Invariances as Side Effects of Control

[Bruce Nevin (2017.07.14.1844 ET)]

So these would be examples of aspects of the (perceived) environment that are stabilized by control but not controlled. It doesn’t resolve the discussion whether environment variables corresponding to the controlled perception are stabilized (Kent’s preference) or controlled (your preference), but it does introduce a different sort of distinction to that discussion.

···

On Fri, Jul 14, 2017 at 3:50 PM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.07.14.1250)]

RM: Most of the debates we’ve been having on CSGNet for the last few years since Bill Powers passed away are repeats of debates that have occurred since the beginning of CSGNet. One debate that that did seen completely new was the one over the power law of movement. But by chance I found a 1995 CSGNet post from Bill that, though not specifically about the power law, is about a phenomenon  that is very much like the power law –  tangential velocity profiles.Â

RM: Like the power law of movement, which has a nearly invariant power coefficient of 1/3 or 2/3 (depending on how the variables are measred), the shape of tangential velocity profiles is found to be nearly invariant across different movement trajectories. And also like the power law, the invariance of these profiles is thought to reveal something important about the fundamental biological and/or kinematic constraints on how organisms produce these different movement trajectories. As Bill put it in the beginning of his post about these tangential velocity profiles:

BP: In a great
deal of modern behavioral research, trajectories of movement
are
examined in the hope of finding invariants that will reveal secrets
of
behavior. This approach ties in with system models that compute
inverse
kinematics and dynamics and use motor programs to produce
actions
open-loop…

RM: So both the power law and tangential velocity profiles are measures of invariant characteristics of movement trajectories that are thought to “reveal secrets” of how movement trajectories are produced. Therefore, it’s not surprising that what Bill says about tangential velocity profiles in his 1995 post, is the largely same as what I (and my co-author) say about the power law in  Marken, R. and Shaffer, D. (2017)
The Power Law of Movement: An Example of a Behavioral Illusion, Experimental Brain Research, 235,
1835–1842).Â

RM: I’ve attached Bill’s post on tangential velocity profiles to this post as a  WORD document and highlighted in italics the parts of his discussion of these profiles that are most relevant to our discussion of the power law. I’ve also added footnotes to these italicized sections that contain quotes or refer to topics in our power law paper that mirror Bill’s discussion of the tangential velocity profiles.

RM: Some things to note if you read the attached post: Bill sees the invariance of tangential velocity profiles in the same way we see the invariance of the power law of movement; as an irrelevant side-effect of controlling. In both cases, evidence that these invariances are side-effects come from the fact that a control model produces movement trajectories with invariant tangential velocity profiles and power law coefficients without considering tangential velocity profiles or power law coefficients. Also, Bill says that research aimed at finding these invariants is going down a “blind alley”. We  implied the same thing by saying that power law researchers were succumbing to a behavioral illusion.Â

RM: The only difference between Bill’s analysis of the invariance of tangential velocity profiles and our analysis of the invariance of the power law coefficients is that we were lucky enough to find a simple explanation for the observed invariance of the power law coefficient.Â

RM: Anyway, I just thought it would be interesting to note that we had discussed an invariance of movement trajectories (in the form of tangential velocity profiles) and the PCT explanation of them was the same as my PCT explanation of the them (in the form of the power law): side effects of control.

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

[From Rick Marken (2017.07.14.1250)]

RM: Most of the debates we’ve been having on CSGNet for the last few years since Bill Powers passed away are repeats of debates that have occurred since the beginning of CSGNet. One debate that that did seen completely new was the one over the power law of movement. But by chance I found a 1995 CSGNet post from Bill that, though not specifically about the power law, is about a phenomenon  that is very much like the power law –  tangential velocity profiles.Â

RM: Like the power law of movement, which has a nearly invariant power coefficient of 1/3 or 2/3 (depending on how the variables are measred), the shape of tangential velocity profiles is found to be nearly invariant across different movement trajectories. And also like the power law, the invariance of these profiles is thought to reveal something important about the fundamental biological and/or kinematic constraints on how organisms produce these different movement trajectories. As Bill put it in the beginning of his post about these tangential velocity profiles:

