
[P(2) - P(1)], [E(2) - E(1)], [M(2) - M(1)]
They are all DIFFERENCES. Likewaise the following parts, one
from each, correspond. They are:
/_\V, /_\Q, /_\N
They are all CHANGES. In each pattern the DIFFERENCE is
multiplied with the CHANGE. Hence the common form to all these
"becoming patterns" are
DIFFERENCE x CHANGE > 0
which we may shorten into
PAIR > 0
In other words, the DIFFERENCE and the CHANGE form together
a PAIR. What strange PAIRs do we not have here?
The CHANGES are each given by an increment (difference) by
/_\V = [V(2) - V(1)]
/_\Q = [Q(2) - Q(1)] and
/_\N = [N(2) - N(1)].
Thus in terms of PURE mathematics it seems as if each pair
consists of merely two differences multiplied by each other. But
remember Fred Nichols' question. It gave me the opportunity to
explain very carefully that in CONTEXT they are very much different.
Every form of energy is made up by two factors. In the three
exemplary forms of energy they are
* pneumatic energy P(pressure) x V(volume)
* electrical energy E(electrical potential) x Q(charge)
* chemical energy M(chemical potential) x N(amount)
All six factors correspond because all are quantities which each
can be measured by an appropiate instrument in terms of its
own standardised unit. All six factors also correspond in that
each of them can change and that any change in one may cause
a change in any of the other five.
But they also differ in a very important facet. The first factor in each
(P, E, M) is an INTENSIVE quantity and the second factor in each (V, Q, N)
is an EXTENSIVE quantity. This difference can be observed when scaling the
system, i.e increasing or decreasing the system in size. When the system
is merely scaled, all the extensive quantities get scaled too while all
the intensive quantities stay the same. Thus the extensive quantities help
us to form the concept of becoming while the intensive quantities help us
to form the concept of being.
It is as if the extensive quantities for becoming (verb) play the role of
adverbs while the intensive quantities for being (noun) play the role of
adjectives. Should we allow in our Systems Thinking not only technological
and biological systems, but also philological (language) systems, then
some hair raising possibilities come to the mind. Compare me now with me
as a kid many years ago to introduce scaling. Think of the sentence "I
walk QUICKLY" applying to me now and applied to me as a kid. My walking
now is much quicker than my walking as a kid. This points to an extensive
property. But think of the sentence "I am EXCITED" applying to me now and
applied to me as a kid. My excitement is much the same in both cases. This
points to an intensive property.
To become aware of the difference between intensive and extensive
properties of humans, we will have "to scale" humans. The only scaling
available to us is that provided by evolution and growth in us. It is
unethical to cut down any human to a smaller size. Thus we will have to
work also with children and not only adults in our Systems Thinking to
find out in what properties (the intensive ones) we are clearly the same
and in what properties (the extensive ones) are we clearly different.
Thus I find Andrew Campbell's following contribution LO24081 a jewel of
delight and insight. It is so short that I can quote it in whole:
>For Jessica and all the children whose parents 'tap' and
>'peer' into this box while watched curiously by little faces...
>'It is hard to be brave,' said Piglet, sniffing slightly, 'when you
>are only a very small animal.'
>Rabbit, who had begun to write very busily, looked up and said:
>' It is because you are a very small animal that you will be Useful
>in the adventure before us.'
>(From The Te of Piglet by Benjamin Hoff ISBN 0-14-023016-5)
Dear fellow learners, we as adults and children have to explore hand in
hand the "becoming patterns". Without kids there is no adventure in the
future. Systems Thinking without kids is a barren panorama. Thank you
Andrew for making this point very clear.
