The speed�?curvature power law of movements: a reappraisal

[From Rick Marken (2017.10.28.1745)

···

On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that’s two words But you know how bad I am at math;-)

Best

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

regardless of your helicopter data and RCT mantras, it would be good if someone from CSGnet took seriously the challenge to PCT that the speed-curvature power law entails.Â

any figure panel of our paper proves rick’s mathematical claims wrong: the PL is not a must and when it takes place it is not trivial and can have different exponents.Â

now, how can “control of perception” explain that phenomenon? claiming it is an illusion because it does not fit in the dogma is like creationists insisting that dino fossils are bogus.Â

so, as adam and myself take this job seriously, and given how many optimal control and nonPCT theories explain the data, I think Bill would really find his edifice crumbling, or at least unable. so, take your best shot at it and really challenge your “revolutionary paradigm changing” theory of behavior.

···

On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that’s two words But you know how bad I am at math;-)

Best

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

Alex Gomez-Marin
behavior-of-organisms.org

[From Rick Marken (2017.10.31.2215)]

···

On Tue, Oct 31, 2017 at 9:01 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: regardless of your helicopter data and RCT mantras, it would be good if someone from CSGnet took seriously the challenge to PCT that the speed-curvature power law entails.Â

RM: What challenge? PCT explains it quite nicely as a mathematical property of curved trajectories. This fact explains why it appears as a side effect of intentionally produced curved movement… But apparently no one else on CSGNet sees it that way so your paper has demonstrated to me that no one on CSGNet (no one who posts, anyway) understands PCT. At least, they don’t understand it the way I do. This has convinced me that I must withdraw my Preface to LCS IV because I can’t in good conscience say that the papers in that book will be based on Powers’ theory and, thus, honor his legacy.

Â

AGM: any figure panel of our paper proves rick’s mathematical claims wrong: the PL is not a must and when it takes place it is not trivial and can have different exponents.Â

RM: There is nothing in your paper that proves that any of the claims made in our paper are wrong. We will explain this all in our own “reappraisal” of your “reappraisal”. But for now I’ll just say that our paper didn’t say that the power law was trivial; it showed that the power law is an illusion in the sense that it looks like it is relevant to understanding how organisms produce movement when it is not. Nor did we say that the power law can’t have different exponents; in fact we showed precisely why you do find different exponents for the power law; it’s because you omit a variable from the regression analysis used to determine that exponent.

AGM: now, how can “control of perception” explain that phenomenon? claiming it is an illusion because it does not fit in the dogma is like creationists insisting that dino fossils are bogus.Â

RM: No, we say it is an illusion because it is demonstrably a side effect of controlling perceptions, as demonstrated by the model of toy helicopter pursuit that we present in the paper (and that you simply dismiss as wrong for no apparent reason other than that it just must be).Â

Â

AGM: so, as adam and myself take this job seriously, and given how many optimal control and nonPCT theories explain the data,

RM: I have not seen any control models that explain the data; the term “controlled variable” is not to be found anywhere in your paper or in any other papers I have read in the area. The models I have seen that “explain” the power law are all output generation models – what Powers called “curve fitting” models – that would fail completely if they had to account for the fact that the observed curved movements being modeled are produced in a disturbance prone environment; the curved movements are themselves controlled variables.Â

AGM: I think Bill would really find his edifice crumbling, or at least unable. so, take your best shot at it and really challenge your “revolutionary paradigm changing” theory of behavior.

RM: I think you are right about that. If Bill has been listening in on CSGNet for the last 4+ years he would, indeed, see his revolutionary paradigm crumbling. I knew that people would disagree with me as much as they did with Bill but I was surprised by the intensity and meanness. But I know there are one or two people out there (not on CSGNet) who not only agree with my understanding of PCT (which I’m pretty, pretty, pretty sure is the same as Bill’s) but are also doing excellent PCT research.Â

RM: It’s too bad; I really thought you really considered PCT a possible explanation of the power law. I guess my trusting nature got the football pulled away from me again. You are obviously very talented at research. It would have been great to have you working on doing research based on an understanding of PCT. But, alas, I guess it’s not to be.Â

BestÂ

Rick

Â

On Sun, 29 Oct 2017 at 02:48, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.10.28.1745)

Alex Gomez-Marin
behavior-of-organisms.org


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

On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that’s two words But you know how bad I am at math;-)

Best

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

[From Rick Marken (2017.10.31.2230)]

Martin Taylor (2017.10.31.13.35)--

AGM: now, how can "control of perception" explain that phenomenon? claiming it is an illusion because it does not fit in the dogma is like creationists insisting that dino fossils are bogus.Â

MT: So far as I am aware, only Rick's bogus mathematics has led anyone on CSGnet even close to saying such a thing.

RM: I don't know if you read the "reappraisal" paper but none of their "proofs" that our claims are wrong say that out mathematics are wrong. Indeed, they even cite a paper (that is incorrectly presented as evidence that our omitted variable bias -- OVB -- analysis is incorrect) that makes exactly the same derivation of the relationship between between velocity and curvature that we do; showing log velocity to by a linear function of both curvature and the "cross product" term we call D. There are many other errors in the paper besides the OVB error but that one is perhaps the most obvious. We could have prevented that error from getting into press if we had been invited to review Alex's rebuttal to our paper. But we were not even extended the courtesy of being notified that a rebuttal was submitted for publication. I wonder why that happened? :wink:
BestÂ
Rick
 >

···

so, as adam and myself take this job seriously, and given how many optimal control and nonPCT theories explain the data, I think Bill would really find his edifice crumbling, or at least unable.

Why, if none of the obvious tests have been done?

so, take your best shot at it and really challenge your "revolutionary paradigm changing" theory of behavior.

First, let's define the challenge. You have a considerable body of observations that relate some environmental states to a power-law relationship between local curvature of a track followed by (including produced by) organisms in motion and the tangential velocity of movement along the track. You also have conditions under which the relationship is not followed. What are the essential differences among these conditions? Is the challenge for PCT to predict/explain that? Or is it in general to explain why power laws are observed sometimes and not other times? PCT does offer a generic explanation for the observation of power laws, which Bill and Rick used to explain the Stevens power law for perceived (reported) sensory magnitudes. It is that a power law will result when a perception is controlled of a relationship between two perceptions that have a near-logarithmic relation to their relevant magnitudes. In this case, maybe the challenge resolves into discovering the two perceptions in question. Might that be true? Or is this particular power law not an example of the generic case? Maybe that's the challenge.

If you are going to assert that PCT is "unable" to explain any data, whatever the experiment, you first have to seek a controlled variable. It is highly unlikely in any of the conditions of any of the experiments that the mover controlled a perception either of following a power law relation between speed and curvature, and even if they did, that they were controlling for making the exponent take on some particular value. So the first step is to propose some plausible perception(s) that might be being controlled, and then try to disturb them to include or exclude them from the plausible list. If a perception of the power-law relationship and the particular exponent is implausible, then the power-law itself is a side-effect of control, and the problem becomes one of explaining what environmental conditions affect the perception and the action influence on whatever is being controlled.

