# Reappraising the Power Law Reappraisals

**URL:** <http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628>\
**Category:** CSG2018\
**Created:** [March 8, 2018, 7:26pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628 "2018-03-08T19:26:19Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 8, 2018, 7:26pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/1 "2018-03-08T19:26:19Z")

</div>

[Rick Marken 2018-03-08\_11:24:06]

RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:

[https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)

RM: For those of you who are interested, the full article is available at:Â

[https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)

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 --Antoine de Saint-Exupery

---

<div class="post-metadata">

**Author:** ![Alex\_Gomez-Marin](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/a/ebca7d/32.png) [@Alex\_Gomez-Marin](http://discourse.iapct.org/u/Alex_Gomez-Marin)\
**Post date:** [March 8, 2018, 9:28pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/2 "2018-03-08T21:28:49Z")

</div>

i see…! so now it turns out that one can move in an ellipse at different velocity profiles but the whole issue was that the non-trivial speed-curvature relationship must be just observed output and thus a behavioral illusion by definition. i see… and you needed two papers and fifty emails full of inexcusable mathematical errors, digressions and shell-games to re-quote powers ab nauseaum again and again and again. bravo! this is how the RCT revolution will take place: by being a one man’s field where one can write and say whatever one wishes as long as one inserts quotes from bill here and there. braaavo! you should be proud of keeping up with such shame.

> **···**
>
> Alex Gomez-Marin  
> [behavior-of-organisms.org](http://behavior-of-organisms.org)

---

<div class="post-metadata">

**Author:** ![Abbott](http://discourse.iapct.org/user_avatar/discourse.iapct.org/abbott/32/2879_2.png) [@Abbott](http://discourse.iapct.org/u/Abbott)\
**Post date:** [March 9, 2018, 12:05am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/3 "2018-03-09T00:05:08Z")

</div>

[From Bruce Abbott (2018.03.08.1905 EST])

[Rick Marken 2018-03-08\_11:24:06]

RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:

[https://doi.org/10.1007/s00221-018-5208-4](https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_s00221-2D018-2D5208-2D4&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=dJUxBpGE3Ak5vUWsq0m4VFTh1sSx_Pl3MJozrH1_lsA&s=Tg3pNh-EB0_goAjlQcAmt2Hj80kyT49YDgKKOggdnt8&e=)

RM: For those of you who are interested, the full article is available at:

[https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dropbox.com_s_3m51ko4vs1xdult_MarkenShafferReappraisal.pdf-3Fdl-3D0&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=dJUxBpGE3Ak5vUWsq0m4VFTh1sSx_Pl3MJozrH1_lsA&s=CSBC_mht2YfpfxSST5mUegY6Kcezy2y7YaxMcdysm7Q&e=)

I must say, I admire your chutzpah. However, your analysis is mathematically flawed regardless of your assertions to the contrary and no rebuttal is going to get around that fact. It’s really a shame that you have not put some real intellectual effort in trying to understand what is wrong with it. (It’s not hard; I’m no mathematician by any stretch of the imagination and even I can grasp it.)

I’ve only quickly skimmed your rebuttal thus far, but wish to note a couple places I’ve noticed where straw men are raised.

One is where you cite other researchers’ use or approval of the Gribble and Ostry equations for computing tangential velocity and curvature. You take this as support for your _analysis_ of the curvature equation, when in fact it is support for the _use_ of those equations to compute tangential velocity and curvature. No one in this debate has challenged the validity of those equations, and the fact that other researchers support their use for this purpose has absolutely no bearing on whether your analysis is correct or incorrect. The argument is a straw man. It is not where your critics say the problem lies.

You also that the same data points that are used to compute tangential velocity are also used to compute curvature. Again, nobody disputes that fact, and again, the argument is a straw man. It is not where your critics say the problem lies.

What you have failed to recognize is that the curvature formula employs these numbers in such a way that the resulting curvature (or its inverse, the radius) is _independent_ of tangential velocity, despite the appearances that so confuse you. What you have failed to understand is that velocity along the curve is only a convenient stand-in for distance along the curve. By relating this distance to the change in the angle of the tangent to the curve, the formula for curvature is able to determine the point where lines drawn at right angles to these successive tangents intersect – and this point is at the radius of the curve. (This description is approximate; the actual process involves taking limits.)

In the data, both the tangential velocity and the angle of the tangent to the line change over time as the line is followed. The computation of curvature takes advantage of the fact that if both change as a function of the same increments in time, then one can eliminate time from the result by comparing the change in tangent angle to the change in position along the line. The same curvature (or radius) will be obtained regardless of the speed with which the curve is traversed. (This is true because the rate of change in the tangent angle scales up or down with the tangential velocity). The portion of the curvature formula that you call “D� is not a separate factor that accounts for a deviation from a strict 2/3 power law; rather, it is a portion of the computation that relates the tangential velocity of the point along the curve (and thus distance traveled along the curve during that time) to the change in angle of the tangent. You can’t just pull it out and claim that what’s left shows that the mathematics necessarily imposes an underlying 2/3 power law between velocity and curvature. Well, you can (and in fact have), but when you do you assert a mathematical fiction.

I don’t expect this post to persuade you to reexamine your position (you have far too much invested in it to turn back now, I suspect), but I did want to note two of the straw men you have erected in your rebuttal; having done that, I have said my piece.

Bruce

---

<div class="post-metadata">

**Author:** ![EetuP](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/e/df705f/32.png) [@EetuP](http://discourse.iapct.org/u/EetuP)\
**Post date:** [March 9, 2018, 12:13pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/4 "2018-03-09T12:13:44Z")

</div>

Rick,

have thought at all how in a normal symmetric coordinate system the direction and the speed of the movement of an object could be mathematically and conceptually interdependent? Is it  
possible to predict the speed from the direction? As a velocity these two variables are described in one vector, but this does not make them interdepending. There is no way how the one could be predicted from the other. Instead they can change absolutely independently.

However, you build your argument on an alternative fact that the change in the speed is a consistent mathematical consequence of the change in direction. I think this is the core problem  
in this whole case.

Eetu

Please, regard all my statements as questions,

no matter how they are formulated.

> **···**
>
> [Rick Marken 2018-03-08\_11:24:06]
> 
> RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> 
> [https://doi.org/10.1007/s00221-018-5208-4](https://emea01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.1007%2Fs00221-018-5208-4&data=02%7C01%7C%7Cbdc601efefe64829418b08d5852a983e%7C9f9ce49a51014aa38c750d5935ad6525%7C0%7C0%7C636561340376220957&sdata=ZwP9Bzb5yxgAKfnsbbjk4tFiE%2F3oHnA9OhlAgVHjuMY%3D&reserved=0)
> 
> RM: For those of you who are interested, the full article is available at:
> 
> [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://emea01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dropbox.com%2Fs%2F3m51ko4vs1xdult%2FMarkenShafferReappraisal.pdf%3Fdl%3D0&data=02%7C01%7C%7Cbdc601efefe64829418b08d5852a983e%7C9f9ce49a51014aa38c750d5935ad6525%7C0%7C0%7C636561340376220957&sdata=I8i4BLuAgwd9bkA%2FkmznA2hpb5EL0cS%2FX58b6DQRbdQ%3D&reserved=0)
> 
> Best
> 
> Rick
> 
> –
> 
> Richard S. Marken
> 
> "Perfection is achieved not when you have nothing more to add, but when you
> 
> have nothing left to take away.�
> 
> ```
> --Antoine de Saint-Exupery
> 
> ```

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [March 9, 2018, 5:05pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/5 "2018-03-09T17:05:06Z")

</div>

[Martin Taylor 2018.03.08.23.07]

> [Rick Marken 2018-03-08\_11:24:06]

> 

> ```
> RM: Our reply to the comments of Taylor and Zago et al on
> 
> ```
> 
> our power law paper have been published in the on-line edition  
> of Experimental Brain Research. The abstract is available at:

> 

> [https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)

> 

> ```
> RM: For those of you who are interested, the full article
> 
> ```
> 
> is available at:

> 

> [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)

> 

> Best

> 

> 

```
I realize there's no point in re-arguing the mathematical and

```

logical points of why your paper was utter nonsense. You know all  
these.

```
But I wonder why you felt it necessary to rebut imaginary criticisms

```

that were not made rather than those that were made, and why you  
imputed motives for the criticisms that you knew to be false? I will  
not speak to Alex’s critique. He can do that if he wishes. Nor do I  
wish to rewrite mine, but I would like to know why in your rebuttal  
you do not address the issues I raised, but instead chose to show  
that criticisms not made would have been wrong had they been made.

```
A few examples:

In the very first paragraph you claim that my reason for writing a

```

critique was that the idea that the power law might be a behavioural  
illusion caused “consternation”, whereas I made explicit that  
nothing in my critique had any bearing on that issue. Indeed, I  
finished my critique with the statement that perhaps the power law  
is indeed a behavioural illusion, though M&S sheds no light on  
that issue.

```
M&S say that my critique of your use of Gribble and Ostry's

```

equations is based on my belief that those equations are wrong or  
misleading, whereas I pointed out that they are well known and  
universally accepted equations for using observed data to measure  
the velocity (equation 1) and curvature (equation 2) profiles  
observed in an experiment. Neither Gribble and Ostry nor (so far as  
I know) anyone other than Marken and Shaffer) ever claimed that the  
observed velocity was the only velocity that could be used to get  
the correct curvature from the equation for R.

```
I never said that the derivation of V = R<sup>1/3</sup>D<sup>1/3</sup>
was wrong. I said that since the formula for D was velocity (V)

