To become or not to become. LO23986

From: AM de Lange (amdelange@gold.up.ac.za)
Date: 02/16/00


Replying to LO23954 --

Dear Organlearners,

Greetings to you all,

Fred Nickols asked a very important question in LO23942
(A Question for AM de Lange) which I replied to in LO23956.

He asked:

>When you use /_\ is that a way of representing the symbol
>delta, that is, an increment as in an increment of change?

to which I replied "yes".

To summarise part of the answer to him: /_\X means the "increment in X
between two values" as well as the "difference in two values of X". Should
we mark the two values of X with (1) followed by (2), then /_\X will be
given by
        /_\X = X(2) - X(1)
The compound symbol /_\ is an approximation of the Greek capital letter
"delta". The actual "DELTA" looks like a triangle. This delta is a
reminder of the first letter with which the word "D-ifference" begins.

The rest of my answer took a different direction in which I tried
to point out that /_\X may also be used to symbolise the
"change in X". Here we should not think of "change" as some
STATIC OUTCOME after having performed the "difference" or
"increment" calculation
        X(2) - X(1)
bur rather as a DYNAMIC ACTION which takes X from the value
X(1) to the value X(2). The symbolisation of such a dynamic
action (becoming) with a static symbolic expression (being) such
as /_\ requires much imagination -- perhaps too much to make
it plausible for many people.

My consolation lies in the fact that I cannot type /_\ by one
single key stroke. Three are needed so that in the typing of
/_\ I am acutely aware of it having the dimension of becoming.
You fellow learners should try to type it too just to get that
feeling of becoming while doing it.

Fred's question was very important to me, not for giving me
the oppportunity to explain once again to him in LO23942
what spectrum of meanings /_\X have, but to stress once
again in this contribution the danger of using mathematics as
a specialisation! (This is no reflection on you Fred!) What do
I mean? When we use our mathematical faculty, we should
never fall in the trap by assuming or requiring that we merely
have to use our mathematical faculty and nothing else. Why?

Although there is much (formal, explicit) knowledge to be
gained in doing mathematics for the sake of merely
mathematics, there is little wisdom to be gained by doing so.
Mathematical wisdom emerges only when we blend our
mathematical faculty in full harmony with all our other
faculties. Some people believe that mathematical wisdom
is actually equivalent to Applied Mathematics. But for me
Applied Mathematics is only one of the many beginnings of
the exciting road to mathematical wisdom.

Nevertheless, Applied Mathematics is an important beginning.
The media have a propensity for distorting reality to fit their own
interests. Perhaps you have read many articles trying to explain
computer hardware and software to ordinary folk. But I bet you
have not read one article explaining to you how Applied Mathe=
matics is used to design and optimise computer technology.
Why? Because you cannot walk on the road of mathematical
wisdom if you do not use your mathematical legs. Since these
"explainers" will not use mathematics in the article so as to
please you, they actually amputate your legs so that you cannot
do the walking. I know that I do not please you, but I care for you
-- which is something different. That is why I keep coming back
to mathematics rather than helping to amputate your
mathematcal legs.

Let us now take Fred's question and look at what we have
been doing in my last contribution in LO23954 on "To
become or not to become." I have taken you with a story
to where I sit in the desert's valley of desolation, observing
(seeing and hearing) how air escape from a puncture in the
tyre. There technology is following its own course. I am not
able to control that course for whatever reason. I may call it
stupidity, infatuation or even honeymoon love. But no such
name giving will ever save me. Should I want to be saved, I
will have to save myself using my own creativity.

What I then do, is to formalise that which caused fear in me
mathematically as the inevitable order relationships
        [P(2) - P(1)] x /_\V > 0
        /_\ [[P(2) - P(1)] x /_\V] < 0
Actually, I hide a lot of the baggage by expressing them as
        PAIR > 0
        /_\PAIR < 0
What is so terrifying? That I do manage to give form to the
cause of my fear -- or the very symbolic form of that cause?

