Replying to LO28652 --
Dear Organlearners,
Ben Compton <benjamin_compton@yahoo.com> writes
>This is the resurrection of a dead thread.
>
>The thread was started by At, and I contributed.
Greetings dear Ben,
Any thread in the likes of "where is it going" will attract my attention.
>It was pointed out to me by one of the participants
>that Godel had shown that any axiomatic system
>beyond first order arithmetic is either incomplete or
>inconsistent.
>
>I had never read Godel's theorem, so I bought Godel's
>proof, called "On Formally Undecidable Propositions
>of Principia Mathematica and Related Systems" from
>Amazon.com.
(snip)
>After having read the book, and assuming I understood
>at least a little of what I read, my opinion still stands.
>However, I think Godel made some interesting discoveries
>that are loosely applicable to organizations.
Perhaps it is much more than loosely applicable.
>I think that any organizational design is incomplete, but
>not exactly in the same sense that Godel would have
>used the word.
That i will forgive you because i am going to explore this "incomplete"
even more ;-)
Long before Goedel's theorem, logicians like Russel, Cantor, Skolem and
Burali-Forte who tried their best to reason logically, began to discover
paradoxes. A paradox is a statement intended to be proven as a theorem.
Once the proof is done correctly, the statement is true and false. Russel
and Whitehead had the insight to see that all these paradoxes involved the
relationship between a member and a class (an "individual and its
organisation" so as to say). Many tried to create a logical system which
would have no paradoxes.
But Goedel's theorem shocked them into serious contemplation. The
complete, consistent system which they try to create will show its
incompleteness and inconsistencies sooner or later.
For me Goedel did much the same for metamathematics (logic of mathematics)
what Heisenberg did for physics -- the introduction of uncertainty.
Heisenberg discovered that for the "atomic world" physical quantities come
in pairs. The more precise we measure the one quantity of a pair, the less
precise we will measure the other quantity. The qualification "atomic
world" is crucial. It entails that the measuring instruments are as large
as the objects to be measured.
In the "organisational world" a similar case would be when we "measure"
one organisation with another one of similar size rather than with an
audit. For example, competition can be seen as such a "measure". Think of
two political parties competing for votes and a Gallup poll prediction of
the coming election. But when election comes, the actual voting is far
different to what has been predicted.
Goedel's incompleteness theorem also introduce uncertainty to mathematics,
but here in terms of only one pair of "quantities", namely the true and
false of logic. It says that mathematicians may discover theorems without
ever being able to proof them as true or disproof them as false.
Mathematicians now refer to such possible theorems as conjectures. There
are now several famous conjectures.
How can theorems be discovered without being able to find a proof for
them? Is this not an oxymoron?
One of the saddest idiosyncrasies in the education of mathematics in
school and even in pre-graduate courses, is that learners are taught that
a mathematical theorem exists by way of its proof. This is tripe. Most
theorems had been discovered by contemplating a topic (in mathematics) by
bringing different parts of that topic in different ways together or by
comparing different parts in different manners. In other words, the
mathematician works creatively with different parts of the topic. By doing
so, the mathematician becomes aware of a certain pattern unfolding itself.
The next step is to formulate this pattern symbolically -- the would be
theorem. Finally, the arduous part comes -- to establish a logical proof
for the theorem. The proof is often horrendous so that the endeavour is
usually to find an elegant proof.
Ben, perhaps this is the very reason why you and many fellow learners are
not fond of mathematics. You were forced by your math trainers (i will not
call them teachers) to discover mathematics through the proving of
theorems. But it is for you to say.
We may think that Goedel's theorem comes into play only during the final
stage -- the possibility of never finding a proof for the theorem. But it
plays its role much earlier in the following sense. In the build up of the
proof, the mathematician does with the "parts" of logic much the same as
he did with the parts of the mathematical topic, i.e., he works creatively
with them. These "parts" of logic are nothing but simpler theorems and
inference rules. An inference rule allows one to move from certain
theorems as its input to another theorem as its output. Thus we may think
of theorems as beings and inference rules as becomings. It is as if
Goedel's theorem says that the theorem as the whole may be more than the
logic (sum) of its parts. In other words, Goedel's theorem brings holism
into mathematics.
Jan Smuts saw holism as the emergences which happen as a result of
increasing wholeness. With this in mind we may study the conjectures of
mathematics anew. We will find that in most cases that those who
discovered conjectures worked holistically in doing so. Thus nobody, when
coming to some insight through increasing wholeness, should feel inferior
when somebody else demands a rational explanation and this cannot be
given, neither in mathematics, nor in any other subject. Goethe knew very
well that this is the case. When he discovered his concept "Steigerung",
others demanded from him a rational explanation. He tried to do so, but
for them it was merely irrational gibberish. At last his only defence was
"do as I do and you will know what it means". Nobody wanted to do that.