```

times a constant in spatial variables, the equation is not an  
equation from which one can determine V. The M&S claim that it  
is an equation from which one can determine V is the core of my  
critique.

```
M&S falsely claim that I argue that "it should have been obvious

```

that X-dot and Y-dot are derivatives with respect to time in the  
expression for V, whereas they are derivatives with respect to space  
in the expression for R (p. 5)". On the contrary, I devote the first  
couple of pages of my critique to showing why, despite the radius of  
curvature being a spatial property, nevertheless it is quite proper  
to use time derivatives in the formula for R.

```
M&S say that because Gribble and Ostry correctly transformed

```

Viviani and Stucchi’s expression for R using spatial derivatives  
into one using time derivatives (a derivation with which I started  
my comment), therefore you were correct to say that ONLY the  
velocity found in an experiment can be substituted into the  
numerator of the expression for R, whereas both my derivation and  
that of Viviani and Stucchi (essentially the same) makes it crystal  
clear that this is not true.

```
M&S follow this astounding assertion with an couple of

```

paragraphs to show why the V = R1/3D1/3  
equation is correct, implying that my comment claimed it to be  
wrong. Early in my comment, however, I wrote: “They then write their  
key Eq (6) [V = R1/3D1/3], which is true for  
any value of V whatever…” Any implication that my comment claimed  
the equation to be incorrect is false.

```
Omitted Variable Bias: My comment demonstrated that the finding

```

predicted and reported by M&S was actually a tautology having no  
relation to experimental findings, which will always produce the  
result claimed by M&S to be an experimental result. M&S in  
the paper and in the rebuttal treat it as a discovery that can be  
made only by careful statistical analysis, and do not acknowledge  
the tautology criticism at all.

```
M&S: "At the heart of the criticisms of our paper by Z/M and

```

Taylor is the assumption that the power law is a result of a direct  
causal connection between curvature and speed of movement or between  
these variables and the physiological mechanisms that produce them."  
I have no idea how this astonishing statement can be derived from my  
exposition of the mathematical and logical flaws in their paper. My  
comment is designed to refute exactly M&S’s claim of my  
motivation. The comment shows that there is NO necessary  
relationships, causal connection or otherwise, between curvature and  
speed of movement.

```
Nothing of M&S's so-called "re appraisal" after that will load

```

from the link Rick provided, so I cannot show any later examples of  
mis-statements of the criticisms made, and rebuttals of criticisms  
not made. Maybe later in their reappraisal M&S do comment on a  
criticism that was actually made in my comment, I can’t tell. But I  
think this should be enough to raise some significant questions as  
to the scientific legitimacy of both the original paper and the  
rebuttal comment.

```
I just wonder why the rebuttal was written, if it was not going to

```

address the criticisms made, but had to invent imaginary ones that  
were not made or that were actually opposite to ones that were made.

```
Martin

```

---

<div class="post-metadata">

**Author:** ![EetuP](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/e/df705f/32.png) [@EetuP](http://discourse.iapct.org/u/EetuP)\
**Post date:** [March 9, 2018, 6:48pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/6 "2018-03-09T18:48:29Z")

</div>

Here should be the whole text attached.

[MarkenShafferReappraisal.pdf](http://discourse.iapct.org/uploads/short-url/lpg4SUfjKDVi5UDHCEz7w3kRz33.pdf) (934 KB)

> **···**
>
> Eetu
> 
> **From:** Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net)  
> **Sent:** Friday, March 9, 2018 7:05 PM  
> **To:** csgnet@lists.illinois.edu  
> **Subject:** Re: Reappraising the Power Law Reappraisals
> 
> [Martin Taylor 2018.03.08.23.07]
> 
> > [Rick Marken 2018-03-08\_11:24:06]
> 
> > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> 
> > [https://doi.org/10.1007/s00221-018-5208-4](https://emea01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.1007%2Fs00221-018-5208-4&data=02%7C01%7C%7C119aabbafd854f0d967b08d585dff076%7C9f9ce49a51014aa38c750d5935ad6525%7C0%7C0%7C636562119277484240&sdata=ijDf7zw8%2FfhAjcpJXo32LneshuCZuQa%2FlnyrnkntXVo%3D&reserved=0)
> 
> > RM: For those of you who are interested, the full article is available at:
> 
> > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://emea01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dropbox.com%2Fs%2F3m51ko4vs1xdult%2FMarkenShafferReappraisal.pdf%3Fdl%3D0&data=02%7C01%7C%7C119aabbafd854f0d967b08d585dff076%7C9f9ce49a51014aa38c750d5935ad6525%7C0%7C0%7C636562119277484240&sdata=J5ilTOl0bBrJvv%2FVpOeLB2rJsO%2B5xk5vcgQYP3J0ql4%3D&reserved=0)
> 
> > Best
> 
> I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> 
> But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? I will not speak to Alex’s critique. He can do that if he wishes.  
> Nor do I wish to rewrite mine, but I would like to know why in your rebuttal you do not address the issues I raised, but instead chose to show that criticisms not made would have been wrong had they been made.
> 
> A few examples:
> 
> In the very first paragraph you claim that my reason for writing a critique was that the idea that the power law might be a behavioural illusion caused “consternation”, whereas I made explicit that nothing in my critique had any bearing on that issue. Indeed,  
> I finished my critique with the statement that perhaps the power law is indeed a behavioural illusion, though M&S sheds no light on that issue.
> 
> M&S say that my critique of your use of Gribble and Ostry’s equations is based on my belief that those equations are wrong or misleading, whereas I pointed out that they are well known and universally accepted equations for using observed data to measure the  
> velocity (equation 1) and curvature (equation 2) profiles observed in an experiment. Neither Gribble and Ostry nor (so far as I know) anyone other than Marken and Shaffer) ever claimed that the observed velocity was the only velocity that could be used to  
> get the correct curvature from the equation for R.
> 
> I never said that the derivation of V = R1/3D1/3 was wrong. I said that since the formula for D was velocity (V) times a constant in spatial variables, the equation is not an equation from which one can determine V. The M&S claim that  
> it is an equation from which one can determine V is the core of my critique.
> 
> M&S falsely claim that I argue that “it should have been obvious that X-dot and Y-dot are derivatives with respect to time in the expression for V, whereas they are derivatives with respect to space in the expression for R (p. 5)”. On the contrary, I devote  
> the first couple of pages of my critique to showing why, despite the radius of curvature being a spatial property, nevertheless it is quite proper to use time derivatives in the formula for R.
> 
> M&S say that because Gribble and Ostry correctly transformed Viviani and Stucchi’s expression for R using spatial derivatives into one using time derivatives (a derivation with which I started my comment), therefore you were correct to say that ONLY the velocity  
> found in an experiment can be substituted into the numerator of the expression for R, whereas both my derivation and that of Viviani and Stucchi (essentially the same) makes it crystal clear that this is not true.
> 
> M&S follow this astounding assertion with an couple of paragraphs to show why the V = R1/3D1/3 equation is correct, implying that my comment claimed it to be wrong. Early in my comment, however, I wrote: “They then write their key Eq (6)  
> [V = R1/3D1/3], which is true for any value of V whatever…” Any implication that my comment claimed the equation to be incorrect is false.
> 
> Omitted Variable Bias: My comment demonstrated that the finding predicted and reported by M&S was actually a tautology having no relation to experimental findings, which will always produce the result claimed by M&S to be an experimental result. M&S in the  
> paper and in the rebuttal treat it as a discovery that can be made only by careful statistical analysis, and do not acknowledge the tautology criticism at all.
> 
> M&S: “At the heart of the criticisms of our paper by Z/M and Taylor is the assumption that the power law is a result of a direct causal connection between curvature and speed of movement or between these variables and the physiological mechanisms that produce  
> them.” I have no idea how this astonishing statement can be derived from my exposition of the mathematical and logical flaws in their paper. My comment is designed to refute exactly M&S’s claim of my motivation. The comment shows that there is NO necessary  
> relationships, causal connection or otherwise, between curvature and speed of movement.
> 
> Nothing of M&S’s so-called “re appraisal” after that will load from the link Rick provided, so I cannot show any later examples of mis-statements of the criticisms made, and rebuttals of criticisms not made. Maybe later in their reappraisal M&S do comment on  
> a criticism that was actually made in my comment, I can’t tell. But I think this should be enough to raise some significant questions as to the scientific legitimacy of both the original paper and the rebuttal comment.
> 
> I just wonder why the rebuttal was written, if it was not going to address the criticisms made, but had to invent imaginary ones that were not made or that were actually opposite to ones that were made.
> 
> Martin

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [March 9, 2018, 7:12pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/7 "2018-03-09T19:12:15Z")

</div>

[Martin Taylor 2018.03.09.13.34]

> [Martin Taylor 2018.03.08.23.07]
> 
> > [Rick Marken 2018-03-08\_11:24:06]
> > 
> > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > 
> > [The power law as behavioral illusion: reappraising the reappraisals | Experimental Brain Research](https://doi.org/10.1007/s00221-018-5208-4)
> > 
> > RM: For those of you who are interested, the full article is available at:
> > 
> > [Dropbox - MarkenShafferReappraisal.pdf - Simplify your life](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > 
> > Best
> 
> I realize there's no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> 
> But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? ...

