Efficiency and Emergence LO22426

AM de Lange (amdelange@gold.up.ac.za)
Fri, 6 Aug 1999 10:46:36 +0200

Replying to LO22359 --

Dear Organlearners,

This contribution is linked to
Inattentive Dynamical Qualities LO22359
[It's at http://www.learning-org.com/99.07/0283.html ..Host]
That contibution set the stage for this one.

If you despise long contributions -- please hit the ESC key.

If you love a story, come sit closer to the cyber campfire.

Once again, please forgive my English because it is not my
mother tongue and I seldom speak it.

This contribution will be a story about scientists (like physicists,
chemists and biologists) and engineers. It will contain some
hard core science, but I will explain that carefully. (What is a
story without some hard core stuff in it?) The story will be about
a paradigm shift which IS STILL IN THE MAKING. It will take
you from way back in the past to the future -- the next millenium.

How far back into the past? Well, we can go back approximately
4000 years ago to Moses. He is probably most (in)famous for
giving the Israelites the Ten Commanments of the God of Israel.
In the fourth commandment Moses said in effect the
once every seven days God's people have to make their
work less to reduce its EFFICIENCY so that they can
renew themselves by thinking how He helped them in their
EMERGENCE as a nation from Egypt.

This paraphrasing of the 4th commandment is unusual, but I
hope you will forgive me. If I had any older doumented reference
from Egypt ot Babilonia to use, I would have done so. In that
case few would have minded this paraphrasing. Let us now jump
more than three millenia in time. We will come back to Moses
at the very end.

It took physicists a long time, since the days of Newton in the
17th century AC, to realise that any kind of potential energy
(symbolised by V) is closely related to work (symbolised by W).
By the end of the 19th century they were theoretically quite
sure that a system can deliver work only if it had a source of
potential energy which could be tapped and thus converted into
work. The engineers put that theory into practice. All their efforts
pointed to their great Law of Energy Conservation LEC -- energy
cannot be created or destroyed, but only converted from one
form to another.

The quantity "free energy" (two words, one concept, symbolised
by the symbol F) is the general name for all kinds of potential
energy (chemical, electrical, gravitational, nuclear, etc). Thus we
may also say that the system requires a source of free energy F
in order to convert it into work W. As the system delivers work,
the amount of free energy in the source decreases. Should the
amount of free energy in the source at the beginning of the
conversion be "F(begin)" and at the end "F(end)", then the
amount "F(end) - F (begin)" of the free energy F has disappeared.
Thus scientists and engineers relate F and W through the
F(end) - F (begin) = W

The left part "F(end) - F (begin)" of the equation may be replaced
by the symbolic expression /_\F where the sign /_\ means
change. Thus the change /_\ in free energy F is given by
substracting the free energy at the beginning "F(begin)" from the
free energy at the end "F(end)". (We do the same kind of
calculation when we spend some of our money.) Symbolically:
/_\F = F(end) - F (begin)

Using this equation, we may shorten the relationship between
free energy F and work W into the equation
/_\F = W ------(eq 1)
It says that "the change in free energy" (/_\F) "is equal to" (=)
"the work delivered" (W). Take care -- physicists used to write
this equation as
/_\F = -W
and many still do so. The difference is the - sign. This - sign
arises when we do not think of the system SY, the
surroundings SU and the universe UN all as systems, nor
when we distinguish between being and becoming forms of

This is the physicists' side of the story. In the same time
engineers learnt that the story had a different side to it. They
were the people who innovated (invented and improved)
machines (electric motors, combustion engins, etc) which
could deliver work by converting it from free energy. The
machine does not convert all the free energy into work.
Some of it gets converted into heat Q also. Thus they had
to work with the equation
/_\F = W + Q ------(eq 2)
Take care, engineers still often write this equation as
/_\F = Q - W
We will not follow this confusing practice.

Should we compare equations (1) and (2), they are clearly not
the same. Equation (2) contains the term Q which is absent in
equation (1). Unless there is no heat produced (Q = 0), the
engineers cannot leave the Q out of the relationship between
/_\F and W. So which side "won the conflict of opinions", the
physicists or the engineers?

Neither side. They made the resolution that equation (1) for
the physicists applies to REVERSIBLE transformations while
equation (2) for the engineers applies to IRREVERSIBLE
transformations. (Reversible means that the transformation can
happen in the forward or in the reverse direction. On the other
hand, for example, birth and death are irreversible
transformations.) Only a few scientists like Gibbs and Einstein
really tried to establish which of the following statements apply:
* All transformations are reversible.
* All transformations are irrreversible.
* Some transformations are reversible and the rest are
The rest merely proceeded as if the third statement applies. Were
they not trying to sit on two chairs? Or does LEM of logic (Law of
the Excluded Middle) not apply here?

