Linear thinking LO22819

AM de Lange (
Thu, 7 Oct 1999 15:05:58 +0200

Replying to LO22800 --

Dear Organlearners,

Vana Prewitt <> writes:

>The terminology is not mine, but that of the field of cognitive
>science. I only attempt to explain how these terms have
>meaning when attempting to provide education. As I
>mentioned in my post, the term I find more accessible is
>"branching logic" as it refelcts a different approach to
>understanding than "linear logic." The term "global thinking"
>has been used in the cognitive science literature to describe
>those who use "branching logic."

Greetings Vana,

Allow me to tell about my own perception of logic and how it evolved.

I majored for the BSc in chemistry, phsyics and mathematics and for the
MSc in phsyics. My academical environment was typically the traditional
natural science one which we find all over the world -- strong in logics
and empirics, weak in the humanics and creativity. This environment pushed
upon me the notion that logic and experiment will save the world.

I was willing to give this notion a go, but two issues troubled me. The
one is how logic and experiment are related to each other. The other is
how could logic and experiment save the world while each of most natural
scientists do research on what is but a very small part of a very complex

If a million scientists each make only a few strokes on a picture called
science with a paint called experiment and a brush called logic, how do
they each ensure that the picture will eventually make sense when each
painter care so little about what each other painter is doing. My
lecturers could not resolve these issues for me so that I created my own
answers to them.

However, I soon discovered that my own answers were both far too
simplistic and thus not even worth trying to verify. I then began to
wonder more about why I created such simplistic answers rather than trying
to create a complex answer. It took me more than ten years to understand
why -- my concepts of logics and empirics were far too simplistic. Let us
focus on how in those days I had been conceptualising logic. It is a sad
story of how I had been learning blindly about logic.

I assumed that "logic is out there" and that I merely had to open myself
so that "logic will come into me". All logic within me came orginally from
outside me. The logic outside me is one coherent system working easily and
perfectly while the logic within me is a shattered image of this system,
an image which was difficult and inferior to work with. Creating a good
image of this "logic out there" was the work of specialists called
logicians. The best which I could do myself is to find the best image and
then merely apply it. So began my search for more than a decade for the
best image to apply in my own work.

My own work was interdisciplinary (like chemistry, physics, mathematics,
soils, biology on the one hand and like operational research, history,
anthropology, economy, psychology, politics and theology on the other
hand). Why such a "jack of all trades"? I wanted to know what learning
and creativity amounts to so that I could teach better. I jumped into
every subject wherever creativity and learning (my own as well as that of
my students) took me to.

Thus, Vana, I fit that description of "branching logic" (right brain
thinking, one-to-many-mapping) perfectly. But why do I fit that
description? Because I was trying with "linear logic" (left brain
thinking) to find a one-to-one-mapping (functional relationship) between
creativity and learning. In other words, I also fit the other side!

As a teacher I became aware of some strange "logical patterns" among
questions and others among learning objectives. I extended my search for
the best logical system in declarative logic (logic of statements) to
interrogative logic (logic of questions) and imperative logic (logic of
commands such as learning objectives). I soon changed my viewpoint on
logics dramatically. Why?

I realised that logic, the "holiest of disciplines" had feet of clay.
More than 99.99% of all advancements in logic were in declarative logic --
the logic concerning statements which are sentences fixed in time. Very
little research has been done in interrogative logic and imperative logic
-- logics concerning sentences which have an arrow like time. Even less
advancements have been made in this research because the logical patterns
among questions and among commands seemed to be much more complex than in
statements. In other words, the advancements in declarative logic seemed
to be the easy and simple option. I became deeply under the impression of
just how complex the logic of teaching is because a good teacher has to
use questions and commands as frequently as statements when exploring the
winding path of truth.

I also realised that "deep logic" (concerning statements, questions and
commands) had its own theory AND practice, rather than being merely a
theory taking care of truth in the abstract world. This helped me to
perceive that most logicians busy themselves only with the theory of
declarative logic and not also the practice. In other words, these
logicians were trying to create a closed logical system within which all
logical inferences have to happen. I was very mad at myself for being a
fool such a long time by assuming "logic is out there". Truth is not only
to be found inside the closed logical system.

The logical system is rather a "system of minimum logical awareness" to be
used as a "sensory organ" to observe truth in the whole of reality "inside
and outside me". The theory of logic is to create a "sensory organ" with
as little distortions as possible and the practice of logic is to apply
this "sensory organ" to whatever topic from reality which comes to mind by
way of statements, questions and commands. I began to discover how certain
logicians like Frege, Peirce, Lukasiewicz, Brouwer and Rosser seemed to
have felt the same, but did not express this felling clearly.

I realised a number of other things also. But to prevent this contribution
from becoming too lengthy, I will restrict myself to the most important
realisation of them all. I began to realise that creativity as a whole,
whatever it supposedly involves, is a prerequisite of logical thinking. We
cannot think about the logical patterns (patterns which preserve truth) in
our thoughts unless we create such thoughts. Every example used by every
logician to illustrate some logical pattern concerned thoughts which were
first created by that logician. The nature of the logician's creativity
thus influences the logical theory which the logician will create, the
application of that theory and the very practice (complexity of thoughts)
to which it will be applied. Should the logician create thoughts in a
linear or non-linear pattern, so will his theory and practice of logic
also respond. In other words, the linearity in thinking is not due to the
very nature of logic, but to the nature of the creativity sustaining that

I began to search for logical studies reflecting some contemplations on
the role of creativity in logic. There was even less to be found than
logical studies on questions and commands. Wheras I began to become
intensely aware of logical patterns in creativity and creative patterns in
logical systems, a sort of "cold war" took place between thinkers on logic
and thinkers on creativity. The prevailing consensus was that logic and
creativity excluded one another -- another sad case of academical

I did find one wonderful man, L E Brouwer, who thought much about the
roles of "construction" and "intuition" in logic. In those days before
WWII the word creativity was seldom used. Because of his disregard for
the exclusitivity between logic and creativity, he was unwelcome among his
peers in logic for the greater part of his life. But (through his own work
and guidance to a younger generation), constructionism and intuitionism
eventually caused a major revolution in mathematics, eventhough almost
half a century later. Perhaps the most remarkable of this revolution is
that it helped to break through linear thinking which prevailed so much in
mathematics, bringing new hope for consistency and coherency in

>I also agree with Chuck Mays comment that "linear" thinking
>excludes; nonlinear feedback, double-loop learning, delayed
>feedback, leveraged action, power laws and other "systems"
> and complexity qualities. Thus, linear thinking is nonsystemic.

Vana, you have made a most profound statement to which I agree: ""linear"
thinking excludes". I think this exclusivity <==> linear thinking is such
an important insight that we have to scrutinise it more carefully in our
dialogue at some later time.

We must be very careful of what I call "hyper linear thinking". It means
that we make use of "linear thinking" in order to escape/emerge/deny/.....
"linear thinking". Fred Nichols, for example, sensed something strange
going on his "hyper linear thinking". (See my reply to him).

Now, should we see the correspondence exclusivity <==> linear thinking how
can we exclude nonlinear feedback, double-loop learning, delayed feedback,
leveraged action, power laws and other "systems" and complexity qualities
from linear thinking?

To curtail any system which behaves basically non-linear into one which
behaves linearly, we cannot exlude nonlinear feedback, double-loop
learning, delayed feedback, leveraged action, power laws and other
"systems" and complexity qualities. Should we do so, we will end up with
a system not changing at all. To curtail the non-linear system into a
linear mode, we have rather to make EXCLUSIVE ADJUSTMENTS to the nonlinear
feedback, double-loop learning, delayed feedback, leveraged action, power
laws and other "systems" and complexity qualities! In other words, we
adjust the system so that it will operate linearly by excluding all
possibilities in every system quality except those which force the system
to operate linearly.

Let me give an example. Consider a person of whom the heart does not
operate normally. If we want that person to live like someone with a
normal heart, we cannot take out the abnormal heart because the person
will die. We cannot even replace the abnormal heart with a technological
heart which operates perfectly, but otherwise do not fit into the rest of
the physiology of the human body. The closest we can come to a perfect
replacement, is to use the heart of another person. That is why heart
transplants developed in the first place.

The operation of a heart is normal because it can operate under a variety
of conditions for each factor which influence its operation. The heart is
normal because it can "dance to its changes". The abnormal heart fail to
make some steps in this dance. It cannot make changes in its regular
changes. It requires exclusive dances rather than participating in all
sorts of dances. To bring it back into a normal operation, it has to
"learn" (operation, medicine, excercise, diet) how to cope with conditions
excluded in its abnormal operation. This "learning" requires nonlinear
feedback, double-loop learning, delayed feedback, leveraged action, power
laws and other complexity qualities.

