[Bruce Nevin (2017.11.05.19:56 ET)]
I’ve been trying unsuccessfully to track this discussion, without being able to focus on it. I may be wildly off base, but this is my take after looking through the two papers this evening.
Rick Marken (2017.11.05.1220) –
What we showed is that the curved paths taken by both pursuers and a PCT model of those pursuers (a model that accounts for on average 93% of the variance in the curved paths taken by pursuers on 41 different trials ) exhibits a power law relationship between speed and curvature. This is evidence that the power law is a side-effect of the outputs that produced the curved paths as the means of controlling for intercepting
Sounds to me like this is the central finding. But it’s not so clear that this is the main point of Marken & Shaffer (2017)Â (posted by Alex on March 19, Subject: Power Law Publication). What you say there is “The present paper shows that the power law is actually a statistical artifact that results from mistaking a correlational for a causal relationship between variables… a mathematical consequence of the way that these variables are calculated.”
Zago, Matic, Flash, Gomez-Marin, and Lacquaniti (2017), which Alex posted at the start of this thread on 10/28, does not talk about control theory and mentions control systems only once (on p. 12 of the unpagenated reprint: an “experimental finding … implies that the control systems are [cap]able of establishing non-trivial co-regulations of path geometry and kinematics”). I may be mistaken, but it seems to me that the few and sporadic other uses of the word control in the article refer to motor control systems in a conventional way that does not invoke negative-feedback control.
We know that that negative-feedback control systems that use movements to control their input do not calculate the path geometry or kinematics of those movements, though the movements in the cases considered here can be described with path geometry and kinematics. Indeed, that is the final point of the Marken & Shaffer paper. The problem appears to be that the brief mention of this experimental finding at the end of the paper is dwarfed and obscured by the protracted critique that precedes it and which has every appearance of being presented as the main point of the paper.
Zago, Matic, et al. do not refer to the control-system model discussed in the short final sections of the Marken & Shaffer paper (called there a COV model), nor do they acknowledge the assertion thatÂ
The movements produced by the COV model accounted for an average of 93% of the variance in the movements of the actual pursuers over all trials … without any attempt to produce trajectories that followed a power law. Nevertheless, the model trajectories, like those of the actual pursuers, followed a power law with an exponent equivalent to that found in other studies of similarly curved movement trajectories… [T]he observed power law is a mathematical “side effect” of the model’s purposeful behavior. Specifically, it is a mathematical property of the trajectories that result from the model acting (varying ox and oy) to achieve its purpose of keeping the controlled perceptual variables…at the specified reference values.
Zago, Matic, et al say that Marken & Shaffer claim “that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated”. This is almost a direct quote of the passage cited above, here again: “a statistical artifact that results from mistaking a correlational for a causal relationship between variables… a mathematical consequence of the way that these variables are calculated.” Substitute “speed and curvature” for “variables”.
Zago, Matic, et al critique the assertion that “Since neither of these variables is manipulated under controlled conditions, any observed relationship between them cannot be considered to be causal.” However, the final claim at the end of Marken & Shaffer is that the power law is not a consequence of calculating speed and curvature, but rather a consequence of control. Isn’t this the real basis for the argument that correlation is not causation?Â
It appears to me that  the rejoinder by Zago, Matic, et al overlooked the demonstration that is the real point of the paper, and that they did so because the critique of statistical methods of power law analysis takes up the central and largest sections of the Marken & Shaffer paper and seems to be its main argument. It also follows, I think, that however the mathematical quarrel between you and Martin is resolved, it will have no bearing on that substantial point: control systems produce ‘power law’ effects without doing power law calculations.
Thus, Zago, Matic, et al say “D cannot be considered an independent predictor of A (or V), because D itself depends on A (or V),” etc., echoing Martin’s objection to predicting V from V. But however the power law is calculated, it is descriptive, whereas a control model is generative, and errors or misconstruals in that calculation are beside that main point.
They rather acknowledge this in concludingÂ
The issue that remains to be solved concerns the physiological origins of the power law. But this is a different topic to be covered in a forthcoming article.
It is a different topic which was covered in Marken & Shaffer (2017) only in the appendix-like concluding sections. I wonder, will their forthcoming discussion of “the physiological origins of the power law” recognize that control systems behave according to the power law without an elaborate physiological account? Will that future paper refer to the final sections of Marken & Shaffer (2017)?
···
On Sun, Nov 5, 2017 at 6:15 PM, Richard Marken rsmarken@gmail.com wrote:
[From Rick Marken (2017.11.05.1515)]
Bruce Nevin (2017.11.05.1755 ET)
Rick Marken (2017.11.05.1220) –
What we showed is that the curved paths taken by both pursuers and a PCT model of those pursuers (a model that accounts for on average 93% of the variance in the curved paths taken by pursuers on 41 different trials ) exhibits a power law relationship between speed and curvature. This is evidence that the power law is a side-effect of the outputs that produced the curved paths as the means of controlling for intercepting
BN: Does this hold also for the paths taken by people catching baseballs?
RM:Yes, and it also holds for people catching footballs thrown to themselves (based on the data from Shaffer, D. M., Marken, R. S., Dolgov,
I. and Maynor, A. B. (2015) Catching objects thrown to oneself: Testing the
generality of a control strategy for object interception, *Perception,*44, 400-409).
BestÂ
Rick
–
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery
