Non-linear Thinking LO20572

AM de Lange (amdelange@gold.up.ac.za)
Fri, 5 Feb 1999 12:19:01 +0200

Replying to LO20559 --

Dear Organlearners,

Leo Minnigh <L.D.Minnigh@library.tudelft.nl> writes, on what was
Subject: Essentiality - "quantity-limit" (spareness) LO20559

>In my search for clarity of characteristics of each of the 7 axes
>(named 'essentialities) of the creativity-space (thus 7-dimensional),
>At responded some other wise words:

>>Leo, I had to snip your summary. But I want to draw your attention
>>and that of fellow learners to the fact that you have used the other
>>essentialities (like wholeness) to enrich your insight on spareness.
>>Now what has happened here? You are thinking NON-LINEARLY.

>I had a big smile. My whole life and thinking is a continuous
>multidimensional meandering. I have indeed difficulties with straight
>lines.
>
>If we number the axes of the 7-dimensional space:
>1. "becoming-being"-(liveness)
>2. "identity- categoricity" - (sureness)
>3. "associativity-monadicity"-(wholeness)
>4. "connect-beget"- (fruitfullness)
>5. "quantity-limit"- (spareness)
>6. "quality-variety"-(otherness)
>7. "open-paradigm"- (openness)
>
>At forced me to think only in (0,0,0,0,n,0,0), along the axis of
>spareness, whereas I left it and was somewhere at (0,1,3,1,11,0,0).
>I hope to be able to think one-dimensional (linear) again; that is a
>tough task. (I hope you realise that I write this with a grin).
>I realise that particularly with the essentiality spareness, it is a
>great mistake to pull the other essentialities into its characteristics.

Greetings Leo,

Before we go any further, let me use your call "Let your thoughts
meander towards a sea of ideas" in your signature to explain once
again nonlinearity. Let us think of a river meandering from the
mountains towards the sea. The motion of something drifting on this
river will be described by the moving point (x,y,z) in 3D space. The z
coordinate (altitude) will decrease all the way. At every rapid it
will decrease faster than other wise. The x and y coordinates describe
the horisontal motion. Sometimes the x will increase faster than the
y. It means that the river is swerving into the one direction. When it
swerves into the other direction, y will increase faster than x. In
other words, the wondering of the river means that there is no uniform
increase in x AND y AND z. As soon as the river moves in a linear
fashion line like in a straight channel, all three of x, y and z
change uniformly.

OK, let us leave the 3D space of a meandering river to go into a 7D
space of something similar.

Leo, I did not force you to think linearly along the axis
(essentiality) spareness. I forced myself to do so when I discussed
this essentiality. I also had to do it in the case of all the previous
essentialities: liveness, sureness, wholeness and fruitfulness. As you
have noted with a grin "that is a tough task".

Why is the task tough? Is it because the essentiality spareness (like
every other essentiality) is difficult to understand? No. It is
because I have to write about the essentiality spareness while keeping
the other six out of the picture as far as possible. In other words,
its is because I have to move along the axis (0,0,0,0,n,0,0).

Let me try to explain what Leo means by the symbolic expression
(0,0,0,0,n,0,0). This expression is called in mathematics the
coordinates of a point in a 7th dimensional space. Leo calls it the
creative space which is nice descriptive term. The six zeros mean that
there is no extention into any of the six other dimensions. The number
n in the fifth place means that the point has moved some distance
along the fifth axis (dimension) called spareness. In other words, the
point has already uncovered some information concerning spareness.
When n increases, it means that the point moves further along that
axis. Since this axis, like the other six axis, is a straight line,
the motion of the point is linear. In other words, the point is busy
uncovering information on spareness in a linear fashion.

In this fashion my initial contribution on the previous (fourth)
essentiality fruitfulness can be symbolised by (0,0,0,m,0,0,0).
Compare (0,0,0,m,0,0,0) for fruitfulness with (0,0,0,0,n,0,0) for
spareness. In (0,0,0,m,0,0,0) the number m tells us how much
information we have uncovered on the essentiality fruitfulness.

Should we encounter the coordinate expression (0,0,0,m,n,0,0), it
tells us that are now moving on a plane (flat surface) which contain
both the linear axis (0,0,0,m,0,0,0) and (0,0,0,0,n,0,0). Our mental
movement (uncovering of information on fruitfulness and spareness) can
have many forms. It can be a straight line which have the equation
a<m> + b<n> = c
It can also be an open curve like a parabola which has the equation
a<m^2> + b<n> = c
It can also be closed loop like an eclipse which has the equation
a<m^2> + b<n^2> = c
(For a circle a=b=1)

[Host's Note: Eclipse? Probably ellipse. ...Rick]

If I now say that I think nonlinearly about the seven essentialites,
what does it mean in terms of fruitfulness and spareness? It means
that I avoid thinking in terms of any straight line on the plane
(0,0,0,m,n,0,0). First of all, it means that I have to stay clear from
moving along the two axis (0,0,0,m,0,0,0) and (0,0,0,0,n,0,0) because
they are also straight lines. It does not mean that I cannot touch one
of them in a sort of collision (skidding) motion or even cross one of
them. It only means that I must not move along any one of them as if
moving in a groove. Secondly, how will I ensure that I do not move on
any other straight line in the plane (0,0,0,m,n,0,0)? By introducing a
third essentiality, say wholeness. In other words, by enriching my
motion to (0,0,l,m,n,0,0), I avoid straight lines in (0,0,0,m,n,0,0)

I can follow all sorts of paths in (0,0,l,m,n,0,0). Most of them will
be nonlinear paths, either open curves or closed loops. However, the
possibility of straight lines also exists in (0,0,l,m,n,0,0). Three of
them is the axis (0,0,l,0,0,0,0) for wholeness, (0,0,0,m,0,0,0) for
fruitfulness and (0,0,0,0,n,0,0) for spareness. They can be avoided by
not thinking exclusive about any one of them. But how can the infinite
many other straight lines in (0,0,l,m,n,0,0) be avoided? By
introducing another essentiality, say sureness. Thus (0,k,l,m,n,0,0)
motions prevent straight lines in (0,0,l,m,n,0,0).

