Taylor's "Comments on Marken and Shaffer: The power law of movement: an example of a behavioral illusion"

{paper attached}

Abstract

Many researchers who have studied movements along curved paths, under a variety of conditions, by di erent organisms,
mostly human but a couple with non-human organisms, have found a consistent form of relation between the tangential
(along-track) instantaneous velocity V and the local radius of curvature R. The consistent relation is that V ≈ cRk, where k
is a constant less than unity, often near 0.33 but sometimes far from 0.33, and c is a proportionality constant appropriate to
the organism and the situation (see Zago, Matic, Flash, et al. (2017) for many examples in which the power law holds with
widely varying values of the power, as well as cases of simple systems for which everything can be calculated exactly and
in which the power law fails badly). Marken and Sha er (Exp Brain Res 235:1835–1842; 2017), following a challenge by
Gomez-Marin to see whether it is possible to use Perceptual Control Theory (Powers 1973/2005) to explain the power law
results (Alex Gomez-Marin posting to CSGnet@lists.illinois.edu 2016.05.03), claim to have found a mathematical argument
that proves the true exponent of the power relating velocity and radius of curvature always to be 1/3. They say that deviations
from this value occur because researchers have omitted a critical correction “cross-productâ€? factor that the authors label
“Dâ€?. This note questions the logic of the analysis o ered by Marken and Sha er, and argues that even had the analysis been
correct, it would not a ect future research into the reasons why and when the power law is observed and the circumstances
that determine the value of the power found when it is observed.Â

powerHigh.pdf (850 KB)

Cheers Alex

···

On 24 Feb 2018, at 08:41, Alex Gomez-Marin agomezmarin@gmail.com wrote:

{paper attached}

Abstract

Many researchers who have studied movements along curved paths, under a variety of conditions, by di erent organisms,
mostly human but a couple with non-human organisms, have found a consistent form of relation between the tangential
(along-track) instantaneous velocity V and the local radius of curvature R. The consistent relation is that V ≈ cRk, where k
is a constant less than unity, often near 0.33 but sometimes far from 0.33, and c is a proportionality constant appropriate to
the organism and the situation (see Zago, Matic, Flash, et al. (2017) for many examples in which the power law holds with
widely varying values of the power, as well as cases of simple systems for which everything can be calculated exactly and
in which the power law fails badly). Marken and Sha er (Exp Brain Res 235:1835–1842; 2017), following a challenge by
Gomez-Marin to see whether it is possible to use Perceptual Control Theory (Powers 1973/2005) to explain the power law
results (Alex Gomez-Marin posting to CSGnet@lists.illinois.edu 2016.05.03), claim to have found a mathematical argument
that proves the true exponent of the power relating velocity and radius of curvature always to be 1/3. They say that deviations
from this value occur because researchers have omitted a critical correction “cross-product� factor that the authors label
“D�. This note questions the logic of the analysis o ered by Marken and Sha er, and argues that even had the analysis been
correct, it would not a ect future research into the reasons why and when the power law is observed and the circumstances
that determine the value of the power found when it is observed.

<powerHigh.pdf>

Shall we be enlightened with Rick’s official response?

···

On Sun, Feb 25, 2018 at 7:52 AM, Warren Mansell wmansell@gmail.com wrote:

Cheers Alex

On 24 Feb 2018, at 08:41, Alex Gomez-Marin agomezmarin@gmail.com wrote:

{paper attached}

Abstract

Many researchers who have studied movements along curved paths, under a variety of conditions, by di erent organisms,
mostly human but a couple with non-human organisms, have found a consistent form of relation between the tangential
(along-track) instantaneous velocity V and the local radius of curvature R. The consistent relation is that V ≈ cRk, where k
is a constant less than unity, often near 0.33 but sometimes far from 0.33, and c is a proportionality constant appropriate to
the organism and the situation (see Zago, Matic, Flash, et al. (2017) for many examples in which the power law holds with
widely varying values of the power, as well as cases of simple systems for which everything can be calculated exactly and
in which the power law fails badly). Marken and Sha er (Exp Brain Res 235:1835–1842; 2017), following a challenge by
Gomez-Marin to see whether it is possible to use Perceptual Control Theory (Powers 1973/2005) to explain the power law
results (Alex Gomez-Marin posting to CSGnet@lists.illinois.edu 2016.05.03), claim to have found a mathematical argument
that proves the true exponent of the power relating velocity and radius of curvature always to be 1/3. They say that deviations
from this value occur because researchers have omitted a critical correction “cross-productâ€? factor that the authors label
“Dâ€?. This note questions the logic of the analysis o ered by Marken and Sha er, and argues that even had the analysis been
correct, it would not a ect future research into the reasons why and when the power law is observed and the circumstances
that determine the value of the power found when it is observed.Â

<powerHigh.pdf>

[Rick Marken 2018-02-25_12:54:18]

···

On Sun, Feb 25, 2018 at 10:32 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: Shall we be enlightened with Rick’s official response?