I hadn't intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.

> **···**
>
> =============  
> Under the heading "Power Law as Behavioural Illusion" M&S say: "As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause�effect pprocess."
> 
> Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that "movement production is a cause-effect process", velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> 
> M&S go on to say: "This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints."
> 
> This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: "Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints" .
> 
> Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of "reappraisal" was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the "reappraisal" would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> 
> I hope to say no more on this very distasteful topic.
> 
> Martin

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 9, 2018, 11:31pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/8 "2018-03-09T23:31:06Z")

</div>

[philip 2018.03.09]

Dear Rick,

In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance. In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:

1. The relationship between the cursor movement and the disturbance; and

2. The relationship between the mouse movement and the disturbance.

Why have you not shown the disturbance in figure 1?

[![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon)  
Virus-free. [www.avast.com](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link)

> **···**
>
> On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > [Martin Taylor 2018.03.09.13.34]
> > 
> > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > 
> > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > 
> > > > [https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)
> > > > 
> > > > RM: For those of you who are interested, the full article is available at:
> > > > 
> > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > 
> > > > Best
> > > 
> > > [Martin Taylor 2018.03.08.23.07]
> > > 
> > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > 
> > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> > 
> > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > 
> > =============
> > 
> > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect process.”
> > 
> > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > 
> > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > 
> > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > 
> > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > 
> > I hope to say no more on this very distasteful topic.
> > 
> > Martin

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 9, 2018, 11:57pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/9 "2018-03-09T23:57:30Z")

</div>

[Rick Marken 2018-03-09\_15:57:13]

> [philip 2018.03.09]  
> Dear Rick,

In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.

RM: Where does he say that?? Page and paragraph please.  
Best  
RickÂ

>  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that "the cursor movements are the voluntary movements that follow the power law". Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:  
> 1) The relationship between the cursor movement and the disturbance; and

2) The relationship between the mouse movement and the disturbance.  
Why have you not shown the disturbance in figure 1?     Â

> **···**
>
> > Â
> > 
> > &nbsp;&nbsp;\> \<[Safe emailing Mac | Avast](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon&gt;&gt); \<[https://ipmcdn.avast.com/images/icons/icon-envelope-tick-round-orange-animated-no-repeat-v1.gif&gt;&gt](https://ipmcdn.avast.com/images/icons/icon-envelope-tick-round-orange-animated-no-repeat-v1.gif&gt;&gt); \> Virus-free. \<[https://www.avast.com/sig-email?utm\_medium=email&utm\_source=link&utm\_campaign=sig-email&utm\_content=webmail&utm\_term=link&gt;www\.avast\.com](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link&gt;www%5C.avast%5C.com)  
> > On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor \<\<mailto:mmt-csg@mmtaylor.net\>mmt-csg@mmtaylor.net\> wrote:
> > 
> > > [Martin Taylor 2018.03.09.13.34]
> > > 
> > > > [Martin Taylor 2018.03.08.23.07]
> > > > 
> > > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > > 
> > > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > > 
> > > > > \<[https://doi.org/10.1007/s00221-018-5208-4&gt;&gt;&gt;&gt;&gt](https://doi.org/10.1007/s00221-018-5208-4&gt;&gt;&gt;&gt;&gt); [The power law as behavioral illusion: reappraising the reappraisals | Experimental Brain Research](https://doi.org/10.1007/s00221-018-5208-4)
> > > > > 
> > > > > RM: For those of you who are interested, the full article is available at:
> > > > > 
> > > > > \<[https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0&gt;&gt;&gt;&gt;&gt](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0&gt;&gt;&gt;&gt;&gt); [Dropbox - MarkenShafferReappraisal.pdf - Simplify your life](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > > 
> > > > > Best
> > > > 
> > > > I realize there's no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > > 
> > > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? ...
> > > 
> > > I hadn't intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > > 
> > > =============  
> > > Under the heading "Power Law as Behavioural Illusion" M&S say: "As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect process."
> > > 
> > > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that "movement production is a cause-effect process", velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > > 
> > > M&S go on to say: "This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints."
> > > 
> > > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: "Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints" .
> > > 
> > > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of "reappraisal" was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the "reappraisal" would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > > 
> > > I hope to say no more on this very distasteful topic.
> > > 
> > > Martin
> 
> --  
> Richard S. Marken  
> "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 --Antoine de Saint-Exupery

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 10, 2018, 12:50am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/10 "2018-03-10T00:50:33Z")

</div>

Chapter 1

> **···**
>
> On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> [Rick Marken 2018-03-09\_15:57:13]
> 
> > [philip 2018.03.09]
> 
> > 
> 
> > Dear Rick,
> 
> > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> RM: Where does he say that?? Page and paragraph please.
> 
> Best
> 
> RickÂ
> 
> >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > 
> > 1. The relationship between the cursor movement and the disturbance; and
> 
> > 1. The relationship between the mouse movement and the disturbance.
> 
> > Why have you not shown the disturbance in figure 1?     Â
> 
> > 
> 
> > 
> 
> > 
> 
> > Â
> 
> > 
> 
> > 
> 
> > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon)  
> > Virus-free. [www.avast.com](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link)
> 
> –  
> 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 --Antoine de Saint-Exupery
> 
> On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > [Martin Taylor 2018.03.09.13.34]
> > 
> > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > 
> > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > 
> > > > [https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)
> > > > 
> > > > RM: For those of you who are interested, the full article is available at:
> > > > 
> > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > 
> > > > Best
> > > 
> > > [Martin Taylor 2018.03.08.23.07]
> > > 
> > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > 
> > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> > 
> > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > 
> > =============
> > 
> > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect process.”
> > 
> > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > 
> > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > 
> > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > 
> > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > 
> > I hope to say no more on this very distasteful topic.
> > 
> > Martin

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 10, 2018, 12:50am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/11 "2018-03-10T00:50:46Z")

</div>

I mean chapter 2

> **···**
>
> On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Chapter 1
> 
> On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> [Rick Marken 2018-03-09\_15:57:13]
> 
> > [philip 2018.03.09]
> 
> > 
> 
> > Dear Rick,
> 
> > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> RM: Where does he say that?? Page and paragraph please.
> 
> Best
> 
> RickÂ
> 
> >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > 
> > 1. The relationship between the cursor movement and the disturbance; and
> 
> > 1. The relationship between the mouse movement and the disturbance.
> 
> > Why have you not shown the disturbance in figure 1?     Â
> 
> > 
> 
> > 
> 
> > 
> 
> > Â
> 
> > 
> 
> > 
> 
> > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon)  
> > Virus-free. [www.avast.com](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link)
> 
> –  
> 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 --Antoine de Saint-Exupery
> 
> On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > [Martin Taylor 2018.03.09.13.34]
> > 
> > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > 
> > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > 
> > > > [https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)
> > > > 
> > > > RM: For those of you who are interested, the full article is available at:
> > > > 
> > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > 
> > > > Best
> > > 
> > > [Martin Taylor 2018.03.08.23.07]
> > > 
> > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > 
> > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> > 
> > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > 
> > =============
> > 
> > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect process.”
> > 
> > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > 
> > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > 
> > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > 
> > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > 
> > I hope to say no more on this very distasteful topic.
> > 
> > Martin

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 10, 2018, 1:12am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/12 "2018-03-10T01:12:23Z")

</div>

[philip 2018.03.09]

If one varies a distal stimulus q(d) and observes that a measure of  
behavior q(o)Â shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.

Rick,  
Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion: Â

   Â

> **···**
>
> On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > I mean chapter 2
> 
> On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Chapter 1
> 
> On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> [Rick Marken 2018-03-09\_15:57:13]
> 
> > [philip 2018.03.09]
> 
> > 
> 
> > Dear Rick,
> 
> > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> RM: Where does he say that?? Page and paragraph please.
> 
> Best
> 
> RickÂ
> 
> >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > 
> > 1. The relationship between the cursor movement and the disturbance; and
> 
> > 1. The relationship between the mouse movement and the disturbance.
> 
> > Why have you not shown the disturbance in figure 1?     Â
> 
> > 
> 
> > 
> 
> > 
> 
> > Â
> 
> > 
> 
> > 
> 
> > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon)  
> > Virus-free. [www.avast.com](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link)
> 
> –  
> 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 --Antoine de Saint-Exupery
> 
> On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > [Martin Taylor 2018.03.09.13.34]
> > 
> > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > 
> > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > 
> > > > [https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)
> > > > 
> > > > RM: For those of you who are interested, the full article is available at:
> > > > 
> > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > 
> > > > Best
> > > 
> > > [Martin Taylor 2018.03.08.23.07]
> > > 
> > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > 
> > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> > 
> > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > 
> > =============
> > 
> > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect process.”
> > 
> > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > 
> > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > 
> > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > 
> > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > 
> > I hope to say no more on this very distasteful topic.
> > 
> > Martin

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 10, 2018, 1:14am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/13 "2018-03-10T01:14:57Z")

</div>

I am sorry, I meant to say “correlation between the mouse movement and the disturbance”.

