Got Ideas?

[Alex_Gomez-Marin]

rick, seriously, do you intend to create more noise than signal, or is it just by chance? if you had reac my first emails when i had the patience to answer to tou bit by bit, while you were high on adrenaline imagining you were going to be the next revolutionary that would change the world by denouncing all behavioral illusions… you would know what you are asking now!!? anyways:

1. very very grave that you still use letters on axis, without phenomenologically thinking and feeling what they are an how they make sense. V is not V, it is V/R=A, in the y axis. it told you that!! so, yes, everyone slows down at higher curvature

2. if you don’t like the name power-law because nothing can be a law dictating anyhthing to an organism becauae of this obsession with freedom that pct stems from, then call it a power-function.

if you are serious about the question, read whitehead’s adventures of ideas, chapters on laws of nature.

3. the law is a constraint; or the law refelcts a constraint on movement. because it shows empirically that kinematics is bound by geometry in a particular ways. once we know where the law comes from, we should be sble to say where that constraint emerges from.

···

On Fri, Aug 26, 2016 at 2:28 PM, Chad T. Green Chad.Green@lcps.org wrote:

[From Chad Green (2016.08.26.1728)]

Â

We appear to be stuck in a double bind, an everyday occurrence which according to Gregory Bateson represents the conflict between different logical types, i.e.,
the information communicated through semiotics (“you can criticize meâ€?) and that which is communicated through actions or metacommunication (“your criticism is unwelcomeâ€?).Â

Â

According to Deleuze and Guattari (1983) double binds are undecidable “until we do away with both the problem and the solution� altogether and instead aim for
constant evolution (becomings or plateaus of intensity). Otherwise schisms such as what we now have are inevitable (i.e., schismogenesis). Food for thought.

Â

Best,

Chad

Â

Chad T. Green, PMP

Research Office

Loudoun County Public Schools

21000 Education Court

Ashburn, VA 20148

Voice: 571-252-1486

Fax: 571-252-1575

Â

“We are not what we know but what we are willing to learn.� - Mary Catherine Bateson

Â

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Thursday, August 25, 2016 6:13 PM
To: csgnet@lists.illinois.edu
Subject: Re: Got Ideas?

Â

[From Rick Marken (2016.08.25.1510)]

Â

On Thu, Aug 25, 2016 at 1:18 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: what an elegant way, dear rick, to retire for a while from the spread-shit power-law discussion, than suggesting that nobody but you in the csgNet can have ideas. bravo!

Â

RM:I didn’t mean to imply that nobody but me on CSGNet can have ideas. I just predicted that, since I have now left the power law discussion, there wouldn’t be any ideas forthcoming in answer to your question about why
or how the control of perception may give rise to the power law. I did say that to be provocative because I would like to hear how others would answer your question (note that I said that I hoped my prediction would be wrong) but also because I would like
to hear something other than that my ideas are all wrong. I would like to know what ideas people think are right:Â why or how might the control of perception (PCT) give rise to the power law? Inquiring minds want to know;-)

Â

Best regards

Â

Rick

On Thursday, 25 August 2016, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.08.25.1015)]

Â

Rick Marken (2016.08.24.0850)

Â

RM: What I think would be most productive now would be for me to drop out of this discussion of the power law. This should certainly resolve the conflict over the power law.Â

Â

RM: What I suggest is that we hit the reset button and start all over from your initial question, but without me in the mix. Your initial question, Alex, was excellent:

Â

AGM: Any ideas why or how “the control of perception” may give rise to this power law constraining geometry and kinematics in humans, and now in fruit fly larvae?

http://biorxiv.org/content/early/2016/07/05/062166

Â

RM: Now that I am no longer in this discussion, I predict that there will be no ideas forthcoming in answer to Alex’s question. Silence will prevail, showing that it was all about trying to show that my idea is wrong rather than showing
that their idea is right; because I believe they have no idea.Â

Â

RM: I hope my prediction is as wrong as they think my analysis is.