RM: I think there is no benefit to thinking that people will not be “enlightened” by my research, writings and demonstrations so I will say “yes, you shall” and try my best to believe it. But after nearly 40 years of working on PCT – and particularly after the years on CSGNet after Bill passed away – I’m pretty sure that Lucy is going to pull the football away again.Â

Best regards

Rick

On Sun, Feb 25, 2018 at 7:52 AM, Warren Mansell wmansell@gmail.com wrote:

Cheers Alex

On 24 Feb 2018, at 08:41, Alex Gomez-Marin agomezmarin@gmail.com wrote:

{paper attached}

Abstract

Many researchers who have studied movements along curved paths, under a variety of conditions, by di erent organisms,
mostly human but a couple with non-human organisms, have found a consistent form of relation between the tangential
(along-track) instantaneous velocity V and the local radius of curvature R. The consistent relation is that V ≈ cRk, where k
is a constant less than unity, often near 0.33 but sometimes far from 0.33, and c is a proportionality constant appropriate to
the organism and the situation (see Zago, Matic, Flash, et al. (2017) for many examples in which the power law holds with
widely varying values of the power, as well as cases of simple systems for which everything can be calculated exactly and
in which the power law fails badly). Marken and Sha er (Exp Brain Res 235:1835–1842; 2017), following a challenge by
Gomez-Marin to see whether it is possible to use Perceptual Control Theory (Powers 1973/2005) to explain the power law
results (Alex Gomez-Marin posting to CSGnet@lists.illinois.edu 2016.05.03), claim to have found a mathematical argument
that proves the true exponent of the power relating velocity and radius of curvature always to be 1/3. They say that deviations
from this value occur because researchers have omitted a critical correction “cross-productâ€? factor that the authors label
“Dâ€?. This note questions the logic of the analysis o ered by Marken and Sha er, and argues that even had the analysis been
correct, it would not a ect future research into the reasons why and when the power law is observed and the circumstances
that determine the value of the power found when it is observed.Â

<powerHigh.pdf>

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

I meant something very simple: are you going to face our critique seriously, or play shell-game again?

···

On Sun, Feb 25, 2018 at 9:54 PM, Richard Marken rsmarken@gmail.com wrote:

[Rick Marken 2018-02-25_12:54:18]

On Sun, Feb 25, 2018 at 10:32 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: Shall we be enlightened with Rick’s official response?

RM: I think there is no benefit to thinking that people will not be “enlightened” by my research, writings and demonstrations so I will say “yes, you shall” and try my best to believe it. But after nearly 40 years of working on PCT – and particularly after the years on CSGNet after Bill passed away – I’m pretty sure that Lucy is going to pull the football away again.Â

Best regards

Rick

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

On Sun, Feb 25, 2018 at 7:52 AM, Warren Mansell wmansell@gmail.com wrote:

Cheers Alex

On 24 Feb 2018, at 08:41, Alex Gomez-Marin agomezmarin@gmail.com wrote:

{paper attached}

Abstract

Many researchers who have studied movements along curved paths, under a variety of conditions, by di erent organisms,
mostly human but a couple with non-human organisms, have found a consistent form of relation between the tangential
(along-track) instantaneous velocity V and the local radius of curvature R. The consistent relation is that V ≈ cRk, where k
is a constant less than unity, often near 0.33 but sometimes far from 0.33, and c is a proportionality constant appropriate to
the organism and the situation (see Zago, Matic, Flash, et al. (2017) for many examples in which the power law holds with
widely varying values of the power, as well as cases of simple systems for which everything can be calculated exactly and
in which the power law fails badly). Marken and Sha er (Exp Brain Res 235:1835–1842; 2017), following a challenge by
Gomez-Marin to see whether it is possible to use Perceptual Control Theory (Powers 1973/2005) to explain the power law
results (Alex Gomez-Marin posting to CSGnet@lists.illinois.edu 2016.05.03), claim to have found a mathematical argument
that proves the true exponent of the power relating velocity and radius of curvature always to be 1/3. They say that deviations
from this value occur because researchers have omitted a critical correction “cross-productâ€? factor that the authors label
“Dâ€?. This note questions the logic of the analysis o ered by Marken and Sha er, and argues that even had the analysis been
correct, it would not a ect future research into the reasons why and when the power law is observed and the circumstances
that determine the value of the power found when it is observed.Â

<powerHigh.pdf>

[Rick Marken 2018-02-25_14:43:05]

···

On Sun, Feb 25, 2018 at 2:13 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

I meant something very simple: are you going to face our critique seriously, or play shell-game again?

RM: I’m afraid that will be up to you to decide. Though I’m pretty sure I know what decision you’ll make.

BestÂ

Rick

Â

On Sun, Feb 25, 2018 at 9:54 PM, Richard Marken rsmarken@gmail.com wrote:

[Rick Marken 2018-02-25_12:54:18]

On Sun, Feb 25, 2018 at 10:32 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: Shall we be enlightened with Rick’s official response?