>>the eater who starts with soup, goes on to salad, then
>>entree, then dessert is a linear eater, right?
>I have to assume this is a facetious question, but the
>answer is "not really.". More to the point, the person who
>eats all his lamb before touching the rice, or who eats all
>the crust before eating the fruit in the pie is a linear eater.
>The person is focused on details rather than the big picture,
>and approaches the task by taking pieces apart rather
>than absorbing it as a whole.

Vana, do we not think exclusively and thus linearly again by focusing on
the big picture rather than the detail and by synthesising rather than
analysing? We cannot use telescopes to look at the stars and microbes. We
cannot use jumping to cross rifts and stacks of eggs in trays. What we
have to try and understand, is that our structures and process have to
commute. When we want to loosen a bolt, we use a spanner and when we want
to pull a spine out of the flesh we use a tweezer. In other words, our
beings and becomings have to harmonise.

We not only have to seek harmony between beings and becomings, but also
harmony (commutation) between pairs of becoming-being. For example, assume
a person eats first that (lamb or rice) which he if most fond of. This
assumption is no law. Another person may want to eat last that which he is
most fond of. The first person may have a smaller capacity for food than
the second person.

Sometimes it is sheer joy to eat sequentially the various dishes during
dinner to experience the otherness (diversity) among the dishes. I do
this after I have "read" the mind of my wife or one of my daughters who
have prepared that specific dinner. If the cook had otherness in mind when
preparing the dinner, seek to fulfill the expectations of the cook.
Sometimes I try to be "naughty" just to see how far my experiments will go
in these essentialities. For example, I will making a "stew" out of the
otherness which the cook have so carefully prepared, or separate the
various components of a stew into different "dishes"
-- if looks could kill ;-)

Making a stew by carefully blending different dishes at various times
during cooking is a wonderful way to experience wholeness at dinner. We
call it "potjiekos" (pot food) in my mothertongue Afrikaans. Making
"potjiekos" is an art, rich in theory and practice. It requires much
non-linear thinking to prepare with what is available. But making a stew
every day or two, week in and week out, buying the same ingredients
repeteadly, is not an art any more. It is a banality. It makes one rather
wanting to eat saw dust. Why? Because what was once non-linear cooking has
now become linear cooking.

>>If this is so, one possibility is that hypertextual thinking,
>>channel surfing, to much globalizing, doesn't help students
>>learn to find the "line," the "thread," the pattern that brings
>>"all relevant parts together at the end."
>I'm afraid I do not understand this hypothesis and would
>welcome your help. Could you provide examples or

Obviously, I cannot clarify on behalve of Steve. But what I have to do for
myself, is to clarify the little understanding between Vana and Steve.

Winfried, this is for you because you seems to be the only one who
followed my example of the political interaction between Herzog and Smuts
(father of holism). They were two prime ministers of South Africa before
WWII and thus the era of apartheid. Vana reminds me of Smuts (perceiving
wholeness as the key to undertanding) and Steve reminds me of Herzog
(perceiving sureness as the key to understanding). Each party assumed the
same two essentialities (sureness and wholeness) to have an order of
presedence. But since the ordering of the two parties were opposite, they
were not able to understand each other. Bring in another five
essentialities and we have 7x6=42 different binary orderings possible.

Herzog and Smuts debated far too much on things which concerned sureness
and wholeness directly and thus far too little on things which concerned
liveness, fruitfulness, spareness, otherness and openness. Thus, although
they succeeded in a mutual understanding (almost like a truce) in the
middle thirties (because of the Depression), this understanding was too
fragile to sustain the destructions of WWII. Something as bad as a war
requires a mutual understanding on all seven essentialties to prevent all
parties from becoming insane. Herzog died in the beginning of WWII, but
Smuts became a leaning pillar for the allied forces. (See Churchill's
acknowledgements on Smuts.)

Smuts often commented on the "insanity of humankind" during WWII ,
surprised by the fact that identity and wholes alone were not sufficient
to prevent the insanity. After WWII Smuts perceived a much greater
insanity developing in his own country, one to which he eventually lost
the election of 1948. It was apartheid in the making. All his guidance on
wholeness and that of Herzog on sureness could do nothing to prevent
people from getting intoxicated by the ideology of apartheid.