Â

BestÂ

Â

Rick

–

Richard S. MarkenÂ

“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

Â

–

Richard S. MarkenÂ

“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. MarkenÂ

“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

[MartinT]

[Martin Taylor 2016.08.27.09.04]

[Martin Taylor 2016.08.27.00.28]

[From Kent McClelland (2016.26.1100)]

Hi Alex,

      Well, I have an idea, although I won’t be offended

if you tell me it’s hopelessly naive. And, I’m sorry to say,
it does involve a spreadsheet simulation (mine, not Rick’s).

…
I have no idea whether this control-system output
conforms to the power law, but i would argue that it shows how
the velocity of controlled movement must to slow down through
sharp turns (and presumably tight curves, as well), in order
for the control systems to maintain control of their
perceptions.Â

      My spreadsheet is attached, so anyone who wants to

can check my calculations, (and tell me where Iâ€ââ„¢m going
wrong!).Â

  I didn't do more than a cursory scan of your calculations, but

assuming they are correct, I thought it would be interesting to
make a scattergram of log radius of curvature vs. log velocity…

I really shouldn't try to think too hard just before going to bed!

Of course the limiting speed is that of the constant-speed reference
track. The interesting point is the slowdown around curves where the
control system can’t follow the infinite curvature at the track
corners.

Here are four scatterplots from McClelland's spreadsheet, with two

different lags and two different gain rates (including the one I
posted last night. All of them conform to V = R0.2 reasonably well
so long as the velocity is not limited by the reference velocity.

![icibhpmjdenhaijd.jpg|707x652](upload://jtKFGINaFbJpHUjgXrPFH5eIEXl.jpeg)

The slope is rather close to 0.2 for all the parameter settings. I

don’t know what this means in relation to the 0.33 power law found
so often or the 0.25 power law found for the fly larva and the
finger drawing in water. Perhaps it’s a sign that McClelland’s
controlled variable (perceived deviation from track y value) is not
the one controlled by subjects in the studies? Either way, it’s an
interesting result.

Martin

[Kent]

[From Kent McClelland (2016.08.27.1530)]

Here’s one more simulation to consider. Using Martin’s version of the spreadsheet (in which the calculations look OK to me, Martin, but as I say, I’m no expert on the equations), tried a different kind of simulation. Instead of a preset path for
the control system to follow (as specified by a vector of XY references), I set the references to zero and introduced a smoothly varying XY disturbance vector. The first simulation I shared had had the XY disturbances set to zero.

This change to a random disturbance removed the constant-speed effect of the preset path, because the distance traveled by the disturbance vector changes randomly at each iteration (with the distances more or less normally distributed). And the
other important change is that the control system in this version is controlling for tracking smooth curves instead of sharp angles.

Here is the disturbance vector I used:

PastedGraphic-5.pdf (29.1 KB)

ATT000012.htm (56 Bytes)

PastedGraphic-6.pdf (28.1 KB)

ATT000021.htm (56 Bytes)

PastedGraphic-7.pdf (26.7 KB)

ATT000031.htm (56 Bytes)

PastedGraphic-8.pdf (17.3 KB)

ATT000041.htm (56 Bytes)

ATT00005.htm (55 Bytes)

McClellandXY POWER-LAW SIMULATIONS (version 2).xlsx (142 KB)

ATT00006.htm (55 Bytes)

[rsmarken]

[From Rick Marken (2016.08.27.1340)]

This is just too much fun; I can’t stay out of this any more than I can stop eating ice cream.Â

Kent McClelland (2016.26.1100)–

KM: If I understand the power-law articles that I’ve looked at, the phenomenon to be explained is that when an organism is making a controlled motion, the speed of movement decreases as the curves get tighter or the angles to be negotiated get sharper, in a fashion that’s described by the so-called power law.