A perceptual variable that is available to larvae and to humans would naturally be more plausible than a requirement that different species control different variables but wind up with the same results. But it may prove that several different perceptual controls working through similar environmental constraints would all give the same power law. A power law is, after all, the result of subtracting one logarithm from another, and since most perceptions do seem to have a near logarithmic relation to the relevant environmental variable (Weber-Fechner Law), such a result is not too far-fetched to contemplate.

Whatever the controlled variables might be, difficulty in finding them is not the same as proof that they do not exist, or that PCT is a crumbling edifice. It helps if the search has been at least begun without successful conclusion, but such searches sometimes take thousands of years. Ptolemy's laws explained the planetary motions relative to the starts well enough not to be discarded for a thousand years, within one conceptual frame -- Earth-centred Universe. Kepler and Newton provided a better explanation, and that was good enough in a different conceptual frame -- a Universe conceptually known synoptically by an omniscient being. But it had little niggles in it such as the advance of the perihelion of Mercury. Einstein came up with a better explanation in a third conceptual frame -- "what you see is what you get" (relativity), but it also has niggles in its incompatibility with quantum chromodynamics, so I guess the next advance is a fourth conceptual frame yet to be found.

PCT is, I think, in the relativistic conceptual frame -- "what you perceive is what you get". Earlier theories that base behaviour strictly on the environment are in the Newtonian conceptual frame "You would know it all if you were God". As with Ptolemy-Newton or Newton-Einstein, the earlier and older theories explain the data pretty well, because that's what they are designed to do. In each case, the newer theory explained a wider range of data and explained it more accurately because it started from "why", not "what". Newton's "why" for the planetary motions was the gravitational law that produced Kepler's ellipses, which were a descriptive improvement on Ptolemy's epicycles. Einstein's "why" for Newton's gravitational law was the distortion of space-time by mass-energy. I suppose the next conceptual revolution in that area of physics will be the finding of a "why" for space-time deformation that resolves the problems with quantum theory. One "why" is simpler than a whole lot of "whats" in the Occam's Razor sense.

PCT offers a relativity-level "why" for a whole mass of data that is observed and for which many people have provided Ptolemy or Newton-level "what" explanations. Maybe optimal control theory does, too, but PCT has the advantage of not having to do complex computations of such things as joint angles and of not having to make special provision for the effects of unexpected external events and forces, since dealing with them is built into the structure. I am not aware of optimal control theory having been applied to sociology, but I suppose it must have been. However that may be, I suspect that another change of conceptual framing will someday provide a "why" for the "whats" of PCT, further simplifying science as a whole.

Enough philosophy of science. It would be nice to be able to figure out what controlled perceptions in what environmental circumstances lead to power laws, and with what exponents when power laws are found. Incidentally, has anyone ever analyzed movies of a skater doing school figures? It is my impression that their skates move faster along the ice when the curvature is high (low radius of curvature), but that may be an illusion.

Martin

On Sun, 29 Oct 2017 at 02:48, Richard Marken <<mailto:rsmarken@gmail.com>rsmarken@gmail.com> wrote:

[From Rick Marken (2017.10.28.1745)
On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin <<mailto:agomezmarin@gmail.com>agomezmarin@gmail.com> wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that's two words But you know how bad I am at math;-)

Best
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

--
Alex Gomez-Marin
<http://behavior-of-organisms.org>>> behavior-of-organisms.org

--
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

I totally disagree, Warren! I admire you but your political correctness, which can be a virtue, is often annoying to me: Marken’s was really really bogus. A shame it went through. Ours is very solid.Â

A different thing is that so far we did not restrict the interpretation we could not make of the power law in terms of perceptual control. That is for the future.

What I think is literally “a failure of effective peer review” is the blablabla on CSGnet (except in some cases).

···

On Wed, Nov 1, 2017 at 9:56 AM, Warren Mansell wmansell@gmail.com wrote:

Hi folks, the clearest message coming out of this for me is that there has been a failure of an effective peer review process for both articles!

On 1 Nov 2017, at 07:47, Boris Hartman boris.hartman@masicom.net wrote:

Down ….

Â

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Wednesday, November 01, 2017 6:15 AM
To: csgnet@lists.illinois.edu
Subject: Re: The speed�curvature power law of movements: a reappraisal

Â

[From Rick Marken (2017.10.31.2215)]

Â

On Tue, Oct 31, 2017 at 9:01 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: regardless of your helicopter data and RCT mantras, it would be good if someone from CSGnet took seriously the challenge to PCT that the speed-curvature power law entails.Â

Â

RM: What challenge? PCT explains it quite nicely as a mathematical property of curved trajectories. This fact explains why it appears as a side effect of intentionally produced curved movement… But apparently no one else on CSGNet sees it that way so your paper has demonstrated to me that no one on CSGNet (no one who posts, anyway) understands PCT. At least, they don’t understand it the way I do. This has convinced me that I must withdraw my Preface to LCS IV because I can’t in good conscience say that the papers in that book will be based on Powers’ theory and, thus, honor his legacy.

Â

HB : Good that you’ll withdraw your Preface. This is the way to preserve Powers theory. With not contributing RCT to any published literature.

Â

AGM: any figure panel of our paper proves rick’s mathematical claims wrong: the PL is not a must and when it takes place it is not trivial and can have different exponents.Â

Â

RM: There is nothing in your paper that proves that any of the claims made in our paper are wrong. We will explain this all in our own “reappraisal” of your “reappraisal”. But for now I’ll just say that our paper didn’t say that the power law was trivial; it showed that the power law is an illusion in the sense that it looks like it is relevant to understanding how organisms produce movement when it is not.

Â

HB : Maybe I could agree with you about the way »Power Law« was presented till now. It seems that it can’t explain how organisms function. Or even how nervous system function. And how by your oppinion organisms produce movements ??? With independent control units like you described in your artcile about »Power Law«. If I compare the »nothing« explained about how organisms function by your example of »helicopter« and »Power Law« I’d say that »Power Law« include less of »nothing« than your example with helicopter. It’s worse. Helicopter example shows »stimulus . respons«. People move in accordance to movement of helicopter. Where did you see this in reality ? Amd this should be the case of »purposefull behavior«.Â

Â

RM : Nor did we say that the power law can’t have different exponents; in fact we showed precisely why you do find different exponents for the power law; it’s because you omit a variable from the regression analysis used to determine that exponent.

Â

AGM: now, how can “control of perception” explain that phenomenon? claiming it is an illusion because it does not fit in the dogma is like creationists insisting that dino fossils are bogus.Â

Â

RM: No, we say it is an illusion because it is demonstrably a side effect of controlling perceptions, as demonstrated by the model of toy helicopter pursuit that we present in the paper (and that you simply dismiss as wrong for no apparent reason other than that it just must be).Â

Â

HB : As I said above. You demonstrated with helicopter example that »environment is controlling« people movement. You proved simple »stimulus-respons« theory. There is no »purposefull« behavior in your example  so that we could answer the question how people decide for their behaviors. In your case people »decide« to move along with helicopter movement probably because they were told to do so. How will you understand from this example how people form purposefull behavior.