It is possible to reform equation (2) in such a way that it consists
of exactly the same quantities /_\F and W as equation (1). This
is done by leaving out the heat term Q. Then the = sign cannot
apply anymore. The result of this reformation is
/_\F < W ------(eq 3)
where the sign < means "is smaller than". Should we compare
equation (1) with "equation" (3), the only difference is in the signs
= or <. Let us summarise this dual situation by
REVERSIBLE CHANGES ------ /_\F = W ------(eq 1)
IRREVERSIBLE CHANGES ------ /_\F < W ------(eq 3)

The physicists were unhappy with "equation" (3) with its < sign
rather than the = sign like in equation (1) -- a true equation. Why?
To understand them, we will have to play with some numbers.

When a system delivers work, its free energy has to decrease
because some of it is converted into work. Since the free
energy F decreases, the value of /_\F is negative, say -4J. (The
J stands for "joule", the unit for any kind of energy.) Using
equation (1), phsyicists can predict EXACTLY that the free energy
decrease of -4J IS EQUAL TO the work -4J. In other words,
/_\F = W
-4J = -4J
What can be nicer than that? The value for /_\F is exactly equal
to the value for W. Get the value for the one (W) and we
immediately have exactly the same value for the other one (/_\F).

Mathematicians will call equation (1) a ONE-TO-ONE mapping.
Physicists needed this ONE-TO-ONE mapping because they
could, thanks to good old Newton, measure the quantities
involved with work and thus calculate the work itself. They used
the formula
work = force x distance (scalar product)
Newton told them what the "force" is, how to measure its parts
and thus to calculate it. We do not know for sure who told them
that work is given by the above formula. It was definitely not
Newton in his Principia.

Fortunately, somebody (perhaps Leibniz?) did it. By calculating
the work done, physicists used the ONE-TO-ONE mapping in
each case to determine the change in potential energy. Except
for this ONE-TO-ONE mapping, they had no idea of what the
potential energy amounted to. Thus they established step by
step and one by one the values of changes in all kinds of
potential energy. Hence they slowly created detailed knowledge
on every kind of potential energy and thus free energy in

A linear equation like "ax+b=0" has one root (solution). Finding
this root is a ONE-TO-ONE mapping from the LINEAR equation
to its root. A non-linear equation like "ax^3+bx^2+cx+d=0" has
three roots. Finding these roots is a ONE-TO-MANY mapping
from the NON-LINEAR equation to its roots. Likewise we may
call any problem with many solutions rather than one solution
a non-linear problem.

We may call "equation" (3) a ONE-TO-MANY mapping, but
mathematicians usually call it an ORDER relation. To
understand why, consider an IRREVERSIBLE conversion of -4J
of free energy F into work W. We cannot say that -4J of free
energy becomes -4J of work because the conversion is
irreversible. But the system can deliver, among innumerous
other possible values, the following values of work: -3J, -2J and
-1J. In each case "equation" (3) applies (is valid):
/_\F < W /_\F < W /_\F < W
-4J < -3J -4J < -2J -4J < -1J
(The expression "-4J < -3J" means that -4J is smaller than -3J.)

The following situation is also possible where the value of W
rather than /_\F gets fixed:
/_\F < W /_\F < W /_\F < W
-4J < -3J -5J < -3J -6J < -3J
In each case we measure the parts (force and distance) of the
work and calculate it. Let us assume it stays -3J for some
reason. Observe that in the last case (-6J) much more free
energy is needed to deliver -3J work than in the first case (-4J).

Which one of the three cases will apply when we (from the
physicist's perspective) ONLY KNOW that the work is -3J and
from this have to infer the UNKNOWN free energy change /_\F?
With no further information it is impossible to know which one
of the three cases apply. ("no further information"? -- note how
wholeness creeps into the picture.) Thus this ONE-TO-MANY
mapping made physicists very unhappy because their minds
UNKNOWN. Except for Newton's ONE known step into the
unknown, they knew of no other step to obtain the same results.

The engineers were also very unhappy with "equation" (3) with
its < sign rather than the = sign like in equation (1). Why?
Their reason is different. Their sorrows begin with equation (2).
They want all the free energy to be converted into work W and
not some of it into heat Q also. They want their machines to be
"effective slaves", utilising all the free energy into work. But
when the machine generates heat Q also, they have to built in
extra coolers which make the machines costlier. They will also
need more free energy for which they have to pay more.

