[Martin Taylor 2018.07.17.17.16]

Let’s try again.

```
Rick, could you help me correct my "bogus mathematics" by pointing
```

out by page and paragraph or by equation number specifically where

the mathematics in my comment on the Marken and Shaffer paper is

“bogus”.

```
You can do this without referring either to your rebuttal or to the
```

eight falsehoods that I asked you not to try to justify at this

point. My question is not about them, but specifically about what in

my mathematics you have shown to be bogus. Your previous response

did not address this question.

```
Martin
```

## ···

[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

- 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

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.

`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