Replying to LO26360 --
Dear Organlearners
Gavin Ritz <garritz@xtra.co.nz> writes:
>What I would like to see is, how specifically one
>can measure the state of an organization (entropy)
>(in the business sense) with respect to (and some
>nice real life examples).
Greetings dear Gavin,
You ask a very difficult question because much of the answer is not yet
known. I will answer you as far as literature can help us. Then I will
then add to that answer from my own experiences on the discovery that LEP
has not only a physical dimension, but also a spiritual one too.
CHANGES IN entropy S was first "measured" some hundred and fifty years
ago. I cannot stress enough this "changes in entropy" /_\S rather than the
entropy S itself. When a system receives an amount Q of heat reversibly,
the entropy change is given by dividing the heat q (measured in the unit
joule or J) by the absolute temperature T (measured in the unit kelvin or
K), i.e.
. /_\S = Q/T
In other words, first the heat Q and temperature T are measured and then
the change in entropy /_\S is calculated from these two measurements. This
is why I began this paragraph by putting "measured" in quotation marks.
Knowing the value of a change in entropy /_\S involves not only
measurements, but also a calculation! This cannot be avoided because it is
impossible to measure entropy directly.
So how did physicists came to know the entropy of a system when they could
measure only changes in entropy? They made use of two assumptions. The
first is a mathematical assumption. If the system's entropy was at a value
S(begin) and then changes by /_\S, then the system's entropy reaches the
value S(end) given by
. S(end) = S(begin) + /_\S
Somehow they needed an original value to which they can add all these
changes which they can calculate based on measurements. So they made a
second assumption that
. S(zero kelvin) = 0 J/K
It is often called the "zeroth law", but it is not actually a law. It is
rather a conjecture, namely that at the lowest possible temperature in
nature all systems have no thermal energy and thus no "thermal entropy".
The basic idea of the reversible Carnot cycle in thermodynamics was to
justify the first assumption, namely that the entropy S is indeed a
systemic quantity. The second assumption also needed justification. Thus
the quest for reaching the lowest possible absolute temperature began.
Unfortunately, the second assumption caused among far too many physicists
the mental model that entropy is purely a thermal property. Furthermore,
this second assumption together with the endeavour of few physicists like
Boltzmann to explain the second law of thermodynamics (LEP) in terms of
Newtonian mechanics by using principles of statistics caused also another
mental model among most physicists. Since (by assumption) the entropy S is
zero at zero temperature and since the crystal order of matter is not
disturbed by thermal energy at zero temperature, entropy can express only
chaos and not order too.
Gavin, we have to delve deeper in this last mental model otherwise it will
constrain our thinking on complex systems seriously. The "thermal entropy"
is indeed zero at zero temperature. But to assume that when this zero
"thermal entropy" is added to the remaining entropy of the system the sum
will still be zero (the "zeroth law") is to assume indirectly that this
remaining entropy is also zero. However, we can also assume any other
finite, constant value for it and not necessarily zero as the constant
value. Should we do this, we will not endanger the first assumption, but
only make it more complex. Firstly, we will have to think more relatively.
Secondly, we will have to interpret this constant, non-zero value. I think
that the best interpretation possible is that this non-zero remaining
entropy expresses the "structural entropy" which exists even at zero
temperature. Once we have freed ourselves from this last mental model, we
will be able to think of entropy as expressing both chaos (such as
"thermal entropy" does) and order (such as "structural entropy" does).
So, is there any example for thinking about "structural entropy" in a
sensible manner? Fortunately, yes. JW Gibbs showed through profoundly
holistic work how to compute the "chemical entropy" of a chemical
substance. This "chemical entropy" is the entropy which a substance has
because of its chemical organisation and not merely because of its
temperature. Unfortunately, this computation is complex because it
requires many measurements covering many different changes, even that
change better known as the chemical reaction. It also requires a high
degree of relativity. Not only is it assumed that the thermal entropy at
zero kelvin is zero, but also that the chemical entropy of all elements
(but not compounds) at zero kelvin are constant. Since chemists work
basically with changes /_\S rather than the boundaries S(begin) and
S(end), what better constant value than the value zero could be given to
the "structural entropy" for each of the elements at zero temperature? To
begin at zero with a complex string of additions to follow is the easiest.
