[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