Dear Organlearners and Winfried,
Please forgive me. I made an error in my previous post. I was in a great
hurry because my wife and granddaughter were waiting for me. I promised
them a few days at the ocean (Richards Bay where my eldest son works for a
computer firm) and they were waiting impatiently upon me to finish the
contribution.
> The problem with the equality sign = in mathematics is that many
> people use it to equate only "beings" with each other. For example,
> in 1 + 1 = 2 the left side 1 + 1 is perceved as a "being" which has
> resulted AFTER the operation (action, process) + has exhausted
> itself. The 2 on the right hand side is a "being". Thus the equation
> 1 + 1 = 2 itself is perceived as a "being" and hence the = (to equate
> - - an action) as a sign of reversibility. Mathematicians call this the
> reflexivity property, saying that (1 + 1 = 2) = (2 = 1 + 1)
The property symbolised above is not the reflexisive property, but
the symmetric property! The symbolisation of the reflexisive property
is (1 + 1 =2) = (1 + 1 =2)
You have questioned my use of the sign "=" in describing
holism as
1 + 1 "=" 3
wondering why I did not use the conventional sign < ("is smaller
than") . To that I replied:
> You are right. I cannot use the ordinary sign = (to equate or to
> identify) when comparing 1 + 1 with 3. Mathematicians would use the
> sign < for such a comparison, i.e, 1 + 1 < 3. The sign < is used to
> signify the action "having been ordered". and is read as "is smaller
> than". I could have used the expression 1 + 1 < 3 to signify Smuts'
> central idea in holism that the the whole is more than the sum of the
> parts. I have contemplated to use it, but decided against it because
> the sign < indicates in no way how this higher order emerged. It
> merely accepts the fact that this higher order has indeed emerged.
Note that he mathematical sign for order, namely >, is not symmetric.
In other words,
1 + 1 < 3
is true, but
3 < 1 + 1
is not true.
Excatly the same applies to 1 + 1 "=" 3.
Winfried, you once mentioned that the book "The self-organising
universe" by Eric Jantsch had a great influence on you. In that book
he discusses the fact that entropy production (the Second Law) is
symmetry breaking and how much it contributed to diversity and
self-organisation. The expression 1 + 1 "=" 3 merely summarises what
he had written about!
Holism is defined as "the whole is more than the sum of the parts".
Its direct symbolisation is 3 > 1 + 1. Thus the wording of
1 + 1 < 3 should rather be "the sum of the parts is less than the
whole". Our use of language is such that the two phrases
"the whole is MORE than the sum of the parts" and
"the sum of the parts is LESS than the whole"
means exactly the same thing. Thus these two phrases are not
symmetrical.
The SYMMETRICAL counterpart of the phrase
"the whole is MORE than the sum of the parts"
would be
"the sum of the parts is more than the whole".
Whereas the phrase
"the whole is MORE than the sum of the parts"
is true, the phrase
"the sum of the parts is more than the whole" is false.
(Sorry, I cannot help the following pun. The latter phrase is true in
the motor industry. Should we assemble a car by buying all the spare
parts individually, it will cost roughly five times as much as buying
a whole asembled car, ...grin...)
What is very worrying to me, is how much a lot of people in many
walks of life live up to the phrase "the sum of the parts is more
than the whole". They buy and swop parts like furniture, books,
concepts and even employees, adding them to the parts which they
already have. Thus they increase the sum of the parts, making this
sum more and more. It is as if they hope that one day the phrase "the
sum of the parts is more than the whole" will indeed become true.
The phrase will never become true because the "sum of the parts" and
the "whole"differ from each other through a very, very important
phenomenon - the "emergence". Since emergences are extremely
contingent, they will never happen automatically when merely
bringing the parts together to form the sum. The complexity of the
contingencies (requirements) can be unfolded by the seven
essentialities.
While staying with my son, I worked through a couple of his
electronic books to refresh my mind and explore new developments.
One of the books devoted a whole chapter on the physics of
semiconductors - p-type (positive) and n-type (negative) conductors.
It struck me how p&n conduction in semiconductors are a fine example
of holism!
The beginning material in a semiconductor is either the element
silicon (or the element germanium) in a very, very pure form. Silicon
(or germanium, like the element carbon) belong to group 4 of the
periodic table. It means that a silicon atom has four outer
electrons. These four outer electrons can combine with 4 outer
electrons coming from other atoms so that the atom becomes saturated
with eight outer electrons. The is exactly what happens to every
silicon atom in a silicon crystal (from which wafers are cut to
manufacture the so-called chips). All the atoms are packed into a
neatly arranged pattern called the crystal structure.
To form a n-type (negative) conductor, a very a small amount of
phophor P is introduced to the pure silicon Si. The ratio is
roughly 1 P atom to every million of Si atoms. Phosphor belong to
group 5 of the periodic table. Thus a P atom has 5 outer electrons
and needs only 3 additional electrons from other atoms to become
saturated with outer electrons. But in the Si crystal, a single P
atom, surrounded by a million of Si atoms, are forced by their
collective action (remember Smuts' "manifestating force of the
whole") to behave like a Si atom (which has four electrons) and not
as a P atom (which has 5 electrons) any more. Thus the P atom, trying
to behave like an Si atom, makes its fifth electron available for
conduction (to get rid of it). Since an electron is negatively
charged, the mode of conduction is called n-type.
In a p-type (positive) conductor, a very small amount of the
element Gallium Ga (group 3) is introduced, again at a ratio of
roughly one Ga atom to every million of Si atoms. A Ga atom has only
three outer electrons. But in the Si crystal, surrounded by millions
of Si atoms (4 electrons), the Ga atom is now forced to behave like a
Si stom. Thus it needs a fourth electron as if its nucleus has
increased by one proton (positively chaged). Whereas a n-type
conductor behaves as if it is electron enriched, a p-type conductor
behaves as if it is electron deficient.
A semiconductor device is created when a p-type conductor and a
n-type conductor are connected to each other. The simplest of devices
is the diode - merely n and p connected. (The next complex device is
a transistor - two p-type conductors separated by a thin piece of
n-type conductor.) All through the n-type conductor (except at the
junction) the electrical resistance is linear (behaves acording to
Ohm's law). The same is true of the p-type conductor. But at the
junction itself the resistance becomes non-linear (non-ohmic)! Thus
the resistance of the whole device becomes non-linear. In the case of
a diode, it will have a low resistance to current in the one
direction, but a high reistance to current in the other direction.
Whats strikes me, is that in the realm of human affrairs we also have
these "manifestating force of the whole" - the masses influencing
the individual to behave like part of the mass, giving up its
individualistic properties. For example, notice what happens when one
individual comes up with a new idea - new to a million of his (her)
former pears. They want him to conform. But this forces the new idea
(like the fifth electron) into the "conduction state" - it becomes
public domain. Let is call this "conductive state" the "n-discourse".
In the next stage a second person gets another idea in anology to the
first idea. Usually, the sceond idea exludes the first idea or even
opposes it. In such a case, again under influence of the millions of
pears, it now leads to a "p-discourse". The non-linear fun really
begins when the "n-discourse" and "p-discourse" comes into contact
with each other, forming a "dialogue device" rather than an
"electronic device". Like in a physical diode, ideas begin to flow
much easier in the one direction than in the opposite direction! See
if you can spot these non-linear flows of ideas in your favourite
list-servers.
Best wishes
--At de Lange Gold Fields Computer Centre for Education University of Pretoria Pretoria, South Africa email: amdelange@gold.up.ac.za
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