RM: I think there is no benefit to thinking that people will not be “enlightened” by my research, writings and demonstrations so I will say “yes, you shall” and try my best to believe it. But after nearly 40 years of working on PCT – and particularly after the years on CSGNet after Bill passed away – I’m pretty sure that Lucy is going to pull the football away again.Â

Best regards

Rick

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

On Sun, Feb 25, 2018 at 7:52 AM, Warren Mansell wmansell@gmail.com wrote:

Cheers Alex

On 24 Feb 2018, at 08:41, Alex Gomez-Marin agomezmarin@gmail.com wrote:

{paper attached}

Abstract

Many researchers who have studied movements along curved paths, under a variety of conditions, by di erent organisms,
mostly human but a couple with non-human organisms, have found a consistent form of relation between the tangential
(along-track) instantaneous velocity V and the local radius of curvature R. The consistent relation is that V ≈ cRk, where k
is a constant less than unity, often near 0.33 but sometimes far from 0.33, and c is a proportionality constant appropriate to
the organism and the situation (see Zago, Matic, Flash, et al. (2017) for many examples in which the power law holds with
widely varying values of the power, as well as cases of simple systems for which everything can be calculated exactly and
in which the power law fails badly). Marken and Sha er (Exp Brain Res 235:1835–1842; 2017), following a challenge by
Gomez-Marin to see whether it is possible to use Perceptual Control Theory (Powers 1973/2005) to explain the power law
results (Alex Gomez-Marin posting to CSGnet@lists.illinois.edu 2016.05.03), claim to have found a mathematical argument
that proves the true exponent of the power relating velocity and radius of curvature always to be 1/3. They say that deviations
from this value occur because researchers have omitted a critical correction “cross-productâ€? factor that the authors label
“Dâ€?. This note questions the logic of the analysis o ered by Marken and Sha er, and argues that even had the analysis been
correct, it would not a ect future research into the reasons why and when the power law is observed and the circumstances
that determine the value of the power found when it is observed.Â

<powerHigh.pdf>

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

[Martin Taylor 2018.02.25.17.55]

[Rick Marken 2018-02-25_14:43:05]

Are you going to answer Alex’s question without going lawyerly?

Let me ask it in another way. If this isn't what Alex was asking, I

will apologize to him, but it is the question to which I would like
an answer.

Which of the following choices is true of your EBR response: (1)

already published, (2) accepted but not yet published. (3) submitted
but not yet accepted, (4) not yet submitted but in progress, (5) not
yet being written but not abandoned, or (6) abandoned.

One, and only one, of those possibilities must be true. Which is it?

Martin
···

On Sun, Feb 25, 2018 at 2:13 PM, Alex
Gomez-Marin agomezmarin@gmail.com
wrote:

              I

meant something very simple: are you going to face our
critique seriously, or play shell-game again?

          RM: I'm afraid that will be up to you to decide. Though

I’m pretty sure I know what decision you’ll make.

Best

Rick

[Rick Marken 2018-02-25_16:15:39]

···

Martin Taylor (2018.02.25.17.55)–

MT: Are you going to answer Alex’s question without going lawyerly?

RM: In what world is that answer “lawyerly”? I thought my answer was quite straight-forward, especially considering the “When did you stop beating you wife?” style of the question.Â

Â

MT: Let me ask it in another way. If this isn't what Alex was asking, I

will apologize to him, but it is the question to which I would like
an answer.

RM: Wow, you didn’t understand what Alex was asking and nevertheless you say that my answer to him was “lawyerly”. Do you guys ever get tired of yourselves?

MT: Which of the following choices is true of your EBR response: (1)

already published, (2) accepted but not yet published. (3) submitted
but not yet accepted, (4) not yet submitted but in progress, (5) not
yet being written but not abandoned, or (6) abandoned.

RM: Well, that’s a pretty weird way of asking. But the answer is (2). I assumed you guys already knew since you seem to have an “in” with at least one of the editors.Â

Rick

One, and only one, of those possibilities must be true. Which is it?



Martin


Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

              AGM: I

meant something very simple: are you going to face our
critique seriously, or play shell-game again?

          RM: I'm afraid that will be up to you to decide. Though

I’m pretty sure I know what decision you’ll make.

[Martin Taylor 2018.02.25.23.14]

[Rick Marken 2018-02-25_16:15:39]

I didn't think Alex's question had any "beating your wife" aspect,

since you had refused to answer his earlier question, but instead
seemed to be doing what you could to avoid answering it. So when he
asked what I thought was a quite reasonable follow-up question,
referencing the style of your earlier answer, your lawyerly (using
tiny loopholes to answer something different entirely) response
prompted me to ask my question in the form of a forced-choice
selection that I thought you could not answer with a lawyerly
weasel-out. And it worked, so I guess it wasn’t a weird way of
asking, after all.

Don't you get tired of being infallible? You know exactly what

people mean that isn’t what they wrote, better than the writers do.

Bruce, for example, points out that equilibrium systems as well as

control systems resist disturbances, and he gives you a dramatic
example of an equilibrium system that resists a disturbance, so you
tell him he’s wrong because his example isn’t a control system and
only control systems resist disturbances. I think that’s called
chutzpah, is it not? Anyway, I’m sure that Bruce now knows that he
didn’t write that equilibrium systems resist disturbances, and will
thank you for letting him know :frowning:

In my message earlier today I suggested that you might actually read

the message that you were criticizing for things it did not say. Now
you say that I didn’t understand Alex, which wasn’t what I wrote in
the quoted sentence that led to your assertion. (I don’t suppose you
want to know, but what I did was allow for the possibility that I
might have misinterpreted Alex, so as to give him a way to correct
me if that was the case, in the knowledge that he would not offend
me by so doing.)

