Commutation in the LO LO12877

Mnr AM de Lange (
Thu, 13 Mar 1997 14:11:38 GMT+2

Dear organlearners,

Please have patience with me in this contribution. I will stress an
important word with CAPITAL LETTERS

Clausius discovered the Second Law of Thermodynamics, namely that the
entropy of the universe CAN ONLY INCREASE. This law came as a shock to
physicists. This Law deals with quantities which they were USING almost
EVERY DAY, namely heat and temperature. It showed them that the great
MYSTERY why other forms of energy could be completely converted into
thermal energy, but not vice versa, is itself a law of nature! But the
shock was in the fact that whereas they could CONNECT the other
fundamental laws of physics into one ORGANISATION by Newton's Laws of
motion, this METHODOLOGY was not possible with the Second Law. Thus the
Second Law became the mystery, and not the PECULIARITIES of energy CHANGES
(transformations) anymore.

They were so SURE of their METHODOLOGY that they then did something
extraordinary. Through the creative genius of Boltzmann, they managed to
DERIVE the Second Law in terms of three things: the laws of mechanics, the
transition from the microscopical-individual things to
macroscopical-collections of things and the laws of statistics concerning
UNCERTAINTIES. They succeeded and an important branch of physics
developed, namely statistical mechanics. Thus they began to accept
mystery/uncertainty as part of the makeup of the physical OBJECT, rather
than the makeup of the physicist (SUBJECT). With that they burried the
mystery of the peculiarities and hence the mystery of the Second Law.
Furthermore, they had a new mental creation to devote their attention to,
namely quantum mechanics. So they had very little reason to wake up the

Then came Ilya Prigogine, not willing to bury what is not dead. The first
mystery which gribbed him, was how does entropy get increased (created).
He solved this mystery by deriving the equation for entropy production
(dissipation). This led to the development of an important branch of
thermodynamics, called IRREVERSIBLE thermodynamics. The second mystery
which gribbed him, was the peculiarities of energy changes. Many years
before him, Planck, discoverer of the quantum effect, was also intrigued
by these peculiarities, probably even more than the quantum effect itself.
In fact, he discovered the quantum effect while trying to solve the
mystery of the peculiarties! The most peculiar thing was that whenever
thermal energy and the CHAOS in it was concerned, the Second Law popped up
like a Jack-in-the-box or the Joker-in-the-pack.

Prigogine also solved this second mystery, not because he was a physicist,
but also because he was a chemist! Why? The concept of ORDER and STRUCTURE
(organisation) is central to chemistry. In other words, by OPENING up to
chemistry as well as physics, he became creative enough to retrace the
origin of the mystery in the subject (researcher) and not the research
object. His stotion to the second mystery was to realise that as far as it
goes for the material world, the Second Law is responsible for not only
chaos, but also for the change from chaos to order.

However, by then, physicists have immensely to PURE (conservative) physics
as a mental ORGANISATION. However, the role of Second Law in this
conservative organisation was still dead as they have buried it long ago.
For prigogine the third mystery was very much alive. He believed, like
Plnack and Eddington, that the Second Law was MOST BASIC (fundamental). If
that is the case, what sense is there in deriving the Second Law as
Boltzmann did it originally. Rather use the peculiarities of the Second
Law to crack open the other branches of physics until its counterpart in
such a branch is manifested.

Thus also this third mystery became solved. For all what physicists had to
say about their hermitian quantum mechanics, they did not realised that it
was one leg of a two legged creature, the other legged now to be called
star-hermitian quantum mechanics. The other leg became born and the
mystery was solved. Now what is the hermitian and star-hermitian business
in quantum mechanics all about? Let me summrise it with two words:
protection and production. The traditional physics of conservative systems
gave birth to PROTECTION (hermitian) quantum mechanics whereas the
physics+chemistry of irreversible systems gave birth to PRODUCTION
(star-hermitian) quantum mechanics.

Now what has this all to do with our topic Commutation in the LO? Well,
allow me this one paragraph and I will come directly to the point. For all
the insights to be gained by it, star-hermitian quantum mechanics have not
made the slightest dent in chemistry. Chemists still use the traditional
hermitian quantum mecanics to solve their problems of chemical structure.
One day, while I was teaching Lewis structures (ORGANISATION of electrons
in molecules) to chemistry students, I wondered what will become of Lewis
structures if I employ star-hermitian quantum mechanics in it. I had a
reason for this. Students create simple Lewis structures easily, but as
soon as the structures become COMPLEX or they have to cope with the CHAOS
of possibilties of simple compounds, they get utterly confused. From then
onwards, it becomes night for them. Thus I began to apply the Liouvile
operator of star-hermitian quantum mechanics to predict the EMERGENCE of
atomic and molecular orbitals. As soon as I did this, the concept of
commutation emerged within me! I found a wonderful way for students to
create complex Lewis structures by using the concept of commutation.

Now. let us leave physics and chemistry behind. But let us not forget that
all reality is one whole in which patterns in one part of it, is reflected
in some other parts of it also. I which now to reflect the concept of
commutation, together with the Second Law, in the organisation of humans.
So, what is commutation?

Commutation is the interactive sharing of any number of minor
organisations between any number of major organisations for any number of
times, thereby causing the emergence of a hyper-organisation. The
magnitude of commutation may be expressed by the Commutation Number CN.

Let us see what happenss if we begin with one KERNEL (major organisation)
and one TRON (minor organisation), slowly increasing the mumber of trons.
If one kernel shairs (sic!) only one tron with itself, then CN=1. The
shairing results in a monokernel, monotronic hyperorg. If one kernel
'shairs' three trons with itself, then CN=3 while forming a monokernal,
tritronic hyperorg. If one kernel 'shairs' twelve trons with itself, then
CN=12 while forming a monokernel, polytronic hyperorg. Thus, we use
prefixes such a mono-, di-, tri-, tetra-, penta-, etc when the number are
still less than 10, but for large numbers we us the prefix poly-. We may
even consider a number like five as too a large a number, but definitely
not the numbers 1 and 2.

Let us see what happenss if we begin with two KERNELs (major
organisations) and one TRON (minor organisation), slowly increasing again
the mumber of trons. If two kernels shair one tron between them, CN=2. The
shairing results in a dikernel, monotronic hyperorg. If two kernels shair
three trons between them, CN=6 while forming a dikernel, tritronic
organisation. If two kernels shair fifteen trons between them, CN=30 while
forming a dikernel, polytronic organisation.

Let us see what happenss if we begin with five kernels and one tron,
slowly increasing again the number of trons. If five kernels shair one
tron between them, CN=5. The shairing results in a dikernel, monotronic
hyperorg. If five kernels shair six trons between them, CN=30. The
shairing results in a pentakernelkernel, hexatronic hyperorg. If we
consider any number larger than 2 as too a large a number, then we may
simply say that the shairing of five kernels and six trons results in a
polykernel, polytronic hyperorg.

Now, for the beautiful and spinechilling part of it. Let us see what
happens when two monokernel, polytron hyperorgs A and B begin it commute.
Let us asuume that the CN of A is 5 and the CN of B is seven. CN(A)=5
means that A has one kernel with 5 trons commuting with it. CN(B)= 7 means
that B has one kernel with 7 trons commuting with it. Thus the total CN
for the system before any further commutation is CN = CN(A)+CN(B) = 5+7 =
12. For the new commutation A and/or B have to donate some of their trons.
Say A donate ONE tron and B donate TWO trons. In other words, at A there
will be 4 'single shaired' trons and 1 double shaired tron while at B
there will be 5 'single shaired' tron and 2 double shaired trons. Thus the
total CN INCREASES from 5+7=12 to (4x1+1x2)+(5x1+2x2)=15. We will call a
'single shaired' tron nothing but an UNSHAIRED tron and any double,
triple, quadruple, ...shaired tron simply a SHAIRED tron.

What do we have now. Two things which do the same thing.
* The one thing is the Second Law of thermodynamics which says
that entropy has to increase when anything happens, even when a
complex structure emerges from lesser complex structures. Few of
you know enough about the quantity entropy to be comfortable
with calculating it from measurements, or to calculate changes
in it.
* The other thing is the CN (Commutation Number) of an
organisation which also increase when a more complex
organisation emerge from lesser complex orgnaistations. The CN
LESSER PARTS BEFORE THE EMERGENCE! Do you still remember the
definition of holism: the whole is more than the sum of the
In other words, by means of the definitions of commutation and
commutation number I have given you the tools to go and
calculate HOLISTIC EVENTS. This is possible because the
increase in the CN TRACES the increase in the entropy during
such a holistic event.

(Just for the record: the tracing comes from the relationship beteen the
trace operator and the Liouvile operator of star- hermitian quantum
mecahnics. The concept holism was probably first created by the South
African field marshall, statesman and naturalist Jan Smuts. The reason is
that South Africa is such a complex country that should a person open
himself up to commutation with this complexity, the CN jumps skyhigh, i.e
massive entropy production follows.)

Do some of you get the idea where we are moving to now? Do you feel the
exitement? Here it comes:

Each person which subscribes to this list can be consider as consisting of
a kernel (which is the physical body) and a vast number of trons (which is
all the distinct thoughts, not necesarily all articulated yet). In other
words, each person is a hyperorg with a CN much higher than that of any
other living organism.

At de Lange
Gold Fields Computer Centre for Education
University of Pretoria
Pretoria, South Africa


"Mnr AM de Lange" <>

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