Replying to LO24065 --
Dear Organlearners,
Greetings to you all.
Please, do not get frustrated by the "mathematical traffic" in this
contribution. I have purpose in this "madness". This "mathematical
traffic" was introduced and explained in LO23887, LO23921, LO23954 and
LO23986 by careful systems thinking. Read those contributions once more to
refresh your mind and thus to put it at ease.
As I was driving to the university this morning, trying to resolve my
frustration with the road traffic by systems thinking on some or other
topic, I became aware how few people actually know that vehicles on the
road traffic function in terms of the two relationships expressed by the
mathematical expressions (see LO23954)
P(1)xV(1) = P(2)xV(2) = .... = constant
and
[P(2) - P(1)] x /_\V > 0
The first expression symbolises Boyle' law (see LO23921). It is already
known for 340 years. Millions of pupils and students had to study it. It
makes use of the "equivalence relationship =" of being. The second
expression does not even have a name (see LO23954 and LO23986). It is
barely known for 50 years to only a few thousand of post graduate students
in irreversible thermodynamics. It makes use of the "order relationship >"
of becoming.
This is what happens in the conventional (4 stroke) petrol engine which
powers the vehicles. A piston moves up and down in a cylinder. This linear
motion is converted by the crankshaft into a circular motion which is
eventually linked to the wheels. On top of the cylinder are two valves --
inlet and outlet -- which close and open by means of a camshaft. The
camshaft is linked synchronously to the crankshaft by a belt or chain.
When the cylinder moves on its first stroke downwards, the inlet valve
opens. The cylinder becomes an open system. A mixture of air and fuel is
sucked in from the carburettor. It happens so that the difference in
pressure between that in the cylinder and that of the atmosphere can
decrease. It happens according to the expression
[P(2) - P(1)] x /_\V > 0
where both [P(2) - P(1)] and /_\V have negative values (< 0). Hence
their product is again positive (> 0).
When the cylinder moves upwards on its second stroke, the inlet
valve becomes closed like the outlet valve. The cylinder becomes
a closed system. Since the volume of the cylinder decreases, the
pressure increases. It happens, as a crude approximation,
according to the expression
P(1)xV(1) = P(2)xV(2) = .... = constant
Should we want to imbetter the approximation, we will have to
include temperature too like in the ideal Gas Law. In any case,
we have to make use of an expression based on the equivalence
relationship "=" of being.
Just before the cylinder moves downwards again on its third
stroke, a spark in the plug ignites the air-fuel mixture so that it
explodes, breaking the fuel molecules up into many smaller gas
molecules at a much higher pressure and temperature. It is this
explosion which forces the piston downwards and supplies the
energy and momentum to complete its four strokes. As the
piston moves downwards in the closed system, the volume
increases so that the pressure decreases. Again it happens,
as a crude approximation, according to the expression
P(1)xV(1) = P(2)xV(2) = .... = constant
The cylinder then moves again upwards on its fourth stroke. The
outlet valve opens so that the cylinder becomes an open system.
The inreasing pressure as a result of the decreasing volume forces
the combusted gases out of the cylinder. It happens according to
the expression
[P(2) - P(1)] x /_\V > 0
where now both [P(2) - P(1)] and /_\V have positive values (< 0)
so that their product is also positive (> 0).
The fifth stroke is an exact replica of the first stroke, the sixth an
exact replica of the second, etc. Now picture in your mind these strokes
just going on and on. Picture how two consecutive strokes (first outlet
open and then inlet open) make use of the order relationship ">" of
becoming while the following two strokes (unburnt and burnt mixture) make
use of the equivalence relationship "=" of being. The synchronisation of
">" amd "=" depends on the careful linking of the camshaft to the
crankshaft by means of the cam belt. It sets up a harmony between being's
"=" and becoming's ">". Thus the engine becomes "alive" by converting
chemical energy into first gas-exploding energy and then into mechanical
energy.
The difference between the 4 stroke conbustion engine and our own
respiratory system is that the engine spends regularly half of its time on
the equivalence relationship "=" of being. But it does not imply that all
animals make use only of the order relationship ">" of becoming. Mammals
like whales and birds like penguins who have to swim under water, will
also make use of the equivalence relationship "=" of being from time to
time. But in their case the "regular" harmony becomes rather a "rhythmic"
harmony.
Let us finally take leave of "gas-exploding" (PV) energy and focus on a
new form of energy. Think of the spark plug used to ignite the mixture by
means of dissipating electrical energy through an electrical spark. The
coil and condensor in the ignition system is used to increase the
difference in electrical potential over the gap in the spark plug. Let the
body of the spark plug and its lip be at an electrical potential E with
value E(1). Let its shaft in the centre have an electrical potential with
value E(2). Thus the difference in electrical potential is [E(2) - E(1)].
First of all, shall we write it as [E(2) - E(1)] or as /_\E? Again it
depends on whether electrical potential E is an intensive or extensive
quantity. How will we find out? Apply as before (see LO23986) the order
relationship ">" to any electrical system and see whether E gets ordered
or not? Take a torch cell and cut a segment out of it parallel to its axis
to produce two parts. Each part will be fully operative since it contains
each sub system (carbon centre, zinc outside, black mulch inside) of the
cell. Measure the potential difference of each part. Result? They are
equal and exactly the same as that of the whole cell. Thus electrical
potential E is an intensive quantity so that we will write the difference
in it as [E(2) - E(1)].
The spark itself is nothing else than a flow of electrical charge Q over
the gap of the spark plug. It happens by ionising the gas molecules. The
charge on the one side of the plug decreases to the value Q(1) while it
increases on the other side to the value Q(2). Hence we have to deal with
the difference [Q(2) - Q(1)]. But again, as before, shall we write it as
[Q(2) - Q(1)] or as /_\Q? Again as, before, we have to determine whether
electrical charge is intensive or extensive. Again, as before, we apply
the order relationship ">" to an electrical system such as a torch cell.
The smaller a part of the cell, the less electrical charge it can produce.
Hence electrical charge is an extensive quantity so that we will have to
write the difference as the flow /_\Q.
When the spark jumps over the gap, it happens as a result of
releasing some of its electrical energy which has build up over
the gap by means of the coil and condensor. This energy is
released in a manner which may be described mathematically
by the relationship
[E(2) - E(1)] x /_\Q > 0
(See any introductory textbook on physics on the meaning of
the expression [E(2) - E(1)] x /_\Q .) Compare the form of this
relationship with the now well known relationship
[P(2) - P(1)] x /_\V > 0
for "gas-exploding" (PV) energy. They have exactly the same
form. Thus both of them can be symbolised once again (see
LO23954) by
PAIR > 0
This is a first order relationship because it contains one /_\ in
it, but which is not shown in this collapsed form. This first order
relationship drives the spark positively. The spark quickly
dissipates (in a split of a second) because of the second order
relationship
/_\PAIR < 0
It is called a second order relationship because it contains two
/_\'s of which the one inside the PAIR is not shown. It controls
the spark negatively. It is no different than a tyre which bursts
suddenly rather than getting a slow puncture.
Again, as as been indicated in LO24065, the relationship
[E(2) - E(1)] x /_\Q > 0
may be derived within a few lines from Prigogine's very complex
formula for
/_\(irr)S(sys) > 0
refering to the irreversible production /_\(irr) of the entropy S(sys)
in the system. Once again we will not indulge in this kind of
derivation.
But it in this case, unlike for gases, its also possible to derive
the order relationship
[E(2) - E(1)] x /_\Q > 0
from Ohm's law for electrical conductors. Ohm's law (1827) is
one of the many equivalence relationships "=" discovered for
electricity. Please browse through the electricity section of a
physics textbook to see how many equations for electricity there
are. Try to find one single order relationship ">" in that section.
The chances are very good that you will find none! Why? Is it
because the derivation is difficult? No -- see how easy it is.
Here is the derivation. Ohm's law may be symbolised by
E = R x I
where E is the difference in electrical potential E (measured in
volt) over the ends of an conductor and I is the current (measured
in ampere) flowing through it. The resistance R (measured in
ohm) is constant for some conductors. Actually, we should
have written Ohm's law as
[E(2) - E(1)] = R x I
since it concerns a "difference" in electrical potential which drives
the current I. The current I itself is defined (using again "=") by
I = /_\Q div /_\t (div means "divided by")
where /_\t is the increase in time for an amount of charge /_\Q
to flow past a certain point in the conductor. Hence we may write
[E(2) - E(1)] = R x /_\Q div /_\t
Multiply both sides by /_\Q which results in
[E(2) - E(1)] x /_\Q = R x /_\Q x/_\Q div /_\t
In the right side the resistance R is always positive as is the flow
in time /_\t. Furthermore is the square /_\Q x /_\Q always positive.
