Reification LO21847

AM de Lange (
Mon, 7 Jun 1999 15:21:27 +0200

Replying to LO21834 --

Dear Organlearners,

Andrew Campbell <> writes:

>My name is Andrew Campbell. I live in a small community near
>the city of Oxford. I have been reading from you list for about a
>year. A few weeks ago I wrote this contribution privately on the
>general subject of creativity in the ***creative course of our
>to Mnr At de Lange.
>He replied,

>>It is a beautiful piece. I was moved by it. Your mind is far more
>>mathematically tuned than you would ever believe. You are, what
>>I would call, a classical example of someone intimidated by the
>>formalism of mathematics, loosing all his mathematical wits as
>>a result -- Digestor action par excellence. Scrape the daring
>>together and send it to the LO list.

Greetings and welcome Andrew,

There are so many thigs that I want to write about. So I will rather
stick to the main things.

First of all, why did I say that your mind is far more mathematically
tuned than you would ever believe? To answer this, we need a
definition or an epitome of mathematics.

A definition of something is the beginning of the creation of that
thing. For example, the definition of life is the replication of
complex molecules making use of catalysts. Another example, the
definition of a crystal is the seed crystal which is the smallest
number of building blocks to set up a regular lattice capable of

An epitome of something is the summary of all the creation involved
with such a thing. For example, the epitome of life is that all
existing life forms derive from living antecedents. Another example,
the epitome of a crystal is the crystalline state competing with the
amorphous solid state, liquid state and gaseous state.

A definition is like the beginning of a movie whereas and epitome is
like its end. In some movies the end suggests a new beginning, leading
to successive cycles when the first cycle proves to be a block buster.
Mathematics is like such movies for me. Therefore I like the following
definition of mathematics very much, a definition which also serves as
its epitome: Mathematics is the study of the form of any content so as
to create new content.

After the first time reading through your contribution, I was struck by
the beautiful way in which you expressed your life. Then I went
through it once again counting how many times you proceeded from form
to content. When I reached thirty, I stopped counting to go back to
another thing which you have mentioned. It is:

>I recall when sitting in the classroom the sheer terror of not
>being able to apply the mathematical model to the world, I felt
>alienated from it, frozen. I suspect one way and another this
>experience is common at all stages of our development as

I have had a similar experience my first year in secondary school as a
thirteen year old teenager.

But first I must tell about my years in primary school. I seldom, if
ever, learned by memorising things. (For "sunday school" at church I
had to memorise verses from the Bible and the hymn book. I did it in
the fifteen minutes I had to walk to church, but I hated it every
minute. It meant that I did not have time to connect to the world
around me as when going back from church to home. Today I cannot
remember even a single line of the thousands which I had to memorise.)
All those years at primary school I was always one of the top 5%
performers. I was continually puzzled by two perceptions. Firstly, the
majority of my fellow 5% performers relied on rote (parrot) learning
to perform. Secondly, the majority of the low performers (the bulk of
the class) failed because of their inability to memorise things. None
of it applied to me. However, I never got so far as trying to
understand the way in which I learn. Nobody ever told me to think
about the "learning of learning". (Today I understand how the second
learning corresponds to form and the first learning to content!)

After a couple of months at high school, we got to the topic of
integers (positive and negative whole numbers) in the math class. In
primary school we were never told about the existence of "signed
numbers". I do not know what happened, but after a week I suddenly
became aware that I do not understand a single thing about these
"signed numbers". It was the first time such a thing ever happened in
my life. Cold fear took hold of me. I often heard stories how pupils
fell out from high school because learning got too tough for them. Was
this what "too tough learning" is about? Was this my first step to
failure? I desperately tried to memorise what the teacher had told us
about "signed numbers".

My fright got even worse when I experienced that, although I seldom
had to memorise things, my memory failed utterly to memorise the
theory of signed numbers. When I turned to my friends, high and low
performers alike, most of them admitted that they also did not
understand a thing. A few of the high performers (sustained by
excellent rote learning) exclaimed proudly that they understood
everything. I felt cheated out of a secret -- not realising that for
them understanding means the ability to remember. My senior cousins
who also struggled with mathematics could not help me. My father and
mother could not help me because they did not learn such things in
their days at school. The teacher became so irritated because his well
meant efforts went up in flames that he was not patient enough to help
us through the crisis. After three weeks I wanted to leave school, but
my parents reminded me that I am still under age. I did not know what
to do.

So one day, about a month of utter dispair, I sat in the pidgeon pen,
staring at my pidgeons, trying to think what to do. If they can find
their home after a thousand killometer journey from anywhere, why
cannot I do the same in mathematics? Surely, pidgeons are not more
clever than me! What do they do when released in a strange place. I
have seen it many times -- the puzzling look of utter bewilderment and
firm conviction in their eyes when they are let out of their baskets.
Then they begin to circle around and around, increasing the diameter
until suddenly one breaks lose from the pack into the right direction,
soon to be followed by some others. Eventually the remaining flock
would follow these individuals, but never catching up with them (as
far as I could see by using binoculars). My father and I usually
rushed to home, trying to see wheter it is these individuals who
arrived first at home. It was often the case.

