I’m sure the researchers who study the power law are doing it because they think it tells them something important about how movement behavior is produced. They might not say it explicitly in their papers but they have certainly said it implicitly by having produced over 40 years of research and publications on the power law. The publications are in journals having to do with motor control and the neural basis of behavior, which suggests that the researchers thought that their work on the power law had something to do with understanding motor behaviors, such as curved movement.
Yes, it certainly would and it certainly has. Generative control models of movement behavior have shown that the power law is an irrelevant side effect of control.
Here is a pertinent segment copied from Bill Powers’ 1978 Psych Review paper that speaks to this question.
The data from investigations of the power law were collected to solve an “old puzzle” – the puzzle of the power law relationship between speed and curvature that is observed when organisms produce curved movements – that the new PCT paradigm shows to no longer need solving. So, from a PCT perspective, the data from investigations of the power law are no more important to the study of movement behavior than the data from investigations of the properties of phlogiston are to the study of combustion.
My aim in the apparently never ending power law debate has been to show that this is the case – that the power law is a problem that no longer needs solving – and to encourage power law researchers to drop their investigations of the power law and redirect their considerable skills to the study of movement behavior as a control phenomenon. Unfortunately (or, possibly, fortunately) this discussion has shown Powers to have been right about what he said in the highlighted portion of the Psych Review quote. Consistent with Bill’s prediction, my explanation of the PCT view of the power law has resulted in a battle between the new paradigm and those who are unwilling to bypass altogether the old power law puzzle that they insist needs solving.
Paradigm shifts, like breaking up, are (as Neil Sedaka told us) hard to do.
Best, Rick