[Martin Taylor 2018.07.19.10.27]

`[Bruce Nevin`

2018-07-19_09:46:11 ET]

Martin Taylor 2018.07.17.17.16 –

```
Nor am I.
```

`Rick, Martin listed "eight ... falsehoods you`

incorporated in your rebuttal." You replied “they are not

“falsehoods” but the best we could do to understand your

criticisms.” That seems to affirm that you did not

understand his criticisms very well.Â

`I know of two ways to demonstrate understanding,`

and both of them involve a test of understanding that is

akin to the Test for controlled variables. One of the two

ways is to apply what is understood. This demonstrates

control of the perceptions intended by the words. The

other way is to paraphrase in different words and ask if

the paraphrase is correct. This is similar to e.g. the

Coin Game.

`Would it be a fair paraphrase of your to enclose`

each of the eight pairs (statements in Martin’s list and

your rejoinders to them) in this frame?

`When you said [quote from Martin's rebuttal] it`

appeared to us that you meant [quote from your rebuttal of

the rebuttal]. Is that what you intended? If so, [further

rebuttal].

`You actually did this, in effect, at this point`

of your reply:

`It seems to me, naively,`

that this is not an accurate paraphrase. I think Martin’s

point isÂ

`a. that one form of the`

equation is a generalization across all possible

velocities,Â

`b. that the other form of`

the equation can be applied only to particular velocity data

from a particular experiment, andÂ

`c. that you employed the`

latter (b) as though it were equivalently (a) a

generalization across all possible velocities.

`Only Martin can say whether`

or not I have accurately paraphrased what he wrote. If he

affirms that I did, are these paraphrase statements incorrect?

```
Nearly, but not quite. In your (a) there are not two forms of one
```

equation, but two different equations that use the standard

Cartesian expression for velocity, namely v=sqrt((dx/dt)^{2}+(dy/dt)^{2} ).

One equation (my 4) is simply a restatement of the fact that when an

experimenter measures dx/dt and dy/dt for something that moves,

these numbers can be used to produce a velocity (and, incidentally,

a direction of movement). That velocity is a particular finding for

a one-time movement.

```
In your (b) my equation (5) is a standard expression for determining
```

a radius of curvature. If you take any specific curved track and

move along it at arbitrary velocities and changes of velocity, this

expression will give you the same result for the curvature no matter

how the velocity changed. My equations 1, 2, and 3 – all quite

standard – show why this is the case. My equation (3) shows that

one expression for the radius of curvature at a point is V^{3} /D,

where D is Marken and Shaffer’s “cross-product correction factor”.

They use D to show that the “correct” value of the power law is R^{1/3}

= V, and that people report other values of the power only because

they did not know to use this obscure (!) correction factor, D that

they “discovered”.

```
Your (c) is correct as is.
```

`I think you have a kind of`

important typographical error here:

`I think you meant to say`

“we said that your critique was based on your misunderstanding

of those equations.” Is that correct?

```
I leave it to Rick to answer that one. I interpreted them as meaning
```

what was written in the first sentence of the quote, that I thought

that they misunderstood the equations. I did, and do, think so.

However, Rick’s second and third sentences in your quote contain the

falsehood. My claim was never that the derivatives were different.

They aren’t. That I said they were is the falsehood. The claim is

actually what you paraphrased above, that the values substituted in

the expression for R need not be the values found in some particular

movement trace. It is merely convenient to use those readily

available values of the derivatives, whereas Marken and Shaffer

proceed as though ONLY those values could legitimately be used in

the expression.

`Are there possibly other misstatements`

confusing the discussion?

```
Yes, many.
Martin
```

## ···

Rick Marken

2018-07-17_10:31:31 --â€‹

```
This dispute
```

seems at last to be converging toward common

perceptions of what is in dispute, but I still

am not understanding it.

```
RM: What you are saying is that we made the mistake
```

of taking the dot derivatives in the two

Gribble/Ostry equations as being time derivatives.

RM: No,

â€‹â€‹

```
we said that your critique was based on our
```

misunderstanding of those equations. Specifically that

the derivatives in the curvature equation were

different from those in the velocity equation. Your

claim that these derivatives are different is simply

wrong and, thus, invalidates your mathematical

critique from the get go.

```
[Rick Marken
```

2018-07-17_10:31:31]

[Martin Taylor 2018.07.16.15.12]

`MT: As well you have known for a very long time,`

I have insufficient hubris to attempt a model of

observed behaviour before trying the TCV to

figure out what variable(s) might be being

controlled during the task. I have no means to

do the TCV needed, so I refrain from suggesting

a model. You are not so inhibited.

```
RM: You have to have had some idea of what the
```

controlled variable might be when people make

curved movements or you wouldn’t know that the

power law is "almost certainly a side-effect inÂ any

of the experiments that find velocity to have a

near power-law relationship to the radius of

curvature ", as you note in your rebuttal.

In PCT, a “side-effect” is a relationship between

variables that exists because a variable is under

control but this relationship not part of the

process that results in control of that variable.