For example, we do it in topographic maps by assume the height at sea
level to be zero. Should we have taken the height at to bottom of the
deepest trench in the sea to be zero, obviously the height at sea level
will be non-zero. Despite this, we will still be able to draw lines of
equal increases in height on topographic maps.
The computation of the entropy of chemical substances is so complex,
tedious and expensive that the entropy of only a few thousand of the
millions of known substances have been computed after almost a century.
(Note also that most students in physical chemistry struggle immensely
with this complex part of the course ;-) Usually it is substances with
immense industrial value or laboratory significance of which the entropy
eventually became calculated. Once we look at such known entropy values of
chemical substances, the notion of the physicists that entropy express
thermal chaos has to be abandoned. These values for chemical compounds
also express order in chemical structure!
Perhaps the most important thing we can learn from chemistry is that other
quantities which depend on the entropy S and total energy E of a system,
become more important in managing chemical reactions than S and E. Here
the free energy F or the Gibbs' free energy G (somewhat more complex than
F) stands first in the row. One look at /_\G of a reaction tells the
chemist far more than the /_\S and /_\E of that reaction. The chemist will
know how far the reaction will proceed (chemical efficiency) and what
concentrations for the compounds at equilibrium conditions can be
expected.
Another very important thing we learn from chemistry is that all kinds of
chemical reactions are associated with a change of entropy. In other
words, each kind of chemical reaction (like acid-base and redox) is a
different manifestation of entropy production. It means that the
knowledgable chemist begins to expect changes in entropy not because
measurements and calculations tell it, but because the peculiar
manifestations of such entropy changes tell it. The more complex a
reaction becomes, the more its unique behaviour becomes the telling
indication of its unique entropy production.
When we plan and build an entire chemical industry, then we will use the
exact entropy values determined by Gibbs' empirical procedure. But when we
want to explore new grounds and speculate on possibilities, the complexity
of Gibbs' procedure becomes a constraint. We need simpler procedures to
get quickly some indication of where we are heading to. Any such a
procedure is based on a model for the entropy of a complex chemical system
rather than its empirical determination. One such a modelling technique
has already been used by physicists employing Newtonian mechanics and
principles of statistics. It is better known as statistical mechanics.
However, this model of statistical mechanics is of little help to the
chemist because it considers all mechanical objects as points without
inner structure. Furthermore, since most chemists are interested in the
various chemical manifestations of entropy production rather than the
entropy production itself, little advancement has been made in creating
models suitable for chemistry.
I myself wanted at some stage to establish a causality pattern between
entropy production and its chemical manifestations. So I have devised a
model based on my concept of commutation. This model made it possible to
compute in a non-standard way (i.e not measuring heat and temperature) the
entropy of a molecule and thus determine the best fitting structure for
it. Because of the experience gained in creating this commutation model,
I think it is possible to devise other models too, each with its own
non-standard computation of the "entropy" of a system. I put the entropy
in quotation marks because this "entropy computed according to the model"
is not exactly equal to the empirically determined entropy.
Nevertheless, we ought trying to improve each such a model so that its
non-standard computations make comparisons possible which are isomorphic
(similar form but not equal content) to comparisons based on standard
entropy values.
Such non-standard models become crucially important with respect to living
systems. We cannot apply the standard procedure to living systems because
we will have to cool them off to absolute zero temperature. No living
system will survive it. One way open to us, is to consider the living
system as the emergent whole of a complex bio-chemical system consisting
of hundreds, if not thousands, of bio-chemical reactions. We then add all
these hundreds of chemical reactions together, also making provision for
how they interact with each other so that the whole is more than the sum
of the parts. The calculations will be hideously complex. I once did it
for a simple bacterium and it took me months to compute the entropy of the
bacterium.
Gavin, the extensive account above on the chemical viewpoint of entropy
(involving ordered structures) is in line with my own experiences rather
than in line with what you can find anyway in standard textbooks on
chemical thermodynamics. My own experiences with entropy involve not only
chemistry and physics, but also soils, plants and animals up to 1983.
