Hi Adam
amatic
November 5
RM: They are not controlling the position of the cursor relative to the moving target; they are matching their movement pattern to the target movement pattern.
AM: Yes! That is exactly what I hoped you would notice. Position control is not enough to explain this task.
RM: Right. You need a higher level “trajectory control” system varying position over time. That’s what my model was.
AM: This task, the fast drawing of ellipses, is where the 2/3 power law phenomenon happens. In other shapes, it is different exponent or no power law. In lower speeds it is low r2 and also different exponent.
RM: Yes, that was the point of our paper. The power “law” is found only for certain trajectories, those with an affine velocity component that is constant.
RM: This is actually closer to the model I proposed (and the one described in our reply to the criticisms of our paper. In my model, the subject is assumed to be moving the reference for the cursor position in an elliptical pattern. These variations in the reference are assumed to be made by the outputs of a higher level system that is controlling for seeing an elliptical movement trajectory.
My model was rejected because it was considered to be cheating to put an autonomously varying reference for elliptical movement into the model. In other words, giving the model autonomy (the very essence of what we think of as the behavior of a living system) was cheating.
AM: It is slightly closer. The problem is that the reference was precalculated and was not really an output from a higher level control system. The cheating part is that the reference trajectory already has a power-law pattern. It slows down in the corners.
Another problem is - make it fast, and the pattern produced looks nowhere near the reference pattern. So, that model does not explain the power law phenomenon in fast drawing of ellipses.
RM: It’s not cheating to put in a reference that can account for the observed variation in position. Though it would be better to have derived this variable reference from the data. One way to do this is described by Powers (1989) Quantitative measurement of volition, Chapter 13 in Hershberger (ED) Volitional Action, Amsterdam, North Holland.
RM: I will try to eventually get to this; but I’m not in a bog rush because I’m detecting a great deal of hostility to what I think of as the PCT approach to understanding the power law. So I’ve got plenty of other problems in my life so unless you are really interested in continuing this discussion I think maybe we can just drop it now.
AM: I don’t think I was hostile in this topic, but I certainly do disagree with your approach.
RM: OK. I guess my problem with your approach is that there’s no “there” there, the “there” being your model that explains the power law. Do you even have a model that explains the power law?
AM: I hope you’re also detecting serious inconsistencies in your story. For example, in the second or third post in this topic you said that position control model explains the power law. In your latest post, you write it is not position control. Somewhere in between, you wrote it might be the affine velocity.
RM: My “story” is simply the very simple control model that I proposed. Of course it controls position the position of the moved entity (the cursor), as does the human, as evidenced by resistance to disturbances to position. But in my model position is controlled to achieve a higher level goal, which is to produce a particular trajectory of positions. SO my “story” is not that position control explains the power law; it’s the higher level system that varies the reference for position in a way that results in observed trajectories that fit the power law that explains the power law.
RM: But I don’t think it’s worth my time to continue this discussion; you acknowledge that you don’t like my approach, which is based on testing models. And I don’t care for your approach, which is not based on model testing at all. This, of course, gives you a tremendous advantage in the “how do you explain the power law” discussion since it means that there is no possibility that I can show that your explanation of the power law wrong because you have none.
AM: I’m perfectly fine with dropping the power law story. It was just an example from your presentation where you claim to have found a controlled variable.
RM: Yes, we really have to drop it. PCT research is not about “finding controlled variables”; it’s not like mining for gold. PCT research STARTS with the observation that a variable is under control because you can see that the variable is being protected from disturbance. That observation leads to your initial hypothesis, which is a formal definitions of the controlled variable. Now you apply disturbances to test that hypothesis (or put that hypothesis in a model and see if it accounts for the data). My initial hypothesis about one of the variables controlled when you move a cursor around the screen is the position of the cursor; and, indeed, that hypothesis pans out. But there are other variables that are surely being controlled in this situation and research should be aimed at discovering what they are. That’s the research I’m interested in. The power law is a red herring; a side effect of controlling. I believe you have no good explanation (model) for the power law because there is none other than that it is a side-effect of control. And that seems to be unacceptable to carry on as you wish. But you won’t have Dick Marken to kick around any more;-)
Best
Rick
