# Submitted comments on Marken Shaffer Power-law paper

[Martin Taylor 2017.11.23.23.23]

I have submitted the attached Word (.doc) file to Experimental Brain
Research.

Martin

MarkenShafferComment.doc (96 KB)

Thanks for sending a copy. It seems that the mathematical error was exactly where you point. I’ve been rereading Rick’s paper, and it seems there are conceptual misunderstandings of what exactly is the phenomenon of the power law of movement, way before doing any math.

For example, in non-mathematical terms, when people draw ellipses, the pen moves more slowly in the curved part of the path, and faster in the straighter part of the path. That is an empirical finding, and when the movements are sufficiently fast and rhythmical, there is a relatively precise relationship between the curvature and speed. Calling the law a statistical artifact is meaningless because the speed really is correlated with curvature. When moving sufficiently slowly, you could do the opposite, draw an ellipse where you move faster on curved parts and slower on straighter parts, and get a different exponent o
r just a non-power law movement.

The existence of a power-law with a specific exponent has a physical meaning, and it seems Rick, Dennis and their reviewers skipped over that part.

···

On Fri, Nov 24, 2017 at 5:54 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2017.11.23.23.23]

I have submitted the attached Word (.doc) file to Experimental Brain Research.

Martin

[From Rick Marken (2017.11.24.1610)]

···

AM: For example, in non-mathematical terms, when people draw ellipses, the pen moves more slowly in the curved part of the path, and faster in the straighter part of the path.

RM: A fact that we acknowledge in the paper. But what we also point out is that this is a correlational relationship and that the speed and curvature cannot be causally related because they are measures of of the trajectory that are occurring simultaneously.

AM: Calling the law a statistical artifact is meaningless because the speed really is correlated with curvature.

RM: It’s not the correlation between the variables that is the artifact; it is the power law relationship between those variables that is that artifact.

AM: The existence of a power-law with a specific exponent has a physical meaning, and it seems Rick, Dennis and their reviewers skipped over that part.

RM: Well, following Warren Mansell’s lead in trying to find the strengths in what people say I will say that this statement is completely correct; the existence of the power law with a specific exponent does have a physical meaning and Dennis and I and the reviewers and the action editor skipped over that part, mainly because it was not relevant to our analysis. But thanks to a reference in the Zago et al “reappraisal” of our paper I’ve learned that our “cross product” variable (which we call D) is actually a measure of the affine velocity at each point in the movement trajectory and when this value is constant the trajectory, regardless of how it’s produced, will be found to satisfy the 1/3 or 2/3 “power law”. In other words, whether or not a movement trajectory is found to follow the power law depends on properties of the trajectory itself, not on how that trajectory was generated (whether it was generated by a living system, a non-living system or a mathematical equation). The idea that the power law does tell you something about how the movement was generated is an example of a behavioral illusion, a fact that could have been seen without all the mathematical analysis but just from looking at the behavior (moving in curved trajectories, in this case) through control theory glasses.

RM: But all this will be explained in our rebuttal to Zago et al and now to Taylor et none as well.

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.â?
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery

On Fri, Nov 24, 2017 at 5:54 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2017.11.23.23.23]

I have submitted the attached Word (.doc) file to Experimental Brain Research.

Martin

···

AM: The question is why does the pen move slower in more curved paths, and faster in straight paths, and “that is just a correlation” is not much of an answer. Saying it is an illusion is denying the physical meaning to the movement.

AM: The power law relationship is the correlation between logs of those variables. It is not "a mathematical artifact’. The pen really does move more slowly when the trajectory is curved, and if the relationship is strong, you can tell in which part of the trajectory the pen is. When you say it is an artifact, what does that mean, if not that the relationship doesn’t exist?

I also notice you haven’t published r2 for any of the trajectories in your paper, and that is an important part of establishing the relationship.

AM:

The meaning of the data should be relevant. Otherwise, well, you get meaningless results.

AM: You keep saying that, but everyone (and I mean everyone in all the papers on the power law that I’ve seen) already agrees with that!

It is simply interesting that it was found in living systems and not in planets.

AM: You’d still need some math and experiments to prove the behavioral illusion, The behavioral illusion is not that trivial. If you say that the trajectory is the controlled variable, what would you correlate it with? What is the disturbance?

