Dear Organlearners,
John Gunkler <jgunkler@sprintmail.com> writes:
>One of the classic descriptions of chaotically complex systems is
>that they are extremely sensitive to initial conditions -- or that the
>flapping of a butterfly's wings in South America changes the
>weather in Minneapolis many weeks later. Doesn't this say that if
>someone, intentionally, changes the right initial condition that large
>effects can occur?
Greetings John,
I like the butterfly metaphor very much in the sense that it show how a
feeble change might be amplified into a catastropic change.
It reminds me of an old joke -- An elephant walks over a hang bridge with
an ant riding on its trunk. The ant observes the swaying of the bridge and
shouts excitedly: "See how we sway the bridge!".
The butterfly metaphor have a number of disadvantages.
* It hides the actual process responsible for the amplification.
* It gives the impression that humans are in no way capable
of amplifying a feeble change or influencing the amplification.
Here is an interesting experiment which all of you can do. Although the
experiment is cheap to perform, it is highly instructive. You will need a
source of electrical energy, a number of IDENTICAL bulbs and their sockets
as well as some connecting wire. A multimeter will also be very handy. The
safest and cheapest components are to use a motor car battery (say 12
volt) and small bulbs used in cars (say 5cp -- candel power). Make sure
that all the bulbs (6 will be enough) are from the same batch so that they
are as identical as possible. Number the bulbs from 1 to 6. Measure their
cold resistance (not glowing) and notice any difference.
Those interested in the seven essentialities, might try to spot them in
this experiment and how they influence its outcome.
Now first connect all the bulbs in parallel and then to the battery.
The following is a schematic diagram.
_____________________________
| | | | | | |
|-|-|- (1) (2) (3) (4) (5) (6)
|_________|___|___|___|___|___|
The battery is on the left side. The bulbs are indicated by (1), (2), ....
The wires are indicated by lines. Observe that they all glow with the same
intensity. Observe that they convert electrical energy not only into light
(which can be seen), but also into radiant (infrared) heat (which can be
felt some distance away) and thermal heat (which can be felt upon touch).
Remove any bulb. The others will still burn. In other words, each bulb is
supplied with electrical energy INDEPENDENTLY (on its own).
Now reconnect the bulbs as follow after having allowed them to cool
off. Make the connection to the battery last.
___________________
| | | |
| | | (4)
| | (2) |
|-|-|- [12V] (1) | (5)
| | (3) |
| | | (6)
|_________|___|___|
Connect (2) and (3) in series. Also connect (4), (5) and (6) in series.
Connect then parallel as indicated. Bulb (1) will always glow brightly as
if on its own. Either bulb (2) or bulb (3) will glow brighly with the
remaining one much less. Either bulb (4), (5) and (6) will glow brightly
with the remaining two less. Should you have measured the cold resistance,
compare the resistance of the bulb glowing the brightest with the
resistances of other bulbs in that series. The one with the highest
resistance, eventhough it may be very slight, usually glow the brightest.
Disconnect from battery and allow at least 10 minutes of cooling so that
all the bulbs can be equlibrated to room temperature. Now observe the
"butterfly ability" of your fingers! Take one of the bulbs (4), (5) or (6)
which glowed feebly and hold it in your warm fingers for a couple of
minutes. Release and immediately reconnect to battery. This bulb will now
glow brightest!
Remove any bulb in a series. The others will stop glowing. In other words,
the supply of electrical energy is DEPENDENT on the supply to the others.
The theory behind it all is as follows.
The current(I)-potential(V) relationship in a bulb is not linear.
Should it have been linear, the result would have been Ohm's law
V = R x I
where V (volt) is the potential difference, I (ampere) is the current
and R (ohm) is the resistance which has a CONSTANT value. The
resistance R in a bulb is NOT constant so that V and I do NOT change
linearly with respect to each other. A the current keeps on flowing
through the filament, it converts electrical energy into radiation
energy and heat at a rate of
P = I x V = R x I x I
The rate of entropy production is
dS/dt = I x V / T
where T is the absolute temperture. The entropy production causes the
temperature of the filament to increase and thus also its resistance
R. As the resistance increases, more and more electrical energy is
converted into (electromagnetic) radiant energy rather than heat
energy.
The bulb in a series with the highest resistance, how small it may be, has
a slight advantage on entropy production and thus the increasing of the
bulb's resistance over that of the other bulbs. By touching the one bulb
with the fingers, its tempearure is raised and thus its resistance
increases above the tolerance for the other bulbs in the series. Sometimes
a bulb with a lower resistance in the series, will glow the brightest.
This is so because its resistance increases faster with a temperature
increase than that of the other bulbs in the series. To identify this
bulb, measure the resistance of the bulbs in, say, boiling water. Compare
that resistance to the cold resistance to identify the bulb of which its
resistance increases fastest with increasing temperature.
After repeating the experiment a couple of times, some of the bulbs will
persist in glowing brightly irrespective how they are connected. This is
because of irreversible changes to the filament because of entropy
production. When glowing, trace quantities of tungsten in the filament
evaporate. This is because entropy production must always be manifested,
evaporation being one of the innumerous ways in which it can happen.The
less tungsten in the filament to conduct electricity, the higher the cold
resistance. It is as if excercise in entropy production increases the
ability to produce entropy. It is as if the bulb learns how to glow the
best.
The latter remark has a bearing on what John writes:
>Also, when one looks at system dynamics models of complex
>systems with an eye to improving some aspect of system
>behavior, often there are one or two "policy" changes that will
>(without altering anything else -- simply letting the system do
>its thing) change the behavior in question.
The bulbs connected in parallel make me think of Personal Mastery. The
bulbs connected in series make me think of Team Learning. The butterfly
touch of the fingers makes me think of a good facilitator or manager,
helping each bulb to glow on occasion. Some people are like butterflies,
usually causing storms elsewhere -- but they are a great benefit to team
learning! I love them. I always try to identify them as soon as possible
in a team. Give them the opportunity to become the mitochondria
(powerhouses) of the cell. (Study a book on cell biology to understand
this metaphor.)
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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