Problem solving and systems thinking LO20323

Leo Minnigh (
Thu, 7 Jan 1999 16:46:34 +0100 (MET)

Replying to LO20274 --

Dear LO'ers,

Now we have entered 1999 - the last prime number (dimensionless) of this
century - it is maybe a good moment to hook on the following issue:

Time, doomsday and dimensionless numbers

On Thu, 24 Dec 1998, AM de Lange wrote:

> >But I also permanently try to 'translate' the entropy
> >concepts to the material and abstract world.
> Read again my recent contribution "A Desert Wonder LO20243".
> Translating the concepts related to entropy from the inanimate to the
> physical living world and then further into the spiritual world is
> very much like switching from a Western way of life to the San
> people's way of life. It requires a total commitment as well as enough
> time to gain sufficient experiences. It is not possible in "one easy
> lesson".

At I have read the Desert wonder, your skelmpie. In LO20243 and in your
article on Doc's site (; with a
beautiful picture of Adenia, looking as an alien) the elements 'time' and
environment (the 'whole') plays important roles. The first element may be
translated into 'patience' and the environment might be translated as
external force. I realise that environment plays other roles too, but I
will try to keep my focus in this contribution to these two elements.

In the Primer on Entropy, it was several times mentioned that speed is of
importence for entropy production. In the iron bar with different
temperatures at both sides, the heat transfer is slow if this difference
is very small. It becomes minimal if there is no difference; transfer is
vice versa and a equilibrium state (reversable) is reached. On the other
hand the transfer is irreversible and fast with temperature differences.

But time alone is not interesting. Words like 'slow' and 'fast' is a
combination of space and time. Space may be translated as distance,
direction, volume, etc.
In the same primer on entropy, At explained a trajectory of entropy
production within the bar. He did this by deviding the bar in a number of
imaginary parts. The jumps of entropy production from one part to the next
one increase from small jumps to higher jumps at the end of the bar. In
his example the final and TOTAL result (adding up all the jumps) is +1J/K.
If we put this trajectory in a graph (distance on the horizontal axis;
entropy on the vertical axis), we will see first a slow rise of the
entropy wich will gradually become steeper and steeper.
So entropy production is the highest at the end of the trajectory of the
heat flux.
If entropy production leads to a bifurcation, we must look for this
bifurcation at the end of the trajectory! There is the place where
'something' might happen (further increase of disorder AND a fall in the
entropy=higher level of order).
The progress of the heat flow through the bar, following the trajectory,
takes time. So after some time we may expect something to happen. But only
if the entropy 'jump' becomes high enough. The travel time of the
heatflow depends on the initial amount of heat (the energy; intensive
quantity) and/or the temperature difference (the environmental force;
extensive quantity).

Three examples came in my mind wich demonstrate the truth of this story.

1. The raindrops on the frontal wind screen of your car is the first
laboratory. For the purpose of this experiment we should park our car;
driving will complicate the experiment and it might be dangerous to be too
much focussed on the rain drops at wind screen while there is havy
traffic. If it is raining (quantity of water is amount of energy), drops
will running downward following some tracks. High on your screen these
drops will follow a fairly straight line; a phenomenon which indicates
laminar flow. But after having travelled some distance on your windshield,
the path of the drop starts diviating from the straight line: meandering
starts. This is the first sign of the beginning of bifurcation. Which thus
happens after some time, when the entropy production passed a certain
If the windshield is large enough (with given inclination this means the
extensive quantity, like the temperature difference in the bar), or the
rain is pouring (quantity of available energy) , we even can see that
meandering may further develop into turbulences (the process of passing
a bifurcation).

2. At present, on the northern hemisphere it is winter. If one has left
his car outside, the condence water (on the outside, not inside the
car!) on the windows of the car might be frozen. Try the following
experiment. Take two buckets with liquid water from home. One is filled
with cold water, the other with warm water. Clean the frost from the
frontal windshield with the cold water. You will easily have the time to
finish this job by wiping and drying the wet glass (ofcourse, it depends
of the temperature of the atmosphere). But now the big surprise. If we try
the same with the warm water at the back window of your car, you will
experience that the initially cleaned window, immediately is frozen again
before you had the time to dry the glass.
Because the temperature difference of the warm water and the window was
apparently too high, sufficient entropy was rapidly produced to reach a
bifurcation point: a part of the water escaped as damp (greater disorder),
an other part of the water became ice (greater order).
If we use too hot water, only vapour may develop and the risk is that the
glass window is broken.
You can easily do this experiment in your home freezer as well: put two
cups of water, one with cold water, the other with warm water) in the
freezer. The warm water will be sooner ice than the other one.

3. The third example is the experiment that Reynolds did. It is somewhat
difficult to do it your self, but nearly in any encyclopedia you will find
the illustration of his demonstration of turbulent flow in a glass tube.
Through the tube some liquid is running. At the beginning of this tube
some coloured liquid is added in the centre of the tube. This coloured
liquid starts to show the turbulences in the flowing liquid. But did you
have noticed that the first part of the track of the coloured liquid is
just a straight line, indicating laminar flow? Only after some distance
the first turbulences start (preceded by a short track of meander
sinusoids). So here again, we see what we expected:
bifurcation after some time and some distance!

But dear readers, what had happened if Reynolds' tube was shorter? A
length which was NOT sufficient to reach the bifurcation point of starting
turbulences?? Although there was entropy produced, it was 'just' a
laminar flow. After a lot of thinking these days and studying the essence
of the Reynolds number, I came to the conclusion that there is something
wrong here. Since the length of the tube is NOT incorporated in the
formula of the Reynolds number, this number seems false. My
conclusion is that turbulences start after passing a critical stage of
entropy production, thus the dimension will be J/K (Joule per Kelvin).

Is this the place for such scientific discussion? I am not sure, because I
become so bewildered. I cannot believe that this conclusion is true. The
scientists of rheology are not stupid, isn't it? Next week I will have
some discussions with experts on this topic here at the university.

But back to LO20274 (Sorry At, I had to skip a most interesting part of
your message (your reaction on push/pull) and tak the thread of the
message at the importance of dimensional analysis and Reynolds number.

> Leo, I am very glad that you have mentioned the Reynold's number. It
> is a dimensionless quantitiy because it does not have an unit. (In
> rheology, the study of flow, a number of dimensionless quantities have
> been discovered since the original Reynold's number. Al of them play
> major roles in designs.) Qunaitites like length (with the meter as a
> unit), velocity (with meter/second as unit) or temperature (with
> celsius as a unit) are dimensional quantities. (If readers want to set
> their teeth into this fantastic subject, they should study the
> literature on the subject "dimensional analysis". For the
> mathematically minded physicists and engineers among you, try to think
> how physics will evolve when we formulate measureable quanitites in
> such a manner that the Law of Energy Conservation and the Law of
> Entropy Production will become dimensionless quanities.)
> Since the Reynold's number is dimensionless, it cannot ever be
> measured directly. It has to be calculated from the measurements on a
> number of other quanitites. The only two dimesional quantities which
> behave the same manner, are energy and entropy, as I have noted in the
> Primer on Entropy. I have hoped that somebody would have found this
> behaviour extraordinary and commented on it. But it now seems that I
> will have to do so because Leo has provided for the "fruchtbare
> Moment". I will do it in terms of the Reynold's number rather than
> energy and entropy, thus saving me a lot of work.

Although I came to the conclusion that the Reynolds number is not the
proper criterion for indicating the start of turbulence in a flow, much of
what At said above, stays. If my conclusion has some sense - that means
that above a critical value of entropy production, turbulences will start
- here too the measurements must be done indirectly and calculations must
be made.

But let's leave this Reynolds number and go directly to the TOOLO number
(Transition from Ordinary Organization to Learning Organization). So I
must again snip.....