AM: For example, in non-mathematical terms, when people draw ellipses, the pen moves more slowly in the curved part of the path, and faster in the straighter part of the path.

RM: A fact that we acknowledge in the paper. But what we also point out is that this is a correlational relationship and that the speed and curvature cannot be causally related because they are measures of of the trajectory that are occurring simultaneously.

AM: Calling the law a statistical artifact is meaningless because the speed really is correlated with curvature.

RM: It’s not the correlation between the variables that is the artifact; it is the power law relationship between those variables that is that artifact.

AM: The existence of a power-law with a specific exponent has a physical meaning, and it seems Rick, Dennis and their reviewers skipped over that part.

RM: the existence of the power law with a specific exponent does have a physical meaning and Dennis and I and the reviewers and the action editor skipped over that part, mainly because it was not relevant to our analysis.

RM: In other words, whether or not a movement trajectory is found to follow the power law depends on properties of the trajectory itself, not on how that trajectory was generated (whether it was generated by a living system, a non-living system or a mathematical equation).

RM: The idea that the power law does tell you something about how the movement was generated is an example of a behavioral illusion, a fact that could have been seen without all the mathematical analysis but just from looking at the behavior (moving in curved trajectories, in this case) through control theory glasses.

[Martin Taylor 2017.11.25.12.34]

[From Rick Marken (2017.11.24.1610)]

``````That's interesting. The drawing that people trace does not exist
``````

before they trace it? The reference for where the moving
fingertip/pencil/whatever should be going during a freely drawn
scribble does not exist before the moving object goes there?

``````This is surely a novel view of PCT. People create the reference
``````

values for what they control by observing what they did, and
drawings can be seen by others only after a subject traces over
them. A new philosophy of Nature, too! This rebuttal may start a
whole new science, just as the original paper introduced a new kind
of logic.

``````Wow! We are cooking with gas here!

If by "artifact" you mean "side-effect", I think everyone has agreed
``````

with that from day one, about 18 months ago.

``````Since your whole paper is based on your mathematical analysis, which
``````

you now say was unnecessary, I suppose your rebuttal consists of
“The Power-law that is observed is a Behavioural Illusion. Why?
Because I say it is.”

``````Of course, you might help your "cause" by redefining "behavioural
``````

illusion" as “side-effect” rather than the usual definition of it as
a misinterpretation of observations because of a failure to
recognize that observed effects depend on the environmental feedback
path between output and the environmental controlled variable rather
than on the details of internal processes so long as they control.
Saying “Behavioural Illusion” is just another name for “side-effect”
might be much easier.

``````If you don't, then you would have to explain a fair amount of PCT to
``````

the EBR readership – which wouldn’t be a bad thing if done
correctly. You would also have to demonstrate what the controlled
perception is in each case, which is what so many of us have been
urging, and which in other situations you insist on. It is, after
all, one thing that “control theory glasses” allow you to see – and
show that you must see before you can say much more about a
situation.

``````Martin
``````
···

``````              AM: For example, in non-mathematical terms, when
``````

people draw ellipses, the pen moves more slowly in the
curved part of the path, and faster in the straighter
part of the path.

``````          RM: A fact that we acknowledge in the paper. But what
``````

we also point out is that this is a correlational
relationship and that the speed and curvature cannot be
causally related because they are measures of of the
trajectory that are occurring simultaneously.

``````              AM: Calling the law a statistical artifact is
``````

meaningless because the speed really is correlated
with curvature.

``````          RM: It's not the correlation between the variables that
``````

is the artifact; it is the power law relationship between
those variables that is that artifact.

``````        [RM]...The idea that the power law does tell you something
``````

about how the movement was generated is an example of a
behavioral illusion, a fact that could have been seen
without all the mathematical analysis but just from looking
at the behavior (moving in curved trajectories, in this
case) through control theory glasses.

``````          RM: But all this will be explained in our rebuttal to
``````

Zago et al and now to Taylor et none as well.