RM: Not quite. The phenomenon to be explained is the power law itself: the tendency for the relationship between measures of curvature and velocity to be fit by a power function with a coefficient of 1/3 (for measures of curvature and velocity in terms of R and V) or 2/3 (for measures of curvature and velocity in terms of C vs A) for some movement trajectories.

KM: The particular model I’ve played around with involves angles, rather than curves, for the sake of providing a clear demonstration of the principle, but I’m guessing the same principle is at work for curves, as well.Â

RM: Excellent! Your model is exactly the same as mine! It’s PCT! The variations in movement produced by your model are produced as they are in my model: by temporal variations in the reference signals going to the systems controlling movement in the X and Y dimensions. Here’s a spatial (X.Y coordinates) picture of the movement produced by your model:

RM: And here’s the temporal picture (the red line is movement in the X dimension).Â

RM: I did an analysis of this movement and got the following results:

RM: For velocity and curvature measured as V vs R, the power coefficient, beta = .12 Â and R^2= .59

RM: [Martin computed V and R somewhat differently than I did. When I use his measures of V and R in a regression I get beta = .10 and R^2 = .77.]

RM: For For velocity and curvature measured A vs C, beta = .88 and R^2 = .99.

RM: So the power relationship between curvature and velocity fits better when curvature is measured as C and velocity is measured as A; but the beta value for the A vs C relationship is .88, which is pretty far from .67 (the 2/3 power “law”). The explanation of this “violation” of the power law (according to my analysis is that in the particular movement trajectory produced by your model (the one seen above) the co-variance between C and the variable omitted from the regression, D, is quite large relative to the variance of C. The ratio of co-variance between C and D to the variance of C determines the “omitted variable bias” (OVB) – the  degree to which the observed power coefficient will over or under estimate the true coefficient of C, .67, due to leaving D out of the regression. Â

RM:  You would get a result closer to the 2/3 power law if your model produced a pattern where the “omitted variable bias” is much smaller. I used my spreadsheet tracking program to produce an up down movement similar to the one produced by your model and was able to produce a movement that was much better fit by both the 1/3 and 2/3 “power laws” than yours. Here’s a trace of my movement:

RM: The results of a regression analysis on this movement trajectory produced the following results:Â

RM: For V vs R, Â beta = .35 and R^2= .54

RM: For A vs C, beta = .65 and R^2 = .80.

RM: So for this movement trajectory the power coefficients are closer to their “lawful” values (.33 and .67) but the fit to a power law (in terms of R^2) is a little worse for each.Â

RM: The results of this analysis show that the fit of the power law to a movement trajectory does not depend on the movement slowing down through curves and speeding up in straightaways. While this happens in the movement trajectory produced by both the model and by me, it is much more pronounced in the model’s trajectory and yet the power law fits the model more poorly than it does my own data.Â

RM: What you can now demonstrate with the model is  that the fit of the power law depends on characteristics of the movement trajectory produced, not on how it was produced. You can do this by using different temporal variations in the reference signals that produce the different movement trajectories. The same model produces all the different movement trajectories but some are fit much better by a “power law” than others (such as the one you used in the spreadsheet you sent out).

RM: Thank you, Kent, for finally providing an alternative to my explanation of the power law; it was a good idea, even though it was actually the same as mine;-)

BestÂ

Rick

···

On Fri, Aug 26, 2016 at 9:11 AM, McClelland, Kent MCCLEL@grinnell.edu wrote:

If I understand the power-law articles that I’ve looked at, the phenomenon to be explained is that when an organism is making a controlled motion, the speed of movement decreases as the curves get tighter or the angles to be negotiated get sharper,
in a fashion that’s described by the so-called power law. (From my PCT background I’m a bit skeptical about “laws� of behavior.) My argument is that when control systems follow a path that involves increasingly tighter curves or sharper angles, they have to
“naturally� slow down to stay in control of their perceptions. The particular model I’ve played around with involves angles, rather than curves, for the sake of providing a clear demonstration of the principle, but I’m guessing the same principle is at work
for curves, as well.Â