You treat other people's words in the same cavalier way you treat

mathematics. The truth is the way you want the world to be, quite
independently of logic or of the evidence before your eyes, just
like your current President and his cronies in Congress. You profess
not to be a Republican, but your approach to asserting the truth
seems very like theirs. It’s tiresome, and not at all conducive to
political discussion, let alone the kind of scientific discussion we
would hope to have when trying to build our understanding of what
organisms individually or in groups do, based on the solid
foundations provided by Bill Powers.

Thanks for an actual answer.

And no, the only "in" I have with any of the editors is that one

(the Editor-in-chief) helped me to get a couple of the equations
that looked fine on my machine to come out properly in their
required format. He did inform me also that you had been asked to
provide a response to be published alongside my comment, but that
you had not done so in spite of being prompted, and that therefore
my comment would be published by itself.

On that basis I expected your answer to be one of 4, 5, or 6. I

would have preferred 1, but failing that, I’m glad your answer was
2. I will be interested to see what you have to say, if it isn’t
hidden behind a paywall. I hope it is mathematically sane, in
contrast to the original paper.

Martin
···

Martin Taylor (2018.02.25.17.55)–

            MT: Are you going to answer Alex's question

without going lawyerly?

          RM: In what world is that answer "lawyerly"?  I thought

my answer was quite straight-forward, especially
considering the “When did you stop beating you wife?”
style of the question.

                            AGM:

I meant something very simple: are you
going to face our critique seriously, or
play shell-game again?

                        RM: I'm afraid that will be up to you to

decide. Though I’m pretty sure I know what
decision you’ll make.

            MT: Let me ask it in

another way. If this isn’t what Alex was asking, I will
apologize to him, but it is the question to which I
would like an answer.

          RM: Wow, you didn't understand what Alex was asking and

nevertheless you say that my answer to him was “lawyerly”.
Do you guys ever get tired of yourselves?

            MT: Which of the

following choices is true of your EBR response: (1)
already published, (2) accepted but not yet published.
(3) submitted but not yet accepted, (4) not yet
submitted but in progress, (5) not yet being written but
not abandoned, or (6) abandoned.

          RM: Well, that's a pretty weird way of asking. But the

answer is (2). I assumed you guys already knew since you
seem to have an “in” with at least one of the editors.

let’s cut the clutter: rick, here is an ellipse, and here are 3 ways of moving on it at different speeds, and one gives 2/3 power law while the other two do not, and there are no statistics to make since the result is analytically exact – doesn’t this invalidate what your wrote in your paper? (and please do not press play and start paraphrasing Powers behavioral illusion blablabla).

···

Martin Taylor (2018.02.25.17.55)–

            MT: Are you going to answer Alex's question

without going lawyerly?

          RM: In what world is that answer "lawyerly"?  I thought

my answer was quite straight-forward, especially
considering the “When did you stop beating you wife?”
style of the question.

                            AGM:

I meant something very simple: are you
going to face our critique seriously, or
play shell-game again?

                        RM: I'm afraid that will be up to you to

decide. Though I’m pretty sure I know what
decision you’ll make.

            MT: Let me ask it in

another way. If this isn’t what Alex was asking, I will
apologize to him, but it is the question to which I
would like an answer.

          RM: Wow, you didn't understand what Alex was asking and

nevertheless you say that my answer to him was “lawyerly”.
Do you guys ever get tired of yourselves?

            MT: Which of the

following choices is true of your EBR response: (1)
already published, (2) accepted but not yet published.
(3) submitted but not yet accepted, (4) not yet
submitted but in progress, (5) not yet being written but
not abandoned, or (6) abandoned.

          RM: Well, that's a pretty weird way of asking. But the

answer is (2). I assumed you guys already knew since you
seem to have an “in” with at least one of the editors.

Alex Gomez-Marin
behavior-of-organisms.org

[Rick Marken 2018-02-26_18:09:28]

···

On Sun, Feb 25, 2018 at 11:34 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: let’s cut the clutter: rick, here is an ellipse, and here are 3 ways of moving on it at different speeds, and one gives 2/3 power law while the other two do not, and there are no statistics to make since the result is analytically exact – doesn’t this invalidate what your wrote in your paper?

RM: No.Â

Best

Rick

Â

(and please do not press play and start paraphrasing Powers behavioral illusion blablabla).

On Mon, 26 Feb 2018 at 06:18, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2018.02.25.23.14]

[Rick Marken 2018-02-25_16:15:39]

I didn't think Alex's question had any "beating your wife" aspect,

since you had refused to answer his earlier question, but instead
seemed to be doing what you could to avoid answering it. So when he
asked what I thought was a quite reasonable follow-up question,
referencing the style of your earlier answer, your lawyerly (using
tiny loopholes to answer something different entirely) response
prompted me to ask my question in the form of a forced-choice
selection that I thought you could not answer with a lawyerly
weasel-out. And it worked, so I guess it wasn’t a weird way of
asking, after all.

Don't you get tired of being infallible? You know exactly what

people mean that isn’t what they wrote, better than the writers do.

Bruce, for example, points out that equilibrium systems as well as

control systems resist disturbances, and he gives you a dramatic
example of an equilibrium system that resists a disturbance, so you
tell him he’s wrong because his example isn’t a control system and
only control systems resist disturbances. I think that’s called
chutzpah, is it not? Anyway, I’m sure that Bruce now knows that he
didn’t write that equilibrium systems resist disturbances, and will
thank you for letting him know :frowning:

In my message earlier today I suggested that you might actually read

the message that you were criticizing for things it did not say. Now
you say that I didn’t understand Alex, which wasn’t what I wrote in
the quoted sentence that led to your assertion. (I don’t suppose you
want to know, but what I did was allow for the possibility that I
might have misinterpreted Alex, so as to give him a way to correct
me if that was the case, in the knowledge that he would not offend
me by so doing.)