So what will I have to about these signed numbers? Circle around them,
looking at them from all viewpoints, thinking where I want to go with
them. Up to this day I cannot remember what happened in that pidgeon
pen, but when I got out of it, I rushed to my books to see if I could
do the excercises. After a couple of failures I got some of them
right, and before the end of that day I could do every exercise. The
next day I felt even more puzzled. I was able to help my friends to
understand "signed numbers". They helped others and eventually the
crisis was rseoved in a few days. But I could not remember what the
things about "signed numbers" were which I could not understand! This
observation puzzled me the next twenty years of my life -- why is it
so difficult to remember things which I do not understand? I became
fond of chess. I could memorise the layout of a partially completed
game in a few seconds, but not the layout of a game by simply placing
the pieces as if a game was partially completed. It had to be an
actual game.

>It is the polyphony of clouds that interests my spirit of learning.
>What I could not know then was that this time in my life when
>I lost the thread of mathematics was called latency, and at this
>time part of my whole creative or 'poetic' sensibility was being
>lost in the artifice of inept maths teaching. In this I lost a
>connection to reality as a whole and today one of my joys is to
>recover the loss by studying the sheer visionary beauty of Mnr.
>de Lange's explanations of the riddles of the whole expressed in

Thank you Andrew for your kind words.

As for my self, up to that terrible month in maths, I was never
conscious of self-learning. (Today I would call it self-organisation
with respect to learning). But that incident made me conscious of
self-learning. However, although I practised self-learning the next
ten years in my academic life, it all happened tacitly! I never
reached the level of articulating this tacit knowledge. I never
encountered the concept of tacit knowledge, even after having obtained
a MSc in physics (1967). (Michael Polanyi formulated the concept in
the same year.) I never knew how much I had been articulating my tacit
knowledge and how I was doing it.

In my second year of reseach into the physics and chemistry of soils,
my technician Frans Visser came to me -- worry written over his
fatherly face. His son was in his first year at secondary school. He
was having difficulties with mathematics. His performance fell from
above 80% in primary school to below 20%. As Frans was painting the
richer picture and I was listening, the haunting ghosts of my own
struggles visited me like in a nightmare. I felt as if I was becoming
sick. I could not believe that my similar experiences so many years
back, almost forgotten, had still such an influence on me. I promised
Frans to do what I can. The next Saturday his son came to my home.
What happened?

After an hour of explaining I realised that his son was compeletely
confused and that no amount of explaining would ever rectify the
situation. I also realised a second thing. I was not trained as a
teacher, although I had contacts with many of them through seventeen
years with my life. I intuitively knew that none of their
methodologies which I was exposed to, will work with Frans' son. I
also realised a third thing. I will have to be completely innovative
in guiding this boy. I already knew that he was extremely fond of
making all sorts of things. So I decided on using the following model.
I would command him to do something mathematically so that he could
become aware of his mathematical BECOMING. Then I would command him to
describe what he has made so that he could become aware of his
mathematical BEING. What crazy idea!

It took us two Saturday mornings for his mathematical crisis to
disappear like mist before the sun. I became very curious about this
strange "becoming-being" thing. Two years later, while I was studying
for my teacher's diploma after hours, I mentioned it to some of my
lecturers. Without exception they said that I was practising
programmed learning, but that it had only restricted application. They
suggested that O should do some reasearch on prgraamed learning so
that I do not have to use the words "becoming" and "being". I followed
their suggestion and soon found out that this "becoming-being" thing
had very little in common with programmed learning. It had, for me,
rather much more in common with creativity. But no book or article on
creativity which I could lay my hands on, afforded me a view point on
this "becoming -being" thing. It was becoming quite a mystery to me.

Another ten years had to pass before this mystery hit me right between
the eyes, together with monadicity (wholeness) and categoricity
(sureness). By then I had matured enough to know that since nobody
else was interested in clearing up my mystery, I had to do it myself
if I wanted the peace of mind for having done so. This led directly to
my discovery of the seven essentialities of creativity,
"becoming-being" (liveness) being one of them.

>Ehrenzweig was convinced that this detached, unsymbolic and
>disconnected or I prefer to say un-integrative and un-symboline
>educational phase in mathematics could and does cause
>permanent damage and retardation.

What a powerful statement!

My mind is not a container with a premanufatured form in which I have
to pour in information like formless liquid so that it can solidify
into a rigid order. My mind is the manufacturer of that container,
giving it the form needed according to my desire. My mind does not
need liquid from the outside which eventually has to fill the
container so as to make that container. My mind uses its own available
raw materials in it scattered all over my past experiences. My mind is
not a consumer of form, but a producer of form. It took me many, many
years to discover how I have become a victim of consumerism like I had
been a victim of other "isms".