Should we divide tacitly (i.e. without showing it) every intensive
quantity like (P, E, M) in our examples above by the temperature,
then the resulting DIFFERENCES which we still will write as
[P(2) - P(1)], [E(2) - E(1)] and [M(2) - M(1)] may all be
called ENTROPIC FORCES. In analogy we will call the CHANGES
/_\V, /_\Q and /_\N by the name ENTROPIC FLUXES. Thus,
should we want to put more form into the "becoming pattern"
DIFFERENCE x CHANGE > 0
ENTROPIC-FORCE x ENTROPIC FLUX > 0
or by using the mathematical symbolism which we have developed
[X(2) - X(1)] x /_\Y > 0
Here X is the intensive factor of a form of energy while Y is its
Ilya Prigogine will simplify the last expression into
XJ > 0
where X is the entropic (thermodynamic) force with form
[X(2) - X(1)] and J is the entropic (thermodynamics) flux with
form /_\V. (See for example p137 of chapter V of Order out of
Chaos or p85 From Being to Becoming). He assumes that
his readers will know that in their minds they have to replace
it by any complexer version such as
[X/T(2) - X/T(1)] x /_\Y > 0
or even by seemingly mathematical monstrosities like
gradX/T x divY > 0
In my next contribution I will go deeper into these entropic force-flux
pairs without invoking any further mathematical monstrosities.
Prigogine can afford to make such an assumption because he writes for
mature thinkers interested in physical evolution. Mathematical literacy
is required for the physical sciences. I cannot afford to make such an
assumption because I write for anybody interested in deep creativity,
physical and spiritual. The evolution in deep creativity involves even
that person's evolution in his/her mathematical faculty! A person may have
experienced many obstructions in the evolution of his/her mathematical
faculty. Yet that person may be more compelled by comprehensive evolution
(TO BECOME) than a professor in mathematics caring nothings for creativity
(NOT TO BECOME).
But neither Prigogine nor I nor the mathematics professor are important.
You and our kids as learners are important. What about you dear fellow
learner, do you want to become or not to become? I seldom make promises,
but the following I can definitely promise you. When you focus in any
becoming on love, peace will come along with that becoming. Let us think
about peace because all my mathematical "traffic" in this topic may have
shattered the peace of many of your fellow learners. So what is peace?
It is something for which year a Nobel Prize is awarded to those who
promote peace best. We seem to recognise the invaluable contributions of
the laureates to peace, but we seem not to understand in what sense they
have contributed. After more than 100 Nobel prizes on chemistry (and the
same for physics) our world has changed technologically beyond recognition
for 19th century people. Our world has definitely not become more peaceful
in the same degree.
It seems as if peace go only skin deep. Anxiety and confusion often
disrupt in the organisations in which we participate. Is it because peace
is fragile? Or is it because we mistake that which goes only skin deep for
The dictionary says that a "truce" is an agreement between belligerents
for a temporary suspension of hostilities. Whereas a "truce" is a
reversible cessation of those activities and differences which cause
agitation, "peace" is an irreversible transformation by which the striving
parties are reconciled into a common destiny. Peace ensues by emerging
relationships which establish concord on those differences which had to be
ignored and activities which had to be forsaken in the truce. Thus it is
easy to distinguish between a truce and peace. In peace we know how to
deal with potentially disrupting differences and contenscious activities
while in a truce we bluntly avoid them. It means a truce involves "not to
become" while peace involves "to become" all the way until one-to-many
love will emerge. In a truce people avoid thinking of entropic force-flux
pairs in the circumstances while in peace people know how to manage them.
Mathematical becoming is a fine activity to illustrate experentially the
distinction between a truce and peace. Bring mathematics persistently into
the LO-dialogue as I did on the topic "To become or not to become" and
observe how it once again agitate some fellow learners. A little bit of it
surfaced into carefully formulated, yet hostile, comments worked into the
replies of other topics.
Perhaps the strategy is to intimidate me into resuming the truce "no
mathematical becoming" so that we can have "peace" once again. A few
fellow leaners have even suggested that I myself may have a hidden agenda
which they will finally expose so that all can know what I am actually
doing to destroy the "peace" among us. I have no hidden agenda. My goal
is clear. I want to help each of you and thus also myself to learn how to
evolve in our personality by healing rather than stunting our spirituality
on fragile issues.
I want for all of us the lasting peace of becoming rather than the fragile
truce of being. That is why I have selected mathematics as the contencious
issue in the topic "To become or not to become". I could have selected
any other pretty contencious topic. But as a teacher for close to thirty
years I have experienced more than enough how the great majority of
learners have been hurt by an educational system selling pure mathematics
through rote learning.
I do not claim that I will heal you who have been hurt so much that you
will stop avoiding mathematics at all costs. My experiences don't sustain
this claim. Some learners did each SELF make peace with mathematics
through my midwifery. But to be honest , I have to admit sadly that I also
experienced how many more learners are still FIGHTING FOR A TRUCE on
mathematical activity. Avoid mathematics! Why? One reason keeps popping
up more than all other reasons together -- they cannot heal spontaneously.
Winston Chuchhill once made the cynical remark: "Peace is so important
that we will fight for it." Dear fellow learners, we may fight for a
truce, but fighting for peace is an oxymoron. It is like invoking hate to
obtain love. Love will overcome and thus replace hate, but love needs
faith rather than hate to emerge. Likewise peace will overcome and replace
violence, but violence does not make peace possible. It is rather the
seven essentialities of creativity which make peace possible. Should we
erronously infer that peace needs violence to emerge, we then infer
wrongly by using the Law of the Excluded Middle (LEM) that we have to
fight for peace.
Why it is not true that peace do not need violence to emerge? I have
often written on bifurcations happening at the edge of chaos. The
bifurcation may result into a constructive emergence of higher order or
into a destructive immergence of lower order. Violence is characterestic
of all immergences. Hence, when a bifurcation finally results in an emerge
rather than immergences as in all previous attempts, then peace become
characterestic of such an emergence with a history of immergences. Peace
is not a characterestic of an emergence for a bifurcation which does not
have a history of past immergences.
We should try not to confuse peace with tranquility. Tranquility
is a generative adjoint (like happiness, curiosity and expectation)
of all emergences, whether their bifurcations had a history of past
immergences or not. In other words, those emergence which
transform problems with a history of war (violence and hurt) into
solutions of higher order define peace. Symbolically
war < peace
It cannot be formulated by the equivalence relationship "=" of
being, but requites the order relationship "<" of becoming. The
closest we can come to it with an "=" is
war = NOT peace
I know that the logic involved between war and peace is extremely
difficult to follow. If it were easy to follow this logic, we would have
had far less war and much more peace on our globe. So let me once again
illustrate the relationship between war and peace by an example. We need
the darkness of the previous night for the brightness of the next day to
emerge. But we cannot say that the dark night causes the emergence of the
bright day. Both are caused by the rotation of the earth on its own axis.
Likewise both war and peace are caused by bifurcations. War is caused
when the bifurcation forks into a destructive immergence. Peace is caused
when that same bifurcation does not fork again into a destructive
immergence, but finally fork into a constructive emergence.
It seems as if peace reverses the irreversiblity of becoming -- peace
become manifested when failures of the past become reversed into the
successes of the future. No, time with its arrow (irreversibility) cannot
be reversed so that the past and the future cannot replace each other. The
immergences of the past are just as irreversible as the emergences of the
future which we seek. Thus we cannot transform past failures into future
successes with the peace which comes with it by denying irreversibility.
Peace comes when we have the wisdom to know what patterns in the past have
to be improved upon so that each kind of bifurcations can fork into an
emerge and not into immergences as before. Trying to undo irreversibility
itself has shipwrecked many an attempt to obtain peace.
Some fellow learners may get the notion that I want to convert all fellow
learners into becoming mathematicans. It is not the case. What I want you
to do, is to carefully consider your mathematical faculty and find peace
in whatever has to become of it. I can think of three possible becomings.
I will not try paint a rich picture of words for the peace of each case. I
will rather make use of the musical expressions of artists who did it far
better than I will ever be able to do with words. I do not think they
intended to compose on peace. But I do think that they composed after
having emerged into peace. It is this peace which is so clearly emminated
from their work.
Some of you may never had this faculty sufficiently to explore
even the simplest of symbolic expression while others have
experienced too soon an irreversible loss in it. Here I am thinking
of the mathematical faculty like the ability to see. Some may
have been born blind while others may have lost their sight
irreversibly at a very young age. You will have to know for sure
that it is indeed this case by looking for the peace which comes
with such certain knowledge. Listen carefully how Joaquin
Rodrigo express in his Concerto for Guitar (Aranjuez) this
Some others of you may be caught up in a preparation period
for your mathematical faculty to emerge into an art which will
take the greater part (dozens of years) of your life. As such
you may often find yourself moving to the edge of chaos where
bifurcations will happen. Since you are not yet ready for the
emergence of this art, use your emotions like anger and
frustration to steer away from any premature bifurcation which
will certainly abort in an immergence. Again you will have to
know for sure that it is indeed this case by looking for the
peace which comes with such certain knowledge. Listen
carefully how Ludwig von Beethoven express in his Concerto
for Violin (op61) this peaceful knowledge.
Some of you may have experienced extreme dispair which
may even have made you temporaly insane. Just as hard as
you try to let your mathematical faculty emerge or keep it
emerged, just as hard the system causes it to immerge. You
know that should the system be kinder to you, you would have
advanced much further on the road of healing. In other words,
although you personally have emerged from the bifurcation,
your environment keeps on trying to reverse that emergence
into an immergence. Consequently you find it very difficult to
grow digestively on that emergence. Once again, you will have
to know for sure that it is indeed this case by looking for the
peace which comes with such certain knowledge. Listen
carefully how Sergei Rachmaninov express in his Concerto
Nr 2 for Piano (op18) this peaceful knowledge.
What goes for your mathematical faculty, goes for any of your other
Perhaps you should listen to all three works in one session so as to be
able to compare them and find out which one describes your peace best.
Perhaps you should also try to read biographies on each composer and try
to establish at what period in the composer's life the particular work
emerged. As for me, I need not listen to them any more and have little
time to do so, although I still love to listen to them. I can recall much
of each from my mind whenever I have the need for their consolation in the
But think again also of what Andrew has pointed to -- our little kids.
Observe them closely. See how they get out of their little boxes when
father and mother come to peace. Peace is vital to them. During a
prolonged absence of peace they become zombies -- their little eyes lose
their creative luster. When these little zombies grow up, they care as
little for humaneness as they care whether they will live tomorrow. They
are programmed only for one thing -- to amplify and spread the hurt which
they themselves had to endure.
My wife and my daughter (Jessica's mother) say that Jessica fools me --
she is an angel when I am close by whereas in my abscence she can be very
demanding. I know it is true what they say. But why is it true? Is it
because I want her to fool me or because I am not clever enough to break
her stance? No, dear fellow learners. It is true because I try my utmost
to provide for her a peaceful environment when she is in my proximity. I
know that little as she is, she experiences daily that life can be hell.
Does she not tell me enough? I want her to experience the opposite --
peace can make life heaven. I want her to grow in those experiences which
she will need so that she can help creating peace when she becomes an
adult. I wish I could help a million other kids as I am helping her.
Peace will not come unless it is nurtured by love and all which
love embodies as well as entails. The Hebrews have the word
"shalom". Those wise to the deeper meaning of the word
"shalom" use it when they mean
I have been living for peace
I came in peace
I work in peace
I will leave in peace
My becoming is peace.
God wants peace because he is Love. What becoming do we want?
With care and best wishes,
At de Lange <email@example.com>
Snailmail: A M de Lange
Gold Fields Computer Centre
Faculty of Science - University of Pretoria
Pretoria 0001 - Rep of South Africa
"AM de Lange" <firstname.lastname@example.org>
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