You treat other people's words in the same cavalier way you treat

mathematics. The truth is the way you want the world to be, quite
independently of logic or of the evidence before your eyes, just
like your current President and his cronies in Congress. You profess
not to be a Republican, but your approach to asserting the truth
seems very like theirs. It’s tiresome, and not at all conducive to
political discussion, let alone the kind of scientific discussion we
would hope to have when trying to build our understanding of what
organisms individually or in groups do, based on the solid
foundations provided by Bill Powers.

Thanks for an actual answer.

And no, the only "in" I have with any of the editors is that one

(the Editor-in-chief) helped me to get a couple of the equations
that looked fine on my machine to come out properly in their
required format. He did inform me also that you had been asked to
provide a response to be published alongside my comment, but that
you had not done so in spite of being prompted, and that therefore
my comment would be published by itself.

On that basis I expected your answer to be one of 4, 5, or 6. I

would have preferred 1, but failing that, I’m glad your answer was
2. I will be interested to see what you have to say, if it isn’t
hidden behind a paywall. I hope it is mathematically sane, in
contrast to the original paper.

Martin

Alex Gomez-Marin
behavior-of-organisms.org

Martin Taylor (2018.02.25.17.55)–

            MT: Are you going to answer Alex's question

without going lawyerly?

          RM: In what world is that answer "lawyerly"?  I thought

my answer was quite straight-forward, especially
considering the “When did you stop beating you wife?”
style of the question.

                            AGM:

I meant something very simple: are you
going to face our critique seriously, or
play shell-game again?

                        RM: I'm afraid that will be up to you to

decide. Though I’m pretty sure I know what
decision you’ll make.

Â

            MT: Let me ask it in

another way. If this isn’t what Alex was asking, I will
apologize to him, but it is the question to which I
would like an answer.

          RM: Wow, you didn't understand what Alex was asking and

nevertheless you say that my answer to him was “lawyerly”.
Do you guys ever get tired of yourselves?

            MT: Which of the

following choices is true of your EBR response: (1)
already published, (2) accepted but not yet published.
(3) submitted but not yet accepted, (4) not yet
submitted but in progress, (5) not yet being written but
not abandoned, or (6) abandoned.

          RM: Well, that's a pretty weird way of asking. But the

answer is (2). I assumed you guys already knew since you
seem to have an “in” with at least one of the editors.Â

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

[Martin Taylor 2018.02.26.22.30]

[Rick Marken 2018-02-26_18:09:28]

Alex, don't forget, Rick uses his own novel version of mathematics,

as yet apparently private or known to only a close circle of
acolytes who have been given entry into the true arcana.

He has shown us a small glimpse of it, however, such as that one of

the R-math axioms must be something along the lines of “if a formula
fits all possible values of a variable, the first one you try is the
only one that is valid in subsequent formulae.” Maybe his “No”
answer to your question comes from some other axiom yet to be
divulged. That axiom must say something near the reverse of the
first, but I can’t guess what it does say. His answer gives no hint,
which is good security for the secret knowledge that gives him great
power to prove anything he wants, but is not very helpful in showing
why “No” is correct.

R-math has another important property. It ensures that there is no

possibility of anything written in the Marken-Shaffer paper ever
being invalidated by either evidence or logic. That paper presents a
basic truth, with which all methods of analysis must conform or
thereby be proved false. I very much hope that the axioms of R-math
will be published in the near future, so that we can all benefit
from this glorious extension of our ability to interpret the new
natural world, in which velocity is a property of every shape,
something we did not know before that paper was published.

Until then, Rick has an unfair advantage, since we are unfortunately

constrained to use only the mathematics and logic known to the rest
of the benighted world. We therefore cannot see his greater truths,
but must muddle along with what has been left for us by the great
mathematicians and physicists of the past. Using only that poor
fragment of the greater knowledge, we have no means at our disposal
for finding any flaw in the Marken-Shaffer paper. There is no flaw,
and there can be none, by definition.

Martin
···

On Sun, Feb 25, 2018 at 11:34 PM,
Alex Gomez-Marin agomezmarin@gmail.com
wrote:

            AGM: let's cut the clutter: rick, here is

an ellipse, and here are 3 ways of moving on it at
different speeds, and one gives 2/3 power law while the
other two do not, and there are no statistics to make
since the result is analytically exact – doesn’t this
invalidate what your wrote in your paper?

RM: No.

Come on, Rick! You went too far and said that it is a mathematical given that speed and curvature should scale like 2/3. But then we demonstrated explicitly and exactly that in the case of an ellipse (the simplest geometry!) one can mathematically move around the same ellipse with different velocity profiles and that for only ONE particular type of profile one gets a 2/3 power law, and for the rest one always gets a violation of the power law. But you still insist in the contrary? THIS IS THE OPPOSITE OF WHAT A SCIENTIST DOES! When faced with undeniable mathematical evidence, one cannot keep on maintaining such initial misconceptions, no matter how sneaky your rhetoric is. HONESTLY, BEING ONE OF THE GREATEST EXPONENTS OF PCT (the theory that claims itself to revolutionise psychology, neuroscience and string theory…) IT IS A SHAME YOU BEHAVE LIKE THAT. A REAL SHAME.