To help them to keep numerical track of their "slave's efficiency"
engineers defined the so-called efficiency factor "EF" of the
machine. (I will use "|" for division because ASCI code does
not have a sign for it it and we have already used the usual / sign
in constructing the symbol /_\ for change.) They do it by dividing
the work by the change in free energy, namely
EF = W | /_\F
The ratio of the output (work W) to the input (change in free
energy /_\F ) gives an indication of this efficiency. To understand
the efficiency EF, we will again have to play with some numbers.

Let us again assume the ONE-TO-MANY mapping above for a
decrease -4J in the free energy. But now we also measure and
calculate the heat Q. As the work decreases from -3J to -1J,
the heat increases correspondingly from -1J to -3J, all according
to LEC. Here are the cases:
/_\F = W + Q /_\F = W + Q /_\F = W + Q
-4J = (-3J)+(-1J) -4J = (-2J)+(-2J) -4J = (-1J)+(-3J)
EF = -3J|-4J = 0.75 EF = -2J|-4J = 0.50 EF = -1J|4J = 0.25

In each case the efficiency EF has been calculated as the ratio
(by division "|") of the work W (only the work and not also the
heat Q) to the change in free energy /_\F. Observe how the
efficiency EF decreases as the value of the work drifts away
from the value of /_\F, becoming more irreversible. "Equation" (3)
gives exactly the same results as equation (2).

The engineers would have loved to work with eqaution (1)
because then the efficiency would have been
/_\F = W
-4J = (-4J)
ef = -4J|-4J = 1.00
In this theoretical ideal the heat would have been zero, i.e Q = 0.
But they learnt by experience that unless they cool off their
machines by taking into account a non-zero value for the heat Q,
their machines would eventually fail by getting too hot.

Albert Einstein, one of the greatest physicists ever, realised the
physicists' need for equation (1). (It is like the need for an
accountant in business, some who balances the books.) They
actually needed the ONE-TO-ONE mapping to get on with the
job begun by Newton and Leibniz three hundred years earlier.
Thus equation (1) and reversibility were the backbone of physics
to him. And were it not? In one of the three papers who made
him famous after 1905, he explained the photo-electric effect by
connecting three concepts into one relationship -- the potential
(free) energy of an electron in a photosensitive substance, the
kinetic energy of an electron and the postulate (wierd at that
time) of Planck that energy is transfered in quantums (packets)
according to the frequency of the transfered energy.

But Einstein also worked in a patent office. There he realised
how important equation (2) and thus "equation" (3) by implication
were to the world of the engineers. However, he did NOT claim
that "equation" (3) (with the < sign, irreversibility) WAS WRONG.
He rather claimed with right that equation (1) (with the =sign,
reversibility) was of paramount importance to the world of the
physicist. His only claim with respect to "equation" (3) (< sign,
irreversibility) was that it pointed to something wrong with the
HUMAN MIND. Our inability to work with "equation" (3) had
something to do with our perceptions.

Physicists' since then checked their physics over and over
again and found nothing wrong. They began to believe that
equation (1) (= sign, reversibility) is real and "equation" (3)
(< sign, irreversibility) is virtual. But they did not examine their
mind for any other perceptions than their physics. Among other
perceptions they believed that nothing was wrong with
specialising in physics and nothing else. It never dawned on
them that the very fragmentation of knowledge into physics and
the rest might be the reason why they favoured equation (1)
rather than "equation" (3). Some even cashed in on this
perception, believing that physics would provide a foundation
for all knowledge, thus setting the stage for the "tyrrany of the

In order to justify their fragmentaristic viewpoint, they carefully
defined physics to be a study of conservative systems,
meaning that equation (1) is valid for such systems. They used
the name "non-conservative systems" for all other systems for
which "equation" (3) is valid. As a consequence of their
fragmentarism many physicists believed non-conservative
systems to be of little importance to physics.

(Skip this paragraph, unless you have had training in physics.)
Should we use for the formula
work = force x distance (scalar product)
the equation
W = F x /_\L
where F is the force and /_\L the displacement in the direction
of the force, then equation (1) becomes, using V for a particular
potential energy rather than F in general for free energy
/_\V = F x /_\L
which can be rearranged into
F = /_\V | /_\L
or the differential equation
F = dV|dL
"force F = divergence of potential energy V"
This equation is basic to the theoretical phsyics of all conservative
systems. On the other hand, "equation" (3) leads to
F > dV|dL
The latter equation means that
"force F is not equal to divergence of potential energy V"
Letting go of the powerful equation
F = div V
so as to study non-concervative systems was too much of a change
in the foundation of theoretical physics.

How great was the intuition of Einstein! But even for his superior
creativity elsewhere, he could not undo this knot. But he was
close to it because of his sensitivity to wholeness. It is because
of this sensitivity that he succeeded in unifying the theories of
Newtonian mechanics and Maxwellian electromagnetism,
resulting in his famous special theory of relativity. This creative
contribution was an advancement to physics in the same order
as that of Newton. In relativity theory space and time have to be
considered as one whole. Mass is merely energy in a
"condensed" form.