What I do know is that many of you will raise objections to it.
Such a mathematical formalisation in the desert is imaginary
-- none of you will ever do it and thus it is most likeable that I
will also not do it. You are quite right. I will not do it. My reason
is different than yours. I have done it in advance many years
earlier.

What I will do, is simply react on the intuitive/tacit level as fast
as possible to regain control. You will also do it. I will be stupid
to formalise when regaining control is the key issue. But I will
be even more stupid trying to regain control without any earlier
preparation which also has to involve "creating form out of
content". I need the "back action" of this higher level of
knowledge on my tacit level so as to complete the cybernetic
circuit needed for control.

Here is a true story. In the early eighties my friend Basjan,
my two young sons and I were travelling in my Combi in the
desolated Huab valley. We were eager to find a gigantic
Adenia pechuelii, so large that we failed to spot it on our
previous visits. We found it easily because we were at last
mentally prepared to recognise such a way-out gaint. I stopped
close to the plant. As I stepped out of the Combi, I heard air
blowing out of the rear, right tyre. I dashed for the tyre, found
the hole and closed it by pressing my finger on it.

Basjan asked with a big frown turning from questioning into
anger: "Why are you doing that?" Since I knew how easily
the lid can blow off his pot, I replied as calmly as possible
"Because our two spare tyres are already flat too!" I will spare
myself typing the detail of the reasons for this. Basjan was
not impressed with those reasons, some of which involved him
too. He began to swear at me, painting a vivid picture of what
will happen to us. It was so vivid that my two sons began
to cry.

"You better make a plan", he said. I replied: "Make us some
coffee while I make us the plan." Then I began thinking. My
problem was to plug the hole such that I could reduce the
order relation
        /_\V > 0
to the equivalence relation
        /_\V = 0
But what will act as a suitable plug, matching the shape of
the hole perfectly? I considered possibility after possibility,
brainstorming time and again for a feasible possibility.
Suddenly I remembered two pieces of epoxy putty under
my seat. I smiled and told my oldest son to fetch them, mix
some of them and hand me a screw driver.

"That plan will not work" Basjan exclaimed. I ignored his
objection. I had a vivid picture in my mind of an epoxy nail,
fitting perfectly into the hole. Its head will have to be on the
inside so that the pressure P(2) will try to blow it out. So I
started to work the putty into the hole with sufficient of it to
protrude on the inside. Then we pushed the Combi a little
backwards so that the "nail-in-becoming" was at the bottom.
Hence the protruding part on the inside could flatten into a
head. The tyre was hot enough to keep it semi-liquid.

We drank coffee and browsed around until the remainder
of the putty mix had hardened too. Then, daringly enough, we
continued with our journey rather than heading back to
civilisation. At first we stopped frequently to inspect the tyre,
but eventually we grew tired of it. The plan worked. We drove
another 400 km with that tyre before we fixed all three tyres
in Omaruru. Basjan and my two sons still marvel today after
nearly twenty years at that plan which worked so good.
None of them remember the swearing, scolding and crying.

That day I did create mathematics while sitting with my
finger in the hole. The mathematics was the transformation
        /_\V > 0 =====> /_\V = 0
which I had to substantiate physically. I learnt about such
expressions as
        [P(2) - P(1)] x /_\V > 0
        /_\ [[P(2) - P(1)] x /_\V] < 0
twelve years earlier in my research on the behaviour of soils.
The famous US brand of epoxy putty did the rest!

Let us now get back to Fred's question. Mathematically,
by applying the definition
        /_\X = X(2) - X(1)
to any two variables P and V, we get
        /_\P = P(2) - P(1)
        /_\V = V(2) - V(1)
Consequently, in terms of PURE mathematics, the following
four order relations are equivalent
/1/ [P(2) - P(1)] x [V(2) - V(1)] > 0
/2/ [P(2) - P(1)] x /_\V > 0
/3/ /_\P x [V(2) - V(1)] > 0
/4/ /_\P x /_\ V > 0

But in terms of CONTEXTUAL mathematics, they are different!
Should I, there in the Huab valley some 20 years ago, not have
been able to select the one order relation appropiate to the Huab
context from the four possibilities, it would have been very
difficult for me to plan a solution amidst all the confusion. How
will I select the correct one?

Let me recall with what I have ended the second contribution
(LO23921):
>Finding harmony between becoming and being is an art

Relations /1/ and /4/ each have an internal symmetry. In the
case of /1/ we have to think of two differences/increments as
"beings". In the case of of /4/ we have to think of either two
shorthand notations which tell the same as /1/, or two changes
imagined as "becomings". There is too little art in /1/ and /4/
for me.

However, relations /2/ and /3/ each have an internal asymmetry.
In /2/ the change in volume act as "becoming" whereas in /3/
the pressure act as "becoming". Thus they have the same
internal art as far as pure mathematics go. But what about
mathematics in context? What is their context? Boyle's law?
In LO23921 Boyle's law has been symbolised as
        P x V = constant
or
        P(1)xV(1) = .... = constant
We have observed carefully that this law concerns "being"
since it employs the equivalence relationship "=".

UNDER this equivalence relationship the two variables P and
V are symmetrical in the sense that each represent a
measured value of a quantity. There is nothing in the symbolism
of Boyle's law even to suspect any asymmetry since the "="
is infertile for asymmetry. Hence there is not enough in the form
of P and V of Boyle's law to help us to make a decision between
/2/ and /3/. Consequently will have to search for a deeper form
-- once again following our mathematical quest. How?

Since the equivalence relationship "=" concerning "being"
was not sufficient, let us seek harmony by trying to find
out what will happen when we bring the order relationship
"<" of "becoming" into the picture. How will we do it?
Divide the tyre in two unequal parts. Since a tyre by its
very technological design prevents this, let us for the moment
imagine one of that sausage shaped balloons used to make
figures. Assume its pressure is P and its volume is V. It is
very easy with a twist of the wrists to divide it into two unequal
parts. Let us mark the SMaller of the two parts by (sm) and the
LArger part by (la).

Let the pressure and volumes in these two parts be given
by P(sm) and V(sm) as well as P(la) and V(la). It is visually
easy to observe that the volume of part (sm) is smaller than
the volume of part (la). This can be symbolised by the
order relation
        V(sm) < V(la)
It is not as easy to observe the relationship between the
pressures P(sm) and P(la) of the two sides. We can hook
a pressure meter to the parts, but let us rather try to guess
the relationship by our sense of touch. Close your eyes,
press first the one and then the other side between the index
finger and thumb. Try to feel any difference. Do it again and
again until you are sure that the difference is neglegible. This
can be symbolised by the equivalence relation
        P(sm) = P(la)

(If you have a very discriminatory touch, you will feel that
the smaller part (sm) actually has a slightly larger pressure.
This is caused by the elastic force of the balloon material
itself.)

Is this not a most interesting result when delving deeper
into form? Under an equivalence relationship "=" the
pressure P and volume V appear to be pure variables.
But under an order relationship they are not since
        P(sm) = P(la)
which is the equivalence relationship "=" of "being" while
        V(sm) < V(la)
is the order relationship "<" of "becoming. It is V rather
than P which responds to shifting from the "being" of "="
to the "becoming" of "<". Thus we will select case /2/
above rather than case /3/.

GN Lewis decided to call quantities which behave like P
"intensive" quantities and quantities which behave like V
"extensive" quantities. He considered this distinction to
be most important, but the rest of the scientific community
thought it to be merely another of Lewis' idiosyncracies.
It never dawned on them that one by one his idiosyncracies
(kernel, electron pair, reaction quotient, .....) eventually
became pivots in future theoretical developments. It took an
Ilya Prigogine to paint this idiosyncracy as a vital part of the
detailed picture on the Law of Entropy Production, thus
earning himself a Nobel Prize.

Sadly, Lewis did not live long enough to see this work of
Prigogine. Neither was he awared a Nobel Prize, although
he was the mentor of three Nobel Prize laureates, a most
exceptional accomplishment. Why? Who knows? Perhaps
it was because, as he often admitted
    "My tolerance for ignorance is zero".
Perhaps it was because he did not want to conform to the
"tyranny of the experts" or claim an opinion as an "experts
on experts".

I must stress once again that we will not be able to create
mathematics while sitting with our finger in a hole.
Mathematics is a creative activity -- an art among the arts.
All arts emerge spontaneously from within a person. Like any
other art it is an emergent phenomenon. As such it cannot
be forced by work and control of any external agency. Any
attempt to coerce or enforce a person to become mathematical
will result in the tragic disaster of destructive immergences.

Sitting with the finger in a hole is just another case of external
enforcement. Feel the force of the pressure in the tyre against
the finger to became aware of it as an external force. That
force will destroy our mathematical becoming in the valley of
desolation as surely as teachers have quenched our
mathematical faculty by coercing us into performances by
using over burdened courses, time tables, tests and problems
never solved to our intuitive satisfaction.

There is a saying in English which does not apply to
South Africa's climate.
        "Make hay while the sun still shines."
It means to prepare oneself as good as possible while there
is still time to do so. It means that a time will come when it
is not possible to make such preparations. Perhaps some of
the hay we need to make is of the mathematical kind. Perhaps
the sun will stop shining when something grave happens to
our technology because, as Lewis might have said, we each
tolerate our ignorance.

I cannot end this contribution with such a depressing note
as a the previous one. Think of Louis Pasteur. He made
most remarkable discoveries upon which much of our present
chemical and biological technologies depend. He of all people
should know better how each of his discoveries was made
possible. He said it himself -- his careful exercises and
preparations rather than waiting for pure luck to strike. It is
exciting and rejuvenating to make discoveries. It helps to fill
up our "fuel tank" for creativity. This fill up is very important
as I will tell in my next contribution with another desert story.

Fritoff Capra, after having contemplated the "web of life" from
many viewpoints, came to the conclusion that three intuitive
concepts are most important for him to understand this
"web of life". I do not remember how he articulated them, but I
do remember that they concern "structure", "process" and
"pattern". One way to discover the ramifications of these
intuitive concepts is to use our mathematical faculty -- to
create form out of content. It is then when we become aware
that
    * the equivalence relation "=" concerns "structure"
    * the order relation relation "<" concerns "process"
    * the harmony between "=" and "<" concerns "pattern".

The mathematical becoming of the mind is reflected by the
mathematical being on paper or screen -- a seemingly
impressive web of symbols. Please, do not let these symbols
intimidate you into not becoming mathematically. They are
but a scare crow. The vital becoming is that which happens
in your spirit rather in the physical world. The excitement and
rejuvenation of arts (which include mathematics) are to give
physical form to this spiritual form so as to proceed from
that physical form back to an even higher level of spiritual form.

To recognise the becoming in any being of art (=artifact)
fills one with such joy that it cannot be expressed in any
other way than the artistic one. Let us take care not to let
jealousy and rivalry get hold of us because they are
unsurmountable obstacles in artistic becoming. They are
like unstable dynamite -- it destroys ourselves before we
even get a change to destroy those artists whom we envy.

I fear that few of us know why we envy artists. Kids are
artists, eventhough immature. Then the system gets hold
of them, killing the artistic becoming of most while they
become adults lacking artistry. The reason for their envy
is obvious -- the system. We will have to correct this in
our own systems thinking. The system caretakers will not
like it because some of them have to much vested interests
in selling art.

With care and 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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