Â

And your assunption is that they produce purposefull behavior with two independent control units. Is this how nervous system function ? Is this a joke ?

Â

AGM: so, as adam and myself take this job seriously, and given how many optimal control and nonPCT theories explain the data,

Â

RM: I have not seen any control models that explain the data; the term “controlled variable” is not to be found anywhere in your paper or in any other papers I have read in the area. The models I have seen that “explain” the power law are all output generation models – what Powers called “curve fitting” models – that would fail completely if they had to account for the fact that the observed curved movements being modeled are produced in a disturbance prone environment; the curved movements are themselves controlled variables.Â

Â

HB : Behavior itself is a »controlled variable« ? How organisms produce »controlled behavior« ?

Â

AGM: I think Bill would really find his edifice crumbling, or at least unable. so, take your best shot at it and really challenge your “revolutionary paradigm changing” theory of behavior.

Â

RM: I think you are right about that. If Bill has been listening in on CSGNet for the last 4+ years he would, indeed, see his revolutionary paradigm crumbling.

Â

HB : You are the one that contributed most of it.

Â

I knew that people would disagree with me as much as they did with Bill

Â

HB : Who said that Bill agreed with you ? He did protect you. But at least once you tryed to aline your and his knowledge and he answered in clear »no«. Your and Bills’ knowledge are not aligned. Anyway you show in every post disalignment with his literature.

Â

RM : ….but I was surprised by the intensity and meanness. Butt I know there are one or two people out there (not on CSGNet) who not only agree with my understanding of PCT (which I’m pretty, pretty, pretty sure is the same as Bill’s) but are also doing excellent PCT research.Â

Â

HB : I’d really like to meet these two people who don’t understand PCT ? You don’t understand PCT. And you never will.

Â

RM: It’s too bad; I really thought you really considered PCT a possible explanation of the power law. I guess my trusting nature got the football pulled away from me again. You are obviously very talented at research. It would have been great to have you working on doing research based on an understanding of PCT. But, alas, I guess it’s not to be.Â

Â

HB : I agree that it would be good for people to use PCT. but not RCT.

Â

Boris

Â

BestÂ

Â

Rick

Â

Â

On Sun, 29 Oct 2017 at 02:48, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.10.28.1745)

Â

On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that’s two words But you know how bad I am at math;-)

Â

Best

Â

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

Alex Gomez-Marin
behavior-of-organisms.org

Â

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

my brief replies to all of you wrote replied:

to martin: you are right, one should seek for control variables, and so, where to start concretely? (but most likely the subtract two logs idea will not work here).

to rick: your infamous claims are not worth answering (not only mathematically, but also that bullshit about us not letting you know that our paper was out nor inviting you as a reviewer. are we crazy? and, did you?) — literally, witth you it feels literally like having to argue with Donald Trump.Â

to warren: PCT could move forward if the guys at the top would dare to call the difference between shit and shinola.

to boris: it is not the PL that needs to explain PCT, but PCT the PL…Â

to eetu: maths are a quite important language for science… but, in some occasions, common sense will do. your Umwelt efforts are welcome.

···

On Wed, Nov 1, 2017 at 10:47 AM, Eetu Pikkarainen eetu.pikkarainen@oulu.fi wrote:

[Eetu Pikkarainen 2017-11-01]

Â

(at the risk to be ridiculed…)

Â

I should be but as a humanist, I try not to be ashamed because of missing mathematical competence. I practice my understanding
by composing a non-mathematical description of what is going on in this case of PCT and Power Law.

Â

When a living being is producing a movement trajectory by moving itself (e.g. crawling) or its organs (e.g. hand in a
drawing task) there seems to be a certain dependence between the curvature of the trajectory (proceeding straight or turning to some direction) and the speed/velocity (understood here as a moved distance along the trajectory during a time unit). The normal
case is that the speed is stable on the straight line but it slows down in a curve.

Â

Now the first question is why that slowdown in the curve takes place. The second question is why the dependence between
curve and speed has those certain values, which have been observed in different situations. That latter question will be postponed.

Â

PCT view is generally that the behavior of an organism is that it controls its certain perception(s) by affecting by its
output some environmental correlates of those perceptions. So when an organism is moving it can be controlling for its distance from some object to be long (if the object is perceived as dangerous) or short (if the object is perceived as desirable). Any regularities
of behavior are often assumed to be side effects of control. (Not side effects of observation.)

Â

At the moment I have no idea what the larvae are controlling in those experiments but introspectively I can imagine some
possible perceptions I would control in a drawing task. First, I control seeing me a helpful aid in science making and being an obedient test subject and following to the rules. Then I would control to see the pen moving in a calm and nice way on the paper.
At the same time, I control that the pen follows the guiding line as strictly as possible. I think that my output function is such that it is easier to follow a line with certain kind of curvature than with another kind. We humans get much practice to draw
just certain kind of lines when we learn to draw and write. But there can also be some more general reasons why we use just those curves in our letters and typical drawings that we use. Anyway, it feels much more natural to draw a circle or looped circles
than rounded polygons.

Â

Therefore, the increased difficulty in controlling of the latter perception (following the line) would draw some effort
away from the control of the first perception (keeping the steady or moderate speed). Or rather the slowing down the speed will make it easier to control the following the line. (A straight line is easier to draw with higher speed than very slowly.) So the
slowdown could be a side effect of control. Perhaps something similar is going on with larvae? Is it easier for them to go straight forward? Is it an additional challenge to turn – to decide to turn and not to continnue forward? Would the slowdown make it easier
to control the perception of the new direction?

Â

Is that at all where the PCT view of Power Law could begin?

Â

Eetu

Â

Â

From: Alex Gomez-Marin [mailto:agomezmarin@gmail.com
]
Sent: 31. lokakuuta 2017 18:01
To: Alex Gomez-Marin agomezmarin@gmail.com; csgnet@lists.illinois.edu
Subject: Re: The speed�curvature power law of movements: a reappraisal

Â

regardless of your helicopter data and RCT mantras, it would be good if someone from CSGnet took seriously the challenge to PCT that the speed-curvature power law entails.Â

Â

any figure panel of our paper proves rick’s mathematical claims wrong: the PL is not a must and when it takes place it is not trivial and can have different exponents.Â

Â

now, how can “control of perception” explain that phenomenon? claiming it is an illusion because it does not fit in the dogma is like creationists insisting that dino fossils are bogus.Â

Â

so, as adam and myself take this job seriously, and given how many optimal control and nonPCT theories explain the data, I think Bill would really find his edifice crumbling, or at least unable. so, take your best shot at it and really
challenge your “revolutionary paradigm changing” theory of behavior.

Â

On Sun, 29 Oct 2017 at 02:48, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.10.28.1745)

Â

On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that’s two words But you know how bad I am at math;-)

Â

Best

Â

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

Alex Gomez-Marin

behavior-of-organisms.org

But how can you openly write a rebuttal to a paper and the editor not consider it important that that one of the authors of the first article are to be one of the reviewers?

