Dear Organlearners,
This going to be a long contribution -- so please either skip it or have
patience.
Winfried Dressler <winfried.dressler@voith.de> writes:
>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)
Greetings Winfried,
I wanted to answer your questions below on m (for lower order) and M
(for higher order). But when I read through your contribition again,
the part quoted above struck me as particularly important.
The origin for the mindset winner/loser, predator/prey and even
competition, is nothing else that digestive development, i.e
evolutionary self-organisation close to equilibrium where the entropy
production is very low. The Digestor is the first model to describe
evolutionary self-organisation whereas Prigogine's Brusselator is the
first model to describe revolutionary self-organisation far from
equilbrium. (One day we must sit down and compare how vastly different
in scope these two models are.)
In a reply to Charlie Saur on the topic "public schools as LOs", I
used his reference to "fragmented" curricula as the handle for him to
make connection between the Digestor and the typical education
provided in public schools. Likewise I want to use your reference to
winner/loser (competition) as the handle for you to make connection
between evolutionary self-organisation and advancement in society.
The smaller crystal (seed crystal, prey) must increase both its m and
M to become a winner. It is called smaller because its value for m is
smaller. Its m can be increased only though digestion. But this is not
possible when it is the prey of the bigger crystal AND its M value is
the same or smaller than that of the bigger crystal. It will remain to
be the prey of the bigger crystal. However, it can become a predator
on the bigger crystal when its own M value exceeds that of the bigger
crystal with a certain amount. In this case we say that the smaller
crystal outsmarts the bigger crystal.
Unfortunately, the smaller crystal can never increase its M value
through digestion (evolutionary creativity). This has to be increased
through revolutionary creativity which happens far from equilibrium.
It is here at the edge of chaos where bifurcations happen. If the
bifurcation results into a constructive emergence, the M value
increases. On the other hand, when the bifurcation results into a
destructive immergence, the M value decreases. In this case the
smaller crystal will become even more easily the prey of larger
crystals.
Obviously, the smaller crystal, although prey to bigger crystals, can
also act as predator on very small crystals (who cannot outsmart it).
This will be the case when it is much closer to the very small
crystals than to the bigger crystal and the mobile phase is more
viscous (lower temperature). (Leo's example of a glacier is the lower
limit. Raising the temperature ensures that the digestion processes
will happen faster. However, since the temperatures of both the system
and the surroundings are increased exactly the same so that the chaos
increases everywhere the same, the system and its surroundings will
remain close at equilibrium. (Think of the Ostwald process on BaSO4.
At room temperature it takes a couple of weeks for the larger or
better crystals to grow sufficiently in size and the smaller or poorer
crystals to disappear. At the boiling point of water it takes only a
couple of hours.)
One main reason why humans have organised the public school system, is
to modify digestive learning -- the evolutionary assymptote of
creativity. Teachers in the public school have to keep too large
crystals (predators) out of the system -- adults who want to abuse or
enslave children for all sorts of reasons (economical, political,
sexual, etc.). Such inscrupulous adults will always use a slogan of
the form "XYZ comes before learning", for example "freedom before
learning". Another, but very subtle example, is "administration before
learning". It is the one encountered by Charlie Saur while trying to
establish "conductive education" for seriously disabled children. The
case which I am particularly sensitive to and which caused me much
trouble in my younger, hot headed days is "teaching before learning".
Teachers in the public school also have to present the learning matter
in such a way that it can act as food (seed crystals) for all sizes of
crystals in the achool RATHER than medium crystals becoming the prey
of larger crystals or the predator of smaller crystals. Unfortunately,
what usually happens in the public school is that the larger crystals
(through giftedness in M or advancement in m) are forced to conform to
medium sized crystals whereas the very small crystals (disabled in M
or retarded in m) are kicked out of the system, sooner or later.
Because of the dismal schooling system in which they have to work,
many teachers fail in guiding children how to acquire a set of seed
crystals in their own mind with which they can digest the seed
crystals in the learning material (environment). In other words, many
teachers fail sadly in providing for emergent learning.
Winfried, forgive me for not going directly to your questions on m and
M because I had to get the above of my heart. Since you gave me the
opportunity ("fruchtbare Moment"), I had to follow it up (the
essentiality fruitfulness).
>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
Yes.
But there is a few technicalities which you and the few others like
you must be aware of. Since these technicalities will be confusing to
most of our fellow learners, I tried to keep them out of the picture
on this LO list. In the actual drivation of the equation I made the
use of the Madelung enthalpy H rather than Madelung internal enery E.
To explain the difference between H and E will only confuse the
picture for most fellow learners with little background in physics and
chemistry. I also made use of the Gibbs free energy change /_\G rather
than Helmholtz's simplification of it into /_\F. Furthermore, it is
only the absolute value of E which increases with increasing m.