BP: In a great
deal of modern behavioral research, trajectories of movement
are
examined in the hope of finding invariants that will reveal secrets
of
behavior. This approach ties in with system models that compute
inverse
kinematics and dynamics and use motor programs to produce
actions
open-loop…

RM: So both the power law and tangential velocity profiles are measures of invariant characteristics of movement trajectories that are thought to “reveal secrets” of how movement trajectories are produced. Therefore, it’s not surprising that what Bill says about tangential velocity profiles in his 1995 post, is the largely same as what I (and my co-author) say about the power law in  Marken, R. and Shaffer, D. (2017)
The Power Law of Movement: An Example of a Behavioral Illusion, Experimental Brain Research, 235,
1835–1842).Â

RM: I’ve attached Bill’s post on tangential velocity profiles to this post as a  WORD document and highlighted in italics the parts of his discussion of these profiles that are most relevant to our discussion of the power law. I’ve also added footnotes to these italicized sections that contain quotes or refer to topics in our power law paper that mirror Bill’s discussion of the tangential velocity profiles.

RM: Some things to note if you read the attached post: Bill sees the invariance of tangential velocity profiles in the same way we see the invariance of the power law of movement; as an irrelevant side-effect of controlling. In both cases, evidence that these invariances are side-effects come from the fact that a control model produces movement trajectories with invariant tangential velocity profiles and power law coefficients without considering tangential velocity profiles or power law coefficients. Also, Bill says that research aimed at finding these invariants is going down a “blind alley”. We  implied the same thing by saying that power law researchers were succumbing to a behavioral illusion.Â

RM: The only difference between Bill’s analysis of the invariance of tangential velocity profiles and our analysis of the invariance of the power law coefficients is that we were lucky enough to find a simple explanation for the observed invariance of the power law coefficient.Â

RM: Anyway, I just thought it would be interesting to note that we had discussed an invariance of movement trajectories (in the form of tangential velocity profiles) and the PCT explanation of them was the same as my PCT explanation of the them (in the form of the power law): side effects of control.

BestÂ

Rick

Powers power law relevant post.docx (28.3 KB)

···


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 (2017.07.15.1020)]

Bruce Nevin (2017.07.14.1844 ET)

BN: So these would be examples of aspects of the (perceived) environment that are stabilized by control but not controlled.

RM: No, these “invariants” are neither controlled nor stabilized. They are simply mathematical regularities in certain aspects of the behavior of a control system.Â

RM: Tangential velocity profiles are plots of the tangential velocity of a curved movement trajectory as a function of the time over which the movement is made. These plots are “normalized” to take into account differences in the magnitude (extent) and duration of a set of different movements. What is invariant is the shape of this normalized plot over the different movements. A more detailed description of how tangential velocity profiles are computed and determined to be invariant can be found in the Atkeson & Hollerback (1985) article referred to in Powers’ post:Â

https://www.dropbox.com/s/qx27ow5je28qwk1/arm_movements.pdf?dl=0

···

RM: Evidence that the invariance of these tangential velocity profiles is a side-effect of control is provided in Powers’ post where he says:Â

RM: That is, Bill showed that the invariance of tangential velocity profiles found in human movements by Atkeson and Hollerback is also found when the same movements are made by a model of a control system (the “Little Man” demo) that is not controlling for keeping tangential velocity invariant.Â

RM: The power law of movement, like the tangential velocity profile, refers to a mathematical regularity that has been observed in curved movement trajectories. The power law is a power relationship between measures of the instantaneous curvature and velocity during a curved movement. What is invariant about the power law (what makes it a “law”) is the shape of this relationship (power function) and, to some extent, the value of the power coefficient over the different movements (1/3 or 2/3, depending on how curvature and velocity are measured). A more detailed description of how the power law of movement is computed and determined to be invariant can be found in Marken & Shaffer (2017):

https://www.dropbox.com/s/g3tcy8p46c957f7/MarkenShaffer2017.pdf?dl=0

RM: In that paper you will see that we determine that the invariance of the power law is a side-effect of control in exactly the same way Powers determined that the invariance of tangential velocity profiles are a side-effect of control. The relevant  quote from our paper is: “The [control] model [like the Little Man] achieved this level of accuracy
without any attempt to produce trajectories that followed a power law”. Â

Â

BN: It doesn’t resolve the discussion whether environment variables corresponding to the controlled perception are stabilized (Kent’s preference) or controlled (your preference), but it does introduce a different sort of distinction to that discussion.

RM: I don’t think there is a way to resolve this empirically. The idea that environmental variables are “stabilized” while the perceptions corresponding to those variables are controlled is simply a misunderstanding of how the PCTmodel works. Environmental variables are not controlled in the PCT model; aspects (functions) of those variables are controlled. The aspects of the environment that are controlled are defined by the perceptual function of the control system. The perceptual variables that are controlled are the outputs of these perceptual functions. So when a perceptual variable (the perceptual signal, p) is controlled, the (variable) aspect of the environment that corresponds to this perceptual variable is also controlled. That’s just the way the model works. There is no difference at all between the perceptual variable that is controlled and the aspect of the environment that is controlled.Â

RM: As I said, I don’t think I will be able to disabuse people of the idea that perceptions are controlled and the environmental correlate of these perceptions are just “stabilized”. It’s probably one of those Zombie ideas, like “trickle down economics”, that won’t die, probably because it serves some other purpose for the people who believe in it. Since the “controlled perception/stabilized environment” zombie is not nearly as destructive as the “trickle down” I’ll try to let it go. As I said, it’s been around since the beginning of CSGNet and if Bill couldn’t kill it I certainly won’t be able to.Â

Best

Rick

Â

/Bruce


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 Fri, Jul 14, 2017 at 3:50 PM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2017.07.14.1250)]

RM: Most of the debates we’ve been having on CSGNet for the last few years since Bill Powers passed away are repeats of debates that have occurred since the beginning of CSGNet. One debate that that did seen completely new was the one over the power law of movement. But by chance I found a 1995 CSGNet post from Bill that, though not specifically about the power law, is about a phenomenon  that is very much like the power law –  tangential velocity profiles.Â

RM: Like the power law of movement, which has a nearly invariant power coefficient of 1/3 or 2/3 (depending on how the variables are measred), the shape of tangential velocity profiles is found to be nearly invariant across different movement trajectories. And also like the power law, the invariance of these profiles is thought to reveal something important about the fundamental biological and/or kinematic constraints on how organisms produce these different movement trajectories. As Bill put it in the beginning of his post about these tangential velocity profiles:

BP: In a great
deal of modern behavioral research, trajectories of movement
are
examined in the hope of finding invariants that will reveal secrets
of
behavior. This approach ties in with system models that compute
inverse
kinematics and dynamics and use motor programs to produce
actions
open-loop…

RM: So both the power law and tangential velocity profiles are measures of invariant characteristics of movement trajectories that are thought to “reveal secrets” of how movement trajectories are produced. Therefore, it’s not surprising that what Bill says about tangential velocity profiles in his 1995 post, is the largely same as what I (and my co-author) say about the power law in  Marken, R. and Shaffer, D. (2017)
The Power Law of Movement: An Example of a Behavioral Illusion, Experimental Brain Research, 235,
1835–1842).Â

RM: I’ve attached Bill’s post on tangential velocity profiles to this post as a  WORD document and highlighted in italics the parts of his discussion of these profiles that are most relevant to our discussion of the power law. I’ve also added footnotes to these italicized sections that contain quotes or refer to topics in our power law paper that mirror Bill’s discussion of the tangential velocity profiles.

RM: Some things to note if you read the attached post: Bill sees the invariance of tangential velocity profiles in the same way we see the invariance of the power law of movement; as an irrelevant side-effect of controlling. In both cases, evidence that these invariances are side-effects come from the fact that a control model produces movement trajectories with invariant tangential velocity profiles and power law coefficients without considering tangential velocity profiles or power law coefficients. Also, Bill says that research aimed at finding these invariants is going down a “blind alley”. We  implied the same thing by saying that power law researchers were succumbing to a behavioral illusion.Â

RM: The only difference between Bill’s analysis of the invariance of tangential velocity profiles and our analysis of the invariance of the power law coefficients is that we were lucky enough to find a simple explanation for the observed invariance of the power law coefficient.Â

RM: Anyway, I just thought it would be interesting to note that we had discussed an invariance of movement trajectories (in the form of tangential velocity profiles) and the PCT explanation of them was the same as my PCT explanation of the them (in the form of the power law): side effects of control.

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