Our thoughts have moved faster than I have expected.
Perhaps it is time to look at Chromatography in Systems Thinking.
It is easy to illustrate the chromatographic effect. Take a strip of cloth
or porous paper. Put an ink blotch near its one end. Put that end into
water so that the water flows past the ink. The ink will slowly disperse
in blotches of different colours moving along with the water. It is as if
we create a profile of blotches. Each blotch represent a different
compound making up the mixture of ink.
The chromatographic effect (differential movements in an effluent) is very
important in life. For example, when water is added to a soil on its top,
some nutrients move faster than others through the soil. If the soil is in
a pot and sufficient water is added so that some of it seeps out of the
pot, the composition of the remaining nutrients in the soil changes. The
soil becomes deficient in the more soluable, faster moving nutrients.
Consider a whole family, children, parents and grandparents going to an
exhibition. They enter the gates simultaneously, but they do not leave
them simultaneously. Perhaps the parents come out first and then the
grandparents. The kids will usually come out last. Not all memebers of a
group come out simultaneously. For example, one kid might appear, then a
few more, and finally everybody have to wait for the last one to appear.
What is very interesting and peculiar of the chromatographic process is
that the longer a particular group of a mixture stays in the
chromatographic system, the wider is the spread between the members of
that group as they come out. In other words, if the parents come out
first, they come out close to each other. If the kids come out last, they
come out in a agonising long progression.
Knowledge management KM has become quite a fashion nowadays. It is seldom
realised that the knowledge pertaining to a subject can be represented in
a profile. When a person has to master that knowledge, the person is
actually moving through that knowledge profile. It opens up a very
important question: Is a chromatographic effect possible when different
people have to master their way through a knowledge profile?
Modern chromatographic instruments are very sensitive. They can easily
identify composite mixtures with one compound as low as one in 1 000 000
000 parts. Think of trying to find one specific person between all the
living humans on this globe -- it is of the same magnitude.
Why is a chromatographic instrument so sensitive? It causes a
differentiation on a macroscopic level by treating all individuals on a
microscopic level as potentially different. A compound may macroscopically
be as little as one in 1 000 000 000 parts, but microcopically that one
part consists of one in 1 000 000 000 000 individual molecules or ions.
What we see macroscopically, even if it were very little, is the
amplifying effect what happens microscopically. This we cannot see with
the naked eyes, but we can certainly see it with our imagination. Let us
try using our imagination.
A chromatographic instrument consists of two things, a solid stationary
phase and a liquid/gaseous moving phase. Both these two phases concists of
molecules/ions. In the solid phase the molecules are connected together so
that they cannot move one by one. The molecules in the liquid phase can
move freely with respect to each other. They can also drift together
through the solid phase if some collective force (pressure) is applied to
the one side.
A small sample of the mixture is now injected into the liquid phase. Let
us assume the mixture consists of compounds A, B and C. Molecules of A, B
and C are attracted to the molecules of the solid phase. Should they
connect with molecules of the solid phase, they remain motionless for some
time. But they are also under pressure by continiuous collisions of
molecules of the liquid phase. Thus each of them may again be hit loose
from the molecule of the solid to which it is bounded. Once loosened, it
quickly gets accelerated by collisions until it reaches the velocity of
the liquid molecules.
In other words, every molecule of every compound in the mixture is
attracted/immobilised and collided/accelerated many times during its stay
in the chromatographic column. Think of each molecule of the mixture as a
(motor) car having two pedals -- accelerator and break. The molecules of
the solid phase act as break pedal on the mixture's molecules while the
molecules of the liquid phase act as the accelerator pedal.
So where does the chromatographic separation comes in? The molecules of A
are the same, but different to all the molecules of B which are the same.
The same for C. Because a molecule of A differs from a molecule for B and
one for C, its preferance for molecules of the solid phase differs from
that of molecules B and C. The molecules of the compound having the
highest affinity for molecules of the solid phase, stays the longest in
the chromatographic column. It is because they spend most of their time
motionless when attracted to the solid which does not move and hence least
of their time when thrushed by the liquid which does move.
Thus the chromatographic depends on three things.
