[From Rick Marken (921229.0800)]
In an effort to direct the net discussion toward more tangible
concerns, I would like to discuss some research I started
this weekend on the phenomenon of conflict.
Conflict is a uniquely control system phenomen. It occurs when
two control systems try to keep the same perception at different
reference levels. For example, consider two control systems
that are controlling the two dimensional position of a dot on a
computer screen. One system controls the perception of the
dot in the x dimension, the other controls the perception of the
dot in the y dimension. The systems control these perceptions
by varying lower level perceptions -- such as the horizontal, h,
and vertical, v, position (as sensed) of the mouse.
We can represent the situation like this:
1) x = a1*h
y = b2*v
x and y can be considered the reference values for the position
of the dot on the screen; the subject must vary the lower level
perceptions, h and v, to produce the perceptions that equal the
reference values. Obviously, this can be done in this situation
since it is possible to find values for h and v that produce perceptions
that equal x and y; there is no conflict.
A conflict would exist if we set things up like this:
2) x = a1*h
y = a2*h
Now there is no way to solve for x and y (assuming they x<>y)
because there is only one lower level perception that can be varied
to produce two different perceptions that satisfy both the x and y
references; there is no way to vary h and have the result equal
BOTH x and y if x<>y. There is a conflict -- both goals cannot
be achieved simultaneously (this is what would be called an
"approach-appoach" conflict; other "classic" conflicts -- like
"approach - avoidance" can also be seen as conflicts between
control systems).
It is possible to produce intermediate levels of conflict between
the no-conflict situation of equations (1) and the conflict situation
of equation (2). This is done by having the lower level perceptions
contribute to the perceptions requested by both higher level
references such that:
3) x = a1*h + b1*v
y = a2*h + b2*v
Now the no-conflict case, (1), is the situation where b1 = 0 and
a2 = 0; and conflict exists when b1=0 and b2=0. There is a theorm
in linear algebra (as Oded knows, my favorite math) that says that
there is a solution to a pair of linear equations, as in (3), when the
determinant of the system is not zero. The determinant of (3), D,
is a1*b2 - a2*b1. So there is a solution to (3) when
4) D <> 0.
When b1 = 0 and a2 = 0 (the no conflict case) there IS a solution;
when b1=0 and b2=0 there is no solution (and, indeed, this is
what a conflict means -- there is no way to solve for the two goals
value, x and y, simultaneously).
So if inequality (4) is satisfied, there IS a way to achieve both goals
simultaneously. But some values of the coefficents -- a1,a2,b1,b2 --
result in a determinant that is closer to 0 than others. Indeed, we
can pick coefficients so that D ranges from 0 to infinity (I'll
ignore negative values of D for now because that changes the
polarity of the control task). So D can be considered a measure of
"degree of conflict" -- with small values of D indicatingf high levels
of conflict. But, as long as D>0 there IS a solution to the conflict.
I did an experiment to see if D (closeness to conflict) made a difference
in a control task. My intuition was that it would NOT; if there is a
solution to equation (3) then a pair of independent control systems (one
trying to produce a perception equal to x, the other a perception equal
to y) should find the solution. In fact, it DOES make a difference -- at
least when there are continuously varying disturbances present.
I set up a two dimensional tracking task based on equation (2) except
that continuously varying disturbances were added to x and y so that:
5) x = a1*h + b1*v + dx
y = a2*h + b2*v + dy
where dx and dy are time varying disturbances, h and v are the
horizontal and vertical measures of mouse position and x and y are
the target position of the cursor on the screen (x = 250, y = 150).
I could pick values for the 4 coefficients to determine a D value
of my choice.The subject then performed the tracking task with that
level of D in effect. The results were quite clear -- the subject's ability
to control the cursor (keep it near the x,y target position), as measured
by RMS error, declined as the value the value of D decreased -- the
closer to conflict, the poorer the control.
I was surprised by this but discovered, to my relief, that the basic
control model behaves in exactly the same way. Mouse movements
(h,v values) produced by two independent control systems were almost
exactly the same as those produced by the subject, as a a function of D.
So the control exerted by two independent control systems worsens as
they approach conflict -- D = 0. For both human and model this is
only true when there is a continuous disturbance to the controlled variable;
when there is no disturbance, both human and the control model find
the h and v values that bring the cursor to the goal x,y position.
There are a number of interesting implications of this little set of
experiments:
1) A person can be operating with "nearly" conflicted control systems
with no problems as long as there is no disturbance to the variables
controlled by the conflicted systems. Thus, "nearly" conflicted systems
can act like Martin Taylor's hypothetical "bug" in a control hierarchy --
having no deleterious effect until disturbances start to vary.
2) Control with "nearly" conflicted systems mimics control when there
is no conflict but the control systems themselves are poor (low gain,
for example). So the same behavioral sympton (poor control) could
be the result of poorly functioning control systems -- or from perfectly
functioning control systems that are in conflict (there was nothing
wrong with the control systems used to model conflict -- the same,
high gain systems that produced nearly perfect control when D was
large produced lousy control when D was small; the control systems
were fine; what they were controlling -- mutually -- was the
cause of poor control). I plan to do some further research to see if
there are some simple ways to distinguish poor control due to conflict
from poor control due to poorly developed control system. This
could have interesting practical implications -- if poor control is the
result of conflict then the solution would be some form of therapy --
like "going up a level"; if it's due to a poorly developed control system
then the solution would be some form of training.
3) There is some evidence in that data that when the subject is in a
noticable conflict (because it is impossible to control the cursor) some
reorganization is occuring; the gain of the subject's control system
seems to change a bit when the conflict (actually, the symptoms thereof)
is perceived. This reorganization (or, possibly just the work of higher
level control systems) shows up in slight but apparently systematic deviations
of the subject's behavior from that of the model. Thus, there may be the
seeds of an approach to studying reorganization here -- by varying D.
Any comments, questions or suggestions would be most welcome.
By the way -- all this work (including the modeling) was done in HyperCard
with HyperTalk (inspired by some offline discussions with Rich Thurman).
Take THAT, C freaks.
Best
Rick