Lastly, I have said nothing on the dimension of E, namely J/mol/mol.
>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?)
I have tried to use a description (not explanation) which will fit any
Digestor (crystal, biological, educational) with digestions on many
levels happening simultaneously. Let me give the description of m for
the Crystal Digestor for its simplest case (only two sizes of
crystals). In such a case we have only two orders, a low order meaused
by m and a high order measured by M. (Remember that the postfix SU
attribute m to the surroundings.) The descriotion is: the quantity mSU
is the quantitative size m of the low order in the surrounding SU.
How do we measure m, whether it be mSY or mSU? Consider a crystal,
either from SY or SU. We simply count the basic building blocks
(units) in the crystal. In the case of a BaSO4 crystal a building
block will be the pair of ions Ba++ and SO4--. In the case of Mohr's
salt Fe(NH4)2(SO4)2.6H2O a building block will consist of five ions,
namely Fe++, NH4+ (twice), SO4-- (twice) as well six water molecules.
In the case of a metal crystal, it will usually be single atoms.
Chemists call this "basic building block" by the name "formula unit".
Before we go to crystals of many different sizes, let us first
determine what is M (number of perfections) for a two size system? I
have written that we can measure M indirectly by the counting the
number (say N) of crystal defects. But there is an even more subtle
difference between m on the one side and M, N on the orther sid. It
has important ramifications for extending to Crystal digestor to all
kinds of Digestors. It concerns the difference between extensive and
intensive quantities. I have shown in the Primer on Entropy that an
entropic flux results from a flow (change) in an extensive quantity
whereas an entropic force results from a difference in values for an
intensive quantity. The difference between an extensive and an
intensive quantity themselves is that when a system is scaled like
dividing it in half, its extensive quantities get scaled (halved)
while the intensive quantities remain the same.
Are you getting the gooseflesh? Divide in hlaves a crystal with size
m. The sizes of its two halves will be m/2. But what about M and N? To
get a hold on them, consider only one fairly large crystal deffect
like a plane dislocation. i.e N=1. (In the diamond industry it is
called a "glets".) Now cut the crystal in half. In most cuts the plane
dislocation will be cut in half. Thus each half still contains one
plane dislocation, N=1 for both parts. (In the diamond industry the
art is not to cut the diamond in two halves so that only one contains
the deep "glets", but that the remaning parts of the "glets" in each
part is as close to cut surface.) For more crystals defects, it is
possible to cut the system with a curved/irregular surface such that
the two parts contains a section of each defect. In other words, N is
primarily an intensive quantity. Its values ranges from 0 (perfect), 1
(defect), 2, 3, 4, ... up to m as its upper limit. In other words, the
maximum number of defects occurs when not even two formula units
connect to produce a seed crystal. (Actually, a crystal seed requires
a few more than two formula units to form.)
In order to get M as an extensive unit without having to think how we
will divide the system to prove it, we devide N by the size m of the
crystal, ie. N/m. Here the rule "extensive/extensive=intensive"
applies. Furthermore, in order to invert "defects" (negative thinking)
to "perfections" (positive thinking), we substract N/m from 1 (one).
The result is
M = (1-N/m)
Therefore the perfections M range from
0 when the defects are maximim, i.e N=m, i.e. (1-m/m),
to
1 when the defects are minimum, i.e N=0, i.e. (1-0/m).
Before I go to a Crystal Digestor with more than two sizes of
crystals, let me show just how important this extensive/intensive
diiference between m and N is for other kinds of Digestors. Consider
the educational Digestor. Consider any course in any subject, say
Chenistry I. The size of the course can be measured by the number of
objectives which have to be mastered (competency). For example, the
educational committee of the Amercan Chemical Society have identified
many hunderds of objectives which have to be mastered for a first year
(general) course in chemistry. (Feel sorry for chemistry students!)
But what about the M (number of perfections to be strived at or the
qualitative value) of the course? It is related to nothing else than
the number of goals to be strived for when completing the course.
Educationalists have identified a number of differences between
objectives and goals. For example, an objective serves a short term
behaviour or memory while a goal serves a long term attitude. But here
is one which they have never even thought of. (Do you get the
gooseflesh?) The course is extensive in its objectives, but intensive
in its goals. Divide (scale) the course in two halves. The number of
objectives in the parts become half the original value, but the number
of goals remain pretty much the same.
Actually, any course designed with only one level as in the previous
two paragraphs, although better than nothing, is pretty bad in my
opnion. It should have several levels (layers) just as we may have
several sizes of crystals in the surroundings. At the bottom layer we
have all the objectives as m(1) and some goals as M(1). However, the
M(1) of the bottom layer serves as the objectives m(2) of the second
layer with its own M(2). Here the "objectives" of m(2) is the
collection of all the goals of the chemistry curriculum (all the
courses) and not merely the Chemistry 1 course. The M(2) is the goals
of the subject chemistry. These goals of the subject chemistry also
apply to the course Chemistry 1 in addition to its unique subset M(1).
On the third level we have m(3) and M(3). Here m(3) counts all those
goals of each of the subjects of the lithosphere (physics, chemistry,
geology, physical geography, engineering sciences, etc.) which makes
such a subject unique. The M(3) counts all the goals common to all
these sciences. The m(4) of the fourth level consists of all the M(3)
of the lithosphere sciences and all the M(3) of the biosphere sciences
(botany, zoology, physiology, etc.) The M(4) contains all the goals
common to all the sciences concerning the material world. Even these
M(3) and M(4) apply to Chemistry 1 in addition to the M(1) + M(2).
Thus the intensiveness or quality of Chemistry 1 is given by M(1) +
M(2) + M(3) + M(4) + M(5). But what is M(5)?
On the fifth and last level, M(5) contains all the goals common to all
the sciences of reality which covers both its material and abstract
worlds (see the humanities). Obviously, all of you fellow learners can
imagine how perplexed the lecturers in a chemistry department will be
when one of their colleagues begin to teach in a manner as above --
"madness", "incomprehensible tripe", "abstract nonsense",
"intellectual diarrhoea" -- they would say. How can such a person ever
dare to speak about the humanities when the physical quantity entropy
is the topic? What more is there to say about the relationship between
free energy on the one hand and freedom or free choice on the other
hand except that the word "free" occurs serependitiously in all of
them? What in heavens name does the Ostwald digestion process have to
do with politics, sosiology or education? Keep this colleague away
form teaching and research among peers because he will destroy the
department of chemistry and the subject forever!
Winfried and other fellow learners, think about yourself. Think how
your mind has reeled since a couple of years ago when I introduced the
topic "entropy production" to substantiate self-organisation at the
edge of chaos in human systems. Think how your mind has reacted the
last ten days since Dan Chay has asked me to explain digestive
learning. Suddenly you have been confronted with the Ostwald digestion
process in a solution with a precipitate -- a minute speck in the
greate diversity of topics and subjects in the celestial sky of
academics. Just another mad scientist who wants to sell his toy
(called a Digestor) as God's own remedy for a sick world.
Well, does such a Chemistry 1 course work? I taught such a course for
five years to students who wanted to major in chemistry. The pass
figure and average mark were much better than previous years.
Furthermore, the course allowed me to discover empirically during
1982-83 that entropy production also happens in the world of mind.
Then I was removed from that course to teach another one to first year
engineering students together with a dear colleague of mine, Herman
Potgieter. I convinced him to follow the same pattern and warned him
about its political dangers. For five years we were able to manage a
pass figure of above 80% and a average mark of above 70%. Nobody
wanted to believe us us, but nobody could also find any dirty tricks
because there were none.(Except if acknowledging complexity is a dirty
trick.) Then we were removed from that course.
Afterwards I came to work at the Computer Centre for Education. One of
my tasks is to program CBE lessons. Another task was to "administer"
chemistry 1 to students who failed the course the previous year
dismally in every test as well as the examination. The pass rate of
these "repeaters" the previous year was per definition 0% and the
average close to 30%. But again, helping them to think creatively and
view chemistry as an integral part of the whole academy, they improved
to a pass rate of more than 95% and an average above 70%! So much for
these "repeaters" who were considered to be "hopeless cases".
Winfired, by now you ought to have a better idea of how various levels
of order interconnect in the Educational Digestor. So let us go back
to the Crystal Digestor and see what you have written:
>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.
(snip)
>If mSU is the size of the SMALLEST grains, I understand nothing.
See how beautiful your intuition (tacit knowledge) works. Tacit
knowledge? Yes because with your physics and not chemistry background
I suspect that you never had the opportunity to experience even one
gravimetric analysis of the sulphate content of a sample.
But you must be careful not to rest on your creativity. Let me answer
your question by doing what Einstein so often suggested -- make a
"Gedanken" (thought) experiment. Consider the simplest case of only
three crystals C1, C2 and C3 with m(1), M(1), m(2), M(2), m(3) and
M(3). C1 acts as the system SY and C2 and C3 act as the surroundings
SU. All three of them form again the Crystal Digestor. When we view
only the system SY as system and not also the surroundings SU and
universe UN as systems, we tend to forget thinking what goes on in SU
and UN. But when we think about all three of them, the structure and
process (becoming-being) in the universe (monad) are also important
There are basically two ways in which we can arrange the three
crystals -- in a linear sequence or at the three corners of an
equitriangle. In the non-linear (triangular) case the biggest crystal
will eat both the smaller crystals while occasionally the medium
crystal will eat the smallest one. Its like a lion (biggest crystal)
and a hyena (medium crystal) competing for a share of the lion's kill.
