[From Bill Powers (941031.0700 MST)]
Bruce Abbott (941030.1700 EST) --
Still mulling over your simulation. I've played around with it some more
and understand what is going on better.
When dNut, the integrated change in nutrient level, becomes negative
the organism tumbles. The nutrient gradient is centered on the square
and is modeled as decreasing with the square of the distance from the
center. There is no EXPLICIT reference level in the model, only "good"
(keep going) and "bad" (tumble).
As I indicated last night, there _is_ an explicit reference level: it is
zero. However, it can be set to other values. The general case would be
if dNut < Ref then
tumble(alpha)
where Ref can be set to any value including zero.
This system is a one-way control system with very high gain at one point
in its output response curve. The control region includes only values of
dNut less than the reference signal. The system will act to prevent dNut
from becoming less than the given reference value. For the most part it
succeeds, although because the output effect is in the wrong direction
after half of the tumbles, there are brief moments when dNut goes
considerably negative relative to the reference signal. But it is
quickly brought to the region equal to or greater than the reference
signal, where is is no longer controlled.
You want to say that the behavior of tumbling is "selected" by its
consequence, the time-rate of change of concentration. I don't think
this is any improvement over saying it is "controlled" by its
consequence. The only way to describe the situation that fits your model
(and mine) is to say that the rate at which tumbles occur is driven by
the DIFFERENCE between the actual consequence and some particular
consequence defined by the setting of the reference signal. In your
model, as long as dNut is less than the reference signal, there will be
a tumble on every iteration, the maximum possible rate of tumbling. When
dNut is equal to or greater than the reference signal, there will be no
tumbling at all. So if we plot tumbling rate against dNut, we get
Tumble>rate
>
//////////////////////////////////
> /
> /
-dNut | / +dNut
================================0======//////////////////////////==
> ref^signal setting
If you set Ref := 0 you have the special case illustrated by your
program. You can check for yourself that the following effects of
varying Ref will occur.
It isn't dNut that determines where the drop in tumbling rate will
occur, but the reference signal. If the reference signal Ref is set too
far positive, dNut will never be positive enough to turn tumbling off,
and no progress will be made. If Ref is set too far negative, dNut can
never get negative enough to cause tumbling, so the spot will simply
keep moving in its initial direction.
When the reference signal is between these limits, there is a period of
random tumbling at the start; when tumbling stops, the initial uniform
motion is within some angle of the radius vector to the target. The more
positive the setting of Ref, the narrower the range of angles and the
longer the initial tumbling goes on before uniform motion starts. When
Ref is set just below the maximum positive dNut at the starting radius,
the period of initial tumbling can go on for a long time, but when the
uniform motion starts, it is aimed almost directly at the target.
In E. coli, the transition from maximum tumbling rate to no tumbling is
smooth and occurs over a range of dNut. Individuals can be observed
which show all possible settings of the reference signal. A few always
tumble, although a sufficiently large positive transient in
concentration (artificially induced) can slow their tumbling or stop it.
A few others never tumble, although a large negative transient can
induce a nonzero tumbling rate. Koshland didn't investigate the
conditions under which the apparent reference level in an individual
might change, but we can guess that a sufficiently close approach to a
food source (near contact) might cause tumbling to cease. There would be
a sensor for the actual concentration, Nut, and a higher level of
control that would vary the reference level for dNut.
ยทยทยท
---------------------------------
The flaw in the concept that consequences govern, determine, affect,
influence, control, or select the behavior that causes them is in the
failure to distinguish between the reference-consequence and the actual
consequence. Only the actual consequences of behavior can influence
future behavior. There is nothing to say that any _particular_
consequence will be brought about. Implicit in the concept behind
control by consequences is that a _particular_ consequence is
controlling behavior so as to produce it, a consequence which has not
yet occurred, but will occur if behavior goes on long enough.
Behavior is always having consequences. In a VI-1min schedule, pressing
the bar at a certain rate will have the consequence of a certain average
rate of pellet delivery. If the observed rates are 1 press per hour and
1 pellet per hour, is the consequence of 1 pellet per hour selecting the
behavior of 1 press per hour? If the behavior rate gradually speeds up
so that now there is 1 pellet per minute for 10 presses per minute, is
the 1 pellet per minute consequence now selecting the 10 presses per
minute behavior?
What happens is that the behavior rate gradually increases, and
consequently the pellet delivery rate gradually increases, until some
final rate of pressing and pellet delivery is occurring. This is
explained by saying that the final rate of pellet delivery is the
consequence that controls the final rate of behavior.
But why _that_ final rate and not another? Why not zero? Why not any
observed rate? The problem is that there is nothing to determine what
the final consequence will be, and therefore nothing to determine what
the final behavior rate will be. There is a missing relationship in this
conception.
What is missing, of course, is the reference setting inside the
organism: how much "consequence" the organism wants. What actually
happens is that the organism varies its behavior rate until the
consequence matches the amount of that consequence specified by a
reference signal inside the organism. That is why both the consequence-
measure and the behavior-measure come to a final equilibrium condition.
The final state of the consequence does not reach back through time to
guide behavior toward creating itself. Instead, a present-time setting
of a reference signal (with the associated control system) continuously
determines how both behaviors and consequences will change from their
current states toward a final state. Seeing consequences as determinants
of behavior is a misinterpretation.
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Best,
Bill P.