Dear Organlearners,
Winfried Dressler <winfried.dressler@voith.de> writes:
> I forgot one question regarding "=":
>
> You use two kind of equations to illustrate your reasoning:
>
> 1.) 1 + 1 = 3 and
>
> 2.) (X * Y) * Z = X * (Y * Z)
>
> In the first case, you note that the meaning of "=" is "becoming", thus
> write " "=" " instead. In the latter case, I could think, that the "="
> means just mathematical equalty, as usual. But knowing you, I assume you
> would reject this as reversible mathematics. So how does becoming or
> irreversibility come into associativity?
Winfired, I must make one point very clear. I do not reject
reversible descriptions (which could involve anything, even
mathematics) all together. What I do reject is that reversible
descriptions depict reality while irreversible descriptions are a
worthless illusion. Both reversible and irreversible changes occur.
However, the traditional notion is that only reversible changes are
fundamentally important. Prigogine began to challenge this notion
acouple of years ago. Since few took heed, I find it necessary also
to challenge this notion.
Other readers may ask "What the heck is a reversible description?"
Well, if we read that description backwards, the meaning would be the
same as reading it forwards. (In a language like Hebrew which is
written backwards, the reversion would be to read it forwards1) This
is evidently false in any natural langauge! In other words, natural
languages function irreversibly. Why? To describe reversible
phenomean which supposedly are more important? Never in my or your
life!
Readers may now think that it is incredible stupid trying to read
something backwards. How could we ever experience doing something
that crazy. At de Lange is crazy even to waste our time suggesting
something that crazy. No, I am not wasting your time. You all know
that it is possible to make a movie based on a book. Sometimes the
actual visual image of the movie (video) is extremely close to the
images described in text. Think of such a mvie and book upon which it
is based. Reading the book backwards is exactly like rolling the
movie backwards.
Many of us have seen a movie (or a part of it) rolling backwards.
See, for example, America's Funniest Home Videos. The outcome may be
very funny, but it never happens like that anywhere else than in a
movie. This difference between playing a movie forwards or backwards
indicates irreversibility.. If no difference can be observed, then
the movie depicts a reversible phenomenon.
One of the main problems of the theoretical tools of physics is that
they can produce only reversible descriptions (movies). The only
exception is the Second Law of Thermodynamics concerning "entropy
production". This law says that when ANY SYSTEM changes, only those
changes will happen by which the entropy of the universe will
increase. Playing a movie of real life backwards, will represent
changes by which the entropy of the universe will decrease!
Making a movie of the motion of the planets and playing it forwards
or backwards afford no differences. It means that planetary motion
is reversible. Newtonian mechanics depicts this motion very accurate.
But planetary motion is not the only thing which happens in our solar
system. All the planets, for example, are unceasingly subjected to
ever changing solar winds (plasmas emerging from the sun). (This was
not known in previous centuries and thus to Newton.) Making a movie
of these plama winds and playing them forwards or backwards affords
great differences. Newtonian mechanics depicts the movements of these
solar winds very poor. Thus the notion that our solar system can be
described reversibly, is an illusion.
Is posssible to obtain reversible changes in ANY system (even huamn
systems such as organisations)? Yes, indeed. Two different ways are
possible. The one way is to isolate (close in all respects) the
system. The system will gradually devolve into a reversible
situation in which the only changes will be minute fluctuations
(random changes on a microscopic level). For example, the sanctionas
and boycots against a country are intended to have this reversible
effect
The other way is to make the system completely open, but to ensure
that no differences at all exist between the system and its immediate
surroundings. Any change at the systems boundaries have to be
craefully matched by a similar changein the immediate environment.
With what word will we describe such an environment? Congenial?
Super-soft? I have searched through the dictionaries, but the word
eludes me.
Whatever way we follow (isolation or congenial surroundings), the
reversible outcome is most devastating.
* It paralyse the major role players in any organistion. For example,
leaders become ineffective. What ever they try to do, become
wasted in minor quaarrels.