> **···**
>
> On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > [philip 2018.03.09]
> 
> > If one varies a distal stimulus q(d) and observes that a measure of  
> > behavior q(o)Â shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.
> 
> > 
> 
> > 
> 
> > Rick,  
> > Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion: Â
> 
> > 
> 
> > Â Â Â Â
> 
> On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > I mean chapter 2
> 
> On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Chapter 1
> 
> On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> [Rick Marken 2018-03-09\_15:57:13]
> 
> > [philip 2018.03.09]
> 
> > 
> 
> > Dear Rick,
> 
> > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> RM: Where does he say that?? Page and paragraph please.
> 
> Best
> 
> RickÂ
> 
> >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > 
> > 1. The relationship between the cursor movement and the disturbance; and
> 
> > 1. The relationship between the mouse movement and the disturbance.
> 
> > Why have you not shown the disturbance in figure 1?     Â
> 
> > 
> 
> > 
> 
> > 
> 
> > Â
> 
> > 
> 
> > 
> 
> > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon)  
> > Virus-free. [www.avast.com](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link)
> 
> –  
> 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 --Antoine de Saint-Exupery
> 
> On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > [Martin Taylor 2018.03.09.13.34]
> > 
> > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > 
> > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > 
> > > > [https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)
> > > > 
> > > > RM: For those of you who are interested, the full article is available at:
> > > > 
> > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > 
> > > > Best
> > > 
> > > [Martin Taylor 2018.03.08.23.07]
> > > 
> > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > 
> > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> > 
> > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > 
> > =============
> > 
> > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect process.”
> > 
> > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > 
> > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > 
> > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > 
> > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > 
> > I hope to say no more on this very distasteful topic.
> > 
> > Martin

---

<div class="post-metadata">

**Author:** ![Alex\_Gomez-Marin](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/a/ebca7d/32.png) [@Alex\_Gomez-Marin](http://discourse.iapct.org/u/Alex_Gomez-Marin)\
**Post date:** [March 10, 2018, 5:24pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/14 "2018-03-10T17:24:56Z")

</div>

I can’t help it, but I just found the perfect quote that describes how I feel about the power-law Marken issue: as former president Lyndon Johnson famously said, “It’s like wrestling with a pig. You both get dirty but the pig enjoys it.”

> **···**
>
> On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > [philip 2018.03.09]
> 
> > If one varies a distal stimulus q(d) and observes that a measure of  
> > behavior q(o)Â shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.
> 
> > 
> 
> > 
> 
> > Rick,  
> > Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion: Â
> 
> > 
> 
> > Â Â Â Â
> 
> On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > I mean chapter 2
> 
> On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Chapter 1
> 
> On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> [Rick Marken 2018-03-09\_15:57:13]
> 
> > [philip 2018.03.09]
> 
> > 
> 
> > Dear Rick,
> 
> > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> RM: Where does he say that?? Page and paragraph please.
> 
> Best
> 
> RickÂ
> 
> >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > 
> > 1. The relationship between the cursor movement and the disturbance; and
> 
> > 1. The relationship between the mouse movement and the disturbance.
> 
> > Why have you not shown the disturbance in figure 1?     Â
> 
> > 
> 
> > 
> 
> > 
> 
> > Â
> 
> > 
> 
> > 
> 
> > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon)  
> > Virus-free. [www.avast.com](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link)
> 
> –  
> 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 --Antoine de Saint-Exupery
> 
> On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > [Martin Taylor 2018.03.09.13.34]
> > 
> > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > 
> > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > 
> > > > [https://doi.org/10.1007/s00221-018-5208-4](https://doi.org/10.1007/s00221-018-5208-4)
> > > > 
> > > > RM: For those of you who are interested, the full article is available at:
> > > > 
> > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > 
> > > > Best
> > > 
> > > [Martin Taylor 2018.03.08.23.07]
> > > 
> > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > 
> > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> > 
> > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > 
> > =============
> > 
> > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect process.”
> > 
> > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > 
> > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > 
> > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > 
> > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > 
> > I hope to say no more on this very distasteful topic.
> > 
> > Martin
> 
> Alex Gomez-Marin  
> [behavior-of-organisms.org](http://behavior-of-organisms.org)

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 10, 2018, 7:30pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/15 "2018-03-10T19:30:36Z")

</div>

Please don't jump the gun, Alex. We have yet to decide if Rick's is  
telling the truth. He currently has in his possession empirical data  
which he has not shown us. This is the correlation between the  
disturbance and the output. Consider us now in the process of writing  
a complaint to Rick - the pleading phase. Then we begin the discovery  
phase where we ask Rick to display the correlation data relevant to  
determining whether the established scientific protocol for proving  
"Z/M are in error" was ignored.