What did Goethe do? Most people think that he was just a writer. No, he
increased his wholeness day by day by studying physics, chemistry,
geology, botany, zoology. He did not study information generated in these
subjects, but explored the objects (exemplars) of these subjects self as
if they were never explored before. Thus most specialist scientists
thought and still think of him as the jack of all sciences and a master of
none. But this is by far not the case. For example, his morphogenesis
categorization in botany is still followed today. Few know that the honour
of discovering the last bone in the human skeleton belongs to Goethe.
So what have all this on Goedel, Heisenberg, Smuts and Goethe to do with
organisations? Organisations of which it is a goal to increase their
wholeness, may expect to come to insights which they cannot explain. It
certainly should be a goal of Learning Organisations (LOs) to increase
their wholeness. Senge pointed out that wholeness is one of the 11
essences of a LO, but he did not stress that such wholeness should
increase. Nevertheless, in the case of a LO the insights which may not be
explained rationally are better known as metanoia.
Just as the mathematician works creatively with the parts of a topic to
discover a theorem, the leader of a LO should do the same with its
members. This is called Team Learning. A team is formed to do some new
task while learning together by doing it and then dissolve once the task
has been completed. Hence some of the organisation in a LO is always
informal. To strive for a complete formal organisation in a LO is
contra-productive to its learning.
Yesterday I had been to a meeting of managers in that organisation which I
reported in the topic "Hard work and efficient management" ="success"? I
clearly observed during the whole meeting how the Executive Manager (EM)
wanted to formalise the organisation as well as the meeting in all
aspects. He did it so amiably that nobody had the heart to take exception
to it. But all along the meeting several managers expressed their desire
to learn more in this or that and how something in the formal organisation
hindered them. I got a warm feeling in my heart because I felt that
finally something is happening. We have a fine word in Afrikaans for it --
"ontwikkeling"=development. Literally it means "unshaking", i.e., shaking
loose an organisation which has become rigid. when fruits in a tree is too
high up, shake the tree to get some of that fruits!!!
>So by incompleteness in OD or policies/procedures
>I mean that inevitably an organization will run into a
>scenario where the policies/procedures or OD do not
>provide guidance. It is at such moments, when
>organizational learning is a necessity.
Did you notice how we came to the same conclusion, but followed different
paths? You followed the path in which you perceived a similarity between
policies/procedures of OD and axioms/proofs of logic. It is the path of
liveness ("becoming-being"). I followed the path of wholeness
("identity-associativity"). Goedel himself in developing his theorem
followed the path of sureness ("indentity-context").
>At the same time, because the rules governing the
>evolution of an organization are not as strict as number
>theory, chances are there will be some inconsistencies
>in policies/procedures or OD that emerge.
I like this very much -- inconsistencies which emerge! Should it not have
been inconsistencies which immerge? In most cases no. But as more and more
of these inconsistencies emerge, their total burden on the organisation
becomes too much. It is then when a paradigm shift MAY happen in that
organisation. Afterwards, what appeared before as inconsistencies, are not
inconsistencies anymore.
I write MAY because only when there is "organisational learning" (based on
creativity) in that organisation WILL the paradigm shift happen.
>With this new perspective, I'll be a little more
>patient as those at the top of the hierarchy try to
>work through these issues. . .but I'm sure, in the
>back of my mind, I'll allow myself a laugh or two
>only because I'm so far away from the problem
>that I can afford to not take as seriously as those
>who are in the middle of it.
Dear Ben, those right in the midst of all these incomplete and
inconsistent issues may not recognise the significance of these issues. It
will be the case when they claim "let us manage as in the past which
brought us success" and "add a lot of hard work" so that "we shall
overcome them". I think that any purpose in which the future (or the
complex with its inconsistencies) is made subservient to the past (or the
simple with its axiomatics), will sooner or later end up in failure. This
is another way to think of Goedel's theorem. I know of nothing in the
universe which has such a backwards servitude, except when when humans
begin to organise.
>I wanted to respond before the LO list goes off-line,
>because I took the comment about Godel seriously.
>And I appreciated the comment, because it gave me
>an opportunity to deepen my thinking, not only about
>mathematics (a subject I've never been particularly
>fond of) and about the crazy stuff that goes on in
>organizations.
Crazy, but real as I realised once more during the meeting yesterday.
Learning is indeed a crazy thing. It gives up on the past for the future.
With care and best wishes
--At de Lange <amdelange@postino.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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