···

On Tue, Feb 27, 2018 at 6:04 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2018.02.26.22.30]

[Rick Marken 2018-02-26_18:09:28]

Alex, don't forget, Rick uses his own novel version of mathematics,

as yet apparently private or known to only a close circle of
acolytes who have been given entry into the true arcana.

He has shown us a small glimpse of it, however, such as that one of

the R-math axioms must be something along the lines of “if a formula
fits all possible values of a variable, the first one you try is the
only one that is valid in subsequent formulae.” Maybe his “No”
answer to your question comes from some other axiom yet to be
divulged. That axiom must say something near the reverse of the
first, but I can’t guess what it does say. His answer gives no hint,
which is good security for the secret knowledge that gives him great
power to prove anything he wants, but is not very helpful in showing
why “No” is correct.

R-math has another important property. It ensures that there is no

possibility of anything written in the Marken-Shaffer paper ever
being invalidated by either evidence or logic. That paper presents a
basic truth, with which all methods of analysis must conform or
thereby be proved false. I very much hope that the axioms of R-math
will be published in the near future, so that we can all benefit
from this glorious extension of our ability to interpret the new
natural world, in which velocity is a property of every shape,
something we did not know before that paper was published.

Until then, Rick has an unfair advantage, since we are unfortunately

constrained to use only the mathematics and logic known to the rest
of the benighted world. We therefore cannot see his greater truths,
but must muddle along with what has been left for us by the great
mathematicians and physicists of the past. Using only that poor
fragment of the greater knowledge, we have no means at our disposal
for finding any flaw in the Marken-Shaffer paper. There is no flaw,
and there can be none, by definition.

Martin
        On Sun, Feb 25, 2018 at 11:34 PM,

Alex Gomez-Marin agomezmarin@gmail.com
wrote:

            AGM: let's cut the clutter: rick, here is

an ellipse, and here are 3 ways of moving on it at
different speeds, and one gives 2/3 power law while the
other two do not, and there are no statistics to make
since the result is analytically exact – doesn’t this
invalidate what your wrote in your paper?

RM: No.

[Bruce Nevin 2018-02-27_15:53:52 ET]

Rick, you said your rejoinder has been accepted but not yet published. Any idea when it will be available?

···

On Tue, Feb 27, 2018 at 3:02 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

Come on, Rick! You went too far and said that it is a mathematical given that speed and curvature should scale like 2/3. But then we demonstrated explicitly and exactly that in the case of an ellipse (the simplest geometry!) one can mathematically move around the same ellipse with different velocity profiles and that for only ONE particular type of profile one gets a 2/3 power law, and for the rest one always gets a violation of the power law. But you still insist in the contrary? THIS IS THE OPPOSITE OF WHAT A SCIENTIST DOES! When faced with undeniable mathematical evidence, one cannot keep on maintaining such initial misconceptions, no matter how sneaky your rhetoric is. HONESTLY, BEING ONE OF THE GREATEST EXPONENTS OF PCT (the theory that claims itself to revolutionise psychology, neuroscience and string theory…) IT IS A SHAME YOU BEHAVE LIKE THAT. A REAL SHAME.

On Tue, Feb 27, 2018 at 6:04 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2018.02.26.22.30]

[Rick Marken 2018-02-26_18:09:28]

Alex, don't forget, Rick uses his own novel version of mathematics,

as yet apparently private or known to only a close circle of
acolytes who have been given entry into the true arcana.

He has shown us a small glimpse of it, however, such as that one of

the R-math axioms must be something along the lines of “if a formula
fits all possible values of a variable, the first one you try is the
only one that is valid in subsequent formulae.” Maybe his “No”
answer to your question comes from some other axiom yet to be
divulged. That axiom must say something near the reverse of the
first, but I can’t guess what it does say. His answer gives no hint,
which is good security for the secret knowledge that gives him great
power to prove anything he wants, but is not very helpful in showing
why “No” is correct.

R-math has another important property. It ensures that there is no

possibility of anything written in the Marken-Shaffer paper ever
being invalidated by either evidence or logic. That paper presents a
basic truth, with which all methods of analysis must conform or
thereby be proved false. I very much hope that the axioms of R-math
will be published in the near future, so that we can all benefit
from this glorious extension of our ability to interpret the new
natural world, in which velocity is a property of every shape,
something we did not know before that paper was published.

Until then, Rick has an unfair advantage, since we are unfortunately

constrained to use only the mathematics and logic known to the rest
of the benighted world. We therefore cannot see his greater truths,
but must muddle along with what has been left for us by the great
mathematicians and physicists of the past. Using only that poor
fragment of the greater knowledge, we have no means at our disposal
for finding any flaw in the Marken-Shaffer paper. There is no flaw,
and there can be none, by definition.

Martin
        On Sun, Feb 25, 2018 at 11:34 PM,

Alex Gomez-Marin agomezmarin@gmail.com
wrote:

            AGM: let's cut the clutter: rick, here is

an ellipse, and here are 3 ways of moving on it at
different speeds, and one gives 2/3 power law while the
other two do not, and there are no statistics to make
since the result is analytically exact – doesn’t this
invalidate what your wrote in your paper?

