Replying to LO24208 --
Greetings to you all feeling lost. This is my ninth round to the topic "To
become or not to become". It becomes almost time to give the URLs to all
these rounds so as to follow the "cyberbalade" (?).
I have longed to put the mathematics away for a while. But the uncertainty
prevailing in many fellow learners as they become in becoming tells me
that I cannot. We will have to look carefully at this uncertainty and try
to understand it.
Perhaps the person who did most to articulate uncertainty, was Werner
Heisenberg, the "father of matrix mechanics". He, together with Erwin
Schroedinger as the "father of wave mechanics" can be considered jointly
as the "fathers of quantum mechanics". PAM Dirac was the key figure in
showing that they looked at one and the same thing, now called Quantum
Mechanics (MQ), but only from different viewpoints. Few people outside
physics know anything of Heisenberg's "matrix mechanics", although many
know that he has formulated what is now known as the "uncertainty
principle". Why? The mere name of this principle is already intriguing.
If they were the "fathers", then who were the "grandfathers"? Two persons
stand out remarkedly: Max Planck with the equation E = h x f and Albert
Einstein with E = m x c^2. Without these two equations, quantum mechanics
would never have seen the light. Planck never became fond of the
Uncertainty Principle (UP) and Einstein often argued very strongly
against it. Both felt that they knew too little to make sure claims on
uncertainty. Sureness and plausible ideas are two different things. On the
other hand, Heisenberg, Schroedinger, Bohr, Dirac, Born and others
accepted the UP as inherent to QM. The mathematical formalism of QM allow
the faultless derivation of a mathematical expression which they have to
call some or other name. They used as name for it the most plausible
explanation to them for it -- an explanation which involves uncertainty.
We are very fortunate to have covered in this topic "To become
or not to become" all the mathematics needed to formulate the
mathematical expression for the UP of Heisenberg. Let us do it.
It concerns the tiniest of wholesome particles possible like photons,
electrons and protons. The mathematical form of the UP is nothing
[z(2) - z(1)] x [p(2) - p(1)] > h/(2 x pi)
We can shorten the expression making use of the /_\ notation for
/_\z x /_\p > $h$
Here /_\z = [z(2) - z(1)] is the possible variation in the position z
of a particle and /_\p = [p(2) - p(1)] is the possible variation in
momentum p. The "h/(2 x pi)" is shorten into $h$. Let us now
delve deeper into its form, trying to understand each facet of it.
The variation (not variance, but rather interval) is the difference
between the two outer extreme values, ie. the maximum and the minimum
possible values. The actual position z is somewhere between [z(2) - z(1)]
and the actual momentum is somewhere between [p(2) - p(1)]. In other
words, although we may think of position z and momentum p as having point
values in terms of Newton's classical mechanics, they can only be
presented by an interval of possible values in QM. This interval or
variation of possible values in z or p is then considered as the
uncertainty of the point values in classical mechanics. It means that in
QM we have to work with a collection of values /_\z or /_\p rather than
the singular point values z or p. It is almost like having to work with
organisations rather than individuals in them.
Three things should struck us in the mathematical expression of the UP.
Firstly, it use the "order relationship >" of becoming rather than the
"equivalence relationship =" of being. This ">" came as a shock for
physicists who were used to work only with "=." Up to that time the ">"
appeared in only one other mathematical expression of physics, namely the
Law of Entropy Production (LEP) some 50 years earlier. Since then many
phsyicists like Bolzmann, Maxwell end even Gibbs tried to explain this ">"
in terms of other physical laws which made use of only the "="
relationship of being. The only "plausible explanation" for LEP (rather
accepting it as a sure fact involving a ">") which they could arrive at in
those times was to incorporate statistics and probability theory. This is
why the concept "entropy" became so fuzzy.
Secondly, on the left side of UP we again have two differences (increments
or variations) multiplied by each other. Thirdly, on the right hand side
we have the "h divided by 2 times pi" rather than the "zero" now so
familiar to us in the mysterious "pattern of becoming". Physicists write
it as the letter h with a bar through its neck. We cannot do it because of
our restriction to the ASCII characters of the PC keyboard. We will write
it simply as $h$.
Do you still remember how I introduced the expression
[P(2) - P(1)] x /_\V > 0
by asking you to imagine me sitting there in the desolated Huab
valley in a desert of Namibia? Do you still remember why we wrote
/_\V for the difference [V(2) - V(1)] in volume, but not /_\P for the
diffrence [P(2) - P(1)] in pressure? The symbol P stands for
"pressure" and the symbol V stands for "volume". The (2) and (1)
added to each mark two different values of each at events (2) and
(1). We retain the "difference" notation for pressure because
pressure is an "intensive" quantity, but we think of the "difference"
in volume as a "flow" (symbolised by /_\) since volume is an
"extensive" quantity. Work through all my previous contributions
on the topic "To become ot not become" in which I have explained
it all very carefully.
There seems to be strange connections between Heisenberg's
UP with form
[z(2) - z(1)] x [p(2) - p(1)] > h/(2 x pi)
and the "pneumatic becoming pattern" with expanded form
[P(2) - P(1)] x [V(2) - V(1)] > 0
Let us go deeper into where they differ, but also correspond.
Firstly, the one and only difference. A tiny flash light or the flame of
one candle will transfer roughly one joule of energy as light in one
second. The value of "h divided by 2 times pi" is approximately 1 x
10^(-34) joule-second. This number is very, very, very, very, very, very
small -- roughly a millionth (1st) of a millionth (2nd) of a millionth
(3rd) of a millionth (4th) of a millionth (5th) of a ten thousandth of one
joule of energy transfered in 1 second. How small is that? Should we add
for every teaspoon of matter of the earth one elementary value of $h$
together, we will still be one millionth short of the light energy given
out by one candle in one second. Thus the value of $h$ is very, very,
very, very, very, very close to "zero", but not yet exactly equal to
"zero". In other words, we would have easily made $h$ = 0, but actually
$h$ > 0. Perhaps it tells us that the closest we can come to zero is by
the value of $h$.
Secondly, the correspondence. The position z of any macroscopic
object is an intensive quantity. Scaling the size of that object does
not influence its position as we measure it from some point called
the origin. However, the momentum (mass x velocity) of this
macroscopical object is an extensive quantity. (Think of a gigantic
truck and a cyclist moving at the same velocity -- their momenta
express mechanically the difference between them.) Hence we may
easily have written the UP as
[z(2) - z(1)] x /_\p > $h$
should It apply to macroscopical objects. However, the UP applies
to "atomistic" ("ultra microscopical") objects such as atoms and
subatomic particles. Thus we should take care not to jump from
"macroscopical" insights into making "ultra microscopical"
conclusions. That jump is too immense not to expect some changes
to our thinking. What changes?
Here is an example. We have used macroscopical instruments
(measuring meters for pressure P and volume V) to set up the
[P(2) - P(1)] x /_\V > 0
In the ultra microscopical world of atoms we cannot have such
measuring instruments because these instruments themselves
are made up of trillions of trillions of atoms. We are forced to
"measure" tiny things like a whole atom with things which are as
tiny as a whole atom. It is then when we suddenly discover that
the PAIR have to increase with at least $h$ and not anything closer
to "zero". It means that the smallest increase in the PAIR is a
"quantum jump" equal to $h$. Should we measure the position z
of one atom by bombarding it with another atom, we will also
disturb the momentum p of this atom significantly. Should we try
to measure both the position z and the momentum p of one atom
with two other atoms, one for position z and one for momentum p,
the irreversible disturbance is even greater! In other words, the UP
tells us that we have reached the lower limit of SCALING down
our objects and thus our measuring instruments.
What a wierd conclusion! Let us contemplate it more. Please
distinguish very carefully in the next paragraph between the words
"human" and "person".
Its like observing one human X solely by his/her interaction with merely
one other human Y. We do not make use of something smaller as a human and
thus definitely not use any questionaire. We know to some extend how Y
reacts upon any spiritual issue, say care, through his/her history of
interactions involving care. In other words, Y is not merely a human, but
the person Y. When Y and X now begin to interact so that we can observe
human X through person Y who have a history, the knowledge of person Y on
care (because of a history!) plays a role on the experiences of human X.
We may observe with much certainty based on person Y's history what Y
tells us about the reaction of human X upon care. But this very reaction
of human X changes the whole personality of X through something which we
call learning! Thus human X will not react the same a second time because
human X has changed irreversibly. We begin to think of human X also as the
person X. Obviously, the same applies to Y so that Y self keeps on making
history, thus becoming further in personality.
Dear fellow learners, let me stress it once again. If you want to
understand "deep uncertainty", make use of a whole person B to enquire
anything about whole person A. In other words, make use of personality B
as the mouthpiece ("umlomo", see the associative pattern of wholeness) of
personality A. Forget about making use of questionaires, or even loftier
CVs, or even detailed reports by peers on a specific discipline because
all these things are but parts of a whole which together are forever less
than the whole. Forget even about finding more out through direct contact
by avoiding the "umlomo" because then you have lost the little objectivity
which you had through the "umlomo"!
Obviously, you are not one atom and thus the quantum jump is not one very,
very small $h$. If you are a human of average built, you will consist of
roughly 10 ^ 28 atoms. Thus the quantum jump you have to expect
physically, is roughly a millionth of the energy given by one candle in
one second. It is roughly like the change brought about by a "twinkle in
the eye" which reflects what is going on in the spirit of the human. It is
this very "twinkle in the eye" we tend to symbolise in email by the
strange cluster ;-) It is what Socrates called "the birth of a noble
Just as the "becoming pattern" (order expression)
[z(2) - z(1)] x /_\p > $h$
brings "uncertainty" about in the microscopical world, any
"becoming pattern" like
[P(2) - P(1)] x /_\V > 0
brings "uncertainty" about in the macroscopical world. But what
exactly is this "uncertainty"? Some fellow learners have written
to me in private, expressing the feeling that as they become
aware of more and more "becoming patterns", they feel some
strange anxiety as never before. Please, do not assume that
you are alone in this feeling. Heisenberg spent many a sleepless
night trying to become more sure on merely the UP of but QM.
Einstein argued bravely against using "uncertainty" in explaining
it, creating many a novel "thought experiment" which baffled
others on the frontiers of quantum mechanics. Prigogine, De
Groot and Callen felt the same about the basic "becoming pattern"
of irreversible thermodynamics. I do not know of any authentic
learner who did not felt this strange anxiety.
I myself felt the "Big Question" intensely -- the "Am" who "Become". I
can now paint a rich picture on this "Big Question" by using the
"becoming-being" of liveness, but I still cannot command it formally. It
is rather my personality being commanded by liveness as a "force" far
greater than all my own mental power. Jan Smuts would have said exactly
the same about wholeness. He became extremely mental on wholeness, yet he
had to bow before wholeness as something having far greater power.
Nevertheless, the anxiety of fellow learners compel me to offer some
explanation rather than none.
By fixing our mind on being and its static qualities we become more sure
of it, but less sure of becoming and its dynamic qualities. We can spent
hours on the static snapshot of being, but then during all that time we
cannot spend anything more than a split second to capture the dynamic
movie of becoming. When we go to the opposite extreme by focussing
continuously on the dynamic movie of becoming, we have but a split second
to focus on the static snapshot of being. The anxiety explodes into sheer
terror when we try to apply LEM (Law of Excluded Middle of logic) on these
two facets of liveness, either "being" as the one extreme or "becoming"
as the other extreme, but not both in harmony. Its almost trying to
understand God with logic -- the more the logic we put into it, the less
we understand God.
On the other hand, this anxiety diminishes to solicitude and eventually a
quiet breeze by trying to find harmony between "becoming" and "being",
letting our focus meander between these two so as trying to learn how to
focus on both of them. Its like driving in car looking at the landscape,
say a desert, next to the car. Focus on a particular static object like a
succulent plant next to the car and you may easily forget you are driving
the car! Focus on the swerving road before you because of driving of the
car and you may not find time to focus on even one single succulent plant
at the side! It took me self a couple of years to do both, looking in
front which changes swiftly and looking to the side at something fixed.
Likewise each of us has to learn from the very beginning like a baby how
to focus one mind on at least two things, a becoming and a being -- the
least of all the one-to-many-mappings. The better one become in this
one-to-two-mapping, the less the feeling of anxiety.
It is for some very strange reason that the Western world have fixed its
focus on "being" the past two millenia, thus losing its focus on also
"becoming". Perhaps it was caused by a unique event two to three thousand
years ago. Perhaps this ancient event was caused by something even more
curious having to do with the much earlier evolution of languages. We load
sentences with more nouns than verbs. We tell stories by beginning our
sentences with nouns or some qualification of the noun. Whatever the
cause, historical or pre-historical, the result of our excessive focus on
being makes us too rigid for becoming. Consequently we begin to fear
change itself and not any qualified changes in particular. Perhaps the
anxiety of fellow learners reflects to some extend this collective fear of
change. It was the case for me too.
The diminishing of our anxiety is not the only reason why we have to focus
on both the becoming and being of liveness. Should we recognise only this
reason, we may easily fall into the banalities of a fear-driven society,
seeking a carefree life rather than reaching out to fellow humans with
caring love as the essence of living. No, when we learn how to focus on
both becoming and being, we become aware of the incredible rhythm
pervading all of the universe. This rhythm can be as smooth as a regular
(sinoidal) wave on a river or become as edgy as the fractal pattern of
its banks in a ravine. It can be as close to equilibrium as a crystal
growing in a saturated solution or as close to the edge of chaos as a
crystal thrown in agitated solvent to dissolve.
It is a rhythm both in the "world-outside-me" and the "world-inside-me".
Let me illustrate it with another example from the desert -- Bushmanland.
The main village of Bushmanland is called Pofadder. It had been named
after a famous Khoi (Namakwa) chief Pofadder. The name "pofadder" also
refers to a very poisonous snake often found in the deserts of Southern
Africa -- somewhat resembling a rattle snake or cascavel. It is short and
thick and seems to be too lazy to move. But when it strikes at something
within range, it is as fast as lightning. It fears only one thing --
strange vibrations in the ground. Give it enough time to overcome its
laziness and you will never even see it in your walking.
Drive a few miles to the west of Pofadder so that a vast basin unfolds
itself before you. I need not to tell you where to stop because you will
do so. Seeing such a vast expanse unfolding in front of you is awesome --
perhaps the same as when an astronaut look at our globe earth from a
distance. Escape from your vehicle which is fast becoming a suana.
Westwards the road (now tarred, but still dirt on my first visit)
stretches into nothing before it has even reached the horizon. A regurlar
and almost imperceptable breeze let you forget that the temperature is
100F (38C). Because it is so dry, your sweat evaporates instantly.
This vast, cream colored basin drains gradually to the north into a
gigantic funnel where it reaches a rugged range of purple colored
mountains some 30 miles away. Somewhere between and along these mountains
flows the Gariep (Orange River). On the other side of this fractal
cataclysm the cream expanse flows again, now deeper into Namibia. Try
taking slides with your camera with the widest possible undistorted angle.
It is impossible to image the whole. Whatever scenery you capture, the
picture leaves you extremely disappointed afterwards. So take a video
recorder along so as to try and capture the whole in one gigantic sweep.
Then the greatest surpise will come to you because even this becomes
Whether as snapshot or a movie, they record only the "world-outside-you".
They do not record the "world-inside-you". Thus thy cannot tell how your
internal rhythm begin to harmonise with the rhythm of the world outside
you. They cannot tell how your heartbeat begins to slow down and get
softer with every beat. They cannot tell how your mind begins to let in
little by little the vast expanse all around you. They cannot tell you
what BECOMING THERE IS IN BEING.
After half an hour or so, the becoming within you calls. You cannot just
stand there. So you get back into the vehicle, switch it on and begin to
drive further westwards down into the basin. You will do it very slowly,
almost as if not to disturb the sacredness of your earlier experience.
When you reach the bottom, you suddenly see a dirt road turning out to the
north, marked Pella. You stop, let the engine idle, take a glance at the
map, see that it is not to far away and thus decide to explore Pella. The
sudden heat let you look at the temperature gauge -- the radiator is at
boiling point! With a shock you realise you have to keep moving to keep
the radiator from exploding. With a another shock you realise that you
have to turn down all windows because sweat is beginning to stream down
On either side of it the dirt road is becoming engulfed by a massive hill
of sand, once before history a sand dune. The vast expanse has
disappeared. You are becoming boxed in by sand and heat. "Where are the
rugged mountains and where is the Gariep?" your mind calls out. Then, as
you turn along the last bend, the small village of Pella greets you. The
shade of the biggest tree in sight next to a white church draws you like a
magnet. You switch off your vehicle and scramble out of it, gasping with
relief. Should you have a thermometer with you, it will show 120F (55C) in
But before you even can reach for your camera to capture this new scenery
with its wierd idillic spirit, you become aware how your heartbeat is now
increasing and thrusting harder with every beat. It is because your body
has now become a refrigirator. Each drop of sweat keeps you alive. All the
snapshots and all the movies you will take, will again be a disappointment
when you look at them later. Why? Because they cannot tell what BEING
THERE IS IN BECOMING -- neither in the "world-outside-you" nor in the
"world-inside-you". This new rhythm in Pella is so different from the one
Later that night, as you lay down, staring into the dark sky filled with
bright stars, think of the vast expanse seen from Pofadder. Its the same
rhythm. Then let you imagination draw you closer and closer to any of the
uncountable many stars above so as to feel the rhythm of Pella once again
in you. Open yourself up to this dance of the rhythms. It will awaken you
to the rhythm of the universe, the becoming-being of liveness. The feeling
of anxiety will get displaced, little by little, with the feeling that
finally you are getting closer to home.
Dear fellow learner, if "becoming-being" makes you feel anxious, do not
get desperate or paralyzed. It is the feeling which you get when you leave
something familiar to explore the unknown. But as you come closer to home
which may not be familiar any more, the feeling of anxiety gets displaced
by a feeling of excitement which words cannot describe. Perhaps it
requires the Faraday stance (See Being mental. LO24112)
Sing with laughter and dance with joy.
With care and best wishes
At de Lange <email@example.com> 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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