> **···**
>
> On 3/10/18, Alex Gomez-Marin \<agomezmarin@gmail.com\> wrote:
> 
> > I can't help it, but I just found the perfect quote that describes how I  
> > feel about the power-law Marken issue: as former president Lyndon Johnson  
> > famously said, "It's like wrestling with a pig. You both get dirty but the  
> > pig enjoys it."
> > 
> > On Sat, 10 Mar 2018 at 02:15, PHILIP JERAIR YERANOSIAN \<pyeranos@ucla.edu\> \> wrote:
> > 
> > > I am sorry, I meant to say "correlation between the mouse movement and  
> > > the  
> > > disturbance".
> > > 
> > > On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN \< \>\> pyeranos@ucla.edu\> wrote:
> > > 
> > > > [philip 2018.03.09]  
> > > > Rick,  
> > > > Please note that I am agreeing with your contention that Z/M are making  
> > > > a  
> > > > factual error. I am simply asking you to prove this by showing the  
> > > > correlation between the cursor movement and the disturbance. Please  
> > > > focus  
> > > > on applying the TCV to the cursor movement and not on applying the TCV  
> > > > to  
> > > > the definition of the phrase behavioral illusion. I honestly don't  
> > > > remember  
> > > > if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I  
> > > > assure you that our definitions are mutually consistent. Here is what  
> > > > Bill  
> > > > said in his paper (1978) about the behavioral illusion:
> > > > 
> > > > If one varies a distal stimulus q(d) and observes that a measure of  
> > > > behavior q(o) shows a strong regular dependence on q(d), there is  
> > > > certainly  
> > > > a temptation to assume that the form of the dependence reveals something  
> > > > about the organism. Yet, the comparison we have just seen indicates that  
> > > > the form of the dependence may reflect only properties of the local  
> > > > environment.
> > > > 
> > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN \< \>\>\> pyeranos@ucla.edu\> wrote:
> > > > 
> > > > > I mean chapter 2
> > > > > 
> > > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN \< \>\>\>\> pyeranos@ucla.edu\> wrote:
> > > > > 
> > > > > > Chapter 1
> > > > > > 
> > > > > > On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken \<rsmarken@gmail.com\> \>\>\>\>\> wrote:
> > > > > > 
> > > > > > > [Rick Marken 2018-03-09\_15:57:13]
> > > > > > > 
> > > > > > > [philip 2018.03.09]
> > > > > > > 
> > > > > > > > Dear Rick,  
> > > > > > > > In LCSIII, Bill states that the behavioral illusion refers to the  
> > > > > > > > fact that the behavior does not correlate with the controlled  
> > > > > > > > variable.  
> > > > > > > > Instead, the behavior correlates with the disturbance.
> > > > > > > 
> > > > > > > RM: Where does he say that?? Page and paragraph please.
> > > > > > > 
> > > > > > > Best
> > > > > > > 
> > > > > > > Rick
> > > > > > > 
> > > > > > > > In your paper, the controlled variable is the cursor movement and  
> > > > > > > > the behavior is the mouse movement. PCT would predict that a  
> > > > > > > > correlation exists between the mouse movement and the disturbance,  
> > > > > > > > but not  
> > > > > > > > between the cursor movement and the mouse movement and not between  
> > > > > > > > the  
> > > > > > > > cursor movement and the disturbance. You contend that "the cursor  
> > > > > > > > movements are the voluntary movements that follow the power law".  
> > > > > > > > Please state  
> > > > > > > > exactly that the power relationship between curvature and velocity  
> > > > > > > > for the  
> > > > > > > > mouse movement differs considerably from that for the cursor  
> > > > > > > > movement. Now  
> > > > > > > > you have to show two things:  
> > > > > > > > 1) The relationship between the cursor movement and the disturbance;  
> > > > > > > > and  
> > > > > > > > 2) The relationship between the mouse movement and the disturbance.  
> > > > > > > > Why have you not shown the disturbance in figure 1?
> > > > > > > > 
> > > > > > > > \<[Safe emailing Mac | Avast](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=icon&gt);  
> > > > > > > > Virus-free.  
> > > > > > > > www.avast.com  
> > > > > > > > \<[Safe emailing Mac | Avast](https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail&utm_term=link&gt);  
> > > > > > > > \<#m\_1171410225649325262\_m\_2652284494106488085\_m\_933963387916827761\_m\_5389974439238208080\_m\_-7168124933558332736\_m\_493210360072632837\_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2\>
> > > > > > > > 
> > > > > > > > On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor \>\>\>\>\>\>\> \<mmt-csg@mmtaylor.net\> \>\>\>\>\>\>\> wrote:
> > > > > > > > 
> > > > > > > > > [Martin Taylor 2018.03.09.13.34]
> > > > > > > > > 
> > > > > > > > > [Martin Taylor 2018.03.08.23.07]
> > > > > > > > > 
> > > > > > > > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > > > > > > > 
> > > > > > > > > > > RM: Our reply to the comments of Taylor and Zago et al on our  
> > > > > > > > > > > power law paper have been published in the on-line edition of  
> > > > > > > > > > > Experimental  
> > > > > > > > > > > Brain Research. The abstract is available at:
> > > > > > > > > > > 
> > > > > > > > > > > [The power law as behavioral illusion: reappraising the reappraisals | Experimental Brain Research](https://doi.org/10.1007/s00221-018-5208-4)
> > > > > > > > > > > 
> > > > > > > > > > > RM: For those of you who are interested, the full article is  
> > > > > > > > > > > available at:
> > > > > > > > > > > 
> > > > > > > > > > > [Dropbox - MarkenShafferReappraisal.pdf - Simplify your life](https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0)
> > > > > > > > > > > 
> > > > > > > > > > > Best
> > > > > > > > > > > 
> > > > > > > > > > > I realize there's no point in re-arguing the mathematical and
> > > > > > > > > > 
> > > > > > > > > > logical points of why your paper was utter nonsense. You know all  
> > > > > > > > > > these.
> > > > > > > > > > 
> > > > > > > > > > But I wonder why you felt it necessary to rebut imaginary  
> > > > > > > > > > criticisms that were not made rather than those that were made, and  
> > > > > > > > > > why you  
> > > > > > > > > > imputed motives for the criticisms that you knew to be false? ...
> > > > > > > > > 
> > > > > > > > > I hadn't intended to say anything further on the M&S paper or their  
> > > > > > > > > rebuttal to my published comment, but Bruce Abbott was kind enough  
> > > > > > > > > to send  
> > > > > > > > > me a complete copy of the rebuttal. In it I find a passage so  
> > > > > > > > > breathtakingly false that it blows all the others away. Again I  
> > > > > > > > > cannot  
> > > > > > > > > speak for Alex, but I would be surprised if he felt very  
> > > > > > > > > differently.
> > > > > > > > > 
> > > > > > > > > =============  
> > > > > > > > > Under the heading "Power Law as Behavioural Illusion" M&S say: "As  
> > > > > > > > > noted above, our fundamental theoretical error, according to Z/M  
> > > > > > > > > and  
> > > > > > > > > Taylor, was the failure to see that movement production is a  
> > > > > > > > > cause�effect
> 
> > > > > > > > > process."
> > > > > > > > > 
> > > > > > > > > Nothing could be further from the truth. Any reader of my comment  
> > > > > > > > > would know that the fundamental theoretical error was a failure to  
> > > > > > > > > see that  
> > > > > > > > > a spatial property has no component of time in it. More directly,  
> > > > > > > > > that what  
> > > > > > > > > they took to be a measured value was actually a technique for  
> > > > > > > > > measuring a  
> > > > > > > > > value. Put in an even more superficial way, as in my published  
> > > > > > > > > comment,  
> > > > > > > > > their fundamental error was to take a measured velocity as a  
> > > > > > > > > stand-in for  
> > > > > > > > > the concept of velocity in which every possible velocity would  
> > > > > > > > > serve  
> > > > > > > > > equally well. Since the impression produced on a casual reader by  
> > > > > > > > > the  
> > > > > > > > > original M&S paper could easily be that "movement production is a  
> > > > > > > > > cause-effect process", velocity being caused by curvature, my  
> > > > > > > > > published  
> > > > > > > > > comment was as much a rejection of that view as it was a rejection  
> > > > > > > > > of their  
> > > > > > > > > faulty logic.
> > > > > > > > > 
> > > > > > > > > M&S go on to say: "This can be seen in the fact that their  
> > > > > > > > > criticisms of our paper are all aimed at showing that the speed of  
> > > > > > > > > a  
> > > > > > > > > movement depends on (is caused by) its curvature and/or that the  
> > > > > > > > > relationship between the speed and curvature of a movement depends  
> > > > > > > > > on a  
> > > > > > > > > third variable, such as “physiological constraints."
> > > > > > > > > 
> > > > > > > > > This statement is an outright and presumably deliberate  
> > > > > > > > > contradiction to the entire sense of my comment. They should have  
> > > > > > > > > said:  
> > > > > > > > > "Their criticisms of our paper are all aimed at showing that the  
> > > > > > > > > speed of a  
> > > > > > > > > movement DOES NOT depend on (is caused by) its curvature and/or that  
> > > > > > > > > the  
> > > > > > > > > relationship between the speed and curvature of a movement DOES NOT  
> > > > > > > > > depend  
> > > > > > > > > on a third variable, such as “physiological constraints" .
> > > > > > > > > 
> > > > > > > > > Why M&S choose to completely invert the sense of my entire critique  
> > > > > > > > > is between them and their consciences. I can only assume that the  
> > > > > > > > > submission delay of "reappraisal" was intended to ensure that it  
> > > > > > > > > would not  
> > > > > > > > > appear in the same journal issue as my comment, and that readers of  
> > > > > > > > > the  
> > > > > > > > > "reappraisal" would not take the trouble to check the tenuous  
> > > > > > > > > relationship  
> > > > > > > > > between my comment and their rebuttal.
> > > > > > > > > 
> > > > > > > > > I hope to say no more on this very distasteful topic.
> > > > > > > > > 
> > > > > > > > > Martin
> > > > > > > 
> > > > > > > --  
> > > > > > > Richard S. Marken
> > > > > > > 
> > > > > > > "Perfection is achieved not when you have nothing more to add, but  
> > > > > > > when you  
> > > > > > > have nothing left to take away.�?  
> > > > > > > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;--Antoine de Saint-Exupery
> > > 
> > > --
> > 
> > Alex Gomez-Marin  
> > behavior-of-organisms.org

---

<div class="post-metadata">

**Author:** ![\_Boris\_Hartman](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/e8c25b/32.png) [@\_Boris\_Hartman](http://discourse.iapct.org/u/_Boris_Hartman)\
**Post date:** [March 11, 2018, 11:47am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/16 "2018-03-11T11:47:24Z")

</div>

Dear Alex

> **···**
>
> **From:** Alex Gomez-Marin [[mailto:agomezmarin@gmail.com](mailto:agomezmarin@gmail.com)]  
> **Sent:** Saturday, March 10, 2018 6:25 PM  
> **To:** csgnet@lists.illinois.edu  
> **Subject:** Re: Reappraising the Power Law Reappraisals
> 
> I can’t help it, but I just found the perfect quote that describes how I feel about the power-law Marken issue: asformer president Lyndon Johnson famously said, “It’s like wrestling with a pig. You both get dirty but the pig enjoys it.”
> 
> HB : I like this quote very much JJJ, although It’s not by Barbs standards.
> 
> Best Regards,
> 
> Boris
> 
> On Sat, 10 Mar 2018 at 02:15, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > I am sorry, I meant to say “correlation between the mouse movement and the disturbance”.
> 
> > On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > [philip 2018.03.09]
> 
> > Rick,  
> > Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion:
> 
> > If one varies a distal stimulus q(d) and observes that a measure of behavior q(o) shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.
> 
> > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > I mean chapter 2
> 
> > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Chapter 1
> 
> > On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> > [Rick Marken 2018-03-09\_15:57:13]
> 
> > > [philip 2018.03.09]
> 
> > > Dear Rick,
> 
> > > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> > RM: Where does he say that?? Page and paragraph please.
> 
> > Best
> 
> > Rick
> 
> > > In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > > 
> > > 1. The relationship between the cursor movement and the disturbance; and
> 
> > > 1. The relationship between the mouse movement and the disturbance.
> 
> > > Why have you not shown the disturbance in figure 1?
> 
> > > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dicon&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=dwsP6Ogi9pn7sLnICnQDCnljVgBE_KgJRnR5JKErtBc&e=)
> 
> > > Virus-free. [www.avast.com](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dlink&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=2vEy3im7aaa8URTG5NBe0NtjtoLdRelFZQJK87ygNNg&e=)
> 
> > > On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > > [Martin Taylor 2018.03.09.13.34]
> 
> > > [Martin Taylor 2018.03.08.23.07]
> 
> > > [Rick Marken 2018-03-08\_11:24:06]
> > > 
> > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > 
> > > [https://doi.org/10.1007/s00221-018-5208-4](https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_s00221-2D018-2D5208-2D4&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=NP_Wa7eCfk_THQzTRPdkXv_WZZpglADKQ6FZjQLKlGc&e=)
> > > 
> > > RM: For those of you who are interested, the full article is available at:
> > > 
> > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dropbox.com_s_3m51ko4vs1xdult_MarkenShafferReappraisal.pdf-3Fdl-3D0&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=3t_VmGppk-oX9gm8A-AXJkZWVm_C7h13Q5yaBP02Olk&e=)
> > > 
> > > Best
> 
> > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > 
> > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> 
> > > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > > 
> > > =============  
> > > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effect processs.”
> > > 
> > > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > > 
> > > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > > 
> > > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > > 
> > > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > > 
> > > I hope to say no more on this very distasteful topic.
> > > 
> > > Martin
> 
> > 
> 
> > –
> 
> > Richard S. Marken
> 
> > "Perfection is achieved not when you have nothing more to add, but when you  
> > have nothing left to take away.�  
> > –Antoine de Saint-Exupery
> 
> –
> 
> Alex Gomez-Marin  
> [behavior-of-organisms.org](https://urldefense.proofpoint.com/v2/url?u=http-3A__behavior-2Dof-2Dorganisms.org&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=vOVZxt6c8jFAXNHCcs3nESzkZdFUtOCJIOAuaqPndO0&e=)