For example, the relationship between disturbance

and output in a tracking task is a side effect of

controlling the position of the cursor but is not

part of the process that results in control of

cursor position. In order to know that the power

law is, indeed, a side-effect, you had to have an

idea of what variable is under control when people

make curved movements as well as having an idea of

how the instantaneous curvature and velocity of

these movements are related to this variable. This

should have been enough to let you develop a first

approximation to a model of curved movements that

would demonstrate why the instantaneous

curvature and velocity of these movements is a

side effect of controlling this variable. The

model itself would have been a basis for the

TCV; it would be a test of the correctness of

your hypothesis regarding the variable under

control.Â So it would not have been hubris

to model the behavior before doing the TCV since

you presumably had to have had the essential

components of the model in mind when you said that

the power law is almost certainly a side effect.Â

`MT: For the record, here`

are just eight of the falsehoods you

incorporated in your rebuttal of my comment on

the Marken and Shaffer paper (copied from

[Martin Taylor 2018.03.08.23.07]). Despite

having been made aware of their falsity, yet you

continue to repeat some of them on CSGnet. Why

do you do that?

```
RM: BecauseÂ they are not "falsehoods" but the
```

best we could do to understand your criticisms.

Â

`----------begin quote`

(replacing references to “you” with references

to “they”, and added numbering)-------`* MT: (1) 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.*

```
RM: Since, as I noted above, you came up with
```

no hypothesis about what variable might be

controlled, I dismissed your claims of accepting

that the power law is a behavioral illusion

because you gave no evidence of understanding what

a behavioral illusion is.

Â

`MT: (2) M&S say that`

my critique of their 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.*

```
RM: No, we said that your critique was based on
```

our misunderstanding of those equations.

Specifically that the derivatives in the curvature

equation were different from those in the velocity

equation. Your claim that these derivatives are

different is simply wrong and, thus, invalidates

your mathematical critique from the get go.

Â

`MT: (3) I never said`

that the derivation of V = R**

^{1/3}D^{1/3}** 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.*

```
RM: And we never said that you said that the
```

derivation of * V

= R**^{1/3}**D**^{1/3}**Â * was

wrong. We said that what you said about it not

being an equation that can be used to predict V

using linear regression is wrong. Which it is.Â

`MT: (4) 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.*

RM: But that’s what you argued, right here:Â

```
RM: What you are saying is that we made the
```

mistake of taking the dot derivatives in the two

Gribble/Ostry equations as being time derivatives.

But that was not mistake. The mistake is all

yours.

`MT: (5) 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 they 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.*

```
RM: Well, that would be news to all the power
```

law researchers who computed velocity and

curvature the way I did in my analyses, using time

derivatives.

Â

`MT: (6) M&S follow`

this astounding assertion with an couple of

paragraphs to show why the V = R**^{1/3}D^{1/3}** 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 = R**^{1/3}D^{1/3}** ],

which is true for any value of V whatever…”

Any implication that my comment claimed the

equation to be incorrect is false.*

```
RM: What we showed is that that equation has
```

been used by others to show what we showed in our

paper – that using only R (curvature) as the

predictor in a regression on V (speed) – will

result in an estimate of the power coefficient of

R that deviates from 1/3 by an amount proportional

to the correlation between R and D (radial

velocity).Â

Â

`MT: (7) 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.*

```
RM: Your demonstration that our findings are a
```

“tautology” made no sense to us. You made this

claim based on your derivation of an equation for

V of the form V = V. But this is true for any

equation. If X = f(Y) then you can substitute X

for the right side of the equation and write the

equation X = X. That’s not a tautology; that’s

just an irrelevant observation.

`MT: (8) 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 relationship, causal connection

or otherwise, between curvature and speed of

movement.

*

```
RM: You were apparently trying to show,
```

mathematically, that the curvature and velocity of

a curved movement are physically independent, like

the disturbance and output in a tracking task.

Since you didn’t speculate about the controlled

variable that might be simultaneously affected by

these two variables I assumed that you were dong

this to justify the assumptions of power law

researchers that these two variables are either

causally related or simultaneously caused by a

third variable.Â

Â

--------end quote-------

`MT: I repeat from my last message: *"* What's`

the advantage to you of refusing to deal with

scientific points people bring up about your

work?"

```
RM: We dealt with your confusing rebuttal as
```

best we could. There was nothing scientific about

it inasmuch as it was purely mathematical.

Best

Rick

Â

`Well, I guess predictions aren't always`

wrong, and I am indeed not surprised.

`Martin`

–

Richard S.

MarkenÂ

```
"Perfection
```

is achieved not when you

have nothing more to add,

but when you

have

nothing left to take

away.â€?

Â

Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â --Antoine de

Saint-Exupery

Best

Rick

Â

`What's`

the advantage to you of

refusing to deal with

scientific points people bring

up about your work? In what

perception you control would

it create error if you were to

accept normal mathematics or

physics as being valid? When

your work is good, it’s good,

but when you make a mistake,

why does it seem so difficult

for you to correct it? In the

curvature paper none of the

criticisms were relevant to a

PCT interpretation, but you

make out that all of them were

intended to refute a “correct

PCT analysis” of the

experimental findings. Why?`I don't expect an answer to a`

question raised, but I

wouldn’t be surprised at an

answer to something completely

different.