···

On Wed, Nov 1, 2017 at 9:42 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

I totally disagree, Warren! I admire you but your political correctness, which can be a virtue, is often annoying to me: Marken’s was really really bogus. A shame it went through. Ours is very solid.Â

A different thing is that so far we did not restrict the interpretation we could not make of the power law in terms of perceptual control. That is for the future.

What I think is literally “a failure of effective peer review” is the blablabla on CSGnet (except in some cases).

On Wed, Nov 1, 2017 at 9:56 AM, Warren Mansell wmansell@gmail.com wrote:

Hi folks, the clearest message coming out of this for me is that there has been a failure of an effective peer review process for both articles!

On 1 Nov 2017, at 07:47, Boris Hartman boris.hartman@masicom.net wrote:

Down ….

Â

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Wednesday, November 01, 2017 6:15 AM
To: csgnet@lists.illinois.edu
Subject: Re: The speed�curvature power law of movements: a reappraisal

Â

[From Rick Marken (2017.10.31.2215)]

Â

On Tue, Oct 31, 2017 at 9:01 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: regardless of your helicopter data and RCT mantras, it would be good if someone from CSGnet took seriously the challenge to PCT that the speed-curvature power law entails.Â

Â

RM: What challenge? PCT explains it quite nicely as a mathematical property of curved trajectories. This fact explains why it appears as a side effect of intentionally produced curved movement… But apparently no one else on CSGNet sees it that way so your paper has demonstrated to me that no one on CSGNet (no one who posts, anyway) understands PCT. At least, they don’t understand it the way I do. This has convinced me that I must withdraw my Preface to LCS IV because I can’t in good conscience say that the papers in that book will be based on Powers’ theory and, thus, honor his legacy.

Â

HB : Good that you’ll withdraw your Preface. This is the way to preserve Powers theory. With not contributing RCT to any published literature.

Â

AGM: any figure panel of our paper proves rick’s mathematical claims wrong: the PL is not a must and when it takes place it is not trivial and can have different exponents.Â

Â

RM: There is nothing in your paper that proves that any of the claims made in our paper are wrong. We will explain this all in our own “reappraisal” of your “reappraisal”. But for now I’ll just say that our paper didn’t say that the power law was trivial; it showed that the power law is an illusion in the sense that it looks like it is relevant to understanding how organisms produce movement when it is not.

Â

HB : Maybe I could agree with you about the way »Power Law« was presented till now. It seems that it can’t explain how organisms function. Or even how nervous system function. And how by your oppinion organisms produce movements ??? With independent control units like you described in your artcile about »Power Law«. If I compare the »nothing« explained about how organisms function by your example of »helicopter« and »Power Law« I’d say that »Power Law« include less of »nothing« than your example with helicopter. It’s worse. Helicopter example shows »stimulus . respons«. People move in accordance to movement of helicopter. Where did you see this in reality ? Amd this should be the case of »purposefull behavior«.Â

Â

RM : Nor did we say that the power law can’t have different exponents; in fact we showed precisely why you do find different exponents for the power law; it’s because you omit a variable from the regression analysis used to determine that exponent.

Â

AGM: now, how can “control of perception” explain that phenomenon? claiming it is an illusion because it does not fit in the dogma is like creationists insisting that dino fossils are bogus.Â

Â

RM: No, we say it is an illusion because it is demonstrably a side effect of controlling perceptions, as demonstrated by the model of toy helicopter pursuit that we present in the paper (and that you simply dismiss as wrong for no apparent reason other than that it just must be).Â

Â

HB : As I said above. You demonstrated with helicopter example that »environment is controlling« people movement. You proved simple »stimulus-respons« theory. There is no »purposefull« behavior in your example  so that we could answer the question how people decide for their behaviors. In your case people »decide« to move along with helicopter movement probably because they were told to do so. How will you understand from this example how people form purposefull behavior.

Â

And your assunption is that they produce purposefull behavior with two independent control units. Is this how nervous system function ? Is this a joke ?

Â

AGM: so, as adam and myself take this job seriously, and given how many optimal control and nonPCT theories explain the data,

Â

RM: I have not seen any control models that explain the data; the term “controlled variable” is not to be found anywhere in your paper or in any other papers I have read in the area. The models I have seen that “explain” the power law are all output generation models – what Powers called “curve fitting” models – that would fail completely if they had to account for the fact that the observed curved movements being modeled are produced in a disturbance prone environment; the curved movements are themselves controlled variables.Â

Â

HB : Behavior itself is a »controlled variable« ? How organisms produce »controlled behavior« ?

Â

AGM: I think Bill would really find his edifice crumbling, or at least unable. so, take your best shot at it and really challenge your “revolutionary paradigm changing” theory of behavior.

Â

RM: I think you are right about that. If Bill has been listening in on CSGNet for the last 4+ years he would, indeed, see his revolutionary paradigm crumbling.

Â

HB : You are the one that contributed most of it.

Â

I knew that people would disagree with me as much as they did with Bill

Â

HB : Who said that Bill agreed with you ? He did protect you. But at least once you tryed to aline your and his knowledge and he answered in clear »no«. Your and Bills’ knowledge are not aligned. Anyway you show in every post disalignment with his literature.

Â

RM : ….but I was surprised by the intensity and meanness. But I know there are one or two people out there (not on CSGNet) who not only agree with my understanding of PCT (which I’m pretty, pretty, pretty sure is the same as Bill’s) but are also doing excellent PCT research.Â

Â

HB : I’d really like to meet these two people who don’t understand PCT ? You don’t understand PCT. And you never will.

Â

RM: It’s too bad; I really thought you really considered PCT a possible explanation of the power law. I guess my trusting nature got the football pulled away from me again. You are obviously very talented at research. It would have been great to have you working on doing research based on an understanding of PCT. But, alas, I guess it’s not to be.Â

Â

HB : I agree that it would be good for people to use PCT. but not RCT.

Â

Boris

Â

BestÂ

Â

Rick

Â

Â

On Sun, 29 Oct 2017 at 02:48, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.10.28.1745)

Â

On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that’s two words But you know how bad I am at math;-)

Â

Best

Â

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

Alex Gomez-Marin
behavior-of-organisms.org

Â

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

Dr Warren Mansell
Reader in Clinical Psychology

School of Health Sciences
2nd Floor Zochonis Building
University of Manchester
Oxford Road
Manchester M13 9PL
Email: warren.mansell@manchester.ac.uk
Â
Tel: +44 (0) 161 275 8589
Â
Website: http://www.psych-sci.manchester.ac.uk/staff/131406
Â
Advanced notice of a new transdiagnostic therapy manual, authored by Carey, Mansell & Tai - Principles-Based Counselling and Psychotherapy: A Method of Levels Approach

Available Now

Check www.pctweb.org for further information on Perceptual Control Theory

[From Rick Marken (2017.11.01.1720)]

···

Bruce Abbott (2017.11.01.0945 EDT)–

Â

RM: What challenge? PCT explains it quite nicely as a mathematical property of curved trajectories. This fact explains why it appears as a side effect of intentionally produced curved movement… But apparently no one else on CSGNet sees it that way so your paper has demonstrated to me that no one on CSGNet (no one who posts, anyway) understands PCT. At least, they don’t understand it the way I do. This has convinced me that I must withdraw my Preface to LCS IV because I can’t in good conscience say that the papers in that book will be based on Powers’ theory and, thus, honor his legacy.

Â

BA: You can resolve this controversy yourself quite easily. Next time you are on campus, stop by the Mathematics Department and ask a faculty member who is competent in analytical geometry to review the mathematical basis of your paper. Be sure to give this person both your disputed paper and the Gribble and Ostry (1998) paper from which you get the equations you rely on.

RM: I wrote the power law paper and submitted it for publication in EBR because I felt that my mathematical/statistical analysis was correct and the criticisms I was getting on the net in our net discussion over a year ago were wrong. I thought that if the paper were accepted in a peer reviewed journal – the very journal where much of the research on the power law is published – that might convince you that your criticisms of my analysis were themselves wrong. And the paper was reviewed and accepted for publication and the result was that the criticisms became even more earnest. So I don’t think that getting my paper reviewed by someone in the Math department is going to help. But I actually did have a senior researcher from RAND review it and he thought it was just fine. But I’m sure this will carry no weight with you even if I tell you that he is got his PhD in applied math from Harvard under Nobel Prize winner Kenneth Arrow. You’ll just say he was the wrong kind of mathematician.Â

BA: The dispute is not with PCT, it is about the soundness of your mathematical analysis.Â

RM: So you say. But, in fact, the dispute is all about PCT because the fact that the power law is an example of a behavioral illusion is not based on the math; it’s based on the fact that an intentionally produced curved movement is a controlled result produced by variable means. The math just shows why researchers have consistently found a power law relationship between two measures – velocity and curvature – of the time varying state of this controlled result.Â

Â

BA: It is obvious that the power law is a side-effect of controlling certain variables

RM: Only when the curved movement is produced intentionally. If the movement is produced via causal processes – like the curved path of a Frisbee – it is simply a mathematical property of curved trajectories.Â

BA: – neither people nor larvae are controolling for moving in conformance with the power law. But contrary to your belief, the power law is not a mathematical property of curved trajectories, and therefore cannot “explain why it appears as a side effect of intentionally produced curved movement.â€?Â

RM: So you say.Â

Â

BA: It follows that the emergence of the power-law relation during curved movements remains to be explained. Developing a PCT explanation will require applying the test for the controlled variable.

RM: Well, I look forward to seeing your control theory explanation of the power law in terms of a variable that is being controlled. You’d think you would have found the controlled variable by now. But it’s hard to find because it’s right in front of your eyes: the movement trajectory itself.

Â

 BA: So again, I encourage you – indeed implore you – to submit your analysis (and its context) to a mathematiciaan on campus for review. You may not be happy with the result, but at least you will learn why so many of us on CSGnet have been asserting that your mathematical analysis of the power law is unsound. What have you got to lose?

RM: See above.Â

Best

RickÂ

Â

Bruce

Â

Â


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

[From Rick Marken (2017.11.01.1745)

···

On Wed, Nov 1, 2017 at 7:11 AM, Warren Mansell wmansell@gmail.com wrote:

WM: But how can you openly write a rebuttal to a paper and the editor not consider it important that that one of the authors of the first article are to be one of the reviewers?

RM: Good question!! That is the proper way to do it. The fact that this didn’t happen, even after I wrote to the journal to inquire about the existence of a rebuttal to our paper, could be because one of the authors, Lacquaniti, is on the editorial board of EBR. As Powers said: "Scientists are all too human: when they see that
the new idea means their life’s work could end up mostly in the trash-can,
their second reaction is simply to think ‘That idea is obviously
wrong.’"Â I think we’re seeing the second reaction.Â

Best

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

On Wed, Nov 1, 2017 at 9:42 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

I totally disagree, Warren! I admire you but your political correctness, which can be a virtue, is often annoying to me: Marken’s was really really bogus. A shame it went through. Ours is very solid.Â

A different thing is that so far we did not restrict the interpretation we could not make of the power law in terms of perceptual control. That is for the future.

What I think is literally “a failure of effective peer review” is the blablabla on CSGnet (except in some cases).


Dr Warren Mansell
Reader in Clinical Psychology

School of Health Sciences
2nd Floor Zochonis Building
University of Manchester
Oxford Road
Manchester M13 9PL
Email: warren.mansell@manchester.ac.uk
Â
Tel: +44 (0) 161 275 8589
Â
Website: http://www.psych-sci.manchester.ac.uk/staff/131406
Â
Advanced notice of a new transdiagnostic therapy manual, authored by Carey, Mansell & Tai - Principles-Based Counselling and Psychotherapy: A Method of Levels Approach

Available Now

Check www.pctweb.org for further information on Perceptual Control Theory

On Wed, Nov 1, 2017 at 9:56 AM, Warren Mansell wmansell@gmail.com wrote:

Hi folks, the clearest message coming out of this for me is that there has been a failure of an effective peer review process for both articles!

On 1 Nov 2017, at 07:47, Boris Hartman boris.hartman@masicom.net wrote:

Down ….<

Â

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Wednesday, November 01, 2017 6:15 AM
To: csgnet@lists.illinois.edu
Subject: Re: The speed�curvature power law of movements: a reappraisal

Â

[From Rick Marken (2017.10.31.2215)]

Â

On Tue, Oct 31, 2017 at 9:01 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: regardless of your helicopter data and RCT mantras, it would be good if someone from CSGnet took seriously the challenge to PCT that the speed-curvature power law entails.Â

Â

RM: What challenge? PCT explains it quite nicely as a mathematical property of curved trajectories. This fact explains why it appears as a side effect of intentionally produced curved movement… But apparently no one else on CSGNet sees it that way so your paper has demonstrated to me that no one on CSGNet (no one who posts, anyway) understands PCT. At least, they don’t understand it the way I do. This has convinced me that I must withdraw my Preface to LCS IV because I can’t in good conscience say that the papers in that book will be based on Powers’ theory and, thus, honor his legacy.

Â

HB : Good that you’ll withdraw your Preface. This is the way to preserve Powers theory. With not contributing RCT to any published literature.

Â

AGM: any figure panel of our paper proves rick’s mathematical claims wrong: the PL is not a must and when it takes place it is not trivial and can have different exponents.Â

Â

RM: There is nothing in your paper that proves that any of the claims made in our paper are wrong. We will explain this all in our own “reappraisal” of your “reappraisal”. But for now I’ll just say that our paper didn’t say that the power law was trivial; it showed that the power law is an illusion in the sense that it looks like it is relevant to understanding how organisms produce movement when it is not.