I’ve done a simulation of a control-system tracking movement in an x-y plane in which the path to be followed consists of a series of line segments of the same length set at increasingly sharp angles from each other. I constructed the line segments
by taking varying angles of the radii of a circle, and as the segments are connected together each angle in the path to be negotiated is 0.1 radians larger than the last. I used this path as to create a set of references for my control systems to follow (more
or less like a tracking experiment). All the line segments are exactly the same length, because they’re all created from radii of the same circle. Here is a graph of this reference path:

–
Richard S. MarkenÂ

“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

[rsmarken]

[From Rick Marken (2016.08.27.1400)]

···

On Sat, Aug 27, 2016 at 12:14 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: rick, seriously, do you intend to create more noise than signal, or is it just by chance? if you had reac my first emails when i had the patience to answer to tou bit by bit, while you were high on adrenaline imagining you were going to be the next revolutionary that would change the world by denouncing all behavioral illusions… you would know what you are asking now!!? anyways:

RM: I’m sorry I’m upsetting you, Alex. And I appreciate your taking the time to answer my questions. But I’m afraid I still don’t understand your answers. But I’ll try to figure out the answers on my own.Â

BestÂ

RickÂ

1. very very grave that you still use letters on axis, without phenomenologically thinking and feeling what they are an how they make sense. V is not V, it is V/R=A, in the y axis. it told you that!! so, yes, everyone slows down at higher curvature

2. if you don’t like the name power-law because nothing can be a law dictating anyhthing to an organism becauae of this obsession with freedom that pct stems from, then call it a power-function.

if you are serious about the question, read whitehead’s adventures of ideas, chapters on laws of nature.

3. the law is a constraint; or the law refelcts a constraint on movement. because it shows empirically that kinematics is bound by geometry in a particular ways. once we know where the law comes from, we should be sble to say where that constraint emerges from.

On Saturday, 27 August 2016, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.08.26.1645)]

OK, I know I promised not to get involved but I just have a couple questions about some things I’ve read. I think this is ok because they are not comments on criticisms of anything anyone else has said.Â

1. Why is it said that the the power law shows that movement slows down through curves? A power relationship between curvature and velocity looks like this:Â

So the 1/3 (or 2/3) power law seems to show that the greater the curvature, the faster the movement velocity. The fractional power just says that the rate of increase in velocity with curvature decreases as curvature increases. What am I missing?Â

2. In what sense is the power law a law?

3. In what sense is the power law a constraint on movement?

Answers to these questions would help me better evaluate my crackpot ideas.Â

Thanks

BestÂ

Rick

–

On Fri, Aug 26, 2016 at 2:28 PM, Chad T. Green Chad.Green@lcps.org wrote:

[From Chad Green (2016.08.26.1728)]

Â

We appear to be stuck in a double bind, an everyday occurrence which according to Gregory Bateson represents the conflict between different logical types, i.e.,
the information communicated through semiotics (“you can criticize meâ€?) and that which is communicated through actions or metacommunication (“your criticism is unwelcomeâ€?).Â

Â

According to Deleuze and Guattari (1983) double binds are undecidable “until we do away with both the problem and the solution� altogether and instead aim for
constant evolution (becomings or plateaus of intensity). Otherwise schisms such as what we now have are inevitable (i.e., schismogenesis). Food for thought.

Â

Best,

Chad

Â

Chad T. Green, PMP

Research Office

Loudoun County Public Schools

21000 Education Court

Ashburn, VA 20148

Voice: 571-252-1486

Fax: 571-252-1575

Â

“We are not what we know but what we are willing to learn.� - Mary Catherine Bateson

Â

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Thursday, August 25, 2016 6:13 PM
To: csgnet@lists.illinois.edu
Subject: Re: Got Ideas?