Let us see what the this "wrongness of the mind" has to do with
wholeness? The great theorist Willard Gibbs pointed out, near
the end of the previous century another clue to solving the
problem. By then both the Law of Energy Conservation (LEC)
and Law of Entropy Production (LEP) were known. They can be
formulated as
LEC: E(un) = constant or /_\E(un) = 0 ------(eq 4)
LEP: S(un) "=" increase or /_\S(un) > 0 ------(eq 5)
where E(un) is the energy of the universe UN and S(un) is the
entropy of the universe UN. See my earlier contribution "Primer
on Entropy" for how that story developed, beginning with the URL

Note that in equation (4) we again have the = sign, the much
beloved ONE-TO-ONE mapping -- the monogamous outcome.
But in "equation" (5) we again have the < sign, the much
despised ONE-TO-MANY mapping -- the polygamous outcome.
In his time Gibbs was perhaps the only person able to work with
"equation" (3) which has a higher complexity than equation (1).
Like Einsten his creativity was superior. He succeeded by
combining equation (4) for LEC with "equation" (5) for LEP into
one wholesome formula.The volume of this highly orginal paper
(more than a hundred pages) staggers the mind, even today.

What was the result of combining equation (4) and "equation"
(5) into ONE WHOLE? Nothing else than "equation" (3), namely
IRREVERSIBLE CHANGES ------ /_\F < W ------(eq 3)
Thus he established in principle that the two great laws of the
universe, LEC and LEP, pointed to irrversibility rather than
reversibility as the common factor of the universe. Gibbs' work
was known to Einstein. Yet Einstein could not let go of this one
last rock (equation 1, = sign, reversibility) and flow forward
(panta rhei) with the stream to encounter many rocks
("equation" 3, < sign, irreversibility).

But the great cosmologist Sir Arthur Eddington was one of the
few people who realised the significance of Gibbs' work based
on LEP. Eddingtton is famous for saying that entropy is the
arrow of time. But even he could not put the puzzle together.
Why not? He was a physicist, cosmologist and mathematican
of great stature. But what about chemistry or biology? Did he
knew enough of each to realise what their central features were
in order to seek their relationships with entropy production?
When striving for wholeness, where can we stop without

Meanwhile, that creative bunch of people called chemists
seized on "equation" (3) to open up a wealth of chemistry for
them. Like the engineers, they have thrown away the heat Q
part of equation (2), resulting in "equation" (3). But unlike the
engineers, their reductionism went further. They even threw
away the work W part by concentrating only on those chemical
systems delivering no work (W = 0). What remains for them?
Nothing else than
SPONTANEOUS CHANGES ------ /_\F < 0 ------(eq 6)

And did they not seize upon the wonderful spontaneous changes
in chemical systems to produce hundreds of thousands of new
chemical compounds. In order to keep track of what they were
doing, they gradually developed their own theory of chemistry.
Study any modern college textbook of chemistry to get an idea
of that theory. So happy were they with their successes that we
will not find the "equation" (3) in these textbooks. "Equation" (3)
is seldom mentioned in even advanced textbooks on physical
chemistry -- that complex discipline of chemistry connecting
with physics and which drives chemistry students crazy. But we
will find "equation" (6) often in any modern college textbook of
chemistry. It is almost as if "equation" (6) makes these
textbooks modern!

Equation (6) is a reduction of equation (3). Dare we say that this
is reductionism -- a destructive immergence? Is this not what
happens when we define spontaneous changes by "equation"
(6), but never tell how (6) results from (3)? Just like "equation"
(3) we will also never find the word "emergence" in any college
text book of chemistry. Chemists call every compound on the
right hand side of a chemical equation a product because it has
been produced by the reactants depicted on the left hand side
of the equation. But not one chemist, as far as I could ascertain,
has ever even thought of calling any product an emergent. Why
should they since specialisation in chemistry was at the order
of the day? Chemistry had its own terminology. Why should the
specialists seek consistency and coherence with the
terminology of other subjects?

With the help of Gibbs' work chemists went even so far as to
create many other kinds of electrochemical cells since the
days of Galvani, Volta and Le Clanche. In each such cell they
used a chemical reaction and the emergence of its products to
deliver an electrical current which could perform work. The
engineers among them observed that when the cell becomes
more efficient by converting the chemical potential (free) energy
more fully into work, the reaction happens slower. In other
words, the more reversible and efficient the cell works, the
slower the emergence (production) of products. When a cell
work100% efficient, it will take an infinite length of time for
the reaction to be completed. Yet they never thought of the
relationship between "the emergence of products" and "efficiency
of delivering work".