Â

HB : Maybe I could agree with you about the way »Power Law« was presented till now. It seems that it can’t explain how organisms function. Or even how nervous system function. And how by your oppinion organisms produce movements ??? With independent control units like you described in your artcile about »Power Law«. If I compare the »nothing« explained about how organisms function by your example of »helicopter« and »Power Law« I’d say that »Power Law« include less of »nothing« than your example with helicopter. It’s worse. Helicopter example shows »stimulus . respons«. People move in accordance to movement of helicopter. Where did you see this in reality ? Amd this should be the case of »purposefull behavior«.Â

Â

RM : Nor did we say that the power law can’t have different exponents; in fact we showed precisely why you do find different exponents for the power law; it’s because you omit a variable from the regression analysis used to determine that exponent.

Â

AGM: now, how can “control of perception” explain that phenomenon? claiming it is an illusion because it does not fit in the dogma is like creationists insisting that dino fossils are bogus.Â

Â

RM: No, we say it is an illusion because it is demonstrably a side effect of controlling perceptions, as demonstrated by the model of toy helicopter pursuit that we present in the paper (and that you simply dismiss as wrong for no apparent reason other than that it just must be).Â

Â

HB : As I said above. You demonstrated with helicopter example that »environment is controlling« people movement. You proved simple »stimulus-respons« theory. There is no »purposefull« behavior in your example  so that we could answer the question how people decide for their behaviors. In your case people »decide« to move along with helicopter movement probably because they were told to do so. How will you understand from this example how people form purposefull behavior.

Â

And your assunption is that they produce purposefull behavior with two independent control units. Is this how nervous system function ? Is this a joke ?

Â

AGM: so, as adam and myself take this job seriously, and given how many optimal control and nonPCT theories explain the data,

Â

RM: I have not seen any control models that explain the data; the term “controlled variable” is not to be found anywhere in your paper or in any other papers I have read in the area. The models I have seen that “explain” the power law are all output generation models – what Powers called “curve fitting” models – that would fail completely if they had to account for the fact that the observed curved movements being modeled are produced in a disturbance prone environment; the curved movements are themselves controlled variables.Â

Â

HB : Behavior itself is a »controlled variable« ? How organisms produce »controlled behavior« ?

Â

AGM: I think Bill would really find his edifice crumbling, or at least unable. so, take your best shot at it and really challenge your “revolutionary paradigm changing” theory of behavior.

Â

RM: I think you are right about that. If Bill has been listening in on CSGNet for the last 4+ years he would, indeed, see his revolutionary paradigm crumbling.

Â

HB : You are the one that contributed most of it.

Â

I knew that people would disagree with me as much as they did with Bill

Â

HB : Who said that Bill agreed with you ? He did protect you. But at least once you tryed to aline your and his knowledge and he answered in clear »no«. Your and Bills’ knowledge are not aligned. Anyway you show in every post disalignment with his literature.

Â

RM : ….but I was surprised by the intensity and meanness… But I know there are one or two people out there (not on CSGNet) who not only agree with my understanding of PCT (which I’m pretty, pretty, pretty sure is the same as Bill’s) but are also doing excellent PCT research.Â

Â

HB : I’d really like to meet these two people who don’t understand PCT ? You don’t understand PCT. And you never will.

Â

RM: It’s too bad; I really thought you really considered PCT a possible explanation of the power law. I guess my trusting nature got the football pulled away from me again. You are obviously very talented at research. It would have been great to have you working on doing research based on an understanding of PCT. But, alas, I guess it’s not to be.Â

Â

HB : I agree that it would be good for people to use PCT. but not RCT.

Â

Boris

Â

BestÂ

Â

Rick

Â

Â

On Sun, 29 Oct 2017 at 02:48, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.10.28.1745)

Â

On Sat, Oct 28, 2017 at 3:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

attachedÂ

RM: Finally! Thank you, Alex. I hope the journal gives us an opportunity to respond. But for now I have only one word for you: helicopter movements. Oh, that’s two words But you know how bad I am at math;-)

Â

Best

Â

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

Alex Gomez-Marin
behavior-of-organisms.org

Â

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

[From Rick Marken (2017.11.02.0950)]

Bruce Abbott (2017.11.01.2140 EDT)

Rick Marken (2017.11.01.1720)]

BA: You can resolve this controversy yourself quite easily. Next time you are on campus, stop by the Mathematics Department and ask a faculty member who is competent in analytical geometry to review the mathematical basis of your paper. Be sure to give this person both your disputed paper and the Gribble and Ostry (1998) paper from which you get the equations you rely on.

RM: I wrote the power law paper and submitted it for publication in EBR because I felt that my mathematical/statistical analysis was correct and the criticisms I was getting on the net in our net discussion over a year ago were wrong. I thought that if the paper were accepted in a peer reviewed journal – the very journal where much of the research on the power law is published – that might convince you that your criticisms of my analysis were themselves wrong. And the paper was reviewed and accepted for publication and the result was that the criticisms became even more earnest.

BA: Well, that’s what I thought you’d say, but it’s disappointing nevertheless. It’s too bad that Richard Kennaway has not weighed in on this as I imagine that you would be more inclined to believe his judgment on this issue. Have you asked him?

RM: No, but I’d love to hear from him. Richard, if your listening I’d be interested in hearing what you have to say about the mathematics (statistics really) in my power law paper. In case you haven’t read it it’s available at https://www.dropbox.com/s/g3tcy8p46c957f7/MarkenShaffer2017.pdf?dl=0.

Best

Rick

rick, your comments are shame after shame.

···

Alex Gomez-Marin
behavior-of-organisms.org

[From Rick Marken (2017.11.05.1220)]

image384.png

···

Martin Taylor (2017.11.03.17.35)–

RM: I shouldn’t respond to this but I can’t seem to focus on other things until I do.Â

Â

RM: Throughout the Marken-Shaffer paper, D1/3 = Velocity*(a
function of spatial variables) is used to “correct” an observed
relationship between the physical curvature of a path in space and
the velocity with which that path is travelled. In a section on
“Omitted Variable” analysis, they show that the observed
relationship is “predictable” by including D, which means simply
that it is predictable by including V to explain V.

RM: This is not what we show. What we show is that leaving D (the cross product variable) out of the regression analysis (D being the “omitted variable”) results in a biased estimate of the coefficient of the actual mathematical power function (1/3 or 2/3 depending on how velocity and curvature are measured) relating velocity to curvature in curved movements.Â

Â

MT: Following that, they purport to provide a PCT model that explains

the power law, though the model they provide shows no relation to
the power law at all. All it does is show a possible PCT model for
how a person controls for following a toy helicopter. That has no
implications whatever for the power law. Nevertheless, they find
that both helicopter and human move in a manner that exhibits the
power law between velocity and curvature, which they then predict
with amazing accuracy by using V (as D1/3) to predict V.

RM: 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 the helicopters.

Â

MT: In spite of the fact that the PCT model they provide for how humans

follow toy helicopters has absolutely no implications for the power
law,

RM: The fact that the power law is found for the curved trajectories produced by the PCT model suggests that the model has a least one implication for the power law: that is is a side-effect of control.