Â

[From Rick Marken (2016.08.25.1510)]

Â

On Thu, Aug 25, 2016 at 1:18 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: what an elegant way, dear rick, to retire for a while from the spread-shit power-law discussion, than suggesting that nobody but you in the csgNet can have ideas. bravo!

Â

RM:I didn’t mean to imply that nobody but me on CSGNet can have ideas. I just predicted that, since I have now left the power law discussion, there wouldn’t be any ideas forthcoming in answer to your question about why
or how the control of perception may give rise to the power law. I did say that to be provocative because I would like to hear how others would answer your question (note that I said that I hoped my prediction would be wrong) but also because I would like
to hear something other than that my ideas are all wrong. I would like to know what ideas people think are right:Â why or how might the control of perception (PCT) give rise to the power law? Inquiring minds want to know;-)

Â

Best regards

Â

Rick

On Thursday, 25 August 2016, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.08.25.1015)]

Â

Rick Marken (2016.08.24.0850)

Â

RM: What I think would be most productive now would be for me to drop out of this discussion of the power law. This should certainly resolve the conflict over the power law.Â

Â

RM: What I suggest is that we hit the reset button and start all over from your initial question, but without me in the mix. Your initial question, Alex, was excellent:

Â

AGM: Any ideas why or how “the control of perception” may give rise to this power law constraining geometry and kinematics in humans, and now in fruit fly larvae?

http://biorxiv.org/content/early/2016/07/05/062166

Â

RM: Now that I am no longer in this discussion, I predict that there will be no ideas forthcoming in answer to Alex’s question. Silence will prevail, showing that it was all about trying to show that my idea is wrong rather than showing
that their idea is right; because I believe they have no idea.Â

Â

RM: I hope my prediction is as wrong as they think my analysis is.

Â

BestÂ

Â

Rick

–

Richard S. MarkenÂ

“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

Â

–

Richard S. MarkenÂ

“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. MarkenÂ

“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. MarkenÂ

“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

[Alex_Gomez-Marin]

honestly, this whole csgnet thing looks more an entertainment for you than a serious attempt to continue to push pct forward. i wanted to engage again but i’ll let it pass; there is just too much ego-noise for me to spend my time and energy. anyone seriously interested in the power law, please write to me directly (cc-ing whoever you like) as i will resume research next week and we can test your ideas on real data and new experiments.

···

On Sat, Aug 27, 2016 at 12:14 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: rick, seriously, do you intend to create more noise than signal, or is it just by chance? if you had reac my first emails when i had the patience to answer to tou bit by bit, while you were high on adrenaline imagining you were going to be the next revolutionary that would change the world by denouncing all behavioral illusions… you would know what you are asking now!!? anyways:

RM: I’m sorry I’m upsetting you, Alex. And I appreciate your taking the time to answer my questions. But I’m afraid I still don’t understand your answers. But I’ll try to figure out the answers on my own.Â

BestÂ

RickÂ

1. very very grave that you still use letters on axis, without phenomenologically thinking and feeling what they are an how they make sense. V is not V, it is V/R=A, in the y axis. it told you that!! so, yes, everyone slows down at higher curvature

2. if you don’t like the name power-law because nothing can be a law dictating anyhthing to an organism becauae of this obsession with freedom that pct stems from, then call it a power-function.

if you are serious about the question, read whitehead’s adventures of ideas, chapters on laws of nature.

3. the law is a constraint; or the law refelcts a constraint on movement. because it shows empirically that kinematics is bound by geometry in a particular ways. once we know where the law comes from, we should be sble to say where that constraint emerges from.