You may experience this relationship yourself by driving a car.
When the car has gained sufficient velocity to engage its top
gear, press the fuel pedal as little in as possible to maintain
the lowest velocity and yet a smooth operation of the engine.
The engine is now working less irreversible and more efficiently.
You will get much more work (mileage) out of the gasoline's
chemical free energy. But it will take also a much longer time
to use up all the fuel.

So what do we now have? Physicists who are happy with
equation (1) (the = sign, reversibility), engineers happy (?) with
equation (2) so long as Q could be reduced to maintain a high
efficiency and chemists happy with "equation" (6) (the < sign,
irrversibility) so long as the irreversibility afforded them with
spontaneous changes leading to a wealth of new compounds.
But in none of these three subjects "equation" (3) got the
attention WHICH IT DESERVED when thinking interdisciplinary.
Now where does Einstein comes in with his brilliant intuition
that "equation" (3) pointed to something wrong with the human
mind? Einstein gave us no clear answer. Is it not that the
minds of physicists, engineers and chemists gave too little
attention to "equation" (3) which would have compelled them
to think more interdisciplinary and eventually transdisciplinary?

The cow has not only three nipples. It also has a fourth one
on which the biologists were sucking. But as the chemist's
system is more complex than the physicist's system or even
the engineer's system, the biologist's system is of an even
higher order complexity. They got the least milk from the udder
while the physicists got the most. They had to struggle with a
biodiversity which baffles the mind. The organisation of their
biological systems (which they call morphology and physiology)
is much more complex than the organisation of the chemist's
system (which they themselves call structure [composition]
and reaction mechanism).

But early in the previous century Wolfgang Goethe, a man who
worked on many disciplines, already noted that from ONE
species MANY species could have developed. Few know of
this and his other decisive contributions to biology. This theme
(ONE-TO-MANY species) was taken further by Charles Darwin
who accepted it as a fact and offered natural selection (the
"fittest survive") as the reason for it. When Jan Smuts took it
one step further by saying that wholeness (holism) rather than
natural selection is the reason for evolution (the name by then
accepted for this ONE-TO-MANY mapping or speciation),
most biologists thought it too thick for a dollar to be genuine.

The task of biologists was made even more difficult because
of a particular physicist's claim that since entropy is chaos
and the entropy of the universe has to increase so that chaos
increases, life has to proceed with a different principle because
evolution is about increasing order. He called this different
principle "negentropy", but never even defined it as Clausius a
century before him carefully did define entropy. Thus this man
sent the biologists on a red herring track for many decades to
come. Hence not one of them even suspected that "equation"
(3) -- taking together equation (4) for LEC and "equation" (5)
for LEP -- was the great driving force behind biodiversity.

Why should they? Biology was their subject. They relied on
chemists to inform them with chemistry priciples so that they
could advance in their own biochemistry. From chemists they
learnt a little of "equation" (6), but nothing of "equation" (3).
Furthermore, the far majority of them hated to learn even of
"equation" (6) because it was physical chemistry, far too
close to physics for their liking.

So who was needed now to fit another piece into the puzzle?
A creative man who himself was not satisfied with merely
equation (4) -- LEC. He accepted with all his mind and heart
also "equation" (5) -- LEP. He accepted THAT the entropy of
the universe has to increase. But he went one step further.
He then wanted to know HOW the entropy of the universe
increases. For searching this "how" he was often told that it
was a crazy venture. Scientists merely accept and describe
a natural law when they are fortuante enough to discover it.
Except for describing it as precisely as possible, they do not
try to understand HOW it works because that is the work of
the gods. Science and religion do not mix.

But this man persisted with youthful enthusiasm. Eventually
he did discover HOW entropy is produced, making use of the
work of Gibbs and later Duhem. But this equation describing
HOW entropy gets produced, proved to be extremely complex.
On the other hand, most scientists wanted equations to be
simple. This equation for entropy production did not fit into
their list of wants. He also succeeded bringing together
hithertho many unconnected phenomena (called "effects" like
the Peltier effect and the Dufour effect) under one umbrella.
Since these effects could not be explained by the impressive
theories of physics constructed upon equation (1) (the = sign,
reversibility), he was not much in favour with those traditional
physicists who subsribed to equation (1). Even when he,
Ilya Prigogine, was awarded the Nobel prize in chemistry (not
physics!) in 1977, they spoke little about him.

Why? The paradigm of physicists has not yet shifted. But
Prigogine went even one step further -- he not only knew
HOW entropy is produced, but also began to wonder WHY
it should be produced. As one body most physicists answered
"to produce chaos". They knew perfectly well that the LEP
says that the entropy of the universe has to increase and that
LEP says nothing about chaos per se. But except for classical
thermodynamics (the thermodynamics of REVERSIBLE
processes), they could not make out the head or tail of
entropy. Since the eminent Maxwell suggested that entropy is
a "measure of chaos", who could differ from such a great man
and offer another interpretation?

But Prigogine thought anew -- why should it be "only chaos
and not also order"? In other words, is it correct to interpret
entropy merely as chaos? Soon enough he saw hundreds of
possibilities in the inanimate world where entropy production
caused not only "chaos", but also "order", for example, the
Bernhardt convection patterns when a liquid is heated.

Then came a truly gigantic step. He began to speculate with
the idea that somehow or other not even complex patterns in
the animate world EMERGE as a result of entropy production,
but also chemical patterns of the biological world. Most
extraodinary are the so-called biochemical reaction cycles. He
designed his theoretical Brusselator to reflect the common
part to most biochemical cycles. It then afforded by computer
simulation astounding insights -- non-linear behaviour and
strange attractors. Even the development of a slime mould gave
him the clue that it looks very much like the patterns in a
chemical clock reaction.

The bullet went through the shrine of tradition. The LEP was
not merely destructive and degrading as in the eyes of
physicists and engineers, but it also has a constructive and
upgrading side to it. Biologists did not need the mysterious
(although enticing) notion of negentropy to explain biological
evolution. Biological diversity was a consequence of LEP --
entropy production. But how?

Crucial to the next step of insight was how fast entropy gets
produced. The faster it is produced, the more the system is
forced away from equilibrium, linear changes and ONE-TO ONE
mapping. But to where is it forced? There is a limit to it -- the
edge of chaos! But what happens when the edge has been

Here comes in a fifth, but very diverse, bunch of people who did
not even have a nipple of the cow to suck on -- thinkers like
Morgan, Alexander, Bergson and Whitehead. Although diverse,
they can be considered together for three things. The first thing
is that they had little formal exposition, if any, on entropy
production. The second thing is that they all struggled with the
idea of emergence, searching for its web of consequences, but
seldom for its web of cause. The third is how people reacted to
their efforts. More than two millenia ago the so called expert
leaders exclaimed to Socrates that only the gods know what will
emerge -- that it is not for ordinary humans to know this great
mystery (obviously, excluding leaders like themselves). These
bunch of thinkers similarly experienced strong opposition from
the ignorant. If not enough, these claims of the "ignorance is OK"
mongers won easily support from the common people. Why?
Emergences sought became more than often the opposite,
namely destructive immergences.

To explain how an emergence happens, Prigogine had to bring
another concept into play, namely that of a bifurcation
("bi"=two, "furcation"=forking). Opposition rocketed sky high.
To know the future, one has to have a ONE-TO-ONE mapping
-- measure one thing now in order to know ONE thing about
the FUTURE. It is far too complex to measure one thing now
to know TWO things about the future. In other words, a
ONE-TO-TWO mapping is out of the question. Hence a fully
ONE-TO-MANY mapping is shear madness. Who wants to
deal with such complexity when everybody wants simplicity?

However in the background looms "equation" (3) with the
> sign and not the = sign, with irreversibility and its
ONE-TO-MANY mapping and not reversibility with its
ONE-TO-ONE mapping. So Prigogine persisted and gained
some followers with his ONE-TO-TWO mapping. These
followers began to use the word complexity to distinguish
their work from those demanding simplicity. But soon
enough the word complexity became fashionable, stripped
from its historical context in terms of emtropy production.

Now what has the bifurcation and emergence as its one
possible outcome have to do with "equation" (3), namely
IRREVERSIBLE CHANGES ------ /_\F < W ------(eq 3)
When an emergence happens, the system goes into a higher
level of order. The system uses its own sources of free energy
F rather than external work W done upon it to make this
change in organisation. Since the system uses its own free
energy to produce self entropy and thus change its own
organisation, it has very little left over to deliver external work.
Thus equation (1)
REVERSIBLE CHANGES ------ /_\F = W ------(eq 1)
will definitely not apply.

If it is possible, we should rather try to stress the < in
"equation" (3), almost like
VERY IRREVERSIBLE CHANGES ----- /_\F << W ----(eq ?)
But this is actually what biologists intuively know about
evolution. For example, it was first articulated by Dollo that
the evolution of species has never repeated itself. In other
words, Dollo's Law says that evolution does not backtrack
its path or follows the same route twice. (So much so for one
business wanting to copy the successful emergence of another.)
Also, for example, biologists now realise that a sudden
"explosion" in biodiversity has happened four or five times
(opinions differ) in the history of planet earth, each time as a
result of immense irreversible changes in the rest of the plante's
physical makeup (geology, atmoshpere, etc.)