[From Rick Marken (2017.11.26.1050)]

···

RM: It’s not the correlation that is an illusion; it’s the idea that this correlation tells you something about how the trajectory was generated.Â

Â

RM: It’s actually the idea that there is a 1/3 (or 2/3) power "law"Â that is the artifact.Â

RM: Actually, we did mention that the average r2 fit of the power law to our data (pursuer and helicopter trajectories) is a bit over .9.Â But thanks for bringing this up. I’ll be sure to discuss the goodness of fit issue in the rebuttal even though I have not seen many discussions in the literature regarding what the "critical"Â r2 value is that would allow one to declare that the power law fits (or doesn’t fit) the data.

Â

RM: You can say that again!

Â

RM: I think they are also trying to figure out why that’s true, aren’t they? For example, they have come up with models that purport to explain how these power law compliant trajectories produced by living organisms are generated.Â If power law researchers were interested only in the fact that something close to the 1/3 power law is always found in living systems and not in planets then I would have no beef with them. But I was asked how PCT would explain the existence of the power law as it is found in the trajectories produced by living organisms, which is presumably asking howÂ Â these trajectories are generated. I provided the PCT explanation, was roundly (and rudely) criticized on CSGNet for giving it, submitted the explanation for publication in the hopes that it would get a better reception from a peer reviewed journal, it did, and now the expected hysteria from the so-called “PCT experts” moves to the journal.Â Which is exactly what I was hoping for.Â

RM: What is unquestionably controlled when people produce curved movements is the position of the moved entity (finger, cursor, etc) at each instant during the movement. The disturbance to this variable when a finger is moved in a curved trajectory, for example, is the varying effects of gravity as the arm and finger change their position in space. If the curved movement is that of a cursor on a computer screen then known disturbances can be applied at each point in the movement and it can be shown that the resulting cursor trajectory is produced by outputs (mouse movements) that follow a very different power law than the one that characterizes the resulting cursor trajectory.Â

RM: All this (and more) will be made clear in our rebuttal to Zago et al and Taylor et none (assuming they publish the latter, which I have no doubt they will).Â

Best regards

Rick

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.â€?
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery

AM: The question is why does the pen move slower in more curved paths, and faster in straight paths, and “that is just a correlation” is not much of an answer. Saying it is an illusion is denying the physical meaning to the movement.

AM: For example, in non-mathematical terms, when people draw ellipses, the pen moves more slowly in the curved part of the path, and faster in the straighter part of the path.

RM: A fact that we acknowledge in the paper. But what we also point out is that this is a correlational relationship and that the speed and curvature cannot be causally related because they are measures of of the trajectory that are occurring simultaneously.

AM: The power law relationship is the correlation between logs of those variables. It is not "a mathematical artifact’. The pen really does move more slowly when the trajectory is curved, and if the relationship is strong, you can tell in which part of the trajectory the pen is. When you say it is an artifact, what does that mean, if not that the relationship doesn’t exist?

AM: I also notice you haven’t published r2 for any of the trajectories in your paper, and that is an important part of establishing the relationship.Â

RM:Â the existence of the power law with a specific exponent does have a physical meaning and Dennis and I and the reviewers and the action editor skipped over that part, mainly because it was not relevant to our analysis.

AM: The meaning of the data should be relevant. Otherwise, well, you get meaningless results.Â

AM: You keep saying that, but everyone (and I mean everyone in all the papers on the power law that I’ve seen) already agrees with that!Â It is simply interesting that it was found in living systems and not in planets.Â

RM: In other words, whether or not a movement trajectory is found to follow the power law depends on properties of the trajectory itself, not on how that trajectory was generated (whether it was generated by a living system, a non-living system or a mathematical equation).

AM: You’d still need some math and experiments to prove the behavioral illusion, The behavioral illusion is not that trivial. If you say that the trajectory is the controlled variable, what would you correlate it with? What is the disturbance?

RM: The idea that the power law does tell you something about how the movement was generated is an example of a behavioral illusion, a fact that could have been seen without all the mathematical analysis but just from looking at the behavior (moving in curved trajectories, in this case) through control theory glasses.

[From Rick Marken (2017.11.26.1100)]

···

[Martin Taylor 2017.11.25.12.34]

``````MT: Of course, you might help your "cause" by redefining "behavioural
``````

illusion" as “side-effect” rather than the usual definition of it as
a misinterpretation of observations because of a failure to
recognize that observed effects depend on the environmental feedback
path between output and the environmental controlled variable rather
than on the details of internal processes so long as they control.
Saying “Behavioural Illusion” is just another name for “side-effect”
might be much easier.

``````MT: If you don't, then you would have to explain a fair amount of PCT to
``````

the EBR readership – which wouldn’t be a bad thing if done
correctly.Â

Â RM: Thanks for all the advice. I’ll try really hard to do it correctly, knowing PCT experts of your caliber will be watching;-)

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.â?
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery

[Martin Taylor 2017.11.26.17.40]

``````A pity you put the smiley there, because it would indeed be nice if
``````

you were to do it correctly. You only need to do two things to
produce a perfect rebuttal: (1) Show that your equation 2 is valid
only for the velocity recorded by equation 2, and (2) for the
Omitted Variable analysis, show that D, considered as an expression
on its own is not V*(function of spatial variables). Once you have done those two things, the rebuttal will be complete.
No more would be necessary. Without them, it will fail as science,
though perhaps it would still be useful as a public relations
exercise aimed at the mathematically challenged.
Just a bit of friendly advice.
Martin

···

On 2017/11/26 1:59 PM, Richard Marken
wrote:

[From Rick Marken (2017.11.26.1100)]

[Martin Taylor 2017.11.25.12.34]

``````            MT: Of course, you might help your "cause" by redefining
``````

“behavioural illusion” as “side-effect” rather than the
usual definition of it as a misinterpretation of
observations because of a failure to recognize that
observed effects depend on the environmental feedback
path between output and the environmental controlled
variable rather than on the details of internal
processes so long as they control. Saying “Behavioural
Illusion” is just another name for “side-effect” might
be much easier.

``````            MT: If you don't, then you would have to explain a fair
``````

amount of PCT to the EBR readership – which wouldn’t be
a bad thing if done correctly.

``````          RM: Thanks for all the advice. I'll try really hard to
``````

do it correctly, knowing PCT experts of your caliber will
be watching;-)

3

···

AM:

Right, my bad, I see it. Important issue, I agree.

AM:

Position is not unquestionably controlled, though. Position could be a side-effect of controlling something else, just like trajectory can be.

Hope you don’t rush your publication because you feel offended.

RM: Actually, we did mention that the average r2 fit of the power law to our data (pursuer and helicopter trajectories) is a bit over .9. But thanks for bringing this up. I’ll be sure to discuss the goodness of fit issue in the rebuttal even though I have not seen many discussions in the literature regarding what the “critical” r2 value is that would allow one to declare that the power law fits (or doesn’t fit) the data.

AM: I also notice you haven’t published r2 for any of the trajectories in your paper, and that is an important part of establishing the relationship.

RM: What is unquestionably controlled when people produce curved movements is the position of the moved entity (finger, cursor, etc) at each instant during the movement. The disturbance to this variable when a finger is moved in a curved trajectory, for example, is the varying effects of gravity as the arm and finger change their position in space. If the curved movement is that of a cursor on a computer screen then known disturbances can be applied at each point in the movement and it can be shown that the resulting cursor trajectory is produced by outputs (mouse movements) that follow a very different power law than the one that characterizes the resulting cursor trajectory.

RM: All this (and more) will be made clear in our rebuttal to Zago et al and Taylor et none (assuming they publish the latter, which I have no doubt they will).

[From Rick Marken (2017.11.27.1410)]

···

RM: I kind of agree. But it seems to me that, in order to control the other possible variables a person might be controlling when making curved (or any kind) of movements – variables such as the instantaneous velocity and curvature of the movement – you have to be controlling position as the means of controlling those variables. But these are empirical questions and it would take a very clever researcher to be able to tease out what variables are being controlled when people make curved (or other) movements, as in writing; a researcher who knows a lot about physics, mathematics and instrumentation. A researcher like you and Alex and everyone else in Alex’s lab.Â

RM: I don’t feel offended at all, certainly not by you. You have been a mensch. And, therefore, your comments have been very helpful in suggesting how I might frame my rebuttal and I will take take your advice and take my time on it.Â

AM: Position is not unquestionably controlled, though. Position could be a side-effect of controlling something else, just like trajectory can be.

AM: Hope you don’t rush your publication because you feel offended.

Best regards

Rick

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.â?
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery