flock of birds LO21869

AM de Lange (amdelange@gold.up.ac.za)
Tue, 8 Jun 1999 21:09:41 +0200

Replying to LO21774 --

Dear Organlearners,

Arthur Battram <apb@cityplex.demon.co.uk> writes:

>Complex behaviour need not have a complex explanation. Order will
>emerge from self-organisation. This points the way to a new more
>open and adaptable form of teamwork in which individuals manage
>themselves within clear boundaries.

Greetings Arthur,

Thank you very much for your delightful contribution.

I am going to make your words above applicable in a way which you
might not have expected. My granddaughter Jessica, like all children
of her age in their first year of formal schooling, already behaves in
a very complex manner. She emerges from one level of order to another
like a princess in a fairy tale. This happens without someone
explaining to her in the usual jargon what is happening to her.
Luckily she has a grandfather who understands a little bit of the
complexity within her and encourages her to go for it.

Unfortunately, the movie [the behaviour of a complex system through
the creative course of time] cannot be imaged by a simplistic lines
[collection of sentences]. When it does happen, the movie becomes a
cartoon. I love cartoons because they tend to focus on the essentials.
But I also love movies which zoom out from the essentials to provide a
rich experience.

You write:

>The boids: not a film, not directed by Craig Reynolds
>Reynolds' basic idea was to place a large collection of autonomous,
>birdlike agents - 'boids' - into a computer-generated environment
>of walls and obstacles. Each boid followed three simple rules of
>1. It tried to maintain a minimum distance from other objects in the
>environment, including other boids.
>2. It tried to match velocities with boids in its neighbourhood.
>3. It tried to move toward the perceived centre of mass of boids in

This is exactly what also happens in the laminar flow of any liquid.
m(l) stands for "molecule of liquid". The three laminar rules of a
liquid are:

(1) A m(l) is in close contact with the other m(l)s surrounding it as
well as the surface atoms of any object along its path. This is
usually known my the technical term incompressibility.

(2) A m(l) matches its velocity to that of the surrounding m(l)s as
close as possible to minimise the entropy production. This is ussually
known by the technical term viscosity.

(3) A m(l) moves towards the region of highest kinetic energy because
of the extra velocity it receives from this region.

Note that they correspond in an enticing way to the three rules of

Should we plot the velocity of the m(l)s in the laminar flow of a
liquid in a regular pipe against a cross section of the pipe, we get a
pretty formation, almost like a parbola at lower velocities. Let me
try to draw a picture by using ASCII characters. The xxxxxxx pictures
the wall of the pipe. The ---> picture the velocity of a m(l). The
velocity is highest in the middle of the pipe. These rules afford what
we may call "laminar self-organisation".

Should we increase the overall velocity, the velocity diagram becomes
more V like in shape.

By increasing the velocity, the Reynold's number
R = LengthxVelocityxDensity/Viscosity
also increases. (This is another Reynolds of many years ago who
studied fluid dynamics.) Note that the length of the flowing liquid
(=length of pipe), its density and its viscosity do not change.
Eventually the Reynold's number R reaches a unique value when the
parabola has become a perfect V.

The "laminar self-organisation" now looks pretty much like that of
birds (not boids) flying in a V formation.

As soon as the velocity goes higher than the unique value, the V bends
towards its point as follows, slightly exaggerated

But something extraordinary also happens. A new type of self
organisation arises which we may call "turbulent self-organisation".
Molecules close to the centre of the pipe begin to show a curly
motion. An intense diversification in velocity (magnitude and
direction) becomes superimposed ON THOSE MOLECULES MOVING FASTEST IN
THE PIPE. Some begin to move very slow and others to move very fast
to produce this curly behaviour. Thus we may think of a bifurcation
(forking event) -- slower and faster. The unique value of the
Reynold's Number thus identifies the velocity at which this
bifurcation will happen. The behaviour of the liquid emerges to a new
level of complexity. A couple of months ago, Leo Minningh wrote some
pretty contributions on this phenomenon.

Now what is complexity -- either the laminar flow, or the the
turbulent flow, or both?

Try as we like, its is impossible to explain this "turbulent
self-organisation" by the three rules for "laminar self-organisation".
We need a fourth rule:
[SUM [(deviation entropic flux) x (deviation entropic force)]] > 0
It is known in irreversible thermodynamics as the criterium for
thermodynamic instability.

It may be translated as follows into a language without maths which we
may call the rule for "turbulent self-organisation":
4) A m(l) overcomes the dragging influence (viscosity) from its
surrounding m(l)s by super imposing its own ramming influence
(positive feedback) on them.

Please note that we now have four rules, neither three nor one, to
handle complexity with a new higher level.

I have observed twice in my life how the V flying formation of actual
birds rammed through laminar flow into turbulent flow. Once it was a
large falcon making a dive bomber attack from higher up in the sky on
them. The attack was, strangely enough, not at the point or the ends
of the V shape, but about in the middle of the leg. About four birds
behind the victim had to scatter in all directions. The rest of the
leg closed the gap and the four lucky ones soon attached them to the
end of the leg.

The other event was much more wierd. The V formation, flying lowly,
approached a high electrical power line (half a million volts DC) with
a few meters to spare. However, as soon as the they one by one came
almost above the line, each one veered off in a different direction.
On the other side many were desperately trying to regroup themselves
again. When they disappeared out of my sight, two small V's had
already formed. But some were still flying solitary in a direction of
their own, apparently to a new destination. The magnetic field of that
powerline certainly caused chaos in their little bird brains -- the
three rules forgotten.

To describe the complex flight of actual birds, the four rules above
are by far not enough. We need at least the following two rules:

(5) the rule of metabolism -- the birds have to sustain their
mechanical kinetic energy by a higher entropy production within them
(using the chemical free energy of the carbohydrates in their bodies)
to overcome losses because of the entropy production outside at the
surface of their bodies due to the viscose drag. Without sufficient
carbohydrates in their bodies they cannot fly.

(6) the rule of aerodynamics -- the wings and body must have the
correct shape to make use of the lifting effect of the Bernoulli
principle. Their wings are more rounded on the upper side than on the
bottom side. This shape forces the air to flow faster on the bent
upper side and thus reduces the pressure on the upper side of the wing
with respect to that of the lower side. Without sufficient curvature
on the upper side the bird fas to use too much free energy to overcome
the drag on both sides of its wings, not to speak of its body. Their
wings will fail them.

Arthur, you make one comment most exciting to me:

>Self-organisation points the way to a new more open and
>adaptable form of teamwork in which individuals manage
>themselves within clear boundaries.
>[xref- dialogue, Self-organising For Success]

You have used in one meaningful sentence seven words which are related
to the seven essentialities of creativity:
open == openness
adaptable == liveness
teamwork == wholeness
individuals == otherness
manage == fruitfulness
clear == sureness
boundaries == spareness
It is the first time ever that I have come upon a sentence with a full
score. Congratulations

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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