After discribing the digestive process, in which BaSO4 powder
transforms into crystalline structure (those particles with highest
E(m,M) "eating" the weaker particles in a process close to dynamical
equilibrium), At de Lange asked:
>Do you already, as Jon Krispen often describes it, see the lights
>coming on and hear the bells ringing in your mind?
Dear At,
I feel more like wandering around in a dark, drafty labyrinth with a
candlelight in my hand. Where does the draught come from? What does the
patterns flickering at the walls mean? From time to time I think that I
recognise something known, yet it may have been only a shadow.
>I do hope that the following account of the Digestor will help you
>"to look through the mirror"
Is this how it looks like behind the mirror? Or is it part of "the dog
biting its own tail"?
I will try to grasp some of the flickers. So I will have a close look at
your basic equation:
> /_\F = - /_\n*mSU*[E(mSY, Msy) - E(mSU, Msu)]
Let me start with /_\F.
My guiding idea about the digestive phase of learning is, that the
task of this phase is to increase the systems F: /_\F(SY) > 0
(Side remark: With this F, the system become prepared for a new
emergence, in which such F is converted into S (entropy is being
produced) fast enough, so that the produced S is not totally dispersed
to the systems surrounding but kept within the system. If the
essentialities are fulfilled, such entropy will condense at the
bifurcation point in higher order structure (emergence), otherwise it
will blow up already existing structure and transform the structural
energy into entropy and disperse it to the surrounding (immergence).)
>Remember that a system's free energy F is that part of its total
>energy E which it can use to change its future organisation. By using
>this free energy F, it produces entropy S. The entropy may be
>dispersed as chaos (of becoming) and also be concentrated as order (of
>structure). For any spontaneous change in organisation the system's
>free energy must be used up. Thus spontaneous changes corresponds to
>a negative change (decrease) in free energy, ie /_\F<0. When
>non-spontaneous changes happen, the system's free energy F increases
>so that the change in free energy is positive, i.e /_\F>0. Such
>non-spontaneous changes have to be forced on the system by the
>surroundings SU through working on the system SY.
If I name the total system (SY + SU) "universe" U, is /_\ F in your
equation /_\ F(SY) or is it /_\ F(U)?
I guess that it should be /_\ F(U), because the change is occuring as
a consequence of a force-flux-pair between SY und SU. Thus a
spontanous change only require /_\ F(U) < 0! /_\ F(SY) > 0 is still
possible, as long as
- /_\ F(SU) > /_\ F(SY). As you have written, the surrounding SU is
working on the system SY. But in my understanding, such working is not
forced on the system but happens spontanously, given freely, one may
say.
In the case of the growing BaSO4 crystall as SY, is it not increasing
its F? Does this not happen spontanously? I agree, it wouldn't grow
without the powder as SU in its surrounding "working" on it, "forcing"
it to grow. But what about the powder, decreasing its F in this
process, is this more spontanous? The prey needs the predator in order
to become a prey as well as the predator needs the prey in order to
act as a predator. Or in other words, no entropic flux without
entropic force.
Next, let me try to understand /_\n:
>Firstly, the factor /_\n says that the more the elementary building
>blocks (ion pairs) flowing between the system SY and the environment
>SU, the more the change in free energy is also enhanced.
Because /_\n(U) = 0, I guess we are talking about /_\n(SY). Positive
/_\n(SY) in our example means that the crystal is growing. This is a
spontanous process, because E(SY) -E(SU) > 0 leading to a /_\F(U) < 0.
If we look at a grain of the powder as a system, the spontanous
process require /_\n(SYgrain) < 0 because in this case E(SYgrain)
-E(SUcrystal) < 0 as well - the powder is shrinking.
This is just looking at the same spontanous process from two different
perspectives: the crystal (predator) and the powder grain (prey).
While of course in both cases /_\F(U) < 0, in the first case,
/_\F(SYcrystal) > 0 while in the second case /_\F(SYgrain) < 0.
What does this mean? This means that while one grain, which happens to
have had the most successful emergence in the beginning, starts to
grow from the other emergences around it (the smaller, more impure
grains). While in this process total entropy is being produced and the
total free energy F(U) decreases, F(SY) increases while it grows to
maturity, preparing for another emergence.
Is this a win-lose situtation: win for the crystal, loss for the
grains? I don't think so, because the elementary building blocks are
more valuable (more free energy per building block) in the context of
the crystal than before in the grain.