Prigogine and his school know well that entropy production
tells only one part of the story. Entropy production is a
necessary condition for self-organisation (constructive
emergences). But what other conditions, constraints,
requirements, sufficiencies -- call it what you want -- are
necessary? The Prigoginian school are now researching
heavily all kinds of kinetic models, hoping to discover in this
manner these conditions. Yet they never refer to Smuts who
created a theory of evolution based on wholeness. By
neglecting wholeness, do they not also neglect by implication
other ".......nesses" along with wholeness?

Newton brought order to the physical world by showing with
empirical evidence that his law of gravitation holds - the first
formulated universal law of the physical universe. Then
followed hundreds of other physical laws, among others the
LEC and the LEP. So what will be the first universal law to be
formulated and tested empirically for the spiritual universe?
How is wholeness related to this law? We owe Jan Smuts
an answer!

Let us summarise what the < sign in "equation" (3) tells us.
For engineers it means that the conversion of free energy into
work is not 100% efficient. Thus the < points to less
EFFICIENCY. For biologists it means that the free energy of
the make up of a former species is converted into the
emergence of a new species with a new make up. Thus the
< points to more EMERGENCE.

Perhaps a metaphor from the world of business will illustrate
this summary. Think of any business. Think of its cash
reserves as its free energy. When all the cash is used to
pay the workers for whatever they produce, we have equation
(1) -- the phsyicist's viewpoint, the ONE-TO-ONE mapping.
Now think of some of the cash used to pay for advertisements
also -- some information on the business flying around like in
the chaotic fashion of thermal energy. In other words, the cash
is used to pay for work W and heat Q. Thus we have
equation (2) -- the engineer's viewpoint. Should we consider
this advertisement as a waste of cash, we get to
"equation" (3) -- the ONE-TO-MANY mapping. Not all the
cash goes to the workers. Not all the free energy is converted
into work. Some of the free energy is used to let other things
happen. Some of the cash is used for advertisements. Hopefully
a new customer will emerge.

An emerging biological system can deliver very little external
work because its free energy is used to self-organise itself.
Thus an emerging biological system is very inefficient in the
world view of the engineer. Just ask any expectant mother
about her experience as a factory worker. Since the efficiently
working mechanical system can deliver much work for the free
energy it concumes, it is inapt to emerge because of the little
free energy left over for self-organisation. Thus an efficient
machine is very sterile in the world view of the biologist. The
machine cannot in the same time both work effectively and
create newly, even its own progeny.

Now fasten your seatbelts!

Likewise we will have to make the final choice about the coming
bifurcation in the future of mother earth -- either mechanical
slaves working efficiently for humans or biological organisms
evolving freely to higher order forms of life. A most extraodinary
"still movie" has been made early this century with the name
Metropolis. The clear insight it affords into the future is stunning.
Please to try view it, especially at this point in the contribution.

It is not easy to make that choice. It requires much learning.
It requires us to perceive that not only a ONE-TO-TWO mapping
follows from
IRREVERSIBLE CHANGES ------ /_\F < W ------(eq 3)
but a ONE-TO-MANY mapping. Up to now I have told the story
of the ONE-TO-TWO mapping, namely
* engineer's viewpoint -- efficiency, /_\F into work
* biologist's viewpoint -- emergence, /_\F into new species
But this ONE-TO-TWO mapping, after all which has been told,
concerns merely the physical world to which the brain belongs.
What about the spiritual world to which the mind belongs? Is
it not that equation (3) leads to a ONE-TO-MANY mapping?

In this ONE-TO-MANY mapping we can think about the
* inventer's viewpoint -- innovation, /_\F into novel designs
* learner's viewpoint -- education, /_\F into fresh knowledge
* believer's viewpoint -- religion, /_\F into glad tidings.
These are the things which I have been writing about the past
few years on this list. It requires that we should accept the
physical world and the spiritual world as the two intimately
connected sides of one reality. It requires that we should think
of entropy production which happens in both sides. It requires
that we should see free energy as pertaining to physical and
spiritual entities. Madness?

Think of the business metaphor above used to illustrate the
summary. We may use its cash (free energy) to pay its
workers (to convert into work W) and to pay for advertisements
(to convert into heat Q also). This is a ONE-TO-TWO mapping.
But we may also use its cash to pay for its research and
development division, the case
* inventer's viewpoint -- innovation, /_\F into novel designs.
Thus we have extended the conversion of cash (free energy)
into a ONE-TO-THREE mapping. We may also use its cash to
pay for the education or training of its people, the case
* learner's viewpoint -- education, /_\F into fresh knowledge
The conversion then becomes a ONE-TO-FOUR mapping.

Think of Einstein. What did he say about "equation" (3)? Not
that it is wrong, but rather that something is wrong with the
human mind. What?

This following forms part of my own theory. We cannot proceed
in liveness, wholeness, sureness, fruitfulness, spareness,
otherness and openness because by impairing even merely one
of them, the more our bifurcations will result in destructive
immergences rather than constructive emergences. Even our
understanding of things is a constructive emergence. Yes, our
understanding also includes these seven qualities called the
essentialities of creativity. Should we neglect merely one of
them, say wholeness, the we cannot grow in our understanding
of wholeness, not to speak of the other six.

Let us use the business as metaphor once again. Big
corporations like banks and industries produce yearly a
shining overview of their financial reports under impressive
categories such as "core business", "social responsibility"
and "ecological undertakings". When studying such
overviews, it is difficult to find the gaps between these
categories because of the transdissiplinary thinking required.
But as soon as we use the essentialities liveness, wholeness,
sureness, fruitfulness, spareness, otherness and openness
to let our minds meander what these corporations should
have done given their complex web of business, these gaps
become clear to us.

Finally, this ONE-TO-MANY mapping of "equation" (3) affords
us the acid test in its highest emergent member. It is the
* non-conformers viewpoint -- compassion, /_\F into eternal love.

I have tried to explain how entropy production emerges into
creativity, how creating emerges into knowledge, how learning
emerges into faith and how believing emerges into love. This is
different to saying that the output of creating is culture, the output
of learning is knowledge and the output of believing is faith. I
admit that the explanation is very complex, far more than even I
would have expected thirty years ago. But note how wholeness
weaves such diverse actions like entropy producing, creating,
learning and believing into one whole. Should we impair
wholeness or any of the other six essentialities, we cannot
emerge into the understanding how it all fits together.
Consequently, the more we find ourselves deluged with entropy
production while our sources of free energy are diminishing, the
more we will reap chaos rather than order.

Jesus taught with many parables that the kingdom of God
can be entered only by way of unconditional love. Peter,
John, James and Paul experienced this acid test. Their
testimonies are there for everyone to read. We may despise
these people. We may misuse their teachings for our own
selfish purposes. We may judge the wisdom of the movement
by the acts of those who claim to have follow it. But will we
be able to avoid this acid test when the entropy production
increases explosively? If not unconditional love, what else
will the bifurcation lead to?

Two millenia ago important distinctions were made in the
Greek language between the three concepts of love --
"eros", "phileo" objectificated love (like in philosophy,
"sophia"=wisdom) and "agape" (unconditional love). We can
now formulate a most important distinction:
"phileo" == ONE-TO-ONE mapping between the lover and
specific object loved.
"agape" == ONE-TO-MANY mapping between the lover
and all objects with no distinction made between
The "phileo" works with equation (1) (= sign, reversibility),
but the "agape" works with "equation" (3) (< sign, irreversibility).

Thus the story ends.

What has this story to do with Learning Organisations?
Think of the many people which you encounter in your
organisation and who seem not to be working efficiently.
Are you not perhaps wanting the slice of bread to be buttered
on both sides -- efficiency and emergence? They might be
working less efficiently because they are using their free
energy for actual emergences. Hurray for that. However,
they may also be working inefficiently because they use
their free energy (the little which they still have) to get to
the bifurcation at the edge of chaos, desperately striving
for constructive emergences, but reaping destructive
immergences. It is painfully typical of the continent in which
I live -- Africa. If you want your organisation to emerge into
a LO, you will have to help your fellow learners like
Socrates of old, acting as midwife.

We cannot change the world because each of us has
barely enough own free energy to change ourselves. It is
futile to use external sources of free energy like the
chemical potential energy in bombs to change others. Let
us begin with changing the only person in our power
-- the self -- some days working efficiently, other days
emerging novelly.

The story began with Moses. Let us end with Moses.
Perhaps Moses' sabbatical ratio of 6 to 1 is very wise!
The pharaohs built impressive pyraminds trying to
generate their emergence into a new life. What we observe
today is only one thing -- these monuments needed an
impressive amount of free energy to be converted into work.
Is this not what Moses, once a prince of Egypt himself,
already perceived 4000 years ago?

We will be entering the new millenium soon. Once again we
will have to question ourselves -- can we have our modern
pyramids and our emergence to a new life? Do we have
sufficient CONTENT for both -- the necessary free energy? Do
we have the sufficient FORM for both -- the seven essentialities
liveness, wholeness, sureness, fruitfulness, spareness,
otherness and openness?

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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