Sometime the hyena manages to get in a bite, but never, never will it
take a bite into the lion.
In the linear case the ultimate result will be the same. But should
the smallest crystal come in between the biggest and the medium
crystal, both the biggest and medium crystals will feed on the
smallest crystal. Thus the medium crystal also gets some time to grow
before the smallest crystal between them disappears. After that it is
competition between the biggest and medium crystal. Now, if the medium
crystal has a higher value in M than the biggest crystal, the chances
become very good for the medium sized crystal to become the predator
and the biggest crystal to become the prey. I cannot think of a better
example than IBM (the biggets crystal) who everybody thought to be THE
system and MS (Microsoft, the medium crystal).
The previous paragraph should give you an idea how any LO (family,
public school, business) ought to manage learning. In the big open
world life is usually traingular (non-linear). Let us now take the LO
school and teacher as example. Leo Minningh's descriptions of medieval
guilds as LOs (about a year ago on this list) was so clear that they
can also serve as an example. Between the outside world (biggest
crystal) and child (smallest crystal) stands the teacher as medium
crystal. But in order to safeguard the child, the teacher must become
as humble as child. In other words, the teacher must reduce his m (by
letting only a small number of objectives come through in any
particular lesson) as well as his M (by letting only one or two goals
come through in the same lesson). Usually the lesson's m has to be
learned digestively while its M has to be learned emergently.
Sometimes it takes several lessons to master one or two particular
goals emergently.
When the child gets somewhat big headed, just step aside for some
short interval so that the linear setup becomes a triangle. The child
will soon discover that the big crystal is far worse than the teacher
(little crystal) standing between the child and the outside world. But
the teacher has to remain close by to take the child in his/her caring
arms when the lesson has been learned.
The next steps are to play with arrangements of crystals of four,
five, six, ... different sizes.
Winfried, you also write:
>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.
About the acceleration part you are correct. See the dialogue between
me and Winfried Deijman on a new experience of time where information
on the Crystal Digestor did not yet have any effect on what he had to
say in the first instance. Humankind (medium crystal) is flying faster
and faster away from all other livings species (all smaller sized
crystals) in its evolution. (Some sections within humankind are
accelerating even faster, causing other sections to hate or envy
them.) While this speed is increasing, more and more humans fail to
observe the smaller crystals, thinking of humankind as the only and
biggest crystal. Thus more of them do more things which cause other
biological species becoming extinct at an increasing rate. However,
there are more than enough religions in the world which each cautions
humankind that the biggest crystal is the godhead of that religion and
not humankind.
But also think of virusses as very tiny crystals. A virus is merely a
fragment of DNA with a molecular layer of protein around it to protect
it as its skin. Although very, very small in m compared to the DNA of
humans, the chances of relatively less errors in the DNA of the virus
is also better. (The m in DNA is count in terms of nucleotide base
pairs.) Think of the clever little devil called the HIV virus which
attacks humans where it hurts most -- the human's immunology system,
its only defence (forget about antibiotics) again virusses. Think
about the influenzia virus which got hold of the beta cells in my
pancreas. Where do all these virusses come from? How can we prevent
their increase in diversity and perfections? Why do we fail to find
the categorical answers to these questions?
It is true that a big mSU does not enhance a change in the free energy
through the factor
E(mSY) - E(mSU)
But note that mSU occurs twice in the equation -- the other case as a
factor like the factors /_\n and (Esy - Esu). Because of wholeness
("associativity-monadisity") we cannot think mSU into two separate
cases. It has to be treated as one complex case. Because of this, your
idea of acceleration is not so simple as you think. The change in free
energy accelarates through the factor (Esy - Esu) as the difference
between mSY and mSU becomes greater, but decelerates through the
factor mSU as mSU decreases while mSY increases. To find out which of
the two cases it will be, we need the exact form of E(m, M) and then
find the second derivative of /_\F with respect to mSU.
>Ok, this was hard work. I am looking forward to the graphs!
Winfried, it is even harder work to keep in front of a crystal like
you which keeps on taking bites at me -;)
But all laughter aside ("alle grappeis op 'n stokkie" as we would say
in my own mother tongue), it is a sheer pleasure to work with you and
fellow learners on this list. Let us lift our hats to our host Rick
who provides us with these wonderful opportunities.
Best wishes
--At de Lange <amdelange@gold.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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