Well... but what if a grain wants to preserve its identity, if the
grain feels disadvantage if it is not the one becoming the crystal? If
every grain wants to become the crystal, for example due to a
winner/loser mindset? Ah... we are coming to some important questions!
Some flickers are showing up, will it sustain to become light?
(flickers as grains, light as crystal)
Let me proceed to mSU:
>The richer the environment SU is in lower orders, i.e the greater
>mSU, the more the change in free energy F is enhanced.
First quesiton: Is E(m) increasing with increasing m? My guess: Yes
Second question: What does "greater mSU" mean? Is it a measure for the
quantity of small grains in the surrounding or for the size of the
LARGEST grains in the surrounding? (I don't understand your
explanation: "the quantity mSU (the quantitative size m in the lowest
orders of the surroundings SU)" - what does "lowest order" mean? Are
you talking of the size of the SMALLEST grains?)
My guess: mSU reflect the size of the largest grains in the
surrounding. Otherwise I don't see, how E(mSY) could be bigger than
E(mSU) as necessary for spontanous growth. I think, that the quantity
of small grains should be reflected in /_\n.
But if my guesses are correct, the equation tells another story than
your sentence which I quoted: Immediately after the precipitate is
built, there is a big quantity of powder and only a few slightly
bigger grains, which slowly start to grow (E(mSY) - E(mSU) is very
small, although mSU is big). So big mSU does not enhance the change in
free energy, due to the small difference compared to the mSY. As this
difference increases while mSU decreases and mSY increases, the
process accelerates until mSU becomes very small and the process comes
to an end, when mSU = 0. I imagine a typical S-shape curve as it
occurs, when an innovation substitutes an older solution in the market
- another model for the Digestor.
If mSU is the size of the SMALLEST grains, I understand nothing.
And the riddle goes on:
>The lower orders of the system itself, expressed by mSU, do not play
>such a role here.
I think this is a typewriting mistake and you meant mSY. In my still
simple image of the BaSO4 example, I have no idea, what you mean by
lower orders of the system itself. I thought mSY is the size of the
crystal (while Msy is its purity). What could be lower orders of the
growing crystal?
>In other words, an environment rich in lower orders enhances the
>system's free energy for digestion and thus evolutionary growth. An
>environment poor in lower orders inhibits the change in free energy.
I understand this, but not as a consequence of mSU, but merely as a
consequence of bigger /_\n: There is simply more food available. (And
this will have a negatively correlated backaction on Msy, making it a
Msy(/_\n) - "eating" too fast will lead to more impurities.)
And now comes, what questions my above flickers again, a huge draught,
a real breeze. So /_\F is meant to be /_\F(SY)?? As I explained above,
I can't make sense of this. After reading your paragraph another three
times, there is hope again. Little changes in your text would bring it
in line with what I have argued above (my changes in brackets and
capitals):
>Thirdly, let us study the factor [E(mSY, Msy) - E(mSU, Msu)]. It is
>made up by the difference between two similar terms for energy as a
>result of order, the one for the system SY and the other one for the
>surroundings SU. When the order in the system SY is greater than the
>order of the surroundings SU, we will have
>[E(mSY, Msy) - E(mSU, Msu)] > 0
>so that /_\F < 0. In other words, when the system SY is more ordered
>than the surroundings SY, the system [UNIVERSE (SYSTEM +
>SURROUNDING) instead of "system"] will behave spontaneously,
>working for its own self-organisation. But when the Surroundings is
>more ordered than the system, the system's organisation can only be
>changed [INCREASED] when forced by the
>surroundings [SOMETHING OUTSIDE THE UNIVERSE instead of
>"the surrounding"] to do so. However, as soon as
>the surroundings SU [THAT SOMETHING] stop working on the system
>SY [UNIVERSE], that organisational
>change will not happen any more. Thus we say that the change was
>non-spontaneous.
Ok, this was hard work. I am looking forward to the graphs! Do you
already have an idea, where they will be published?
Thank you for this farreaching lesson. Either I have got it right, or
you may be able to point me to where I got stuck. I hope, I could
express myself sufficiently clearly.
Liebe Gruesse,
Winfried
--"Winfried Dressler" <winfried.dressler@voith.de>
Learning-org -- Hosted by Rick Karash <rkarash@karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>