MT: and in spite of the fact that the wrongness of the use of V to

predict V has been explained many times over the last year and more,

Â

RM: I am not using V to predict V. I am using a measure of curvature (R or C) and a cross produce variable (D) to predict velocity (V or A). Measures of curvature and the cross product variable D are correlated to varying degrees depending on the nature of the curved trajectory being analyzed. But they are not the same variable.Â

Â

MT: Marken [From Rick Marken (2017.10.28.1745)] still uses the

helicopter model as though it provided a PCT explanation of the
power law, and treats criticism of his paper as denial of PCT.

RM: Not denial of PCT; just not understanding it. Â

MT: That the paper is actually total garbage is irrelevant to the beauty

and power of PCT.

RM: Apparently your opinion of the paper was not shared by two reviewers and the action editor. To say nothing of my co-author and other people who reviewed it for me personally.

Â

MT: What is not irrelevant to the potential

propagation of PCT to the wider world of science is the fact that
the paper has not been withdrawn, and worse, that Rick continues to
refer to it outside the semi-closed society of CSGnet readers as
though it was some kind of triumph of PCT thought rather than a
simple pollution of the literature.

RM: Again, that’s your opinion. And apparently that of many others, including those that wrote the “reappraisal” paper. But I wrote the power law paper only to try to point research on movement production in a direction that is more consistent with an understanding of movement as a control phenomenon: the production of a consistent result (the curved movement) in the face of unpredictable and undetectable disturbances. If that happens – if power law researchers start doing research aimed at understanding how organisms control limb movements --Â then my reason for writing the paper will have been accomplished and I will not submit my rebuttal to the “reappraisal” paper to EBR.

Â

MT: To any mathematically literate

reader who takes the time to work through the formulae, the thought
that Rick might be a typical proponent of PCT as a science, and is
yet capable of seriously publishing such nonsense, must be very
off-putting when it comes to the possibility of looking more deeply
into PCT to see if it has anything to offer.

RM: Here’s calculations made by what appear to be some mathematically literate people who took the time to work through the formulae.Â

Â

RM: In the formulae above, v(t) is their measure of velocity, equivalent to V in our paper, k(t) is their measure of curvature, which is equivalent to 1/R in our paper, and a(t) is equivalent to D in our paper. Because their measure of curvature is the reciprocal of ours, their equation (5) shows the power coefficient for curvature as -1/3 rather than 1/3, as in our paper. The time subscript on their variables is actually unnecessary (which is why we didn’t use them) since the variables are used in a regression analysis which ignores the time sequence in which the variables occur; it just assumes that all three variables: k(t), a(t) and v(t) are measures of characteristics of the curve at the same instant.Â

MT: I just hope that someone is able to figure out just what perceptions

are being controlled when living organisms move fast but smoothly
(which seems to be the condition under which the power law is
observed), and why control of those perceptions leads to a power law
with a particular power, whether the power be as low as 1/6 or as
high as 2/5.

RM: I think someone has already done that;-)Â

MT: If that can be done, we can put this whole disgraceful episode behind us.

RM: That would be nice!

BestÂ

RickÂ


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

[From 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

Does this hold also for the paths taken by people catching baseballs?

image384.png

···

On Sun, Nov 5, 2017 at 3:23 PM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.11.05.1220)]

Martin Taylor (2017.11.03.17.35)–

RM: I shouldn’t respond to this but I can’t seem to focus on other things until I do.Â

Â

RM: Throughout the Marken-Shaffer paper, D1/3 = Velocity*(a
function of spatial variables) is used to “correct” an observed
relationship between the physical curvature of a path in space and
the velocity with which that path is travelled. In a section on
“Omitted Variable” analysis, they show that the observed
relationship is “predictable” by including D, which means simply
that it is predictable by including V to explain V.

RM: This is not what we show. What we show is that leaving D (the cross product variable) out of the regression analysis (D being the “omitted variable”) results in a biased estimate of the coefficient of the actual mathematical power function (1/3 or 2/3 depending on how velocity and curvature are measured) relating velocity to curvature in curved movements.Â

Â

MT: Following that, they purport to provide a PCT model that explains

the power law, though the model they provide shows no relation to
the power law at all. All it does is show a possible PCT model for
how a person controls for following a toy helicopter. That has no
implications whatever for the power law. Nevertheless, they find
that both helicopter and human move in a manner that exhibits the
power law between velocity and curvature, which they then predict
with amazing accuracy by using V (as D1/3) to predict V.

RM: 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 the helicopters.

Â

MT: In spite of the fact that the PCT model they provide for how humans

follow toy helicopters has absolutely no implications for the power
law,

RM: The fact that the power law is found for the curved trajectories produced by the PCT model suggests that the model has a least one implication for the power law: that is is a side-effect of control.

MT: and in spite of the fact that the wrongness of the use of V to

predict V has been explained many times over the last year and more,

Â

RM: I am not using V to predict V. I am using a measure of curvature (R or C) and a cross produce variable (D) to predict velocity (V or A). Measures of curvature and the cross product variable D are correlated to varying degrees depending on the nature of the curved trajectory being analyzed. But they are not the same variable.Â

Â

MT: Marken [From Rick Marken (2017.10.28.1745)] still uses the

helicopter model as though it provided a PCT explanation of the
power law, and treats criticism of his paper as denial of PCT.

RM: Not denial of PCT; just not understanding it. Â

MT: That the paper is actually total garbage is irrelevant to the beauty

and power of PCT.

RM: Apparently your opinion of the paper was not shared by two reviewers and the action editor. To say nothing of my co-author and other people who reviewed it for me personally.

Â

MT: What is not irrelevant to the potential

propagation of PCT to the wider world of science is the fact that
the paper has not been withdrawn, and worse, that Rick continues to
refer to it outside the semi-closed society of CSGnet readers as
though it was some kind of triumph of PCT thought rather than a
simple pollution of the literature.

RM: Again, that’s your opinion. And apparently that of many others, including those that wrote the “reappraisal” paper. But I wrote the power law paper only to try to point research on movement production in a direction that is more consistent with an understanding of movement as a control phenomenon: the production of a consistent result (the curved movement) in the face of unpredictable and undetectable disturbances. If that happens – if power law researchers start doing research aimed at understanding how organisms control limb movements --Â then my reason for writing the paper will have been accomplished and I will not submit my rebuttal to the “reappraisal” paper to EBR.

Â

MT: To any mathematically literate

reader who takes the time to work through the formulae, the thought
that Rick might be a typical proponent of PCT as a science, and is
yet capable of seriously publishing such nonsense, must be very
off-putting when it comes to the possibility of looking more deeply
into PCT to see if it has anything to offer.

