[Hans Blom, 960212]
(Rick Marken (960208.0850))
... can you tell me whether or not the envinronment controls
behavior using this meaning of "control"?
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This question deserves a somewhat longer answer than a simple yes or
no. I'll answer it with an experiment. The essence of my answer may be
familiar to those who participated in this discussion list in 1992.
You are undoubtedly aware of what Brownian motion is: pollen submerged
in water were discovered by Father Brown to make strange, ever chang-
ing random zigzag movements. This random motion of micron-sized
particles in water is now understood in terms of the movement of water
molecules (produced by what is known as 'thermal energy') that bump
against the particle. This movement is statistical in nature: mole-
cules bump into the particle from all sides equally on average, but
over a short time it cannot fail that the number of pushes from one
side is slightly larger than that from the opposite side. The result
is a random fluctuation in the number of bumps against the particle
from all sides causing a particle to move in random-sized steps in
random directions.
In 1905 Einstein himself gave a theoretical foundation for Brownian
motion by relating the particle's thermo-kinetic energy to the drag
forces that arise due to its movement in the fluid (as had already
been described by Stokes). Einstein provided us with the formula
2 k.T
d = ---------- . dt
3.pi.eta.r
where
2
d = the (average) square of the particle's displacement during
a time dt; the direction of the displacement is random
k = Boltzmann's constant
T = absolute temperature
pi = 3.14159...
eta = the fluid's viscosity
r = the particle's (average, effective) radius
Brownian motion is slightly, to say the least, mysterious for those
unfamiliar with it. It introduces seemingly paradoxical results, such
as the answers to the questions "What is the most likely position of
that particle an hour from now?" (answer: "its current position") and
"What is the chance that you will find a particle, say one with a 1
micron radius, within a 10 micron distance of its current position, an
hour from now?" (answer: "practically nil").
Back to the formula. In our simulation, we will sample the particle's
position at multiples of a fixed time interval dt. Due to the vector
addition of random displacements over time, the average size of each
displacement in a time period dt is proportional to the _square root_
of dt. But much more important in this context is the relationship
between the average step size and the particle's radius. From the
formula it is immediately clear that a larger particle will move more
slowly. But that in itself is uninteresting. Let us investigate what
happens when the particle's radius can _vary_ in time.
First of all, we need something that influences the particle's radius.
Assume that we add some chemical to the water that causes the particle
to swell. It is not particularly difficult to find such a chemical for
many types of particle; a great many not too small organic molecules
show a change in shape ("conformation change") in the presence of a
large variety of other, small or large, molecules. Everything else
being the same as before, the now larger particle will move more
slowly.
But things get really interesting if we create a _concentration
gradient_ by dropping a slowly dissolving pellet or trickle a micro-
flow of the chemical into the water. The particle will now be largest
and thus move most slowly in the regions where the concentration is
highest. Our intuition says that the particle will spend more time in
the vicinity of the maximum concentration.
But how, exactly? In order to get to know that, we need to pick some
mathematical formula to describe the relationship between the chemi-
cal's concentration and the particle's radius [r = f (c)], and another
formula for the spatial distribution of the chemical's concentration
[c = g (x, y) in two, c = g (x, y, z) in three, or c = g (x, y, z, t)
in four dimensions]. Now we can compute our particle's movement over
time, using Einstein formula. What do we find?
To simplify matters, I did most of my simulations in two dimensions
and with symmetrical functions g. I picked several different functions
f and g, and different parameters in those functions, but unvaryingly
found that whenever the radius of the particle increased with the
chemical's concentration, the particle tended to persist for a longer
time in those regions where the concentration was highest. As was to
be expected. The particle is "attracted" by the chemical. We know this
phenomenon as chemotaxis. Obviously, chemotaxis doesn't just exist in
living matter (it may be best known in bacteria) but also in dead
matter. In this case, it results from the interaction of a gradient
field, material properties, and thermal energy.
Now, to simplify the calculations, pick an unchanging concentration
profile c = g (x, y). The course of the particle over time now depends
on the nature of the relation r = f (c) between concentration and
radius. On average, of course; any particular trajectory is stochast-
ic. The course is computed by choosing an initial position (x, y) and
by adding, at each sampling time i.dt, i = 1 .. N, a position change
of size
k.T
d = sqrt ( ------------------ . dt )
3.pi.eta.f(g(x,y))
in a random direction. For a wide variety of choices for f(c) and
g(x,y), we find the following results:
1. If the particle's radius cannot vary, we see normal Brownian
motion. It is a characteristic of Brownian motion that d increases
without bound as dt increases. In due time, therefore, the particle
disappears from sight.
2. At small values of the particle's potential radius increase, the
particle will have a tendency to move toward the maximum of the
concentration, but the thermal energy overcomes this tendency and
more or less quickly moves the particle out of sight.
3. With larger values, the particle will tend to climb the gradient as
long as it can 'sense' a strong enough concentration. Although its
random movements sometimes may take it relatively far away from the
concentration's maximum, the particle will remain somewhere in the
vicinity of the maximum concentration. One could say that the posi-
tion is 'controlled', but control is poor.
4. With even larger 'gain' values, the particle stabilizes its posi-
tion increasingly better near the maximum of the concentration. We
now start to have a 'good' control system, where Brownian motion is
apparent only as a small random disturbance that causes jitter in
the particle's position. This seems to be the case, however, only
with rather contrived functions f, which seem quite unrealistic for
large molecules or other 'dead' particles like pollen, but maybe
small bacteria that have extensible but not otherwise controlled
cilia do "navigate" this way.
Note that in this experiment I do not need a "living" organism; it is
sufficient that the material properties of the particle are such that
its size varies with the concentration of some chemical. Yet it looks
as if the particle "controls" its position. The Test will demonstrate
this: pick up the particle and put it somewhere else. As soon as you
let it go, it will start to move towards the chemical's concentration
maximum again.
What do we have here, "control" or simply the result of a combination
of some laws of physics? Both, I would say. In this case, what we call
control is the result of the interaction of physical laws and material
properties. Here, control is an "as if" phenomenon: it is "as if" the
particle controls its position. But we all "know", of course, that a
dead particle cannot control, don't we? So, if there is control -- as
The Test seems to indicate -- who or what does the control? The envi-
ronment? No. Nothing does. Control is a _process_ that unfolds over
time. If you look at the simulated particle for a short time only, you
may not perceive control. Due to the large random component of the
motion, you will be able to see all different kinds of "behavior" at
different times: attraction, repulsion, no change of position, back
and forth movements, etc. In this case, it is only over long time
periods that we discover an "emergence" of an overall pattern that we
could call control. In other cases, the fuzzy classification "control"
might be ascribed much more rapidly.
So my answer to your question is: control is not an all-or-none pheno-
menon; in this example, we see a plastic progression from no control
at all to almost perfect control. Even in dead matter.
Why this extensive discussion? To show you how I prefer to look at
control: as an abstract, emergent phenomenon. The question "what
controls what" is meaningless for me.
I'm not sure this answer will satisfy you ;-).
Greetings,
Hans