Energy and Entropy LO28636

From: AM de Lange (
Date: 05/28/02

Replying to LO28593 --

Dear Organlearners

and greetings to you Dan,

Sorry for ending so abdruptly last time. Who must run, must run ;-)

Last time I took pneumatical energy to explore the paradigm
whether the universe is reversible or irrversible. It may seem that
pneumatical energy is esoteric. It is not. Whenever a wind blows,
pneumatical energy is involved.

I want to explore that paradigm further.

In a reversible universe winds cannot blow. The pressure P has to
be everywhere the same. If the air then moves so slightly that a wind
cannot be felt, the pneumatical work done is
W = P x /_\V
where /_\V is the volume of air displaced. Here the pressure P is the
intensive parameter while the volume V is the intensive parameter. It
means that should we scale the system bigger or smaller -- with a
balloon it is easy -- the pressure stays the same while the volume
cales accordingly. Likewise every other form of energy has an
intensive parameter Y and an extensive parameter X.

In an irreversible universe we accept that winds do blow. When a
wind blows, it blows from a higher pressure P2 to a lower pressure
P1. Again a volume /_\V of air gets displaced. To calculate the
pneumatical work done, we have to take the changing pressure from
P2 to P1 into consideration. As a crude approximation, we may think
of the average pressure (P2+P1)/2. The pneumatical work done is
W = (P2+P1)/2 x /_\V
We may use integral calculus to obtain a much better value.

But see what we did! We reduced two different pressures P2 and
P1 into one average pressure (P2+P1)/2. Is this how otherness
("quality-variety") works -- reducing P2 and P1 into the "sameness"
(P2+P1)/2? Does the difference P2-P1 not also help us to focus on
otherness? As I have said before, the expression
(P2-P1) x /_\V
is proprotional to the entropy produced, namely /_\S. The
proportionality factor is the absolute temperature T. Hence we have
/_\S = (P2-P1) x /_\V / T
This was the crucial discovery of Ilya Prigogine -- how entropy gets
produced by force-flux pairs.

Let us now think of
W = (P2+P1)/2 x /_\V
/_\S = (P2-P1) x /_\V / T
in terms of how we conceive the universe. In a conception that the
universe is reversible, P2=P1=P while P2-P1=0. Thus the work
W reduces to
W = P x /_\V
(P2+P1)/2 = (P+P)/2 = P
Furthermore the entropy production /_\S reduces to
/_\S = 0
(P2-P1)x/_\V/T = (P-P)x/_\V/T = 0x/_\V/T = 0

Dan, is this not shocking? By thinking of the universe as a reversible
system, we end up with
W = P x /_\V
for the more complex
W = (P2+P1)/2 x /_\V
/_\S = 0
for the more complex
/_\S = (P2-P1) x /_\V / T
What can be more simple than this reversible world which your text
book writes about?

W = P x /_\V
/_\S = 0
say that no organisation involving order and chaos has to be minded,
neither for pneumatical energy nor for any other form of energy. But
the expressions
W = (P2+P1)/2 x /_\V
/_\S = (P2-P1) x /_\V / T
say that organisation in which differences occur has to be considered.
Can you percieve the LRC (Law of Requisite Complexity) here?

All my writing on energy and entropy would be irrelevant were it not
possible for us to scale organisations too. Let us scale an organisation.
In the scaled organisation the number of managers stays the same
while the number of subordinates get scaled too. Hence the crucial
difference between leaders and followers is that leaders have to act
intensively while followers have to act extensively. A leader is
someone for whom qualities have decisive meaning whereas followers
toil with quantities leading from such qualities. It is as if a leader thinks
in a
W = (P2+P1)/2 x /_\V
/_\S = (P2-P1) x /_\V / T
manner whereas followers think in a
W = P x /_\V
/_\S = 0
manner. (Look at the number of symbols involved ;-) The leader
embraces complexity while a follower gets intimidated by complexity.
A leader wants to know more of complexity while a follower shies
away from entropy production /_\S, wanting
/_\S = 0
which means a reversible conception of the universe.

Dear Dan, rote learning means
/_\S = 0
whereas authentic learning means to explore
/_\S > 0
Why? In rote learning information which exists outside the mind
flows into the mind by way of memorisation. Its organisation stays the
same so that the entropy does not change, i.e.,
/_\S = 0

In authentic learning a "knowledge kernel" emerges in the tacit
dimension. The entropy has to increase for this emergence. Then
that "knowledge kernel" gets articulated into an idea. Again the
entropy increases. With this idea we then search for information
related to it. This information is organised in many different stacks
(books, papers, files). We digest the appropiate bits of information
and reorganise them with regard to the idea. Again the entropy
increase, but now for digestion slower than for the emergences.
Thus authentic learning involves entropy production, i.e.,
/_\S > 0

When I observe your telling how you work through that physics
textbook (1970) all on your own in far away Alaska, i think you
have been creating a lot of entropy to sustain your creative learning.
I am reasonably sure, given the date of that textbook, that it does
not have explicit information on the intensive-extensive pattern
common to all forms of energy. You had to search self for that
pattern in each from. If you were a rote learner adhering to
/_\S = 0
you would not have created such interesting statements and
compelling questions. Your entropy landscape has now become
quite rugged as a result of your irreversibility along
/_\S > 0
Keep on learn while you create, order or chaos, it does not matter.
ooner or later order will emerge from every chaos.