>I'm less concerned about which theory explains the world
>as I experience it, as I am in understanding that world, being
>able to make sense of it, and manage it effectively. The
>right brain / left brain research does a nice job of helping me
>make sense of varied learning styles, an issue I contend with
>daily as an adult educator.
>Alternative theories will have to be as equally accepted and
>promoted by researchers and scholars to receive recognition
>and promotion within formal educational systems.

Vana, Leo began the topic on "What is love?" with a lovely
contribution. I will respond to that one in due time. But I
think that some time or other we will have to focus our
dialogue on "What is theory?" There are some important
questions to answer, like:
* When is an exposition a theory?
* When is a theory valid?
* When is a theory good?
* What role should time play in a theory?
* How do we create a theory?
* How do we learn a theory?
* Can a theory reflect understanding?
* Can all understanding be reflected by theory?
* How is theory related to practice?
* Which comes first, theory or practice?
* What makes a theory obsolete.
* What can we use when an obsolete theory
cannot be replaced by a better one?

>It seems less a matter of resistance to change as it may
>be that the proof of validity is on the newcomer.

Perhaps the greatest factor for not being able to deal with old and new
theories are one or more deficiencies in our creativity rather than
"resistance" or "lack of proof". I am often astounded at the creativity
of people to find a reason(s) why their creativity took a dip. It is as if
they make use of some tacit knowledge which says: "only creativity can
protect creativity". Is it creativity which protects creativity, or is it
an outcome of creativity which protects it?

Finally, Vana, I want to thank you for widening the web on linear thinking
to include things such as logic food, education, etc. It made my task more
difficult and much more lengthy to reply to most of your contribution in a
fair manner. But it also made my task delightful because it shows that
linearity is something which requires careful Systems Thinking.

You have written "Thus, linear thinking is nonsystemic." I have to differ
slightly from you. Excessive linear thinking is typical of the linear
behaviour of any system at its dying age. It signals that the system is
about to stop acting as a system in its present order. It requires a
profound knowledge of the seven essentialities to perceive what kind of
future the system will fork into. Why? It signals that some bifurcation in
the near furture is emminent. Only the lack of high entropy production
prevents it from plunging so deep into chaos that the very edge of chaos
can be reached.

Operating close to equilibrium into a magnificent digestor does not make
the system less of a system or even a non-system. It calls for the vision
of leaders how to guide people into a new future when the creative
collapse arrives. Linear thinking and simple thinking are closely
related. Since the dawn of humankind the far majority of people have
assumed tacitly that life has to be simple. This simplicity of life is
about to crash. Feel it, smell it, taste it, hear it and see it -- the
assumption of simplicity or linearity cannot serve humankind any more and
will never do so again in the near future.

We may still try to get as much mileage as possible from linear thinking.
But what about our children, grandchildren and all the children after
them. Education does not concern us, but them and their future. Their
future is one in which they will have to assume that reality is complex,
having more pleads than a face withered by the desert. Up to now FORMAL
education had been the last faculty in academics to change because of a
changing reality. If it keeps on doing so, I fear that this will be the
very suicide of formal education. It will do our children and
grandchildren great harm, but they will survive because informal education
cannot die.

The LOs which kept education alive operate mostly in informal education.
These LOs (seemingly insignificant organisations in the community like
families, neighbour caring groups, reach-out societies) will be the rescue
of our children and grandchildren. Should the present formal system
collapse, these LOs will organise a completely new formal education. They
may not know that they are LOs. They may not even know about the five
disciplines, neither creativity nor when it swings to the linear
assymptote. They will probably not even perceive how they non-linear their
organissing of a new formal education is. But because they care for
creating, learning, believing and loving children and thus became LOs in
the first place, they will become the midwifes to the emergence of
humankind to a higher level of consciousness.

The tragedy about the Titanic is that so many believed the ship was
unsinkable and that so few could act in a responsible manner when it began
to sink. The reason for this tragedy was the prevailing linear thinking.
Linear thinking is the ship Titanic -- straight on course to collide with
the iceberg of ignorance, proving once again that ignorance is most

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

Learning-org -- Hosted by Rick Karash <> Public Dialog on Learning Organizations -- <>