RM: Here’s calculations made by what appear to be some mathematically literate people who took the time to work through the formulae.Â

Â

RM: In the formulae above, v(t) is their measure of velocity, equivalent to V in our paper, k(t) is their measure of curvature, which is equivalent to 1/R in our paper, and a(t) is equivalent to D in our paper. Because their measure of curvature is the reciprocal of ours, their equation (5) shows the power coefficient for curvature as -1/3 rather than 1/3, as in our paper. The time subscript on their variables is actually unnecessary (which is why we didn’t use them) since the variables are used in a regression analysis which ignores the time sequence in which the variables occur; it just assumes that all three variables: k(t), a(t) and v(t) are measures of characteristics of the curve at the same instant.Â

MT: I just hope that someone is able to figure out just what perceptions

are being controlled when living organisms move fast but smoothly
(which seems to be the condition under which the power law is
observed), and why control of those perceptions leads to a power law
with a particular power, whether the power be as low as 1/6 or as
high as 2/5.

RM: I think someone has already done that;-)Â

MT: If that can be done, we can put this whole disgraceful episode behind us.

RM: That would be nice!

BestÂ

RickÂ


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

[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

[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

come on, guys!, let us all be clear and fair: rick just wanted some publicity on PCT and so they took their previous papers, cited them q lot, and applied this logic “since helicopter-pursuer system shows power law, therefore power law is a by-product of control” and then added before and after really bogus mathematical and statistical claims (that pretended to generalize for all sustems all powerlaws and all exponents found!), and rhethoric interpretation. we just had to correct that nonsense. and we are still looking for a pct explanation. but one cannot rush to the conclusion with faulty arguments. really, guys, the whole problem with most of PCT attitude now is that since you know from god that you are right, one thinks it is ok to dispense with basic rules of evidence, marhematical correctness and intellectual honesty. this is why me (and others i have talk to) have considered so many timea that being engage with csgnet is hopeless.

···

Martin Taylor (2017.11.03.17.35)–

          RM: I shouldn't respond to this but I can't seem to

focus on other things until I do.Â

Â

            RM: Throughout the Marken-Shaffer

paper, D1/3 = Velocity*(a function of spatial
variables) is used to “correct” an observed relationship
between the physical curvature of a path in space and
the velocity with which that path is travelled. In a
section on “Omitted Variable” analysis, they show that
the observed relationship is “predictable” by including
D, which means simply that it is predictable by
including V to explain V.

          RM: This is not what we show. What we show is that

leaving D (the cross product variable) out of the
regression analysis (D being the “omitted variable”)
results in a biased estimate of the coefficient of the
actual mathematical power function (1/3 or 2/3
depending on how velocity and curvature are measured)
relating velocity to curvature in curved movements.

Alex Gomez-Marin
behavior-of-organisms.org

sure, Fred. but the question is “what would that actually prove?” and whether the conclusion you or rick would draw is independent of the result of the experiment, aka, that pf course pct is right and the power law is an artefact and compulsory…

now, think of a pendulum: curvature is constant, and speed changes all the time. is the PL there given? aha!

···

Alex Gomez-Marin
behavior-of-organisms.org

[From Rick Marken (2017.11.06.0910)]

···

Bruce Nevin (2017.11.05.19:56 ET)

BN: 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.

RM: I think this is a pretty good take on it. Our paper is heavy on the “statistical artifact” and light on the “PCT explanation” for a reason. The original paper had a more detailed discussion of the “PCT explanation” but one of the reviewers didn’t like that part but loved the “statistical artifact” part. So I had to trim the “PCT explanation” considerably. But PCT sneaks in at the beginning of the article in this paragraph:

Although a third variable is a plausible explanation of
the correlation between curvature and velocity, it does not
explain why that correlation is consistently found to follow
a power law, per Eq. 1. A third variable explanation
requires that the cause of movement—the muscle forrces—
consistently affects curvature and velocity in such a waythat velocity is a power function of curvature. However,
this explanation ignores the fact that different muscle forces
are required to produce the same movement trajectory on
different occasions due to variations in the circumstances
that exist each time the movement is produced (Marken
1988). For example, the forces required to move a finger in
an elliptical trajectory are different each time the movement
is produced due to slight changes in one’s orientation relative
to gravity. Therefore, muscle forces will not be consistently
related to the curvature and velocity of the movement;
the same power relationship between curvature and velocity
will be associated with somewhat different muscle forces
each time the same movement trajectory is produced.

RM: This is the PCT explanation of why we though the explanation of the power law might be found in the mathematics of how curvature and velocity are measured; and, as you note, a large part of our paper is dedicated to showing that this is, indeed, the case. But this PCT-based observation alone – that, due to varying disturbances, different muscle forces are being used to produce the same curved movement on different occasions; that variable means must be used to produce consistent results – is enough to lead one to suspect that the power law that is found for the resulting movement can’t possibly be telling us anything about how that movement was produced. That’s why I have been rather surprised (and disappointed) that all these presumed PCT experts here on CSGNet are making out like I’m the great enemy of PCT for pointing out one of the most basic facts about behavior that we get from PCT; consistent results are produced by variable means. It’s called “control” and curved movements (indeed, all movements) are controlled (consistently produced) results of (necessarily variable) muscle forces.

Best

Rick

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)?

/Bruce

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

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

[From Adam Matic 2017.11.6]

···

[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) (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.”

The trajectories of pursuit tracking of helicopters in that particular task is (could be) just one more situation where the power law can be found. Since that is pursuit tracking, where velocity of the target is already given, and not tracing of curves where velocity is not given, the explanation cannot be generalized. Most studies on the production of the power law were done on tracing different curves, or drawing scribbles or letters,. The power law can be found in trajectories of very simple mass on spring systems, or coupled sinusoidal trajectories, and this doesn’t say nothing definite about how this movement is produced in tracing experiments.

BM: 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.

Overgeneralization. In some cases, some control systems can produce a power law. If you accurately follow a pendulum trajectory with your finger, where the curvature is always the same, but velocity changes, then the curvature and velocity will not be related with a power law. This has nothing to do with how you calculate curvature and velocity. However you calculate them, if you plot them on a log-log plot, you will not get a regression line with high r2.

Adam

[From Rick Marken (2017.11.06.1020)]

···

Fred Nickols (2017.11.06.0612 ET)–

Â

FN: Rick:Â While watching a football game yesterday, I speculated that catching a football fit with your catching fly balls work.Â

 RM: Yes, receivers are surely controlling the optical variables controlled by the COV model of catching.Â

FN: I wonder if you could do the same for a quarterback throwing them?

RM: I think that’s a whole different ballgame;-)Â The same optical variables might be involved but there are surely higher level functions of those variables involved since the quarterback is throwing to a moving target. So the quarterback must control for the future optical location of the ball matching the future optical location of the receiver. This requires prediction of the future states of a perception, which can be modeled as an extrapolation in imagination or control of a higher level present time perception. But, whatever, passing is a more difficult control phenomenon to model than catching.Â

Best

Rick

Â

Â

Fred Nickols

Â

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Sunday, November 5, 2017 6:15 PM
To: csgnet@lists.illinois.edu
Subject: Re: The speed�curvature power law of movements: a reappraisal

Â

[From Rick Marken (2017.11.05.1515)]

Â

Bruce Nevin (2017.11.05.1755 ET)

Â

Rick Marken (2017.11.05.1220) –

Â

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

Â

BN: Does this hold also for the paths taken by people catching baseballs?

Â

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).

Â

BestÂ

Â

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

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