* It prohibits the butterfly effect. For example, the actions of the
of followers become merely random fluctuations. There is no
amplification of their output such that the whole organisation
may benefit from it.
The present fashion of intellectual specialisation is little else
than setting up a system of reversible thinking. Reversible systems
thinking has most devastating outcomes as I have decribed in the
previous paragraph. Peter Senge identifies systems thinking as the
Fifth Discipline needed to learn more about Learning Organisations.
Making this fifth discipline reversible will destroy rather than
promote learning organisations..
I am sorry for having written so much about "reversible" and
"irreversible", but what sense will my answer to Winfried make if we
do not know more about the meaning of these words.
> For example, 1 + 1 "=" 3 is a formular for emergence, but 3 "=" 1 + 1
> could be read as immergence. What about X * (Y * Z) = (X * Y) * Z? I would
> say, in a mathematical sense, this is still associativity. But you are
> always good for a surprise.
>
> And why do you use the mathematical sign for equalty "=" and explain
> it with " "=" " as a sign for becoming, instead of using another
> sign for becoming, for instance "->" which more clearly depicts the
> direction of irreversibilty?
Winfried, the only possible surprise is that I try to think
inclusively rather than exclusicely.
The problem with the equality sign = in mathematics is that many
people use it to equate only "beings" with each other. For example,
in 1 + 1 = 2 the left side 1 + 1 is perceved as a "being" which has
resulted AFTER the operation (action, process) + has exhausted
itself. The 2 on the right hand side is a "being". Thus the equation
1 + 1 = 2 itself is perceived as a "being" and hence the = (to equate
- an action) as a sign of reversibility. Mathematicians call this the
reflexivity property, saying that (1 + 1 = 2) = (2 = 1 + 1)
You are right. I cannot use the ordinary sign = (to equate or to
identify) when comparing 1 + 1 with 3. Mathematicians would use the
sign < for such a comparison, i.e, 1 + 1 < 3. The sign < is used to
signify the action "having been ordered". and is read as "is smaller
than". I could have used the expression 1 + 1 < 3 to signify Smuts'
central idea in holism that the the whole is more than the sum of the
parts. I have contemplated to use it, but decided against it because
the sign < indicates in no way how this higher order emerged. It
merely accepts the fact that this higher order has indeed emerged.
Hence I decided to use the expression 1 + 1 "=" 3 to bring in the
element of surprise - to show that "equality" or "identity" is also
possible by way of an emergence. I have read many mathematical
descriptions in my life employing the sign <. But I never have seen
that this sign used to refer to the actual process of emergence
rather than the order as its result.
Winfried, the sign = in X * (Y * Z) = (X * Y) * Z does indicate
reversibility since this equality says exactly the same as its
reflexisve counterpart (X * Y) * Z = X * (Y * Z). But I know you.
You will ask "What has become of the irreversibility?". In order to
have both X * (Y * Z) and (X * Y) * Z so that eventually we can
equate them, we require the basic pattern X * Y * Z (without the
brackets). The irreversibility already occur in this basic pattern
itself. For example, this basic pattern is different to the pattern
Z * Y * Z.
> (I am still trying to "escape from the groove of reversible thinking".)
I wish you all success. If I can give you advice - Do not try to
escape the groove of one mode of exclusive thinking just to fall back
into another groove of exclussive thinking. In other words, try to
avoid the "isms". Do not see reversibility and irreversibility as
contradictories. Reversibility is merely the limiting case of a whole
spectrum of irreversible cases. This limiting case happens when the
system is isolated (fragmented) from the rest of the universe, or
when the diversity of the rest of the universe is hidden by cngenial
surroundings. But the WHOLE itself changes irreversibly - I have no
doubts any more about this.
Best wishes
--At de Lange Gold Fields Computer Centre for Education University of Pretoria Pretoria, South Africa email: amdelange@gold.up.ac.za
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