[From Bill Powers (2003.08.25.0751 MDT)]
The tracking experiment project
There has been considerably difficulty in attempts to replicate some results of tracking experiments described in 1967 by McReuer and Jex. This is important for testing the concept of an "illusion of adaptation," which is a generalized version of the "behavioral illusion" well-known in PCT. I believe, incidentally, that "response" is a more appropriate term than "behavioral, "and will refer to it that way from now on. I now believe that it will be possible to generalize to the illusion of adaptation once we get the right experimental conditions, which seem at the moment to depend primarily on using a control element that is centered by a spring, so the operator must exert a detectable force proportional to displacement to move the control element or handle. Before seeing how that is explained, let us review the situation to date.
The response illusion and the adaptive illusion.
The response illusion occurs when a control system is successfully stabilizing some variable in the environment against disturbances by means of an action. When an observer is unaware that a controlled variable exists, the only obvious relationship is between disturbances (here meaning variables tending to cause changes in the controlled variable) and the action that opposes their effects. The appearance is that the action is a direct response to disturbing variables, as if a simple cause-effect link existed instead of the feedback loop. Since any disturbing variable that can affect a one-dimensional controlled variable will result in the same kind of action (the kind that acts on the controlled variable to keep it from changing significantly), the appearance is that many different disturbing variables are equivalent in their ability to "stimulate the system" to produce the same action. This phenomenon has been called by various names, for example "equifinality." Naming it does not, of course, explain it. The apparent causal relationship is, when control is actually involved, an illusion.
It has been found that a similar illusion exists in the time domain or frequency domain of description. When a person tracks a moving target using a control handle, changing the dynamic properties of the connection between the control handle and the cursor that is supposed to be kept aligned with the target produces an apparent change in the internal dynamic characteristics of the controlling person. McReuer and Jex (1967) observed that the final result was always that the overall relationship getween target and handle movement could be represented by a "crossover model" that behaved in the frequency domain like an amplification factor, a 90-degree phase shift, and a small time-delay. This is equivalent to the control system we have long used for modeling tracking in PCT, consisting (in the time domain) of an input delay, a comparator, and an output function containing an integrator. Since part of the observed relationship was determined by the nature of the element being controlled, "the plant" in engineering terminology, and the characteristics of the plant were changing, it seemed logically that the characteristics of the controlling person must be changing in the opposite way so as to preserve the same overall behavior described by the crossover model.
I discovered that a model involving a hierarchical arrangement of velocity and position control could reproduce this crossover phenomenon without any changes in the parameters of the controlling system. The initial inference was that there must have been something wrong with McReuer's measurements that showed the controlling person's characteristics changing. However, when the same measurements were made of the simulated control system, plotting the ratio of output action to input error, exactly the same changes in controller characteristics were measured, even though it was quite certain that nothing about the simulated controller had changed. Clearly there was no measurement error: this was a true illusion.
The apparent changes in the controller's characteristics were explained by the fact that both velocity and position feedback were used in the controller, so when the characteristics of the plant were altered, they affected both the position and the velocity information entering the control system, thus altering its actions even though its actual parameters remained constant. This model is entirely equivalent to a traditional model with proportional and velocity feedback, but evidently no one had ever thought to measure the apparent input-output characteristics of such a model with plants having varying characteristics. It was simply assumed that if the model retained constant characteristics, its measured input-output function would remain the same. But it does not. McReuer's measurements were correct, but his explanation of them was wrong. Or so, at this time, I strongly suspect.
Replicating the phenomenon
While the adaptive illusion has been demonstrated for the case of pursuit tracking (in which the target moves), and John Flach has worked out a brilliant analytical proof for this case, questions have been raised about the compensatory tracking case in which the target remains stationary and the cursor is disturbed by various means. Since disturbances can be applied in different places with different results, I thought it important to find out exactly what the experimental conditions were, with the hope of replicating the basic phenomenon and measuring it for myself. So far, the trail has been hard to follow, since the basic information is in Air Force technical reports which are hard to obtain. Efforts in that direction continue, of course.
In the meantime, I have been trying to replicate the effect using a simple computer experiment with a mouse as the manipulated element. I find pursuit tracking with the normal (direct or proportional) connection between mouse and cursor quite easy, since it is simply the kind of tracking we have been studying in PCT for 25 years or so. When the external connection is changed so the mouse position determines the cursor _speed_ instead of its position, the task becomes considerably harder. It becomes so much harder, in fact, that it seems that I have to do a lot of learning -- adapting -- to get better at it. And when the third standard condition is introduced, in which mouse position determines the _acceleration_ of the cursor, I find that I can't control at all, and have improved very little with practice. Rick Marken has successfully replicated my failure, if that can be termed a success. So not only is the "adaptive illusion" not illusory for me, it seems much too hard for me in the third of the standard conditions used by McReuer and Jex.
Naturally, I have been wondering whether McReuer and I are talking about the same experimental situation. His subjects apparently maintained control, in the third condition, to some degree with disturbances varying as fast as 2.5 cycles per second. Neither I nor Rick Marken can achieve anything resembling control in that case even with the maximum frequency of the disturbance restricted to 0.25 cycles per second. Something is amiss.
In reflecting on why both the velocity and acceleration conditions are so difficult, I have realized that there is an important feedback missing from the way I am doing the experiment. I can't tell where the mouse is without taking my eyes off the screen to look at it -- and then I can't track. Kinesthetic sensing is just not accurate enough to tell me when the mouse crosses the zero point (and anyway, with time that position shifts as the mouse gains or loses counts). This means that I can't tell how hard I am "pushing" on the cursor or , near zero, in which direction. Watching the cursor provides velocity feedback (the eye is pretty good at that), but visual perception of acceleration is very poor. That's not a problem for a simulation, because the computer always knows where zero is. For a human controller, something more is needed.
What is needed is feedback that indicates acceleration or applied force. While this can't easily be provided in a literal sense, there is a way to provide the same effect: use a spring to center the control handle. With the spring, the controlling person can feel and control how hard and which way he is pushing (by sensing effort as well as skin pressure), and applied force is proportional to acceleration via Newton's formula, F = MA solved for F. According to this idea, simply by using a spring-centered control handle I should suddenly find the two hard tasks to be much easier. As I thought of this only an hour ago, out of a deep sleep, I haven't even been able to put this feature into the simulation yet (the simulation without acceleration feedback also has trouble with the third case). Setting up a physical control handle with a centering spring will take even longer. Of course anyone else who wants to try this is welcome to get there first.
This is where the tracking experiments stand now.
Best,
Bill P.