On Saturday, 27 August 2016, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.08.26.1645)]

OK, I know I promised not to get involved but I just have a couple questions about some things I’ve read. I think this is ok because they are not comments on criticisms of anything anyone else has said.Â

1. Why is it said that the the power law shows that movement slows down through curves? A power relationship between curvature and velocity looks like this:Â

So the 1/3 (or 2/3) power law seems to show that the greater the curvature, the faster the movement velocity. The fractional power just says that the rate of increase in velocity with curvature decreases as curvature increases. What am I missing?Â

2. In what sense is the power law a law?

3. In what sense is the power law a constraint on movement?

Answers to these questions would help me better evaluate my crackpot ideas.Â

Thanks

BestÂ

Rick

–
Richard S. MarkenÂ

“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

On Fri, Aug 26, 2016 at 2:28 PM, Chad T. Green Chad.Green@lcps.org wrote:

[From Chad Green (2016.08.26.1728)]

Â

We appear to be stuck in a double bind, an everyday occurrence which according to Gregory Bateson represents the conflict between different logical types, i.e.,
the information communicated through semiotics (“you can criticize meâ€?) and that which is communicated through actions or metacommunication (“your criticism is unwelcomeâ€?).Â

Â

According to Deleuze and Guattari (1983) double binds are undecidable “until we do away with both the problem and the solution� altogether and instead aim for
constant evolution (becomings or plateaus of intensity). Otherwise schisms such as what we now have are inevitable (i.e., schismogenesis). Food for thought.

Â

Best,

Chad

Â

Chad T. Green, PMP

Research Office

Loudoun County Public Schools

21000 Education Court

Ashburn, VA 20148

Voice: 571-252-1486

Fax: 571-252-1575

Â

“We are not what we know but what we are willing to learn.� - Mary Catherine Bateson

Â

From: Richard Marken [mailto:rsmarken@gmail.com]
Sent: Thursday, August 25, 2016 6:13 PM
To: csgnet@lists.illinois.edu
Subject: Re: Got Ideas?

Â

[From Rick Marken (2016.08.25.1510)]

Â

On Thu, Aug 25, 2016 at 1:18 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: what an elegant way, dear rick, to retire for a while from the spread-shit power-law discussion, than suggesting that nobody but you in the csgNet can have ideas. bravo!

Â

RM:I didn’t mean to imply that nobody but me on CSGNet can have ideas. I just predicted that, since I have now left the power law discussion, there wouldn’t be any ideas forthcoming in answer to your question about why
or how the control of perception may give rise to the power law. I did say that to be provocative because I would like to hear how others would answer your question (note that I said that I hoped my prediction would be wrong) but also because I would like
to hear something other than that my ideas are all wrong. I would like to know what ideas people think are right:Â why or how might the control of perception (PCT) give rise to the power law? Inquiring minds want to know;-)

Â

Best regards

Â

Rick

On Thursday, 25 August 2016, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.08.25.1015)]

Â

Rick Marken (2016.08.24.0850)

Â

RM: What I think would be most productive now would be for me to drop out of this discussion of the power law. This should certainly resolve the conflict over the power law.Â

Â

RM: What I suggest is that we hit the reset button and start all over from your initial question, but without me in the mix. Your initial question, Alex, was excellent:

Â

AGM: Any ideas why or how “the control of perception” may give rise to this power law constraining geometry and kinematics in humans, and now in fruit fly larvae?

http://biorxiv.org/content/early/2016/07/05/062166

Â

RM: Now that I am no longer in this discussion, I predict that there will be no ideas forthcoming in answer to Alex’s question. Silence will prevail, showing that it was all about trying to show that my idea is wrong rather than showing
that their idea is right; because I believe they have no idea.Â

Â

RM: I hope my prediction is as wrong as they think my analysis is.

Â

BestÂ

Â

Rick

–

Richard S. MarkenÂ

“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

Â

–

Richard S. MarkenÂ

“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. MarkenÂ

“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

[rsmarken]

[From Rick Marken (2016.08.27.1430)]

···

Kent McClelland (2016.08.27.1530)–

KM: Here’s one more simulation to consider… Instead of a preset path for
the control system to follow (as specified by a vector of XY references), I set the references to zero and introduced a smoothly varying XY disturbance vector. The first simulation I shared had had the XY disturbances set to zero.

RM: Excellent! This is another great way to show that it’s the nature of the movement trajectory itself, and not how it is produced, that determines how well it is fit by a “power law”. The results of a regression analysis on the output movement trajectory you sent produced the following results:

RM: For V vs R, beta = .35 and R^2= .55

RM: For A vs C, beta = .65 and R^2 = .79.

KM: This change to a random disturbance removed the constant-speed effect of the preset path, because the distance traveled by the disturbance vector changes randomly at each iteration (with the distances more or less normally distributed). And the
other important change is that the control system in this version is controlling for tracking smooth curves instead of sharp angles.

RM: Yes. And these changes are, indeed, the reason why you get the different results. But notice that there was no change in the model itself; the same model generated your first pattern (with the R vs V beta of .1) as the second (with an R vs V beta of a more “lawful” .35).

KM: Here is the disturbance vector I used:

KM: How did you generated the random disturbance? It looks nice.

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

[chadtgreen]

[From Chad Green (2016.09.01.1002)]

"Proposition 10: The power of rationality is embedded in stable power relations rather than in confrontations

Confrontations are part of the rationality of power, not the power of rationality. Because rationality yields to power in open, antagonistic confrontations, the power of rationality, that is, the force of reason, is weak or non-existent here. The force of reason gains maximum effect in stable power relations characterized by negotiations and consensus-seeking. Hence, the power of rationality can be maintained only insofar as power relations are kept non-antagonistic and stable." - Bent Flyvbjerg (Power and Rationality)

Best,
Chad

Chad T. Green, PMP
Research Office
Loudoun County Public Schools
21000 Education Court
Ashburn, VA 20148
Voice: 571-252-1486
Fax: 571-252-1575

"We are not what we know but what we are willing to learn." - Mary Catherine Bateson

···

-----Original Message-----
From: Erling Jorgensen [mailto:kmjorgensen2000@yahoo.com]
Sent: Thursday, September 01, 2016 12:13 AM
To: csgnet@lists.illinois.edu
Subject: Re: Got Ideas?

[From Erling Jorgensen (2016.08.31 2330 EDT)]

Rick Marken (2016.08.31.1750)

Erling Jorgensen (2016.08.31 1545 EDT)--

EJ: The difficulty I have with your present model on the power-law
issue is

that I cannot (yet) trust the conclusions because I cannot trust the math. As many others have pointed out, including myself, there is some kind of fundamental error going on in how you treat the math.

RM: But how could you know that there is an error -- or that others are

correctly pointing out an error -- if, as you say later in your post:

EJ: Cube roots are not really my thing, so I have a hard time getting
an

intuitive sense of the relationship that is being posed.

EJ: Rick, I too have a PhD in psychology, & I can follow the arguments others are making. I have tried on two other occasions to raise with you the sticking point that I have with your math. The closest I can come to expressing it, in verbal form, is that you have to get the change in X and the change in Y over onto the left hand side of your equation for V. Otherwise, you end up essentially using V to predict V. And that is what I call a tautology, which does not yet tell anything very useful.

EJ: On both occasions where I have raised this, & now again in this response to my post, you simply reiterate where you got the formulas & then move on to log-log regression (i.e., conclusion territory), without engaging the question of whether your D term carries velocity components within it. That is why I believe your treatment is "stacking the deck," as has been mentioned by others, rather than telling us something new & useful.

EJ: I find it encouraging that your latest post to Alex [Rick Marken (2016.08.31.1800)] is asking questions of a fellow scientist, not simply making assertions. That is the spirit of the scientist I know you to be, by slowing things back down to check every step. You've had enough input from others to suggest something is amiss here, even though it looks all fine to you. So, yes, collaborating on those pre-conclusion, methodological questions (assuming not all bridges have been scorched) is the way to go here.

EJ: At any rate, it is good to engage with you. It is also late. Sleep summons. So enough for now.
All the best,
Erling

[rsmarken]

[From Rick Marken (2016.09.01.1340)]

···

Erling Jorgensen (2016.08.31 2330 EDT)–

EJ: Rick, I too have a PhD in psychology, & I can follow the arguments others

are making. I have tried on two other occasions to raise with you the

sticking point that I have with your math. The closest I can come to

expressing it, in verbal form, is that you have to get the change in X and the

change in Y over onto the left hand side of your equation for V. Otherwise,

you end up essentially using V to predict V. And that is what I call a

tautology, which does not yet tell anything very useful.

EJ: On both occasions where I have raised this, & now again in this response

to my post, you simply reiterate where you got the formulas & then move on to

log-log regression (i.e., conclusion territory), without engaging the question

of whether your D term carries velocity components within it. That is why I

believe your treatment is “stacking the deck,” as has been mentioned by

others, rather than telling us something new & useful.

RM: I’m sorry Erling. I didn’t mean to be evasive. I just didn’t know how to answer your question. But as I was trying to write this reply I finally realized that the answer to you question is “yes, there is a tautology”! My derived equation for the relationship between R to V – V = D^1/3 *R^1/3 – inasmuch as it shows that power law researchers are unknowingly “stacking the deck” in favor of finding a 1/3 power law between R and V simply because these variables are close to being in a mathematical 1/3 power relationship to each other! I realized this while I was going through a little exercise to show you that my derivation of the relationship between R and V was not a tautology. In doing so, I realized that it is. Here was what led me to this realization:

===========

RM: You say you have trouble dealing with algebraic manipulation with powers (exponents) so maybe I can illustrate the legitimacy of solving two simultaneous equations using equations that don’t have any exponents. Here are two equations, analogous to the ones for V and R:

     A = .5 * (X + Y)                              (1)



     B = (X+Y) * (X-Y)                          (2)

RM: Now I can solve for B as a function of A. All I have to do is note that the multiplier of X in the equation for B – (X+Y) – is part of the expression for A. And,indeed, some algebra on the equation for A gives:

     (X + Y) = A/.5

RM: So now we can substitute A/.5 for (X+Y) in the equation for B:

     B = A/.5 * (X-Y)

RM: And, finally, I can write A as a function of B as follows:

      A = .5*B - (X-Y)                              (3)

RM: This is exactly analogous to what I did with the equations for V and R.

RM: By the way, if X and Y are data points, then if you calculate A and B from the data (using the equations 1 and 2 above) and run a linear regression relating B to A you will not find the coefficient of B to be .5 (as per equation 3) because a variable, (X-Y), has been left out of the analysis. If you don’t know about the variable (X-Y) and you are studying the relationship between A and B in the data, you will find values for the coefficient of B that deviate from .5 – and the size of these deviations will be proportional to the extent to which (X-Y) covaries along with B.

===========

RM: This is exactly analogous to what is happening in the power law research. And it is what made me realize that my equation for the relationship between R and V – V = D^1/3 *R^1/3 – can be considered a tautology in the sense that it shows that power law researchers are studying a relationship between variables that are mathematical functions of each other. The deck is “stacked” in favor of finding a 1/3 power law (relating R to V) or 2/3 power law (relating C to A), the deviation from those “stacked results” being proportional to the covariance between the predictor variables, R or C, with the omitted variable D (where D is analogous to (X-Y) in my example).

RM: So I think a better way of putting it is that my derivation of the relationship between R and V (and between C and A) shows that power law researchers are studying a tautology.

RM: The interesting question (to me) is why did the power law researches notice that the variables they measure in their studies are related “tautologically”). I mean here are two equations sitting right in front of them:

And anyone who knows eighth grade algebra should be able to see how V can be written as a function of R. Yet lots of very smart (and mathematically sophisticated) power law researchers missed this. Why?

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