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 14, 2018, 5:43am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/17 "2018-03-14T05:43:12Z")

</div>

Maybe the power law results from the control of the “linear optical velocityâ€?. The pen moves faster where it curves more because the curvature slows the LOV. On the other hand… Let’s have a person scan an ellipse with their eyes and see what happens. I’ll bet the eye moves slower where it curves more because the curvature speeds the linear optical acceleration.Â

> **···**
>
> On Sunday, March 11, 2018, Boris Hartman [boris.hartman@masicom.net](mailto:boris.hartman@masicom.net) wrote:
> 
> > Dear Alex…
> 
> > Â
> 
> > **From:** Alex Gomez-Marin [[mailto:agomezmarin@gmail.com](mailto:agomezmarin@gmail.com)]  
> > **Sent:** Saturday, March 10, 2018 6:25 PM  
> > **To:** csgnet@lists.illinois.edu  
> > **Subject:** Re: Reappraising the Power Law Reappraisals
> 
> > Â
> 
> > I can’t help it, but I just found the perfect quote that describes how I feel about the power-law Marken issue: as former president Lyndon Johnson famously said, “It’s like wrestling with a pig. You both get dirty but the pig enjoys it.”
> 
> > Â
> 
> > HB : I like this quote very much JJJ, although It’s not by Barbs standards.
> 
> > Â
> 
> > Best Regards,
> 
> > Â
> 
> > Boris
> 
> > Â
> 
> > Â
> 
> > Â
> 
> > Â
> 
> > 
> 
> > Â
> 
> > On Sat, 10 Mar 2018 at 02:15, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > I am sorry, I meant to say “correlation between the mouse movement and the disturbance”.
> 
> > > Â
> 
> > > On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > [philip 2018.03.09]
> 
> > > Rick,  
> > > Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion: Â
> 
> > > If one varies a distal stimulus q(d) and observes that a measure of behavior q(o) shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > > Â Â Â Â
> 
> > > Â
> 
> > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > I mean chapter 2
> 
> > > Â
> 
> > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > Chapter 1
> 
> > > Â
> 
> > > On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> > > [Rick Marken 2018-03-09\_15:57:13]
> 
> > > > Â
> 
> > > > [philip 2018.03.09]
> 
> > > > Â
> 
> > > > Dear Rick,
> 
> > > > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> > > Â
> 
> > > RM: Where does he say that?? Page and paragraph please.
> 
> > > Â
> 
> > > Best
> 
> > > Â
> 
> > > RickÂ
> 
> > > >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > > > 
> > > > 1. The relationship between the cursor movement and the disturbance; and
> 
> > > > 1. The relationship between the mouse movement and the disturbance.
> 
> > > > Why have you not shown the disturbance in figure 1?     Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dicon&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=dwsP6Ogi9pn7sLnICnQDCnljVgBE_KgJRnR5JKErtBc&e=)
> 
> > > > Virus-free. [www.avast.com](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dlink&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=2vEy3im7aaa8URTG5NBe0NtjtoLdRelFZQJK87ygNNg&e=)
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > > > [Martin Taylor 2018.03.09.13.34]
> 
> > > > [Martin Taylor 2018.03.08.23.07]
> 
> > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > 
> > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > 
> > > > [https://doi.org/10.1007/s00221-018-5208-4](https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_s00221-2D018-2D5208-2D4&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=NP_Wa7eCfk_THQzTRPdkXv_WZZpglADKQ6FZjQLKlGc&e=)
> > > > 
> > > > RM: For those of you who are interested, the full article is available at:
> > > > 
> > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dropbox.com_s_3m51ko4vs1xdult_MarkenShafferReappraisal.pdf-3Fdl-3D0&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=3t_VmGppk-oX9gm8A-AXJkZWVm_C7h13Q5yaBP02Olk&e=)
> > > > 
> > > > Best
> 
> > > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > > 
> > > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> 
> > > > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > > > 
> > > > =============  
> > > > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effecct process.”
> > > > 
> > > > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > > > 
> > > > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > > > 
> > > > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > > > 
> > > > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > > > 
> > > > I hope to say no more on this very distasteful topic.
> > > > 
> > > > Martin
> 
> > > > Â
> 
> > >
> 
> > > Â
> 
> > > –
> 
> > > Richard S. MarkenÂ
> 
> > > "Perfection is achieved not when you have nothing more to add, but when you  
> > > have nothing left to take away.�  
> > > Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > –
> 
> > Alex Gomez-Marin  
> > [behavior-of-organisms.org](https://urldefense.proofpoint.com/v2/url?u=http-3A__behavior-2Dof-2Dorganisms.org&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=vOVZxt6c8jFAXNHCcs3nESzkZdFUtOCJIOAuaqPndO0&e=)

---

<div class="post-metadata">

**Author:** ![Alex\_Gomez-Marin](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/a/ebca7d/32.png) [@Alex\_Gomez-Marin](http://discourse.iapct.org/u/Alex_Gomez-Marin)\
**Post date:** [March 14, 2018, 8:02am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/18 "2018-03-14T08:02:58Z")

</div>

We have done that experiment with eye-tracking devices. But we are carefully analyzing it, and repeating it. It is not like you can show 1 cherry-picked case without showing any log-log plot, nor methods nor anything and get it published. Of course you are the world-wide famous proposal and defender what-ever-it-takes of RCT, of course… (we are also trying to reproduce and see all the hidden important details behind Rick’s figure 1…)

> **···**
>
> On Wed, Mar 14, 2018 at 6:43 AM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Maybe the power law results from the control of the “linear optical velocityâ€?. The pen moves faster where it curves more because the curvature slows the LOV. On the other hand… Let’s have a person scan an ellipse with their eyes and see what happens. I’ll bet the eye moves slower where it curves more because the curvature speeds the linear optical acceleration.Â
> > 
> > On Sunday, March 11, 2018, Boris Hartman [boris.hartman@masicom.net](mailto:boris.hartman@masicom.net) wrote:
> > 
> > > Dear Alex…
> 
> > > Â
> 
> > > **From:** Alex Gomez-Marin [[mailto:agomezmarin@gmail.com](mailto:agomezmarin@gmail.com)]  
> > > **Sent:** Saturday, March 10, 2018 6:25 PM  
> > > **To:** csgnet@lists.illinois.edu  
> > > **Subject:** Re: Reappraising the Power Law Reappraisals
> 
> > > Â
> 
> > > I can’t help it, but I just found the perfect quote that describes how I feel about the power-law Marken issue: as former president Lyndon Johnson famously said, “It’s like wrestling with a pig. You both get dirty but the pig enjoys it.”
> 
> > > Â
> 
> > > HB : I like this quote very much JJJ, although It’s not by Barbs standards.
> 
> > > Â
> 
> > > Best Regards,
> 
> > > Â
> 
> > > Boris
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > >
> 
> > > Â
> 
> > > On Sat, 10 Mar 2018 at 02:15, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > I am sorry, I meant to say “correlation between the mouse movement and the disturbance”.
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > [philip 2018.03.09]
> 
> > > > Rick,  
> > > > Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion: Â
> 
> > > > If one varies a distal stimulus q(d) and observes that a measure of behavior q(o) shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â Â Â Â
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > I mean chapter 2
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > Chapter 1
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> > > > [Rick Marken 2018-03-09\_15:57:13]
> 
> > > > > Â
> 
> > > > > [philip 2018.03.09]
> 
> > > > > Â
> 
> > > > > Dear Rick,
> 
> > > > > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> > > > Â
> 
> > > > RM: Where does he say that?? Page and paragraph please.
> 
> > > > Â
> 
> > > > Best
> 
> > > > Â
> 
> > > > RickÂ
> 
> > > > >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > > > > 
> > > > > 1. The relationship between the cursor movement and the disturbance; and
> 
> > > > > 1. The relationship between the mouse movement and the disturbance.
> 
> > > > > Why have you not shown the disturbance in figure 1?     Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dicon&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=dwsP6Ogi9pn7sLnICnQDCnljVgBE_KgJRnR5JKErtBc&e=)
> 
> > > > > Virus-free. [www.avast.com](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dlink&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=2vEy3im7aaa8URTG5NBe0NtjtoLdRelFZQJK87ygNNg&e=)
> 
> > > > > Â
> 
> > > > > On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > > > > [Martin Taylor 2018.03.09.13.34]
> 
> > > > > [Martin Taylor 2018.03.08.23.07]
> 
> > > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > > 
> > > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > > 
> > > > > [https://doi.org/10.1007/s00221-018-5208-4](https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_s00221-2D018-2D5208-2D4&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=NP_Wa7eCfk_THQzTRPdkXv_WZZpglADKQ6FZjQLKlGc&e=)
> > > > > 
> > > > > RM: For those of you who are interested, the full article is available at:
> > > > > 
> > > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dropbox.com_s_3m51ko4vs1xdult_MarkenShafferReappraisal.pdf-3Fdl-3D0&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=3t_VmGppk-oX9gm8A-AXJkZWVm_C7h13Q5yaBP02Olk&e=)
> > > > > 
> > > > > Best
> 
> > > > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > > > 
> > > > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> 
> > > > > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > > > > 
> > > > > =============  
> > > > > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effecct process.”
> > > > > 
> > > > > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > > > > 
> > > > > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > > > > 
> > > > > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > > > > 
> > > > > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > > > > 
> > > > > I hope to say no more on this very distasteful topic.
> > > > > 
> > > > > Martin
> 
> > > > > Â
> 
> > > >
> 
> > > > Â
> 
> > > > –
> 
> > > > Richard S. MarkenÂ
> 
> > > > "Perfection is achieved not when you have nothing more to add, but when you  
> > > > have nothing left to take away.�  
> > > > Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > –
> 
> > > Alex Gomez-Marin  
> > > [behavior-of-organisms.org](https://urldefense.proofpoint.com/v2/url?u=http-3A__behavior-2Dof-2Dorganisms.org&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=vOVZxt6c8jFAXNHCcs3nESzkZdFUtOCJIOAuaqPndO0&e=)
> 
> * * *
> 
> Alex Gomez-Marin, PhD
> 
> Research Group Leader
> 
> Instituto de Neurociencias
> 
> [behavior-of-organisms.org](http://www.behavior-of-organisms.org)

