Hi Rick, if this is the case:
log(V) = .33*log(D) + .33*log (R)
Shouldn't it be possible to know exactly what D is? D might be a value that is actually a composite of the effect of some other complex formulas to do with the kind of variables that Bruce, Martin and Alex are interested in?
Do you just fit the number to the data or can you specify what D will be in advance?
Warren
On 22 Aug 2016, at 00:24, Richard Marken <rsmarken@gmail.com> wrote:
log(V) = .33*log(D) + .33*log (R)
Hi Rick and Henry,
I agree with this and I agree with Rick’s assertion of this too and it fits with some papers in the literature who see the power law in movement merely as a side effect; surely we are trying to push the demonstration further by using PCT to prove it and prove the exceptions. I just think it needs to be shown from PCT models where the CV and the environment do not already contain patterned movement, and the exceptions should be demonstrated on this way too, maybe where certain conditions prevail. For example, Bill showed that the feedback function in the environment accounted for ‘reinforcement behaviour’ rather than the rat itself. I think Rick earlier stated that a similar thing could be going on here with viscosity. The feedback function is still part of the closed loop, just not part of the organism.
Warren
RM: I’m copying this from Henry Yin, with his permission, of course. I have copied Henry on a couple of these posts. He’s a busy guy but I’m thrilled that he took the time to send a reply.
On Sun, Aug 21, 2016 at 12:46 PM, Henry Yin, Ph.D. hy43@duke.edu wrote:
Hi Rick,
I don’t have access to CSG so you may forward my message.
I think this debate is important and interesting. I haven’t had time to follow the details closely, but I did take a look at the Lacquanti et al 1983 paper, which described the power law in some detail. The main conclusion is that angular velocity is
causally dependent on curvature. As the authors stated, curvature is considered the input to a dynamical system, whereas angular velocity its output. This is
wrong , based on incorrect assignment of input and output in systems analysis. Curvature cannot be an independent variable here. Analysis of the mathematical relationship between curvature and angular velocity will not tell us anything useful about the
properties of the system. I believe Bill’s major contribution to science is his elucidation of the behavioral illusion, and this is another good example of it. It reminds me of the more famous ‘matching law,’ another law based on misunderstanding. And
there must be other examples of this. So I think a good way to learn PCT is to train oneself on problems like these. Math is not the challenge here, but correctly identifying the components of the system before writing down the equations.
Henry
On Aug 20, 2016, at 5:00 PM, Richard Marken rsmarken@gmail.com wrote:
[From Rick Marken (2016.08.20.1400)]
–
BA: It would also be nice to hear from anyone else who has been attempting to follow along in this discussion of the power law, on CSGnet or otherwise. At present I have no idea whether anyone is even interested in having this discussion
continued, let alone whether anyone has formed an opinion based on it.
RM: Thanks Henry. It’s a relief to know that there is at least one person around who can carry the PCT torch when I am gone.
Best
Rick
Bruce Abbott (2016.08.20.1130 EST)
BA: Throughout my recent exchanges with Rick on the power-law issue I have assumed that Rick simply did not understand the serious deficiencies in his analysis…
BA: When Alex Gomez-Marin came to CSGnet for help with a scientific problem, here was an opportunity to show a practicing scientist (a physicist with training in neuroscience no less!) what PCT might offer by way of a solution or at least
a start toward a solution. Rick quickly responded with his “solution,� which Alex immediately noted is seriously flawed as it is based on a misconception of what the equation for computing the radius of curvature actually does.
RM: Alex is a very nice guy. I like him very much. I had a very cordial email (and Skype) exchange with Alex before the power law explosion. I knew that the PCT explanation of the power law would be very controversial. So before I posted about it to CSGNet
I wrote to Alex privately saying that I did have the PCT explanation of the power law and that it would be very disturbing to the power law community So I asked Alex if it would it be ok with him if I posted it to CSGNet anyway and he said yes. I didn’t go
into details about what the PCT explanation was but I thought Alex might be excited by it and I invited him to be co-author on the paper I would write describing it. I assumed that a young, smart and ambitious researcher like Alex would jump at the chance
to show that 40+ years of research on movement control was based on an illusion.