By continuing this line of inductive reasoning, we will eventually be
moving in the space (j,k,l,m,n,o,p) of all seven essentialities. But
how will we prevent moving in straight lines in this full 7D space
itself?

One very obvious possibility is to keep on with the line of inductive
reasoning. In other words, we have to find an eight essentiality. But
is it possible? Think about how I discovered the seven essentialities.
I searched for patterns of corrspondence (adjunctions) between
chemistry (material world) and mathematics (abstract world). (See CS
Peirce on adjunctive logic and its relation to deductive logic and
inductive logic). Now, unless some mathematician uncovers a completely
new branch of mathematics or some chemist uncovers a completely new
branch of chemistry, the chances of finding an 8th essentiality is
indeed very slim. Hence there is a limit on the number of
essentialities (spareness working on all of them), the limit the
quantity 7.

Another obvious possibility is to fragment the seven essentialities
into more than seven essences. (For example, Peter Senge works with 11
essences in the five disciplines of a learning organisation. see
Appendix 1 of "Fifth Discipline".) But such a proliferation of
essences by unlimited fragmentation is against the spirit of all seven
essentialities. Furthermore, because of all the complications this
possibility will cause, it will lead to unprecented linear thinking to
simplify the issue.

But let us look for unexpected possibilities by enter the realm of
metanoia, a topic which Winfried Dressler, Arthur da Silva and others
are questioning.

A metanoic possibility is to understand that the seven essentialities
do not say all about creativity. They describe the curved path in
creative space which a person's creativity traces. They help us to
observe all the curves (non-linearity) in that path. In other words,
they help us to describe the mechanics or FORM of that path. But they
do not formulate the dynamics or CONTENT of the path. In other words,
they tell us HOW the path curves, but they do not tell WHY the path
makes this or that curve. In other words, as soon as we busy ourselves
with the HOW (seven essentialities) AND the WHY (???????), then our
motion in the creative space will be nonlinear.

It is almost as if the WHY plays the role of an 8th essentiality! Is
this WHY not actually the 8th essentiality? No. Each of the seven
essentialities has to do with the HOW and not the WHY. The 8th cannot
be different from them. Furthermore, what is the ??????? of the WHY as
the seven essentialities are of the HOW? Or to formulate the question
in other words:

What content has the seven essentialities as form?

What a strange (awkward?) question! Almost like the question "Is
learning our earnest?" Is the word "essentiality" (a new English word
which I had to create) which makes it strange? No, I have explained
several times that the seven essentialities are a unique set of
essences. The nature of their discovery makes them complete. They can
be grouped into less than seven essences or be fragmented into more
than seven essences. They promote emergences. They bridge the material
and abstract world. They are so unique that I had to distinguish them
by the special name "essentialities". Let us then accept the word
"essentiality" not to be awkward. Yet the question will remain to be
akward for most other fellow learners. Why?

Is it because the syntaxis of the question is awkward? No. Here is a
question which concerns chemistry. "What content has the tetrahedron
as form?" Methane, CH4. Should I have written
"What molecule has the tetrahedron as form?", I already would have
supplied more of the answer in the question. This is exactly what I do
not want to do. I must try to keep the question as open as possible.
In this sense I should have asked:

What has the seven essentialities?

by leaving out the qualifiers "content" and "form".

But why did I include the words "content" and "form"? Should I have
left them out, I would have put you in more darkness than the darkness
in which I found myself during their discovery. That would have been
dishonest of me. I would have made the question more complicated than
the implicit complexity which it already has. What content did I know
which made the question "What content has the seven essentialities as
form?" not awkward for me?

Leo, I think the question is not so awkard for you any more because
you have written:

>But as you may realise, any reaction on your original message
>is a result of entropy production. It is the paradox of thinking. I
>must force to slow down the flow within myself. Or maybe, I
>should limit the pulling force of my formal knowledge.

But let us leave the realm of metanoia and continue with nonlinear
thinking. The question "What has the seven essentialities?" is a
nonlinear question. How can we make it linear? By asking ANY ONE of
seven independant questions:

What have the essentialitity liveness?
What have the essentialitity sureness?
What have the essentialitity wholeness?
What have the essentialitity fruitfulness?
What have the essentialitity spareness?
What have the essentialitity otherness?
What have the essentialitity openness?

However, if we want to think nonlinearly, we must ask all seven in
parallel. That is very difficult because of the way in which our
neurological system works. Another way is to ask them sequentially
such that as soon as we answer one additional question, we weave it
into the answer of the former question(s). In other words, we let our
answer meander in terms of the previous answers. I frequently enjoy
the almost effortless way in which you let your latest thoughts
meander trough the context of your older thoughts.

>Thank you for the fine reply. I know of the joy which spareness
>could give and even a linear track does have its endless horizons.

But is it not exciting how spareness and meandering are related to
each other? If we keep to a straight line in out thinking by
considering only one topic as if this topic cannot be exhausted, then
our thoughts cannot not meander to other topics. Or to question it
once again, why do Leo not say:

"Let your thoughts rush straight forward to a sea of ideas."?

Best wishes

-- 

At de Lange <amdelange@gold.up.ac.za> 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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