Yes, I also have my own small business and realise exactly how
important it is for my business to have consumers in order to survive
or even excell. But in my business (growing rare succulent plants) I
have to produce every item (speciman) which I sell -- the strict
Washington Convention (CITES) making sure of it. The only thing which
I cannot produce, is the genetical material which mother nature
supplies me with. I cannot even buy those from other suppliers because
most of the species which I sell were never sold before. I feel with
my purse how other nurseries abroad are catching up on me by buying my
products so as to produce their own. I know exactly how many years it
will take before my sales will drop sharply -- the number of years it
took me to produce my own parent plants from seed. Were it not for the
fact that I have to pay for my dessert trips out of the money which I
make by satisfying consumers or that I learn so much about life, I
would have stopped participating in this deadly race of consumerism.

This consumerism is creating an intense rage within me. During the
apartheid era our country had to manufacture the majority of its own
goods because of sanctions. Thus these sanctions were actually good to
us, although apartheid was very bad to us. But since 1992 when
apartheid was axed, sanctions were lifted and affirmative action took
its place, factories had been closing at a steady rate. Why? People
are appointed to jobs and contracts are awarded because of the colour
of their skin, not their competency. The quality of many products
either could not compete with products of better quality from overseas
or took a bomber dive into oblivion because of bad quality. Closing
down all these failing manufacturers means hundreds of thousands jobs
less per year -- this in a country where already 40% of its people are

In the meanwhile, products imported from abroad are filling our
warehouses and selling shelves. All this have to be paid in foreign
currency. Thus our money (Rand) devaluates steadily. To counteract
this, the reserve bank makes the lending of money so expensive that
manufacturers with massive debts cannot handle it any more. More go
bankcrupt -- a vicious spiral. Sadly, very few people of our nation
are able to see through the FORM of every item imported -- its
CONTENT, namely the work done by someone into another country. In
other words, for every imported item we buy, we pay a worker in
another country rather than some of the millions of jobless people in
our own country. We have become a nation of "form consumers" rather
than "form producers". We are now doing the same thing to our economy
what we had been doing to our education.

Andrew, is this not what you express with:

>So what am I expressing?
>That the dissociation of conscious sensibility from unconscious
>phantasy (which I sense is the 'reservoir' of our deep human
>creativity), in the formal educational delivery and receipt of
>mathematics at a crucial stage in human development is
>matched in the loss to the child of his or her total
>artistic/creative potentiality. Such is this loss that his or her
>learning may forever become frozen or shallow (meagre) as may
>the other products of his imagination.

South Africa like the rest of Africa is becoming "frozen or shallow
(meagre) as may the other products of his imagination". Mathematics is
not only creating form out of content, but also using that form as the
content for a deeper level of mathematical activity. To not be able to
perceive how form can give rise to new content and thus emerge to new
form is to freeze in form. It can heppen in mathematics. It can happen
in education. It can happen in business. It can happen in arts. When
it happens, death sets in.

>If you have wondered why some modern abstract art looks or
>feels shallow and meaningless to you, then you now may have
>one reason, it is probably devoid of feeling. The feeling that
>issues from making contact with the metaphysical aspect.
>Through the power of abstract thought the surface of a painting can
>become renewed through the willing and playful decomposition
>and recomposition (living/dying) of abstracted forms that are
>suggested by the often unexpected or surprising interplay between
>different levels of reality and his growing curiosity in both realms.

Andrew, I must thank you for not letting this topic of "reification"
die away. The reason why I lifted it out of John Gunkler's
contribution, is that we somehow would get to the deep relationship
between reification and reality because of the meandering nature of
learning. Actually, I gave up all hope that we will compare
reification with "learning of reality" until you sent me your
contribution. Then I felt very ashamed. How can I give up all hope?
Here is one swallow indicaiting that he ammounces the coming of

>For an immediate creative reference or appreciation of this you
>might care to examine a late Picasso cubist painting. It probably
>contains the complex geometry of the Greeks via the use of the
>golden section expressed either written as, - The smaller is to
>the larger as the larger is to the whole, or numerically as
>approximately 8:13.

Ah, the beautiful Fibonacci series!
1, 2, 3, 5, 8, 13, 21, 34, 55, 89,......
Better approximations of the golden number are 13/21, 21/34, 34/55,
55/89, ....... One day you must go with me to a dessert so that I can
show you how often this number occurs in life forms there.

>So, all the lines I have written are condensed into one single
>thought or exemplar by the genius of a poetic metaphor from
>Leonardo. In your LO list, as the messages reply to messages
>in a sort of complexifying binary fashion, I see thousands of
>bridges built from words, signs and numbers, and it seems
>very much to me as if in this collective is not so much the
>discovery of bridges but the very construction of them,
>innumerable and polyphonic.

It will not serve as a definition for a LO. But it will definitely
serve as an epitome. Thank you very much Andrew for such a fine
epitome -- as well as the following:

>*** In every instant God creates an immense number of new
>angels, all of whom have only one purpose, to sing the praises
>of God before his throne for a moment before they dissolve to
>(From the ancient Hebrew tradition.)

How much correspondence is there between angels seen from this
viewpoint and the forms which we give to our thoughts?

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

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