Hence the right side is always positive so that for the left side
must also be positive. This is nothing else than what is symbolised
by
[E(2) - E(1)] x /_\Q > 0
I have done this bit of derivation to show you how easily it can be done.
Yet, not one single textbook in physics out of a couple of hundred of them
in our university library tries to harmonise the equivalence relationship
"=" of being in Ohm's law with the order relationship ">" of becoming. Few
of these text books and mainly the very old books mention the date of
discovery. What most of them rather do, is the "wham bam thank you mam"
typical of meiotic thinking. Yet few of them ensure for a nutritional
receptacle required for meiosis.
I have done above such meiosis for the same reason as they did -- to give
a reductionistic account of Ohm's law. I hope that you fellow learners did
not have the same intimidating experiences in learning physics as in
learning mathematics.
Observe that Ohm's law (1827) is very old, almost 200 years. Again its
age indicates a curious state of mind in humankind -- an obsession with
the equivalence relationship "=" of being while neglecting the order
relationship ">" of becoming. Why does this obsession exists up to even
today? Perhaps one day we may have a dialogue on it -- "To be rather than
to become". In my own researches I have traced it back as far as the first
Egyptian civilisations. I suspect that it has very much do with the first
fixed writings of humankind on rock. Those hieroglyphs were sheer wonders,
yet mere beings after all. Their lack of becoming enables us after many
millenia to still gaze upon their being, trying to make sense of what
becoming they suggest.
In my previous contribution I complemented the technology of tyres with
the physiology of our respiratory system to show that the topic of
becoming(>)-being(=) spans both. You may argue that this may be true for
pressure(P)-volume(V) stuff, but that your are sceptical for the
electrical potential(E)-charge(Q) stuff. This makes me happy because
sceptical thinking prevents quick and dirty generalisations. However,
sceptical thinking simultaneously requires painting rich pictures. So let
us apply the findings above, namely
[E(2) - E(1)] x /_\Q > 0
/_\[ [E(2) - E(1)] x /_\Q] < 0
on our body like we did for
[P(2) - P(1)] x /_\V > 0
/_\[ [P(2) - P(1)] x /_\V] < 0
Whereas the latter applied to our respiratory system, the former
will apply to our neurological system.
The building units of our neurological system are the nerve cells
(neurons). They are curiously shaped, elongated cells unlike any other
cells in our body. Some people try to model their action with metallic
conductors, but this model is poor. There are three major kinds of neurons
so let us not now paint the picture too rich. Neurons are almost shaped
like trees growing in a forest with tall trunks. The long axon (nerve
fibre) is like the trunk with the soma (body containing the nucleus)
usually somewhere along it as a thickening. The one end of the neuron
looks like the canopy of branches at the top of the tree so that it is
called the dendrite. It has many spreading branches so as to ensure an
effective connection (synapsis) with other neurons. The other end (base)
of the neuron has less and shorter branches like the roots of the tree.
[By the way, a succulent species grows in the deserts of Namibia which
looks very much like a neuron. Its botanical name is Moringa ovalitifolia.
Its vernacular name is "meel-sak-boom" which translates literally into
flour-bag-tree.]
The effective connection between the ends (dendrite and base) of two
neurons is by no means through an electrical contact. This is why the
model of a metallic conductor for a neuron is so poor. It is rather a
chemical interface through which certain electrically neutral chemicals
(called neurotransmitters) have to move. They are small molecules (usually
proteins) so as to improve their diffusion through this interface.
After the neurotransmitters diffused through the synapse (interface) so
that they enter the end of the cell, they cause a difference in
concentration of potassium (K+) and sodium (Na+) ions, but not chloide
ions (Cl-). This difference is between the inner side and outer side of
the cell wall. It begins at the wall close at the end where the
neurotransmitters have entered. Since the ions are charged, this
concentration difference gives rise to a difference [E(2) - E(1)] in
electric potential between the positive and negative ions. What now
happens, is remarkable. The difference in concentration and thus
electrical potential is propagated as a soliton wave along the wall of the
axon to its other end. At the other end it initiates the production of
neurotransmitters which have to bridge the gap in the synapse before
excitating the next neuron.
A solition wave has only one crest. If you give a long garden hose one
whip lash at its one end, a solition wave will run along it to the other
end. The neurotransmitters act like the whipping hand.
The appearance and subsequent disapperance of the solition at
each position along the axon wall while it moves forward happens
according to the the order relationships
[E(2) - E(1)] x /_\Q > 0
/_\[ [E(2) - E(1)] x /_\Q] < 0
or concisely
PAIR > 0
/_\PAIR < 0
The reason why the soliton wave moves forward and not simply
appears and then disappears at one position, is because the two
order relationships are not in phase. The maximisation first order
PAIR > 0 has a phase which is in advance to the phase of the
minimisation second order /_\PAIR < 0.
A similar kind of thing happens when the neurotransmitters are produced
and subsequently consumed. But in that case it involves chemical energy
rather than electrical energy. We will soon go deeply into this issue
which involves chemical energy with a different example.
Any way, we have now completed the technology of a spark plug with the
physiology of the neurological system. There are abovious differences. For
example, spark plugs use metals and operates in gas mixtures. Neurons use
organic tissue and operates in ionic solutions. But the most remarkable
correspondence is that both happen according to the order relationships
[E(2) - E(1)] x /_\Q > 0
/_\[ [E(2) - E(1)] x /_\Q] < 0
Let us now collapse creatively in order to emerge to an even higher
(deeper ;-) level of harmony between being "=" and becoming ">". Both the
technology of a spark plug and the physiology of the neurological system
are example from the physical world. However, what about the spiritual
(abstract) world to which the mind (not brain) belongs? What possible
relationships are there?
One possible way of thinking is to insist that the difference and hence
order relationship ">" of becoming cannot be harmonised by an equivalence
relationship "=" of being. In other words, the difference is so great that
no correspondences can exist or will ever be found should they exist. This
way of thinking leads to cartesianism, the belief that there is an abyss
between the physical and spiritual worlds which cannot be bridged. It is
most interesting to note that Rene Descarte (1596-1650) was almost a
contemporary of Robert Boyle (1627-1691). Both were fond of mathematics
and for Descarte it was even a profession.
Another way of thinking is to seek harmony between becoming(>) and
being(=) even if we have to explore new unknowns and higher emerging
orders. So let us do it -- let us become.
The more we think in spirit by painting rich pictures in our mind, the
more the physical soliton waves meander over the whole brain rather than
on some localised sections of it. Its like becoming able to move freely
along every road in the city. No traffic congestion and jams. No more a
harmful build up of combusted compounds in being which otherwise in
becoming are beneficial to the function of vehicles. In the city these
vehicles are our cars travelling on roads. In the brain they are solition
waves of concentrated ions travelling along neurons. No more enzymes
necessary to switch off over excited neurons which could not relax by
passing the solitons on to the next neurons. No more headaches of
frustration. It is like as if all the neurons participate in the game
rather than a game played by few players while the rest of the crowd look
on as spectators. Play like a kid, sleep like a kid. Many toys -- many
thoughts. Play with thoughts, sleep on them. But never toss them out of
circulation for whatever system, cursed or praised. A kid without toys
will never sleep peacefully.
These rhythmic meandering (as a result of a phase difference) of the
first and second order relationships
PAIR > 0
/_\PAIR < 0
over our entire neurological system is very important to its well
being. It is not a pure homeostasis, but actually a deliberate
fluctuation around it, yet never leaving it for keeps. It is almost
like a goat attached to a pole so that it can browse around the
pole ithout getting lost. It is like someone sitting at his/her own
PC while browsing through the entire internet of the globe, eating
whatever the WWW can provide. The importance of such rhythmic
meanderings of the order relationships through our whole
neurological network is very important to its well being as our third
example will now show.
Let us think as example for the third form of energy in our body of
chemical energy. Consider glucose as the main source of chemical energy in
our body. The mitochondria in our cells use the glucose molecules as fuel
just as a car would use gasoline. Our digestive system breaks the complex
carbohydrates in food up unto smaller carbohydrate molecules like glucose.
The glucose molecules enter our blood stream where their chemical
potential M have a value M(2). Since each glucose molecule is a chain of
atoms of which its two ends are tied together, its resulting ring shape
makes it "too fat" to pass through the cell walls.