Since then my experiences also involved the mental dimension of entropy
and not merely its material dimension. I now want to stress in terms of
these experiences that we will need more than empirically based
calculations and model based computations to uncover the complex outcomes
of entropy production. Measurements and calculation will bring us to a
certain level of understanding, but to proceed beyond that level into
higher levels of understanding, we will have take more than measuring and
calculating into account. What else will we have to take into account? I
can summarise it one sentence -- patterns persisting through all levels in
any complex system. To work with determinations of entropy production
alone and not also these persisting patterns is like trying to work with
our five senses but not also our brain. Not even a moron will do it.
Allow me to explain it in terms of my own empirical discovery that LEP has
both the material and mental dimensions. In my teaching I became fed-up
with the existing taxonomies of learning objectives because they helped
little, if not actually constraining, the mastery of chemistry. So I
created hundred of objectives which would definitely help the student, how
unfitting these objectives may be with respect to existing taxonomies.
Afterwards I began to search for taxonomical patterns among these
objectives. I felt like Linneaus, trying to find order among so many
herbarium and museum species. Perhaps the most striking pattern for him
was the distinction between plants and animals. When comparing my work to
it, the most striking pattern was the distinction between structural
objectives ("beings") and procedural objectives ("becomings"). I also
discovered two other clear patterns, but articulating them became a
nightmare for me. The closest I came was to call them the categoricity and
monadicity patterns.
I then decided to measure how efficiently this taxonomy with its three
strange patterns helped the students in their learning. I considered
various domains (like logic, ethic and systems systematic) for quantifying
some of their learning. Eventually I decided on logic. I learned as much
as possible of logic in its broadest sense so as to quantify each possible
logical ACT as a CHANGE. My greatest problem at that stage was to decide
between a linear or a non-linear quantification. I chose the non-linear
case because, curiously enough, it was easier for me. Obviously, because
of my choice, I measured only the logical dimension of the students'
learning. My "experiment" began in 1982. I began to plot the learning
performances of the students (based on some 50 000 calculations using some
20 000 logical measurements) graphically. The graphs shocked me. I
expected a statistical indication (bell curve, standard deviation, etc.)
to determine the efficiency of their learning. But the graphs showed a
pattern unique to entropy production in the physical world. Then, as a
scientist ought to do, I first established that this unique pattern could
be repeated. Thereafter in the next year 1983 I established that this
unique pattern could not be falsified.
By way of this unique pattern I had to conclude that LEP acts in both the
physical and spiritual dimensions of reality. This unique pattern is
orders more complex than the pattern
. Q/T(low) - Q/T(high) > 0
which allowed Clausius to infer that a strange law (LEP) was operating
here (see the Primer on Entropy). This latter pattern needs four physical
measurements and three calculations whereas the unique pattern mention
above needed orders more of logical "measurements" and calculations.
However, in both cases the patterns were as crucial in identifying LEP as
the measurmenets and calculations.
Gavin, to conclude, I want to stress six points. Firstly, you will have to
create your own non-standard model for computing the entropic changes of
systems as a result of processes in them. Secondly, when you consider a
complex ensemble of computations according to your non-standard model and
they exhibit no pattern typical to the manifestations of entropy
production, improve the model rather pushing a far-fetched interpretation
on the existing model. Thirdly, you will break new ground and thus cannot
expect much guidance from existing literature which seldom measure up to
what the seven essentialities require. Fourthly, quantify a dimension of
thinking (like I did with logic) of which its structures and processes
have been well established by other thinkers. Fifthly, always try
differentiate between those computations based on form and those
computations based on content because the entropy S is the form of energy
E as its content. Sixthly, when you want to proceed from energy E and
entropy S to work W and free energy F so as to dance with LEP on LEC, seek
for harmony between form and content in the model.
What patterns are typical manifestations of entropy production -- patterns
which your computational model should be able to lift out? I think
foremost is that pattern which will enable you to distinguish between
intensive and extensive variables so that you subsequently can identify
entropic forces and entropic fluxes. Another important pattern is that one
which will enable you to distinguish between changes close to equilibrium
and changes close to the edge of chaos. Then there is also a number of
patterns (like electrophoresis and chromatography) unique to entropy
production. They all have one feature in common -- they depict a
one-to-many-mapping in some or other feature of the system.