(1) the repeated boosting-vs-breaking on each molecule
of each compound in the mixture.
(2) The different macro reponses of molecules of different
substances to this repeated boosting-vs-breaking procedure.
(3) The different micro responses of molecules of the same
substance.
Number (2) leads to a strong differentiation between the various
compounds. Number (3) leads to the slight broadening between members of
the same compound -- those who comes out last are dispersed most among
themselves.
Let us take a grand organisational phenomenon such as democracies. Have
you ever noticed how the growth of democracies among all civilisations
follows a chromatograpic pattern? On some continents democracies have come
fast and in close succession. On other continents they appear much slower
and wider dispersed.
To describe, explain and predict chromatography in terms of statistical
mechanics (= Newtonian mechanics + probability theory) is a never ending
nightmare. The reason is (1) the repeated boosting-vs-breaking on each
molecule of each compound in the mixture
Each such a boosting-vs-breaking invokes the famous H-theorem of Boltzmann
who tried to give entropy a statistic-mechanical interpretation. The
H-theorem itself is very complex so that invoking it many times for every
molecule makes it too a complicated complexity.
Thus the Law of Fick (which describes this differential diffusion merely
mathematically) remains an enigma. But in terms of entropy production
(irreversible thermodynamics) the Law of Fick is merely one instantiation
of many cross inductances depicted by the Onsager reciprocal matrix. In
fact, the "boosting-vs-breaking" on each molecule can serve as a metaphor
how the Law of Entropy Production works.
The first order change in entropy has to increase towards a maximum. This
is the boosting part, the "ramjet of the plane" or the "tailfin of the
fish". But the second order "change of the change" in the entropy has to
decrease towards a minimum. This is the breaking part, the "feedback
controler of the plane" or the "head of the fish".
Entropy production has a pushing tail and a breaking head. It is
manifested everywhere in nature (like the fish with a tail and a head) or
in culture (like the plane with a ramjet and a controler.) Sometimes it is
difficult to see this "boosting-vs-breaking" with the naked eye as in the
case of chromatography. It is then when we have to use our imagination.
Is it so difficult to imagine that in any personality the "heart" acts as
the booster (tailfin of the fish) while the "mind" act as the breaker
(head of the fish)? Perhaps it is not mere imagination, but very real! It
is it not this "heart-vs-mind" which causes different personailties to
move differently through the solid chromatographic column of life.
One last note. If we use two chromatographic columns made from different
solid-stationary phases, the same mixture may produce completely different
chromatographic spectra (profiles). The art of chromatography is to know
which solid phase to use to make the best separation possible between two
compounds (in the mixture) which appears to be the same thing.
Likewise with personalities. We may think that the personalties of two
persons are the same. But suddenly, under certain conditions, they may
differ immensely. (The dessert is one fine place to see this happening.)
That is why it is so dangerous to lump personalties together in one box.
In a LO it is better not to do so because it will be contraproductive to
Personal Mastery. Why?
This I have discovered in 1972, the first year of teaching at a school. In
our earlier study for the teachers diploma, we also had to study
psychology and personality (one of its strongest disciplines in those
days). I thought that putting the personalities of pupils in boxes to
guide them with their self-learning would be very helpful. Within six
months I had a crisis on hand which my mentor helped me to avoid.
"Stop putting pupils in boxes if you want each one to develop fully
according to his/her own potential." he said. Once we stop putting people
in boxes, we will see the unique need of each individual.
Putting a person in a box is like introducing a stickiness in the solide
phase which not even a vast drift in the liquid phase can overcome. The
person stays in the box (sticky phase) and thus cannot develop his/her
personality ("chromatographic potential").
In other words, some chromatographic columns are simply useless. Through
over usage they have become too sticky to allow for any diversification --
they lump too much. It is wise to identify such columns as soon as
possible and avoid them. Refurbish them at a suitable occasion, but do not
expect integration to become differentiation. Such miracles do not happen
to complementary duals. The miracles are rather the complementary duals
themselves.
Boosting-breaking is such a miracle. A fish with a tail and a head is such
a miracle. The heart and mind of a person is such a miracle. Creativity
and love form such a miracle.
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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