> Let us think metaphorically of the Renold's number in relation to
> Learning Organisations. The transition from an Ordinary Organisation
> (OO) to a LO is an emergent phenomenon. Thus we can suspect a TOOLO
> number (like the Reynold's number) which characterises the transition
> from an OO to a LO. Let us assume that it is the case. It means that
> we can wait till doomsday, but an OO will not transform into a LO when
> the value of the TOOLO number is lower than the the threshold value.
> But it also means that we will never be able to express the TOOLO
> number with merely one kind of measurement. We will need at least
> three different kinds of measurements and will have to know how to
> associate them into one single outcome. (TOOLO = Transformation of
> Ordinary Organisation to Learning Organisation)

If my thoughts are correct, than we must think of the initial difference
of potential(like the temperature difference of the two ends of the bar,
or the altitude difference of the top and the bottom of the windshield)
between OO and LO, the resistence between these two (which is an
indication of the length of the distance between the two) and the amount
of externally introduced energy into the system. These three 'values'
define the time and the intensity of the flow, or in other words the time
that a certain amount of entropy is produced.
Thus we must be sure that the flow runs along a slope with a certain
inclination and that this slope should not be a ravine; and cecondly the
length of the slope must be sufficient to transfer the amount of energy
(or water if you like) from a laminar flow into a turbulent flow.

Therefor, if in this case the length of the slope is too short, we
could indeed wait till doomsday. Keep in mind that bifurcation points
might be found near the end of the trajectory, not in the beginning.
We also could wait till doomsday, of the amount of energy (water) is not

Concluding, the TOOLO trajectory might be long, so we should have
patience. On the other hand, enough energy should be introduced. And of
course, we do have an instrument to influence the inclination of the
slope: the will to reach the goal. As long the flow is running (in a
laminar way) and time (patience) is available I am sure that before
doomsday the flow start to meander. At that time we are sure that
turbulences are nearby.

At, your skelmpie (a desert plant wich according to At is probably 1500
years old) has several times 'thought' that it was doomsday: time to die.
But because of its patience (the length of the path is very long) and just
in time some extra energy was supplied, Adenia 'suffered' some fruitful
Unfortunately, the San people suffer too much implied energy from their
(unwanted modern) environment, while standing already on a steep slope
(nearly a ravine). It is hardly possible to escape from such situation.

> I hope my TOOLO number has not shocked you out of your wits. I have
> intended to write about emergent numbers since I read the first
> contributions on measuring learning organisations. But I needed too
> much context to do so in one contribution. While writing the Primer on
> Entropy, I realised that it will give me a marvelous opportunity to do
> so -- to stress in terms of historical events that not all valuable
> things can be measured directly. Read the Primer again to see how I
> have worked this theme into it.

The TOOLO number has not shocked me (you know, I have flexible shock
absorbers). It actually stimulated me in my meandering and I am sure that
the turbulences will follow.

> Now fasten your seatbelts. If learning emerges from creating, then we
> can suspect some dimensionless number to characterise the edge of
> chaos for emergent learning. If believing emerges from learning, then
> we can suspect another dimensionless number to characterise the edge
> of chaos for emergent believing. What will the fearful masters say of
> such emergent numbers since they want to control the knowledge and
> belief of other people by inundating them with their own dogma. Will
> they take kindly to emergences in general? I fear not.

Well, I have already reached the believing stage, but I like to make
regular back loops to sniffle on learning and creating.
I have undergone some inundating in this list. I love it.

> Lastly, assume it is possible that we can measure all the things
> needed for associating them with these emergence numbers, of what
> value will it be when we have determided the values of these emergent
> numbers. (Note that we again have the "dog biting its own tail" when
> we question the "value of a value".) For example, assume that we have
> determined the value of the TOOLO number and that it shows that the
> Ordinary Organisation cannot emerge into a Learning Organisation. How
> much will its value help us in transforming the OO into a LO?

I had with my thinking of the meaning of the Reynolds number a very strong
feeling of "dog biting its own tail". The several factors which compose
this number are so closely related to each other that circular repetitions
are involved. Whereas the most important unit is missing: temperature.

The meaning of numbers is relative. I think it is more important to
understand the principles. But it is still a nice challenge to think of
quantifications. But they never should be declared as 'holy'.

As many others, I intended originally a complete other mail (about cause
and effect). The cause of this message was At's mail. The effect was
different from my initial goal.

dr. Leo D. Minnigh
Library Technical University Delft
PO BOX 98, 2600 MG Delft, The Netherlands
Tel.: 31 15 2782226
Let your thoughts meander towards a sea of ideas.


Leo Minnigh <>

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