I am deeply under the impression that my advice seems to be woolly or even
mystic. However, I am also under the impression that you are learning
creatively about some key issues on entropy production because you write:
>1- Maximum entropy (no flow of energy)
>2- Dynamic equilibrium (i.e. Si increasing and
>Se flowing out)
>3- Not at equilibrium ( Si increasing, Se going in
>or out of the system)
Your issue 1 refers to what chemists generally recognise as the
equilibrium state. Your issue 2 refers to what some irreversible
thermodynamists recognise as thermokinetics -- something between
thermostatics and thermodynamics proper. Your issue 3 refers to the
endless becoming of a system SY together with its surroundings SU. Some
systems become extinct, others exist without change while the rest evolve
into systems with more complex organisations -- all as a result of
non-equilibrium conditions. Thus your three issues indeed cover a very
rich picture.
Lastly, you write:
>This connects with the article on grace and
>learning (LO 26327) the 14th paragraph about
>transfer of E and S to and from a system.
>
>Looking forward to some interesting answers.
I am deeply under the impression that the understanding which I gained by
seeking the wholeness between entropy production from below and loving
grace from above is incomprehensible by many other fellow learners. Even
worse, I have to recommend strongly to fellow learners that they ought to
question my understanding with their own authentic learning rather than
importing it by rote learning. Insight gained by inner irreversible
entropy production /_\(irr)S is vastly superior to understandings imported
from the outside by reversible entropy changes /_\(rev)S. The former
drives all kinds of evolution whereas the latter can easily undo
evolution. The authenticity of fellow learners is much more important to
me than my ramblings on entropy (the picture) and its production (the
movie).
My long answer may not be as interesting as you might have expected. It
says, in a grand summary, that although empirical measurements are
necessary to our understanding, they are not sufficient. We also need to
extend them with computations based on models so as not to destroy the
system when measuring it. With respect to the sufficiency requirement, we
have to rely far more on patterns indicative of entropy production. Our
understanding involves more than measurements because the essentiality
otherness ("quality-variety") cannot ever be reduced to or be replaced by
spareness ("quantity-limit").
Our understanding also involves mental emergences and thus the
essentiality openness. To measure the novel requires an already
established unit which thus cannot self be novel. The innovator has no
peers. Thus it is impossible to identify novel emergences with
measurements. It is easier for a blind person to identify any painting as
a great work of art. To identify the miracle of emergences we have to open
ourselves up to patterns persistent in this miracle.
Gavin, I admire your opening up to new dimensions of understanding. You
have surprised me because I sometimes speculated privately that you are
also a dealer in the proliferating junk of systems thinking. Although I
try to avoid judgement, I cannot avoid speculations because they are
integral to the scientific method as I understand it. I need to make
speculations on my initial observations so as to falsify them. The
remaining speculations which cannot be falsified help me to complexify my
own understanding. You are indeed a thinker struggling with managing the
complexity of human systems. The future of humankind depends on thinkers
like you because managing human systems with simplicity is bringing
humankind to the edge of chaos with its inevitable bifurcation. Simplicity
management will eventually propel humankind into an immergence too ghastly
to contemplate. But complexity management will attract humankind into the
emergence of a higher consciousness where harmony rather than
confrontation will be sought.
The more I explore the dance of LEP on LEC, the more I become convinced
that this dance will play a crucial role in overcoming the looming ethical
dilemmas of lately. These dilemmas stem from the fact that whereas many
humans now create immensely complex systems, very few humans can manage
these complex systems for the better of the entire Creation. Gavin, please
take extreme care when you introduce the complexity of LEP dancing on LEC
to facilitate managers on complex systems. It will not be as mild as
putting a cat among chickens in a pen.
Entropy production is real, even and especially when we merely speak about
it. When we merely speak about it, we deluge others with our own entropy
production rather than guiding them to produce entropy self when learning
about entropy production. Any deluge of entropy is dangerous for all
complex, self-organising systems. How I wish for the seemingly impossible,
namely that every long contribution of mine on entropy production to this
LO-dialogue was not so dangerous. The only way to minimize this danger
when speaking of entropy production, is to do it by way of dialogue in a
LO. Thus I would appreaciate your comments as well as the contributions of
fellow learners very much.
With care and 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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