RM: But obviously my assumption was all wrong. Alex didn’t get excited about the PCT explanation of the power law – not in a good way, anyway;-) – and I don’t blame him. Alex is just starting his career and success in that career will not be achieved
by basically insulting those who can promote that career.
RM: Bill Powers often said that PCT is revolutionary. He meant that it is theoretically revolutionary because it explains behavior in a way that is the exact opposite of the way it is explained by conventional psychology: as control of input rather than control of output. But he also meant that it is
practically revolutionary because it challenges those in positions of power in the academic establishment, particularly those in the psychology/ neuroscience establishment. If PCT is right, then many of the textbooks and the leading scientists in the
field are all wrong.
RM: The practical consequences of a PCT revolution are similar to those of any social revolution; it will cost careers, status, and (most importantly) money. This is why the PCT revolution has not happened and will not happen for quite some time. It will
have to be a PCT evolution, as more people like Henry Yin navigate their way through the conventional programs of academia, get “certified” by the establishment (with tenure, for example) and then start doing and publishing research based on PCT.
BA: I can’t speak for Martin, but I was appalled to find Alex quite rightfully angered at Rick’s refusal to listen, and withdrawing from CSGnet in frustration.
RM: I listened and I never withdrew from the CSGNet discussion. I withdrew (and then un-withdrew) from LCS IV, not CSGNet. I withdrew from LCS IV for the reasons given in my post; I didn’t want to be associated with a work on PCT that would contain many
articles that are based on the very misconceptions about the nature of the behavior that Bill spent his entire professional career trying to dispel. I un-withdrew because Henry Yin pointed out that the contributors to
LCS IV were selected by Bill. So apparently Bill was willing to have non-PCT stuff published in the volume honoring him since he knew that many of the people he wanted as contributors were still mired in an S-R view of behavior.
BA: I hoped that if I could explain Alex’s critique clearly enough to Rick, he would finally see that he was committing a serious error. Then, perhaps, we could get back to the problem Alex had originally asked for help with.
RM: The problem Alex had asked for help with was a PCT explanation of the power law. I have provided it. I believe you don’t accept it for the reasons I gave at the end of my last post to Martin. I think you believe that the power law describes a stimulus-response
relationship between curvature (measured as R or C) and velocity (measured as V or A). All of your “explaining” of why my PCT explanation of the power law is wrong has been aimed at showing that measures of curvature and velocity are two independent measures
of the trajectory of a movement. these measures would have to be independent order for curvature to be considered an independent variable that is the cause of (or “constraint” on) the dependent variable, velocity. My analysis is based on the observation that
curvature and velocity are not independent measures of movement trajectory. This drives you nuts because it blows your S-R view of the power law out of the water.
RM: All of your efforts to cast the power law in S-R terms has obscured the fact that power law research is aimed at understanding how organisms make voluntary movements. And we already have a model of how organisms do that; it’s called PCT. It explains
voluntary movement as the control of perception. The model of voluntary movement that I posted (and post again, correcting a couple of little errors) is the PCT model of how people produce voluntary movement trajectories.
<image.png>
RM: So when Alex asked for a PCT explanation of the power law, this model should have popped into your mind. And then you would ask yourself (as I asked myself) where would the power law fit into this model. It doesn’t fit in with the output functions
(o.x and o.y) since the power law is only based on measures of the controlled variable (the movement trajectory, which is temporal variations in qi.x, qi.y). And, for the same reason, it doesn’t fit in with the feedback functions, kf.x, kf.y. So then you would
realize (as I did) that the power law is an observed relationship between two different variable characteristics of the controlled variable (the movement trajectory) itself!!
