Numbers and Organisations LO28889

From: AM de Lange (
Date: 07/24/02

Replying to LO28877 --

Dear Organlearners,

Chris Macrae <> writes in:

Subject: Individual Competence vs. Organizational Efficiency LO28877

>The trouble is there are a lot of people who use numbers who
>are totally unqualified as mathematicians. A mathematician
>knows the limitation of any logical/science system he or she
>uses. Arithmetic makes one heroic assumption: that everything
>separates in an inanimate way so that 1+2=3. And now you
>know this assumption, you of good conscience can never
>blindly obey an organisational number again.

Greetings dear Chris,

It is good thing that you have touched upon this number mania in

But first i want to defend those who are not qualified mathematicians. My
own training in mathematics had been up to a post graduate level as part
of a comprehensive physics curriculum. I had seen how the numbers of
fellow math students dwindled away until in the fifth year about 2% were
left over. The far majority of them simply could not pass a certain level.
They were "sieved" out of the system, year after year, just as sand is
graded into grains of different sizes.

It is now some 40 years later. Society has change very much here in South
Africa. I work in a different university with a different ethos. Yet the
"sieving" goes on almost like 40 years ago, if not worse.

I think that the most important reason for this "seiving" is that the
focus in the training is to make professional mathematicians out of the
students. Professional mathematicans by large earn an income by
discovering new theorems and proving them correctly, i.e., they work in an
academical niche.

I myself was not too fond of learning theorems and their proofs. I first
had to understand the proofs before i could remember them. This took time.
Sometimes i could not understand them so that i had to memorise them
verbatim. I hated it.

In all my five years at university i never had even one lesson on logic
itself. Six years after i left the university, i began to study upon my
own logic formally. I began to understand why i could not understand some
theorems. Some of them had too much information which obscured the logical
pattern while others had too a complex logical pattern for me to follow. I
think that many students would not have failed maths if the logical
pattern was also highlighted and explained to them in every proof.

What i really loved, is to explore "mathematical forms", first in physical
and chemical objects and later also in geological and biological objects.
It is better known as applied mathematics, but conventional applied
mathematics has become very much hijacked by engineers and staticians.
This exploration helped me to get a better understanding of these objects
by having a sort of plan in the "mathematical form" to work from.
Sometimes i made the error of thinking a "mathematical form" into a object
whereas that object never had this form in itself. I have learned to let
the object suggest the form rather than me assuming a form will suite it.

The reason why i love applied mathematics is that it becomes a vehicle to
travel faster and with less baggage from one point to another point in

Perhaps the greatest benefit to my outlook on mathematics is the vast
Euclidian Geometry we did early in high school. As a result i never
associated mathematics as a number business, but learnt early that it is a
study of regular forms, symbolising them in an efficient as possible

Another thing which received much emphasis in our training in
physics and chemistry is that numbers without units and uncertainty
limits have little meaning, if any. Thus, is N is a number pertinent
to physics or chemistry, it has to be expressed as
(N +/-n)[u]
where N may have any value between N-n and N+n while [u] is
the unit. The unit tells how it was measured, to what kind the number
belongs and thus what relationships to expect from it. The interval
(N-n, N+n) tells how large the uncertainty is.

Very few people are aware that as one begins to combine numbers (each with
its own uncertainty) in whatever way, the uncertainty in the combination
increases. By making successive combinations the uncertainty may grow so
much that the final result is virtually useless. For example, should i say
that the final result is, say 456 with a uncertainty which has grown to
100%, it means the actual value could have been anywhere between 0 and

I often shudder when i see a carefully worked out budget of an
organisation, but with no indication at all of uncertainty limits in any
of the numbers. The same happens in strategic plans involving numbers. Any
report with numbers in it, but no uncertainty limits, may have an
identity, but it certainly has no categoricity. Thus its sureness
("identity-categoricity") fails. Consequently any discussion on such a
report degenerate in a concussive debate. Furthermore, any creative
venture on such a report is in real danger of failing. Finally, crisis
management becomes of necessity in such a venture. (Sureness is one of the
7Es -- seven essentialities of creativity.)

It is possible to represent virtually anything by numbers. People do not
believe it, but the very computer in front of you is an example of this.
Deep down in its hardware on the basic level, it works with only two
numbers, 0 and 1. Letters, numbers, lines, pictures and even sounds are
made up by 0 and 1 sequences according to certain rules to form patterns.
These rules are programmed also by way of 0 and 1 sequences into the
software so that you are not aware of them. But change merely one 0 in a
rule into1 (which many virusses do) and the application will go haywire as
soon as that rule is used.

Although the representation of anything by patterns of 0 an 1
(digitalisation) and then many subsequent operations on them becomes
possible, there is a fundamental drawback in it. The digitalisation brings
in a certain grittiness, a kind of uncertainty in itself. Anyone who has
worked with PaintBrush, trying to draw a smooth curve, will have
experienced it. This experience serves as warning that the same applies
when trying "numberise" any smoothly changing property of an organisation.
It becomes gritty and thus introduces uncertainty. Worse is when anyone
use such numbers without knowing the rules of the "numberisation", the
outcome will go haywire.

I am all for organisations to become "numerate" just as they have to
become literate. Bearing in mind that every number REPRESENTING something
has uncertainty limits, is essential to such "numeracy".

With care and 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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