---

<div class="post-metadata">

**Author:** ![Alex\_Gomez-Marin](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/a/ebca7d/32.png) [@Alex\_Gomez-Marin](http://discourse.iapct.org/u/Alex_Gomez-Marin)\
**Post date:** [March 14, 2018, 8:03am UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/19 "2018-03-14T08:03:29Z")

</div>

I meant: “Of course IF you are”

> **···**
>
> On Wed, Mar 14, 2018 at 9:02 AM, Alex Gomez-Marin [agomezmarin@gmail.com](mailto:agomezmarin@gmail.com) wrote:
> 
> > We have done that experiment with eye-tracking devices. But we are carefully analyzing it, and repeating it. It is not like you can show 1 cherry-picked case without showing any log-log plot, nor methods nor anything and get it published. Of course you are the world-wide famous proposal and defender what-ever-it-takes of RCT, of course… (we are also trying to reproduce and see all the hidden important details behind Rick’s figure 1…)
> 
> * * *
> 
> Alex Gomez-Marin, PhD
> 
> Research Group Leader
> 
> Instituto de Neurociencias
> 
> [behavior-of-organisms.org](http://www.behavior-of-organisms.org)
> 
> * * *
> 
> Alex Gomez-Marin, PhD
> 
> Research Group Leader
> 
> Instituto de Neurociencias
> 
> [behavior-of-organisms.org](http://www.behavior-of-organisms.org)
> 
> On Wed, Mar 14, 2018 at 6:43 AM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Maybe the power law results from the control of the “linear optical velocityâ€?. The pen moves faster where it curves more because the curvature slows the LOV. On the other hand… Let’s have a person scan an ellipse with their eyes and see what happens. I’ll bet the eye moves slower where it curves more because the curvature speeds the linear optical acceleration.Â
> > 
> > On Sunday, March 11, 2018, Boris Hartman [boris.hartman@masicom.net](mailto:boris.hartman@masicom.net) wrote:
> > 
> > > Dear Alex…
> 
> > > Â
> 
> > > **From:** Alex Gomez-Marin [[mailto:agomezmarin@gmail.com](mailto:agomezmarin@gmail.com)]  
> > > **Sent:** Saturday, March 10, 2018 6:25 PM  
> > > **To:** csgnet@lists.illinois.edu  
> > > **Subject:** Re: Reappraising the Power Law Reappraisals
> 
> > > Â
> 
> > > I can’t help it, but I just found the perfect quote that describes how I feel about the power-law Marken issue: as former president Lyndon Johnson famously said, “It’s like wrestling with a pig. You both get dirty but the pig enjoys it.”
> 
> > > Â
> 
> > > HB : I like this quote very much JJJ, although It’s not by Barbs standards.
> 
> > > Â
> 
> > > Best Regards,
> 
> > > Â
> 
> > > Boris
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > >
> 
> > > Â
> 
> > > On Sat, 10 Mar 2018 at 02:15, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > I am sorry, I meant to say “correlation between the mouse movement and the disturbance”.
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > [philip 2018.03.09]
> 
> > > > Rick,  
> > > > Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion: Â
> 
> > > > If one varies a distal stimulus q(d) and observes that a measure of behavior q(o) shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â Â Â Â
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > I mean chapter 2
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > Chapter 1
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> > > > [Rick Marken 2018-03-09\_15:57:13]
> 
> > > > > Â
> 
> > > > > [philip 2018.03.09]
> 
> > > > > Â
> 
> > > > > Dear Rick,
> 
> > > > > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> > > > Â
> 
> > > > RM: Where does he say that?? Page and paragraph please.
> 
> > > > Â
> 
> > > > Best
> 
> > > > Â
> 
> > > > RickÂ
> 
> > > > >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > > > > 
> > > > > 1. The relationship between the cursor movement and the disturbance; and
> 
> > > > > 1. The relationship between the mouse movement and the disturbance.
> 
> > > > > Why have you not shown the disturbance in figure 1?     Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dicon&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=dwsP6Ogi9pn7sLnICnQDCnljVgBE_KgJRnR5JKErtBc&e=)
> 
> > > > > Virus-free. [www.avast.com](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dlink&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=2vEy3im7aaa8URTG5NBe0NtjtoLdRelFZQJK87ygNNg&e=)
> 
> > > > > Â
> 
> > > > > On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > > > > [Martin Taylor 2018.03.09.13.34]
> 
> > > > > [Martin Taylor 2018.03.08.23.07]
> 
> > > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > > 
> > > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > > 
> > > > > [https://doi.org/10.1007/s00221-018-5208-4](https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_s00221-2D018-2D5208-2D4&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=NP_Wa7eCfk_THQzTRPdkXv_WZZpglADKQ6FZjQLKlGc&e=)
> > > > > 
> > > > > RM: For those of you who are interested, the full article is available at:
> > > > > 
> > > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dropbox.com_s_3m51ko4vs1xdult_MarkenShafferReappraisal.pdf-3Fdl-3D0&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=3t_VmGppk-oX9gm8A-AXJkZWVm_C7h13Q5yaBP02Olk&e=)
> > > > > 
> > > > > Best
> 
> > > > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > > > 
> > > > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> 
> > > > > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > > > > 
> > > > > =============  
> > > > > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effecct process.”
> > > > > 
> > > > > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > > > > 
> > > > > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > > > > 
> > > > > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > > > > 
> > > > > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > > > > 
> > > > > I hope to say no more on this very distasteful topic.
> > > > > 
> > > > > Martin
> 
> > > > > Â
> 
> > > >
> 
> > > > Â
> 
> > > > –
> 
> > > > Richard S. MarkenÂ
> 
> > > > "Perfection is achieved not when you have nothing more to add, but when you  
> > > > have nothing left to take away.�  
> > > > Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > –
> 
> > > Alex Gomez-Marin  
> > > [behavior-of-organisms.org](https://urldefense.proofpoint.com/v2/url?u=http-3A__behavior-2Dof-2Dorganisms.org&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=vOVZxt6c8jFAXNHCcs3nESzkZdFUtOCJIOAuaqPndO0&e=)

---

<div class="post-metadata">

**Author:** ![PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/p/bc79bd/32.png) [@PHILIP\_JERAIR\_YERANO](http://discourse.iapct.org/u/PHILIP_JERAIR_YERANO)\
**Post date:** [March 14, 2018, 3:18pm UTC](http://discourse.iapct.org/t/reappraising-the-power-law-reappraisals/9628/20 "2018-03-14T15:18:20Z")

</div>

[philip 2018.03.14]

It looks like Rick is using a version of the “squaring the circleâ€? experiment. Which may or may not be appropriate, and I hope you will see through it. As for the eye-tracking experiments…it helps us distinguish the two classes of behaviors. On the one hand, behaviors that are responses to distal stimuli (muscular forces that orient eyes and other EM sensory organs), and behaviors that are responses to proximal stimuli (haptic forces).Â