The chemical potential of glucose in the cell is much lower because the
mitochondria are using them up for releasing free energy. Say that the
chemical potential M in the cell has the value M(1). Hence there is a
difference [M(2) - M(1)] in the chemical potential of glucose over the
cell wall. It is very much like the pressure difference [P(2) - P(1)] over
the wall of the tyre!
The task of the pancreas is to produce insulin. The insulin molecules
"straighten" the glucose molecules back into an open chain so that they
then can "puncture" through the cell wall. As they move through the cell
wall, they contribute to a flow /_\N of glucose molecules into the cell.
Hence the expression [M(2) - M(1)] x /_\N again forms a PAIR, but now for
chemical energy! It all happens according to the ny now famliar order
relationships
PAIR > 0
/_\PAIR < 0
The netto effect is again a relaxation (decrease) in the difference
[M(2) - M(1)] of the chemical potential by the complementing flow
/_\N.
But what happens when the pancreas cannot produce insulin any more as in
the case of diabetes mellitus? As a result the flow /_\N of glucose
molecules into the cell cannot be maintained. Hence the value M(2) of the
chemical potential of glucose in the blood stream increases as a result of
the excess glucose in it. Furthermore the potential value M(1) in the
cells decreases because of a depletion of glucose by the mitochondria.
Consequently the difference [M(2) - M(1)] in the chemical potential of
glucose increases to a breaking point. The glucose become partially
oxidised in the blood serum itself to gluconic acid. This lowers the pH pf
the blood and increases its viscosity. The change in pH upsets dozens of
other biochemical reaction in the blood which depend on a homeostatic pH.
Let us see how easy it is to write the mellitic diabetes condition
symbolically. The order relationship ">" of becoming
[MC(2) - M(1)] x /_\V > 0
for a healthy pancreas degenerates into a simpler fixed order
relationhip
[M(2) - M(1)] >> 0
together with a restricting equivalence relationship
/_\V = 0
This is mathematical formulation of what happened to me now
almost a year ago when an attack of influenzia incapacitated
my pancreas irreversibly.
The one treatment is to make use of insulin injections. The alternative
pathway is to keep through a careful diet the difference [M(2) - M(1)] as
small as possible by avoiding carbohydrates as far as possible. This
alternative pathway surprised my GP because he is convinced that I need
glucose as a source of energy, especially for the functioning of my brain.
Well, I had to BECOME more like a fish which is the best among all animals
in utilising protein as a source of energy. I sort of had to exhange the
"petrol engine" in my body for a "diesel engine". I kept in mind that a
similar [M(2) - M(1)] expression for ureum (combustion product of
proteins) would increase drastically, thus increasing gout. But I have now
less gout than before. Something fishy going on here, is it not?
Before I exchanged my petrol engine for a diesel engine, I had
extraordinary experiences how the functioning of my neurological system
shut down in a step wise fashion. My eyes shut off most and my smell
least. When the gluose level in my blood was at its highest level with
[M(2) - M(1)] at its greatest because /_\N was zero (no flow of glucose
into my cells), my cognitive faculty on the formal level of knowledge was
at is lowest. Speaking was with effort. I could not recognise most
spelling mistakes. As a result I became extremely aware how my cognitive
faculty on the tacit level was operating just as before. For example, I
observed with intense curiosity what was becoming of my body and mind. But
because of the lack of the "back action" of the higher faculties in my
mind, I was not able to form a cybernetic loop and thus take control of
myself. So the GP was necessary after all to put me back into control.
What he does not like now is that I have taken over the control myself,
doing him out of some bucks.
Dear fellow learners, I have not tried to avoid technicalities and
mathematics. I tried to stick to what is in my opinion essential to this
topic and thus have avoided a lot which you may not be aware off. The
"mathematical traffic" which I did use was not to intimidate or frustrate
you. It is simple mathematics, although its ramifications are immensely
complex as I have taken pains to point out. I used the mathematics to
focus on a melody with verse upon verse to accompany it. We may call it
the Ballade of "becoming-being" -- the essentiality "liveness" of
creativity, one of seven such essentialities. Perhaps some day I will try
to write balades on the other too.
But what about you? You and you alone are responsible for deciding how
your mind will become. The only thing which I can and gladly will do, is
to assist you as a "midwife" or catalyst in whatever becoming (even
mathematical becoming) you plan for your future. However, whatever you
decide and then follow through, please remember that peace is most
important to it all.
Since this contribution has become lengthy, I will go into the subject of
peace my next contribution. It seems as if this ballade has no end.
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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