RM: So without the need for any mathematics, a knowledge of the PCT model of voluntary movement would lead you to see that the relationship between curvature and velocity that is observed in power law research has nothing to do with what power law researchers
think it’s about – how movement trajectories are produced. The relationship between measures of curvature and velocity that is observed in power law research can depend only on the nature of the movement trajectory that is produced, not on how it is produced.
RM: But then why is the observed relationship between curvature and velocity so often close to a 1/3 or 2/3 power relationship? That question might lead you (as it led me) to look at the equations that define the two measures of the controlled variable
– curvature and velocity – that are used in the study of movement control by power law researchers. And what I saw is that these equations do not measure independent aspects of the controlled variable; they measure aspects of the controlled variable that
are mathematically dependent. And the dependence is expressed this way:
V = D1/3 *R1/3
and
A = D1/3 *C 2/3
where D = |dXd2Y-d2XdY|
RM: This was a stunning discovery since the power coefficient of R is 1/3 and the power coefficient of C is 2/3, the very power coefficients that are typically found for these variables in power law research. This seemed like more than a coincidence. And
it’s not. Since the power law is determined using linear regression of log(R) on log(V) and log(C) on log (A) I realized that researchers would find a power coefficient close of 1/3 when regressing log(R) on log(V) and 2/3 when regressing log(C) on log(A)
to the extent that the variance in log (D) for a particular movement trajectory is close to being constant.
BA: It has turned out to be an exercise in futility.
RM: It’s futile, Bruce, because you think movement trajectories are generated by an S-R process (curvature constrains velocity) and I think they are the result of the control of perception (making perception match a possibly varying internal reference
for the state of that perception). As I said above, you could have made the same discovery I did about the power law (that it says nothing about how movement trajectories are generated), without even having to do any math, if you had just understood that voluntarily
produced movement trajectories are the control of perception (per the PCT model above).
BA: If Rick wants to have an honest discussion of his proposal from a scientific point of view, I’m still willing.
RM: That’s great. I’ll go at this as long as you want. And it seems that others are interested in this too. So let’s keep at it. I agree that my finding about the power law is a pretty awful one from the point of view of a conventional psychologist. So
I expect you and Martin to fight it tooth and nail. But there may be some out there who are willing to see the PCT perspective and are not afraid of the revolutionary conclusions that come from looking at behavior through control theory glasses.
BA: That discussion would begin by addressing the criticism that including log D in the regression does nothing more than reveal the equation by which V and D are used to compute the radius of curvature.
RM: OK, I address it by saying that what you say here is a fair way of describing what including log D in the regression does. The only reason I include the regressions with log (D) in my spreadsheet analysis is to show that when you leave it out your
estimate of the power coefficient will deviate from 1/3 (or 2/3) depending on how much log(D) deviates from a constant in the particular movement trajectory that you are analyzing. But this is something that could only be appreciated my multiple regression
mavens.
BA: This exchange might be followed by Rick demonstrating that he understands why using sines and cosines to draw an ellipse enforces movements in which tangential velocity of the point around the ellipse speeds up in the straighter sections
and slows in the sharper curves, thus necessarily producing a relationship between log velocity and log R that conforms to the power law. (Rick’s latest spreadsheet, in which one attempts to keep a small circle inside a larger one that is tracing an ellipse
in this way, enforces this relationship in the motion of the target and, to the extent that the small circle stays within the larger one, the small circle’s as well.)
RM: I already answered this in my reply to Martin in another thread. But here we go again: The idea that an elliptical trajectory “enforces” the 1/3 power relationship between R and V (and 2/3 between C and A) is exactly what my analysis of the situation
predicts.Indeed, the more perfectly your cursor tracks the ellipse, the closer the estimate of beta will be to .33 (for V vs R) or .67 (for C vs A). What is interesting about the demo is that these elliptical movement trajectories are produced by outputs
(mouse movements) that are not very elliptical (due to the disturbances), which is just another proof that the power law that is found for voluntarily produced movement trajectories says nothing about how these trajectories are produced; PCT explains how
they are produced: it’s control of perception.
BA: In fact, it would be nice if Rick could provide a clear explanation for why he believes that the tangential velocity with which a path is traced is not relevant with respect to finding a power-law relation.
RM: I never said that the tangential velocity (V) with which a path is traced is not relevant with respect to finding a power-law relation. It obviously is relevant. It’s the dependent variable in the power law relationship.
BA: If Rick refuses this challenge, it will demonstrate his disinterest in understanding his critics.
RM: I think I answered your challenge. Now how about answering mine: how do you explain the power law?
BA: Repeating the mantra that the data produced by his model “conform to the power law� and thus “prove� his model to be correct (they do no such thing, for reasons already explained) will be counted as unresponsive.
RM: So I’m unresponsive if I show that my model accounts for the data? Seems kind of unscientific. Anyway, the fact that the model fits the data doesn’t “prove” that the model is correct. It just increases one’s confidence in the model. If you don’t think
my model is correct I believe it now behooves you to describe a test that would lead to rejection of the model. And it would help a lot if you would show me your model of the power law so that I can see what you think is going on. I’ve asked you and Martin
to tell me what you think the power law shows – which is basically asking for your mental model of why there is a power relationship between the velocity and curvature of a movement trajectory – but I still have gotten no response. So apparently unresponsiveness
is not unique to me;-)
BA: It would also be nice to hear from anyone else who has been attempting to follow along in this discussion of the power law, on CSGnet or otherwise. At present I have no idea whether anyone is even interested in having this
discussion continued, let alone whether anyone has formed an opinion based on it.
RM: On this, I heartily agree. But we do know that there are apparently a couple others who are very interested in this discussion but don’t feel like joining in. But it would be nice to hear what others think is going on.
Best
Rick
Richard S. Marken
“The childhood of the human race is far from over. We have a long way to go before most people will understand that what they do for others is just as important to their well-being as what they do for themselves.” – William T. Powers
–
Richard S. Marken
“The childhood of the human race is far from over. We
have a long way to go before most people will understand that what they do for
others is just as important to their well-being as what they do for
themselves.” – William T. Powers
[Martin Taylor 2016.08.22.07.34]
Yes, we know what D is. It's V/R in the equation V =
D1/3*R1/3, where “V” is the formal so-called “velocity” vaiable and
R is the radius of curvature. The equation says
log(V) = log(V) + 0.33logR - 0.33log(R)
or
log(V) = log(V)
You have to specify V in advance and therefore D, in order to
legitimize the initial division of the expression for R (D/V)
from which the equation is derived. So although V is quite
arbitrary, it determines D once you have a radius of curvature.
Martin
On 2016/08/22 4:49 AM, Warren Mansell
wrote:
Hi Rick, if this is the case: log(V) = .33*log(D) + .33*log (R) Shouldn't it be possible to know exactly what D is? D might be a value that is actually a composite of the effect of some other complex formulas to do with the kind of variables that Bruce, Martin and Alex are interested in?
3
Do you just fit the number to the data or can you specify what D will be in advance?
3
WarrenOn 22 Aug 2016, at 00:24, Richard Marken wrote: log(V) = .33*log(D) + .33*log (R)
OK thanks Rick!
On Mon, Aug 22, 2016 at 12:41 PM, Martin Taylor mmt-csg@mmtaylor.net wrote:
[Martin Taylor 2016.08.22.07.34]
On 2016/08/22 4:49 AM, Warren Mansellwrote:
Hi Rick, if this is the case: log(V) = .33*log(D) + .33*log (R) Shouldn't it be possible to know exactly what D is? D might be a value that is actually a composite of the effect of some other complex formulas to do with the kind of variables that Bruce, Martin and Alex are interested in?Do you just fit the number to the data or can you specify what D will be in advance?WarrenOn 22 Aug 2016, at 00:24, Richard Marken <rsmarken@gmail.com> wrote: log(V) = .33*log(D) + .33*log (R)Yes, we know what D is. It's V<sup>3</sup> /R in the equation V =D1/3*R1/3, where “V” is the formal so-called “velocity” vaiable and
R is the radius of curvature. The equation sayslog(V) = log(V) + 0.33logR - 0.33log(R) or log(V) = log(V) You have to specify V in advance and therefore D, in order tolegitimize the initial division of the expression for R (D/V3 )
from which the equation is derived. So although V is quite
arbitrary, it determines D once you have a radius of curvature.Martin
–
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
Tel: +44 (0) 161 275 8589
Website: http://www.psych-sci.manchester.ac.uk/staff/131406
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
[Martin Taylor 2016.08.22.10.47]
OK thanks Rick!
You can thank Rick for defining D as V<sup>3</sup> /R, which he did
when first announcing the behavioural illusion, but you shouldn’t
thank him for answering your question, showing that the equation
log(V) = .33log(D) + .33log(R)
translates to
log(V) = log(V),
because he never has acknowledge that it is so, nor that it is a
tautology. He even now uses it as a way of relating V to curvature
(1/R).
That's the kind of "normal science" -- basic mathematics -- that I
have observed Rick to dismiss as irrelevant to PCT on so many
occasions.
Martin
On Mon, Aug 22, 2016 at 12:41 PM,
Martin Taylor mmt-csg@mmtaylor.net
wrote:
[Martin Taylor 2016.08.22.07.34]
On 2016/08/22 4:49 AM, Warren Mansell wrote:
Hi Rick, if this is the case: log(V) = .33*log(D) + .33*log (R) Shouldn't it be possible to know exactly what D is? D might be a value that is actually a composite of the effect of some other complex formulas to do with the kind of variables that Bruce, Martin and Alex are interested in?Do you just fit the number to the data or can you specify what D will be in advance?WarrenOn 22 Aug 2016, at 00:24, Richard Marken <rsmarken@gmail.com> wrote: log(V) = .33*log(D) + .33*log (R)Yes, we know what D is. It's V<sup>3</sup> /R inthe equation V = D1/3*R1/3, where “V” is the formal
so-called “velocity” vaiable and R is the radius of
curvature. The equation sayslog(V) = log(V) + 0.33logR - 0.33log(R) or log(V) = log(V) You have to specify V in advance and therefore D,in order to legitimize the initial division of the
expression for R (D/V3 ) from which the equation
is derived. So although V is quite arbitrary, it
determines D once you have a radius of curvature.Martin
–
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
Tel: +44 (0) 161 275 8589
Website: [http://www.psych-sci.manchester.ac.uk/staff/131406](https://urldefense.proofpoint.com/v2/url?u=http-3A__www.psych-2Dsci.manchester.ac.uk_staff_131406&d=CwMFaQ&c=8hUWFZcy2Z-Za5rBPlktOQ&r=-dJBNItYEMOLt6aj_KjGi2LMO_Q8QB-ZzxIZIF8DGyQ&m=6d2qhytkOw3PC4HSdjnLdPLVnxviUDPPJ4AEpUU4TFg&s=7elwCq0k5bMjj83n_4rYvmeeLd0KAgR2jcPZt5Qmkx0&e=)
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](https://urldefense.proofpoint.com/v2/url?u=http-3A__www.pctweb.org&d=CwMFaQ&c=8hUWFZcy2Z-Za5rBPlktOQ&r=-dJBNItYEMOLt6aj_KjGi2LMO_Q8QB-ZzxIZIF8DGyQ&m=6d2qhytkOw3PC4HSdjnLdPLVnxviUDPPJ4AEpUU4TFg&s=dt-cWgElQa69kVGSJ7gD4WTI3mfJntOG6MW5fEFLQAo&e=)
for further information on
Perceptual Control Theory