> **···**
>
> * * *
> 
> Alex Gomez-Marin, PhD
> 
> Research Group Leader
> 
> Instituto de Neurociencias
> 
> [behavior-of-organisms.org](http://www.behavior-of-organisms.org)
> 
> On Wed, Mar 14, 2018 at 9:02 AM, Alex Gomez-Marin [agomezmarin@gmail.com](mailto:agomezmarin@gmail.com) wrote:
> 
> > We have done that experiment with eye-tracking devices. But we are carefully analyzing it, and repeating it. It is not like you can show 1 cherry-picked case without showing any log-log plot, nor methods nor anything and get it published. Of course you are the world-wide famous proposal and defender what-ever-it-takes of RCT, of course… (we are also trying to reproduce and see all the hidden important details behind Rick’s figure 1…)
> 
> * * *
> 
> Alex Gomez-Marin, PhD
> 
> Research Group Leader
> 
> Instituto de Neurociencias
> 
> [behavior-of-organisms.org](http://www.behavior-of-organisms.org)
> 
> On Wed, Mar 14, 2018 at 6:43 AM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > Maybe the power law results from the control of the “linear optical velocityâ€?. The pen moves faster where it curves more because the curvature slows the LOV. On the other hand… Let’s have a person scan an ellipse with their eyes and see what happens. I’ll bet the eye moves slower where it curves more because the curvature speeds the linear optical acceleration.Â
> > 
> > On Sunday, March 11, 2018, Boris Hartman [boris.hartman@masicom.net](mailto:boris.hartman@masicom.net) wrote:
> > 
> > > Dear Alex…
> 
> > > Â
> 
> > > **From:** Alex Gomez-Marin [[mailto:agomezmarin@gmail.com](mailto:agomezmarin@gmail.com)]  
> > > **Sent:** Saturday, March 10, 2018 6:25 PM  
> > > **To:** csgnet@lists.illinois.edu  
> > > **Subject:** Re: Reappraising the Power Law Reappraisals
> 
> > > Â
> 
> > > I can’t help it, but I just found the perfect quote that describes how I feel about the power-law Marken issue: as former president Lyndon Johnson famously said, “It’s like wrestling with a pig. You both get dirty but the pig enjoys it.”
> 
> > > Â
> 
> > > HB : I like this quote very much JJJ, although It’s not by Barbs standards.
> 
> > > Â
> 
> > > Best Regards,
> 
> > > Â
> 
> > > Boris
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > > Â
> 
> > >
> 
> > > Â
> 
> > > On Sat, 10 Mar 2018 at 02:15, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > I am sorry, I meant to say “correlation between the mouse movement and the disturbance”.
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 5:12 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > [philip 2018.03.09]
> 
> > > > Rick,  
> > > > Please note that I am agreeing with your contention that Z/M are making a factual error. I am simply asking you to prove this by showing the correlation between the cursor movement and the disturbance. Please focus on applying the TCV to the cursor movement and not on applying the TCV to the definition of the phrase behavioral illusion. I honestly don’t remember if Bill used the phrase behavioral illusion in LCSIII chapter 2, but I assure you that our definitions are mutually consistent. Here is what Bill said in his paper (1978) about the behavioral illusion: Â
> 
> > > > If one varies a distal stimulus q(d) and observes that a measure of behavior q(o) shows a strong regular dependence on q(d), there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â Â Â Â
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > I mean chapter 2
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 4:50 PM, PHILIP JERAIR YERANOSIAN [pyeranos@ucla.edu](mailto:pyeranos@ucla.edu) wrote:
> 
> > > > Chapter 1
> 
> > > > Â
> 
> > > > On Fri, Mar 9, 2018 at 3:57 PM, Richard Marken [rsmarken@gmail.com](mailto:rsmarken@gmail.com) wrote:
> 
> > > > [Rick Marken 2018-03-09\_15:57:13]
> 
> > > > > Â
> 
> > > > > [philip 2018.03.09]
> 
> > > > > Â
> 
> > > > > Dear Rick,
> 
> > > > > In LCSIII, Bill states that the behavioral illusion refers to the fact that the behavior does not correlate with the controlled variable. Instead, the behavior correlates with the disturbance.
> 
> > > > Â
> 
> > > > RM: Where does he say that?? Page and paragraph please.
> 
> > > > Â
> 
> > > > Best
> 
> > > > Â
> 
> > > > RickÂ
> 
> > > > >  In your paper, the controlled variable is the cursor movement and the behavior is the mouse movement. PCT would predict that a correlation exists between the mouse movement and the disturbance, but not between the cursor movement and the mouse movement and not between the cursor movement and the disturbance. You contend that “the cursor movements are the voluntary movements that follow the power law”. Please state exactly that the power relationship between curvature and velocity for the mouse movement differs considerably from that for the cursor movement. Now you have to show two things:
> > > > > 
> > > > > 1. The relationship between the cursor movement and the disturbance; and
> 
> > > > > 1. The relationship between the mouse movement and the disturbance.
> 
> > > > > Why have you not shown the disturbance in figure 1?     Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > Â
> 
> > > > > [![](http://discourse.iapct.org/uploads/default/original/2X/a/aa7c81a314df14f3a4acac74f5ba0fa269d58467.gif)](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dicon&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=dwsP6Ogi9pn7sLnICnQDCnljVgBE_KgJRnR5JKErtBc&e=)
> 
> > > > > Virus-free. [www.avast.com](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.avast.com_sig-2Demail-3Futm-5Fmedium-3Demail-26utm-5Fsource-3Dlink-26utm-5Fcampaign-3Dsig-2Demail-26utm-5Fcontent-3Dwebmail-26utm-5Fterm-3Dlink&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=2vEy3im7aaa8URTG5NBe0NtjtoLdRelFZQJK87ygNNg&e=)
> 
> > > > > Â
> 
> > > > > On Fri, Mar 9, 2018 at 11:12 AM, Martin Taylor [mmt-csg@mmtaylor.net](mailto:mmt-csg@mmtaylor.net) wrote:
> 
> > > > > [Martin Taylor 2018.03.09.13.34]
> 
> > > > > [Martin Taylor 2018.03.08.23.07]
> 
> > > > > [Rick Marken 2018-03-08\_11:24:06]
> > > > > 
> > > > > RM: Our reply to the comments of Taylor and Zago et al on our power law paper have been published in the on-line edition of Experimental Brain Research. The abstract is available at:
> > > > > 
> > > > > [https://doi.org/10.1007/s00221-018-5208-4](https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_s00221-2D018-2D5208-2D4&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=NP_Wa7eCfk_THQzTRPdkXv_WZZpglADKQ6FZjQLKlGc&e=)
> > > > > 
> > > > > RM: For those of you who are interested, the full article is available at:
> > > > > 
> > > > > [https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0](https://urldefense.proofpoint.com/v2/url?u=https-3A__www.dropbox.com_s_3m51ko4vs1xdult_MarkenShafferReappraisal.pdf-3Fdl-3D0&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=3t_VmGppk-oX9gm8A-AXJkZWVm_C7h13Q5yaBP02Olk&e=)
> > > > > 
> > > > > Best
> 
> > > > > I realize there’s no point in re-arguing the mathematical and logical points of why your paper was utter nonsense. You know all these.
> > > > > 
> > > > > But I wonder why you felt it necessary to rebut imaginary criticisms that were not made rather than those that were made, and why you imputed motives for the criticisms that you knew to be false? …
> 
> > > > > I hadn’t intended to say anything further on the M&S paper or their rebuttal to my published comment, but Bruce Abbott was kind enough to send me a complete copy of the rebuttal. In it I find a passage so breathtakingly false that it blows all the others away. Again I cannot speak for Alex, but I would be surprised if he felt very differently.
> > > > > 
> > > > > =============  
> > > > > Under the heading “Power Law as Behavioural Illusion” M&S say: “As noted above, our fundamental theoretical error, according to Z/M and Taylor, was the failure to see that movement production is a cause–effecct process.”
> > > > > 
> > > > > Nothing could be further from the truth. Any reader of my comment would know that the fundamental theoretical error was a failure to see that a spatial property has no component of time in it. More directly, that what they took to be a measured value was actually a technique for measuring a value. Put in an even more superficial way, as in my published comment, their fundamental error was to take a measured velocity as a stand-in for the concept of velocity in which every possible velocity would serve equally well. Since the impression produced on a casual reader by the original M&S paper could easily be that “movement production is a cause-effect process”, velocity being caused by curvature, my published comment was as much a rejection of that view as it was a rejection of their faulty logic.
> > > > > 
> > > > > M&S go on to say: “This can be seen in the fact that their criticisms of our paper are all aimed at showing that the speed of a movement depends on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement depends on a third variable, such as “physiological constraints.”
> > > > > 
> > > > > This statement is an outright and presumably deliberate contradiction to the entire sense of my comment. They should have said: “Their criticisms of our paper are all aimed at showing that the speed of a movement DOES NOT depend on (is caused by) its curvature and/or that the relationship between the speed and curvature of a movement DOES NOT depend on a third variable, such as “physiological constraints” .
> > > > > 
> > > > > Why M&S choose to completely invert the sense of my entire critique is between them and their consciences. I can only assume that the submission delay of “reappraisal” was intended to ensure that it would not appear in the same journal issue as my comment, and that readers of the “reappraisal” would not take the trouble to check the tenuous relationship between my comment and their rebuttal.
> > > > > 
> > > > > I hope to say no more on this very distasteful topic.
> > > > > 
> > > > > Martin
> 
> > > > > Â
> 
> > > >
> 
> > > > Â
> 
> > > > –
> 
> > > > Richard S. MarkenÂ
> 
> > > > "Perfection is achieved not when you have nothing more to add, but when you  
> > > > have nothing left to take away.�  
> > > > Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --Antoine de Saint-Exupery
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > > Â
> 
> > > –
> 
> > > Alex Gomez-Marin  
> > > [behavior-of-organisms.org](https://urldefense.proofpoint.com/v2/url?u=http-3A__behavior-2Dof-2Dorganisms.org&d=DwMFaQ&c=OCIEmEwdEq_aNlsP4fF3gFqSN-E3mlr2t9JcDdfOZag&r=G2rjwc9SjlT6Blyc8su_Md8P_xOsOTRMJ5teQVBC2qU&m=5MLBiGH7oop7I0wuw4OlmF0wL67JsuWN7UBmWSYE8zg&s=vOVZxt6c8jFAXNHCcs3nESzkZdFUtOCJIOAuaqPndO0&e=)