Let us investigate one other form of energy and how it affects our
lives. I am going to select electrical energy, a form of energy with
which you seem to have become confident. Think of your computer.
For it to function, the electrical mains does electrical work on it.
This is given by multiplying the electrical potential in volt with the
flow in electrical charge in coulomb (given by current multiplied by
time). All the modules (screen, fan, motherboard, disk drives) in the
computer need that electrical work to function. The total current
drawn by the computer is fairly constant.

However, when the computer functions, it does so in terms of
millions of tiny transistors switched "on" or "off". Each transistor has
a base which switch between a high potential Y2 and a low potential
Y1. (We use Y here to indicate an intensive parameter and X to
indicate its corresponding extensive parameter.) For the duration of
its "on" state with the base at Y2 the transistor draws a flow of
electrical charge /_\X. Entropy gets produced according to the
/_\S(on) = (Y2 - Y1) x /_\X / T
This entropy production happens as the charge flows from the
emitor through the base to the collector in the transistor. We may
say the transistor is far from equilibirum. For the duration of its "off"
state with the base at Y1 the transistor draws zero charge so that
/_\S(off) = 0
We may say that the transistor is close to equilibrium.

The "on" and "off" states are usually designated "1" and "0" rather than
/_\S(on) = (Y2 - Y1) x /_\X / T
/_\S(off) = 0
But it is worthwhile to think of the switching of the transistor between
the states "far from equilbrium"="1" and "close to equilibirum"="0".
Every thing which the computer then has to do, gets done by
operations on "bits". A "bit" has the value either "1" or "0". For example,
umbers may be expressed by the following bits:
0 = 0
1 = 1
2 = 10
3 = 11
4 = 100
5 = 101
6 = 110
In other words, the larger a number gets, the more bits it need to be
presented. It means that the larger a number becomes, the more
entropy producing units (transistors) it requires for its modelling.

There was a time when computers worked with 8 bit "bytes". In other
words, every piece of information (number, text, graphic) was
modelled on a byte consisting of 8 bits. It required the switching of
8 transistors in unison, some to the "on" and some to the "off" state.
Combining this piece of information with another piece of information
(like adding a number to a number) required 8 other transistors as well
as groups of 8 transistors in the processor to do the adding. Then
came the 16 bits per byte computers and thereafter the 32 bit per byte
computers. Computing power increased, but the basic scheme stayed
the same.

What scheme? To have a network of millions of transistors, some in
the "far from equilbrium"="1" state and the rest in the "close to
equilibirum"="0" state. By typing a number, say 6, somewhere in that
network, a group of 8 (or 16 or 32) transistors change their 1-0
configuration into 00000110. Do you now have an image in your mind
of your computer as a rugged entropy landscape? Imagine looking in
the night from a mountain to a city next to it. Some lights go on while
other stay off. Some lights go off while others stay on. This is how
your computer works, relying on
/_\S(on) = (Y2 - Y1) x /_\X / T = "far from equilibrium"
/_\S(off) = 0 = "close to equilibrium"
for each of its millions of transistors.

Despite this fantastic image, the computer is still a poor model for a
living system. The reason is profound. When a transistor works
between a potential difference Y2 - Y1, only an electrical charge
/_\X flows. This is because of the construction of a transistor. But
when a living cell is placed between a potential difference Y2 - Y1,
a lot of things happen. A charge /_\X will certainly flow. But the cell
will also contract, doing pneumatical P x /_\V work. Ionised parts of
molecules may also begin to flow in or out of the cell, doing chemical
G x /_\N work. In other words, the one (Y2 - Y1) x /_\X force-flux
pair induces many other kinds of force-flux pairs. This is where the
Onsager reciprocal ("cross-induction") relationships of irreversible
systems come into the picture.

It is like using chopsticks to lift one worm out of a can. Out come
many worms crawling in all directions. Fellow learner Alan Cotterel
is fond of risk management. This is where risk management comes
into irreversible systems. Make one change to an irreversible and it
maps itself into many different responses. An irreversible system is a
"one-to-mny-mapping" system. Why? As I have shown many times
with mere numbers,
0 = /_\S
is principally a "one-to-one-mapping" whereas
0 < /_\S
is pricipally a "one-to-many-mapping".
Compare the one possibility of
0 = 0
with the many possibilities
0 < 1
0 < 2
0 < 3
0 < 4 .....
Zero gets mapped onto "counting-numbers"! What an important EO
(Elementary Organiser) has "counting-numbers" not become in
modern society. Perhaps it has become too important, preoccupying
our thoughts to much.

With care and best wishes


At de Lange <> 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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