RM: No.

Really, my expectation to read that is too see how much one is able to bend logic and rules of evidence.

···

On Tue, Feb 27, 2018 at 9:54 PM, Bruce Nevin bnhpct@gmail.com wrote:

[Bruce Nevin 2018-02-27_15:53:52 ET]

Rick, you said your rejoinder has been accepted but not yet published. Any idea when it will be available?

On Tue, Feb 27, 2018 at 3:02 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

Come on, Rick! You went too far and said that it is a mathematical given that speed and curvature should scale like 2/3. But then we demonstrated explicitly and exactly that in the case of an ellipse (the simplest geometry!) one can mathematically move around the same ellipse with different velocity profiles and that for only ONE particular type of profile one gets a 2/3 power law, and for the rest one always gets a violation of the power law. But you still insist in the contrary? THIS IS THE OPPOSITE OF WHAT A SCIENTIST DOES! When faced with undeniable mathematical evidence, one cannot keep on maintaining such initial misconceptions, no matter how sneaky your rhetoric is. HONESTLY, BEING ONE OF THE GREATEST EXPONENTS OF PCT (the theory that claims itself to revolutionise psychology, neuroscience and string theory…) IT IS A SHAME YOU BEHAVE LIKE THAT. A REAL SHAME.

On Tue, Feb 27, 2018 at 6:04 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2018.02.26.22.30]

[Rick Marken 2018-02-26_18:09:28]

Alex, don't forget, Rick uses his own novel version of mathematics,

as yet apparently private or known to only a close circle of
acolytes who have been given entry into the true arcana.

He has shown us a small glimpse of it, however, such as that one of

the R-math axioms must be something along the lines of “if a formula
fits all possible values of a variable, the first one you try is the
only one that is valid in subsequent formulae.” Maybe his “No”
answer to your question comes from some other axiom yet to be
divulged. That axiom must say something near the reverse of the
first, but I can’t guess what it does say. His answer gives no hint,
which is good security for the secret knowledge that gives him great
power to prove anything he wants, but is not very helpful in showing
why “No” is correct.

R-math has another important property. It ensures that there is no

possibility of anything written in the Marken-Shaffer paper ever
being invalidated by either evidence or logic. That paper presents a
basic truth, with which all methods of analysis must conform or
thereby be proved false. I very much hope that the axioms of R-math
will be published in the near future, so that we can all benefit
from this glorious extension of our ability to interpret the new
natural world, in which velocity is a property of every shape,
something we did not know before that paper was published.

Until then, Rick has an unfair advantage, since we are unfortunately

constrained to use only the mathematics and logic known to the rest
of the benighted world. We therefore cannot see his greater truths,
but must muddle along with what has been left for us by the great
mathematicians and physicists of the past. Using only that poor
fragment of the greater knowledge, we have no means at our disposal
for finding any flaw in the Marken-Shaffer paper. There is no flaw,
and there can be none, by definition.

Martin
        On Sun, Feb 25, 2018 at 11:34 PM,

Alex Gomez-Marin agomezmarin@gmail.com
wrote:

            AGM: let's cut the clutter: rick, here is

an ellipse, and here are 3 ways of moving on it at
different speeds, and one gives 2/3 power law while the
other two do not, and there are no statistics to make
since the result is analytically exact – doesn’t this
invalidate what your wrote in your paper?

RM: No.

[Rick Marken 2018-02-27_14:20:35]

···

On Tue, Feb 27, 2018 at 12:02 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: Come on, Rick! You went too far and said that it is a mathematical given that speed and curvature should scale like 2/3.

RM: Not quite. I said that speed and curvature are related by exactly a 2/3 power law coefficient when that we called the cross-product variable is included in the regression analysis.Â

Â

But then we demonstrated explicitly and exactly that in the case of an ellipse (the simplest geometry!) one can mathematically move around the same ellipse with different velocity profiles and that for only ONE particular type of profile one gets a 2/3 power law, and for the rest one always gets a violation of the power law.

RM: Which is expected if the cross-product variable (which corresponds to a measure of affine velocity) is left out of the regression.Â

Â

AGM: But you still insist in the contrary?

RM: No, I don’t insist on the contrary. It’s becoming clear to me that you have no idea what I we have shown in our paper.

AGM: THIS IS THE OPPOSITE OF WHAT A SCIENTIST DOES!

RM: Why don’t you just wait to see my reply to your and Martin’s rebuttal to our paper.Â

Best

RickÂ

When faced with undeniable mathematical evidence, one cannot keep on maintaining such initial misconceptions, no matter how sneaky your rhetoric is. HONESTLY, BEING ONE OF THE GREATEST EXPONENTS OF PCT (the theory that claims itself to revolutionise psychology, neuroscience and string theory…) IT IS A SHAME YOU BEHAVE LIKE THAT. A REAL SHAME.

On Tue, Feb 27, 2018 at 6:04 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2018.02.26.22.30]

[Rick Marken 2018-02-26_18:09:28]

Alex, don't forget, Rick uses his own novel version of mathematics,

as yet apparently private or known to only a close circle of
acolytes who have been given entry into the true arcana.

He has shown us a small glimpse of it, however, such as that one of

the R-math axioms must be something along the lines of “if a formula
fits all possible values of a variable, the first one you try is the
only one that is valid in subsequent formulae.” Maybe his “No”
answer to your question comes from some other axiom yet to be
divulged. That axiom must say something near the reverse of the
first, but I can’t guess what it does say. His answer gives no hint,
which is good security for the secret knowledge that gives him great
power to prove anything he wants, but is not very helpful in showing
why “No” is correct.

R-math has another important property. It ensures that there is no

possibility of anything written in the Marken-Shaffer paper ever
being invalidated by either evidence or logic. That paper presents a
basic truth, with which all methods of analysis must conform or
thereby be proved false. I very much hope that the axioms of R-math
will be published in the near future, so that we can all benefit
from this glorious extension of our ability to interpret the new
natural world, in which velocity is a property of every shape,
something we did not know before that paper was published.

Until then, Rick has an unfair advantage, since we are unfortunately

constrained to use only the mathematics and logic known to the rest
of the benighted world. We therefore cannot see his greater truths,
but must muddle along with what has been left for us by the great
mathematicians and physicists of the past. Using only that poor
fragment of the greater knowledge, we have no means at our disposal
for finding any flaw in the Marken-Shaffer paper. There is no flaw,
and there can be none, by definition.

Martin
        On Sun, Feb 25, 2018 at 11:34 PM,

Alex Gomez-Marin agomezmarin@gmail.com
wrote:

            AGM: let's cut the clutter: rick, here is

an ellipse, and here are 3 ways of moving on it at
different speeds, and one gives 2/3 power law while the
other two do not, and there are no statistics to make
since the result is analytically exact – doesn’t this
invalidate what your wrote in your paper?

RM: No.Â

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

[Rick Marken 2018-02-27_14:22:07]

Bruce Nevin (2018-02-27_15:53:52 ET)--

BN: Rick, you said your rejoinder has been accepted but not yet published. Any idea when it will be available?

Soon, I hope. I just did the proofs.
BestÂ

···

On Tue, Feb 27, 2018 at 3:02 PM, Alex Gomez-Marin <<mailto:agomezmarin@gmail.com>agomezmarin@gmail.com> wrote:

Come on, Rick! You went too far and said that it is a mathematical given that speed and curvature should scale like 2/3. But then we demonstrated explicitly and exactly that in the case of an ellipse (the simplest geometry!) one can mathematically move around the same ellipse with different velocity profiles and that for only ONE particular type of profile one gets a 2/3 power law, and for the rest one always gets a violation of the power law. But you still insist in the contrary? THIS IS THE OPPOSITE OF WHAT A SCIENTIST DOES! When faced with undeniable mathematical evidence, one cannot keep on maintaining such initial misconceptions, no matter how sneaky your rhetoric is. HONESTLY, BEING ONE OF THE GREATEST EXPONENTS OF PCT (the theory that claims itself to revolutionise psychology, neuroscience and string theory...) IT IS A SHAME YOU BEHAVE LIKE THAT. A REAL SHAME.

On Tue, Feb 27, 2018 at 6:04 AM, Martin Taylor <<mailto:mmt-csg@mmtaylor.net>mmt-csg@mmtaylor.net> wrote:

[Martin Taylor 2018.02.26.22.30]

[Rick Marken 2018-02-26_18:09:28]

On Sun, Feb 25, 2018 at 11:34 PM, Alex Gomez-Marin <<mailto:agomezmarin@gmail.com>agomezmarin@gmail.com> wrote:

AGM: let's cut the clutter: rick, here is an ellipse, and here are 3 ways of moving on it at different speeds, and one gives 2/3 power law while the other two do not, and there are no statistics to make since the result is analytically exact -- doesn't this invalidate what your wrote in your paper?

RM: No.Â

Alex, don't forget, Rick uses his own novel version of mathematics, as yet apparently private or known to only a close circle of acolytes who have been given entry into the true arcana.

He has shown us a small glimpse of it, however, such as that one of the R-math axioms must be something along the lines of "if a formula fits all possible values of a variable, the first one you try is the only one that is valid in subsequent formulae." Maybe his "No" answer to your question comes from some other axiom yet to be divulged. That axiom must say something near the reverse of the first, but I can't guess what it does say. His answer gives no hint, which is good security for the secret knowledge that gives him great power to prove anything he wants, but is not very helpful in showing why "No" is correct.

R-math has another important property. It ensures that there is no possibility of anything written in the Marken-Shaffer paper ever being invalidated by either evidence or logic. That paper presents a basic truth, with which all methods of analysis must conform or thereby be proved false. I very much hope that the axioms of R-math will be published in the near future, so that we can all benefit from this glorious extension of our ability to interpret the new natural world, in which velocity is a property of every shape, something we did not know before that paper was published.

Until then, Rick has an unfair advantage, since we are unfortunately constrained to use only the mathematics and logic known to the rest of the benighted world. We therefore cannot see his greater truths, but must muddle along with what has been left for us by the great mathematicians and physicists of the past. Using only that poor fragment of the greater knowledge, we have no means at our disposal for finding any flaw in the Marken-Shaffer paper. There is no flaw, and there can be none, by definition.

Martin

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery