Behav. illusions

[PHILIP_JERAIR_YERANO]

The first figure below is the relationship between variables in a PCT experiment. And the second figure below is an example of a PCT experiment. Only the mouse and the disturbance have a high correlation. The cursor and mouse have no correlation. In his reappraisal paper, Rick states that the correlation between mouse and cursor movements is only 0.53. These values are not correlated. I am asking him to show instead the mouse-disturbance correlation because this is where the high correlation lies. And consciousness is where the controlled variable in the first figure below is a reference value.

Â

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···

On Sun, Mar 11, 2018 at 9:43 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2018.03.11.12.24]

  On 2018/03/11 1:31 AM, PHILIP JERAIR

YERANOSIAN wrote:

  When

a person sees that a perception does not cause them to have an
intention, they are conscious because their behavior is now
resisting disturbances to their intention. Consciousness is where
behavior correlates to disturbances of a perception of an
intention.Â

"Curioser and curioser". I feel as though I am talking to

Humpty-Dumpty and will soon be eating “diminish me” mushrooms or
something. Could you relate what you said in this and your last
message to something connected with PCT as it is normally
understood? Or even to everyday experience?

Martin

  On

Saturday, March 10, 2018, Martin Taylor <mmt-csg@mmtaylor.net >
wrote:

[Martin Taylor 2018.03.10.23.31]

On 2018/03/10 11:30 PM, PHILIP JERAIR YERANOSIAN wrote:

              If a person perceives that the

internal processes produce f-¹⁽ AB) and
assumes that they do it autonomously, independently of
the external environment, that is consciousness.

        Explain what that has to do with

consciousness, and whose consciousness you are talking
about, please? Also please explain how this relates to the
topic under discussion, which is the nature of the
Behavioural Illusion, and behind that, why behaviourist
(“Stimulus-Response” or “S-R”) researchers have accepted the
illusory perception as a truth about Nature.

        Martin

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www.avast.com

            On Sat, Mar 10, 2018 at 8:17 PM,

Martin Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.10.23.14]

[philip 2019.03.10]

                        An observed relationship between the

output and the disturbance can only describe
the form f(AB). This relationship cannot be
used to describe the form f^-1(AB).

                 If the function f(.) is invertible, it

completely describes f-1(.), just as the form of a
jigsaw piece determines the form of the piece next
to it in the puzzle. The question is which one is
responsible for the form being what it is. The
Behavioural Illusion is that the internal processes
are responsible, whereas they are capable only of
compensating for the effects between the output and
the CEV that are imposed by the external
environment.

                        These two sentences are the behavioral

illusion doctrine. Please refer to the last
paragraph of page 9 of Bill’s paper (1978):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.

                          The

Behavioural Illusion is in someone’s
perception that the the form of f(AB)
reflects something about f^-1(AB).

                                        No. There's

no illusion there. It’s just a simple fact.
Whether you call it a fact of physics or of
mathematics is up to you, but it is not an
illusion.

                          The term

f(AB) reflects how the distal stimulus
determines the form of the output.

                Yes.

 The term, f^-1 (AB), reflects
how the internal processes determine the
form of the output.Â

                                        If you

replace “how” with “that”, you have a
description of the Behavioural Illusion in
someone’s mind. Another way of putting it is
“The term f^-1 (AB) determines what the
internal processes must do in order for control
to be effective, given that the environmental
function is f(AB). If a person perceives that
the internal processes produce f-¹⁽ AB)
and assumes that they do it autonomously,
independently of the external environment, that
is the Behavioural Illusion.”

                        Martin

                        On Sat, Mar 10, 2018

at 2:41 PM, Martin Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.10.17.23]

                                On 2018/03/10 4:45 PM, PHILIP

JERAIR YERANOSIAN wrote:

                                  The behavioral

illusion doctrine states that an
experimenter cannot use an
observed relationship between the
output and the disturbance to
describe a dependence between the
input and the output. Nor can this
observed relationship between
output and disturbance be used to
describe a dependence between the
input and disturbance. The purpose
of this doctrine is to prevent an
experimenter from using a shown
dependence to reveal something
about the mechanisms that produce
the output.

                             Actually, this isn't correct,

and there is no “doctrine” involved.
It’s a simple requirement of control
loops. The behavioural illusion is based
on a fundamental fact about negative
feedback loops that stabilize their
variables, and therefore about control
loops that control well. If there is a
functional relation f(AB) between the
variation at point A and the variation
at point B going one way around the
loop, the functional relation f(BA)
going the rest of the way around the
loop is the inverse function: f(BA) = f-¹⁽AB).

                            If "A" is the output, and "B" the CEV,

the environmental variable that
corresponds to the controlled perceptual
variable, and if a change in the CEV is
taken to be a “stimulus”, then the
response (output) is determined by the
properties of the environmental link
between A and B. Those properties, which
produce f(AB), are observable, in
principle, and are not influenced by
whatever happens inside the organism.
The internal mechanisms are not
observable, but they must be such as to
produce f(BA) of a specific form, that
form being f^-1(AB).

                            The modelling done in simulations to

analyze the mechanisms that produce the
output relies on this fact (and on the
discrepancy from f^-1 (AB) that
occurs because of imperfect control).
The Behavioural Illusion is in someone’s
perception that the internal processes
determine the form of the output in a
situation for which control is good.

                                Martin

Virus-free.
www.avast.com

                                    On Fri,

Mar 9, 2018 at 3:04 PM, Richard
Marken rsmarken@gmail.com
wrote:

                                            [Rick

Marken
2018-03-09_15:03:56]

                                              [philip

2018.03.09]Â

                                                PY: The

behavioral illusion
refers to the fact
that the behavior
[where the behavior
is the observable
event we are
referring to] does
not correlate to the
controlled variable
[where the
controlled variable
is the perception
which is influenced
by the behavior].Â
Instead, the
behavior correlates
with the disturbance
[where the
disturbance is an
event that is
influencing the
controlled variable
independent of the
behavior].Â

Â

                                              RM: I prefer the

definition given in
our reply paper:Â Â “…the
behavioral illusion
occurs when an
observed
relationship between
variables is seen
as revealing
something about the
mechanisms that
produce a behavior
when, in fact, it
does not. For
example,
the behavioral
illusion occurs when
“reinforcement� is
seen as “selecting�
the behavior that
produced it (Marken
and Powers 1989; Yin
2013, pp. 342–3343)
or when a tap on the
patellar tendon is
seen as the cause of
the knee-jerk
response (Marken
2014b, p. 123). The
illusion occurs when
the behavior under
study is assumed to
be that of
an open-loop,
cause–effect syystem
when it is actually
that of a
closed-loop control
system (Powers
1978)”.

Best

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
 --Antoine de
Saint-Exupery

–

[MartinT]

[Martin Taylor 2018.03.11.17.12]

  Well, I since you are asking Rick, I guess he had better deal

with it.

  For myself, I don't understand how this (or your "consciousness"

figures) relate to HPCT. And I don’t understand why you say that
Rick wrongly computed his mouse-cursor correlation. He did the
experiment, you didn’t. Did he give you the data, from which you
calculated that the mouse and cursor variations are not
correlated, and did you explain to him where his calculations went
wrong? And if you didn’t have his data to recalculate, on what
grounds do you say that the mouse-cursor correlation was (or
should have been) zero?

  By the way, how and when does a "controlled variable" become a

“reference value”? And what does any of this have to do with
Behavioural Illusions?

Martin

···

On 2018/03/11 1:31 PM, PHILIP JERAIR
YERANOSIAN wrote:

      The first figure below is the relationship between

variables in a PCT experiment. And the second figure below is
an example of a PCT experiment. Only the mouse and the
disturbance have a high correlation. The cursor and mouse have
no correlation. In his reappraisal paper, Rick states that the
correlation between mouse and cursor movements is only
0.53. These values are not correlated. I am asking him to
show instead the mouse-disturbance correlation because this
is where the high correlation lies. And consciousness is
where the controlled variable in the first figure below is a
reference value.

      Â 

Virus-free.
www.avast.com

      On Sun, Mar 11, 2018 at 9:43 AM, Martin

Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.11.12.24]

              On

2018/03/11 1:31 AM, PHILIP JERAIR YERANOSIAN wrote:

              When a person sees that a

perception does not cause them to have an intention,
they are conscious because their behavior is now
resisting disturbances to their intention.
Consciousness is where behavior correlates to
disturbances of a perception of an intention.Â

           "Curioser and curioser". I feel as though I am

talking to Humpty-Dumpty and will soon be eating “diminish
me” mushrooms or something. Could you relate what you said
in this and your last message to something connected with
PCT as it is normally understood? Or even to everyday
experience?

              Martin

                On Saturday, March 10, 2018,

Martin Taylor <mmt-csg@mmtaylor.net >
wrote:

[Martin Taylor 2018.03.10.23.31]

                      On 2018/03/10 11:30 PM, PHILIP JERAIR

YERANOSIAN wrote:

                            If a person perceives

that the internal processes produce f-¹⁽ AB)
and assumes that they do it
autonomously, independently of the
external environment, that is
consciousness.

                      Explain what that has to

do with consciousness, and whose consciousness
you are talking about, please? Also please
explain how this relates to the topic under
discussion, which is the nature of the
Behavioural Illusion, and behind that, why
behaviourist (“Stimulus-Response” or “S-R”)
researchers have accepted the illusory
perception as a truth about Nature.

                      Martin

Virus-free.
www.avast.com

                          On Sat, Mar 10,

2018 at 8:17 PM, Martin Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.10.23.14]

[philip 2019.03.10]

                                      An observed relationship

between the output and the
disturbance can only describe
the form f(AB). This
relationship cannot be used to
describe the form f^-1(AB).

                               If the function f(.) is

invertible, it completely describes
f-1(.), just as the form of a jigsaw
piece determines the form of the piece
next to it in the puzzle. The question
is which one is responsible for the
form being what it is. The Behavioural
Illusion is that the internal
processes are responsible, whereas
they are capable only of compensating
for the effects between the output and
the CEV that are imposed by the
external environment.

                                      These two sentences are the

behavioral illusion doctrine.
Please refer to the last
paragraph of page 9 of Bill’s
paper (1978):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.

                                        The

Behavioural Illusion is in
someone’s perception that
the the form of f(AB)
reflects something about f^-1 (AB).

                                                                    No. There's no

illusion there. It’s just a simple
fact. Whether you call it a fact
of physics or of mathematics is up
to you, but it is not an illusion.

                                        The

term f(AB) reflects how
the distal stimulus
determines the form of the
output.

                              Yes.

                                        Â The

term, f^-1 (AB),
reflects how the internal
processes determine the form
of the output.Â

                                                                    If you replace "how"

with “that”, you have a
description of the Behavioural
Illusion in someone’s mind.
Another way of putting it is “The
term f^-1 (AB) determines
what the internal processes must
do in order for control to be
effective, given that the
environmental function is f(AB).
If a person perceives that the
internal processes produce f-¹⁽ AB)
and assumes that they do it
autonomously, independently of the
external environment, that is the
Behavioural Illusion.”

                                      Martin

                                      On Sat,

Mar 10, 2018 at 2:41 PM,
Martin Taylor mmt-csg@mmtaylor.net
wrote:

                                            [Martin Taylor

2018.03.10.17.23]

                                              On 2018/03/10 4:45

PM, PHILIP JERAIR
YERANOSIAN wrote:

                                                The

behavioral illusion
doctrine states that
an
experimenter cannot
use an observed
relationship between
the output and
the disturbance to
describe a
dependence between
the input and the
output. Nor can this
observed
relationship between
output and
disturbance be used
to describe a
dependence between
the input and
disturbance. The
purpose of this
doctrine is to
prevent an
experimenter from
using a shown
dependence to reveal
something about the
mechanisms that
produce the output.

Virus-free.
www.avast.com

                                                  On

Fri, Mar 9, 2018
at 3:04 PM,
Richard Marken rsmarken@gmail.com
wrote:

                                                      [Rick

Marken
2018-03-09_15:03:56]

                                                      [philip

2018.03.09]Â

                                                      PY: The

behavioral
illusion
refers to the
fact that the
behavior
[where the
behavior is
the observable
event we are
referring to]
does not
correlate to
the controlled
variable
[where the
controlled
variable is
the perception
which is
influenced by
the
behavior].Â
Instead, the
behavior
correlates
with the
disturbance
[where the
disturbance is
an event that
is influencing
the controlled
variable
independent of
the
behavior].Â

Â

                                                      RM: I

prefer the
definition
given in our
reply paper:Â Â “…the
behavioral
illusion
occurs when an
observed
relationship
between
variables is
seen
as revealing
something
about the
mechanisms
that produce a
behavior when,
in fact, it
does not. For
example,
the behavioral
illusion
occurs when
“reinforcement�
is seen as
“selecting�
the behavior
that produced
it (Marken
and Powers
1989; Yin
2013, pp.
342–343) or
when a tap
on the
patellar
tendon is seen
as the cause
of the
knee-jerk
response
(Marken 2014b,
p. 123). The
illusion
occurs when
the behavior
under study is
assumed to be
that of
an open-loop,
cause–efffect
system when it
is actually
that of a
closed-loop
control system
(Powers
1978)”.

Best

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
 --Antoine de
Saint-Exupery

                                                      --

                                           Actually, this

isn’t correct, and there
is no “doctrine” involved.
It’s a simple requirement
of control loops. The
behavioural illusion is
based on a fundamental
fact about negative
feedback loops that
stabilize their variables,
and therefore about
control loops that control
well. If there is a
functional relation f(AB)
between the variation at
point A and the variation
at point B going one way
around the loop, the
functional relation f(BA)
going the rest of the way
around the loop is the
inverse function: f(BA) =
f-¹⁽AB).

                                          If "A" is the output, and

“B” the CEV, the
environmental variable
that corresponds to the
controlled perceptual
variable, and if a change
in the CEV is taken to be
a “stimulus”, then the
response (output) is
determined by the
properties of the
environmental link between
A and B. Those properties,
which produce f(AB), are
observable, in principle,
and are not influenced by
whatever happens inside
the organism. The internal
mechanisms are not
observable, but they must
be such as to produce
f(BA) of a specific form,
that form being f^-1 (AB).

                                          The modelling done in

simulations to analyze the
mechanisms that produce
the output relies on this
fact (and on the
discrepancy from f^-1 (AB)
that occurs because of
imperfect control). The
Behavioural Illusion is in
someone’s perception that
the internal processes
determine the form of the
output in a situation for
which control is good.

                                              Martin

[MartinT]

[Martin Taylor 2018.03.11.17.39]

I explained why Philip's explanation of the Behavioural Illusion was

wrong. Would you care to explain why mine was wrong? Simply saying * ex
cathedra* that it was wrong really doesn’t help me correct the
error.

It is possible that your explanation might help to explain why you

think you have shown why the results of velocity-curvature
experiments are behavioural illusions as opposed to simple
side-effects of control. That would be nice.

Martin

···

[Rick Marken 2018-03-10_17:50:34]

[Martin Taylor 2018.03.10.17.23]

                  PY: The behavioral illusion doctrine

states that an experimenter cannot use an observed
relationship between the output and
the disturbance to describe a dependence between
the input and the output…

MT: Actually, this isn’t correct.

RM: Nor is yours.

[PHILIP_JERAIR_YERANO]

MT:Â I don’t understand why you say that Rick wrongly computed his mouse-cursor correlation.Â

I said that I don’t want to see the mouse cursor correlation. It’s correctly computed in the paper but I want to see the mouse disturbance relationship instead. He did not show me THIS number. Do you understand? Go to ricks website and play the “nature of control demoâ€?. It will show you that the mouse cursor correlation is very low while the mouse disturbance correlation is very high.Â

MT: By the way, how and when does a “controlled variable” become a “reference value”?

I’ll tell you what - it’s certainly not through the behavior of muscular forces on physical objects. But if you can suggest an alternate hypothesis, I may change my default opinion. I say that consciousness is when the CV is a reference value. What do you think consciousness is? (without providing proof)Â

···

On Sun, Mar 11, 2018 at 9:43 AM, Martin
Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.11.12.24]

              On

2018/03/11 1:31 AM, PHILIP JERAIR YERANOSIAN wrote:

              When a person sees that a

perception does not cause them to have an intention,
they are conscious because their behavior is now
resisting disturbances to their intention.
Consciousness is where behavior correlates to
disturbances of a perception of an intention.Â

           "Curioser and curioser". I feel as though I am

talking to Humpty-Dumpty and will soon be eating “diminish
me” mushrooms or something. Could you relate what you said
in this and your last message to something connected with
PCT as it is normally understood? Or even to everyday
experience?

              Martin

                On Saturday, March 10, 2018,

Martin Taylor <mmt-csg@mmtaylor.net >
wrote:

[Martin Taylor 2018.03.10.23.31]

                      On 2018/03/10 11:30 PM, PHILIP JERAIR

YERANOSIAN wrote:

                            If a person perceives

that the internal processes produce f-¹⁽ AB)
and assumes that they do it
autonomously, independently of the
external environment, that is
consciousness.

                      Explain what that has to

do with consciousness, and whose consciousness
you are talking about, please? Also please
explain how this relates to the topic under
discussion, which is the nature of the
Behavioural Illusion, and behind that, why
behaviourist (“Stimulus-Response” or “S-R”)
researchers have accepted the illusory
perception as a truth about Nature.

                      Martin

Virus-free.
www.avast.com

                          On Sat, Mar 10,

2018 at 8:17 PM, Martin Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.10.23.14]

[philip 2019.03.10]

                                      An observed relationship

between the output and the
disturbance can only describe
the form f(AB). This
relationship cannot be used to
describe the form f^-1(AB).

                               If the function f(.) is

invertible, it completely describes
f-1(.), just as the form of a jigsaw
piece determines the form of the piece
next to it in the puzzle. The question
is which one is responsible for the
form being what it is. The Behavioural
Illusion is that the internal
processes are responsible, whereas
they are capable only of compensating
for the effects between the output and
the CEV that are imposed by the
external environment.

                                      These two sentences are the

behavioral illusion doctrine.
Please refer to the last
paragraph of page 9 of Bill’s
paper (1978):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.

                                        The

Behavioural Illusion is in
someone’s perception that
the the form of f(AB)
reflects something about f^-1 (AB).

                                                                    No. There's no

illusion there. It’s just a simple
fact. Whether you call it a fact
of physics or of mathematics is up
to you, but it is not an illusion.

                                        The

term f(AB) reflects how
the distal stimulus
determines the form of the
output.

                              Yes.

                                        Â The

term, f^-1 (AB),
reflects how the internal
processes determine the form
of the output.Â

                                                                    If you replace "how"

with “that”, you have a
description of the Behavioural
Illusion in someone’s mind.
Another way of putting it is “The
term f^-1 (AB) determines
what the internal processes must
do in order for control to be
effective, given that the
environmental function is f(AB).
If a person perceives that the
internal processes produce f-¹⁽ AB)
and assumes that they do it
autonomously, independently of the
external environment, that is the
Behavioural Illusion.”

                                      Martin

                                      On Sat,

Mar 10, 2018 at 2:41 PM,
Martin Taylor mmt-csg@mmtaylor.net
wrote:

                                            [Martin Taylor

2018.03.10.17.23]

                                              On 2018/03/10 4:45

PM, PHILIP JERAIR
YERANOSIAN wrote:

                                                The

behavioral illusion
doctrine states that
an
experimenter cannot
use an observed
relationship between
the output and
the disturbance to
describe a
dependence between
the input and the
output. Nor can this
observed
relationship between
output and
disturbance be used
to describe a
dependence between
the input and
disturbance. The
purpose of this
doctrine is to
prevent an
experimenter from
using a shown
dependence to reveal
something about the
mechanisms that
produce the output.

                                           Actually, this

isn’t correct, and there
is no “doctrine” involved.
It’s a simple requirement
of control loops. The
behavioural illusion is
based on a fundamental
fact about negative
feedback loops that
stabilize their variables,
and therefore about
control loops that control
well. If there is a
functional relation f(AB)
between the variation at
point A and the variation
at point B going one way
around the loop, the
functional relation f(BA)
going the rest of the way
around the loop is the
inverse function: f(BA) =
f-¹⁽AB).

                                          If "A" is the output, and

“B” the CEV, the
environmental variable
that corresponds to the
controlled perceptual
variable, and if a change
in the CEV is taken to be
a “stimulus”, then the
response (output) is
determined by the
properties of the
environmental link between
A and B. Those properties,
which produce f(AB), are
observable, in principle,
and are not influenced by
whatever happens inside
the organism. The internal
mechanisms are not
observable, but they must
be such as to produce
f(BA) of a specific form,
that form being f^-1 (AB).

                                          The modelling done in

simulations to analyze the
mechanisms that produce
the output relies on this
fact (and on the
discrepancy from f^-1 (AB)
that occurs because of
imperfect control). The
Behavioural Illusion is in
someone’s perception that
the internal processes
determine the form of the
output in a situation for
which control is good.

                                              Martin

Virus-free.
www.avast.com

                                                  On

Fri, Mar 9, 2018
at 3:04 PM,
Richard Marken rsmarken@gmail.com
wrote:

                                                      [Rick

Marken
2018-03-09_15:03:56]

                                                      [philip

2018.03.09]Â

                                                      PY: The

behavioral
illusion
refers to the
fact that the
behavior
[where the
behavior is
the observable
event we are
referring to]
does not
correlate to
the controlled
variable
[where the
controlled
variable is
the perception
which is
influenced by
the
behavior].Â
Instead, the
behavior
correlates
with the
disturbance
[where the
disturbance is
an event that
is influencing
the controlled
variable
independent of
the
behavior].Â

Â

                                                      RM: I

prefer the
definition
given in our
reply paper:Â Â “…the
behavioral
illusion
occurs when an
observed
relationship
between
variables is
seen
as revealing
something
about the
mechanisms
that produce a
behavior when,
in fact, it
does not. For
example,
the behavioral
illusion
occurs when
“reinforcement�
is seen as
“selecting�
the behavior
that produced
it (Marken
and Powers
1989; Yin
2013, pp.
342–343) or
when a tap
on the
patellar
tendon is seen
as the cause
of the
knee-jerk
response
(Marken 2014b,
p. 123). The
illusion
occurs when
the behavior
under study is
assumed to be
that of
an open-loop,
cause–efffect
system when it
is actually
that of a
closed-loop
control system
(Powers
1978)”.

Best

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
 --Antoine de
Saint-Exupery

                                                      --

[MartinT]

[Martin Taylor 2018.03.11.23.03]

MT:Â I don’t understand
why you say that Rick wrongly computed his mouse-cursor
correlation.Â

        I said

that I don’t want to see the mouse cursor correlation. It’s
correctly computed in the paper but I want to see the mouse
disturbance relationship instead. He did not show me THIS
number. Do you understand? Go to ricks website and play the
“nature of control demo�. It will show you that the mouse
cursor correlation is very low while the mouse disturbance
correlation is very high.

      So what? These correlations depend on the

quality of control, that’s all. Have a look at
to see why. For what reason do you introduce them into a
discussion of the Behavioral Illusion?

    MT: By the way, how and when does a "controlled variable"

become a “reference value”?

    I’ll tell you what - it’s certainly not through the behavior

of muscular forces on physical objects. But if you can suggest
an alternate hypothesis, I may change my default opinion. I say
that consciousness is when the CV is a reference value. What do
you think consciousness is? (without providing proof)

You misunderstand the question. It was gentle way of saying you are

calling an apple an orange, in the hope that you would put your
point in a more clear way. But I suppose one would be likely to wake
up and become consciously aware something strange was going on when
the perception becomes it own reference!

As for what *I* think consciousness is, that's a long story

that can be summarized as “I don’t know, but I can suggest some
possible properties, and maybe reasons why mobile organisms are
likely to have some version of consciousness.” Possibly “I can only
guess” might suffice.

Martin

···

http://www.mmtaylor.net/PCT/Info.theory.in.control/Control+correl.html

[PHILIP_JERAIR_YERANO]

Martin, your site speaks about the correlation between p and d. I am looking for the correlation between b and d. The correlation between mouse movement and disturbance. This correlation is not shown in ricks paper but is the most important one. When you say “theseâ€? correlations depend on the quality of control, are you referring to all 3 correlations (B-D, B-P, & P-D)?

···

On Sun, Mar 11, 2018 at 9:43
AM, Martin Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.11.12.24]

                      On 2018/03/11 1:31 AM, PHILIP JERAIR

YERANOSIAN wrote:

                      When a person sees that

a perception does not cause them to have an
intention, they are conscious because their
behavior is now resisting disturbances to
their intention. Consciousness is where
behavior correlates to disturbances of a
perception of an intention.Â

                   "Curioser and curioser". I feel as though

I am talking to Humpty-Dumpty and will soon be
eating “diminish me” mushrooms or something. Could
you relate what you said in this and your last
message to something connected with PCT as it is
normally understood? Or even to everyday
experience?

                      Martin

                        On Saturday, March 10,

2018, Martin Taylor <mmt-csg@mmtaylor.net >
wrote:

[Martin Taylor 2018.03.10.23.31]

                              On 2018/03/10 11:30 PM, PHILIP

JERAIR YERANOSIAN wrote:

                                    If a person

perceives that the internal
processes produce f-¹⁽ AB) and assumes that
they do it autonomously,
independently of the external
environment, that is
consciousness.

                              Explain what that

has to do with consciousness, and
whose consciousness you are talking
about, please? Also please explain how
this relates to the topic under
discussion, which is the nature of the
Behavioural Illusion, and behind that,
why behaviourist (“Stimulus-Response”
or “S-R”) researchers have accepted
the illusory perception as a truth
about Nature.

                              Martin

Virus-free.
www.avast.com

                                  On Sat, Mar

10, 2018 at 8:17 PM, Martin Taylor
mmt-csg@mmtaylor.net
wrote:

                                        [Martin Taylor

2018.03.10.23.14]

[philip 2019.03.10]

                                              An

observed relationship
between the output and
the disturbance can
only describe the form
f(AB). This
relationship cannot be
used to describe the
form f^-1(AB).

                                       If the function f(.)

is invertible, it completely
describes f-1(.), just as the
form of a jigsaw piece
determines the form of the
piece next to it in the
puzzle. The question is which
one is responsible for the
form being what it is. The
Behavioural Illusion is that
the internal processes are
responsible, whereas they are
capable only of compensating
for the effects between the
output and the CEV that are
imposed by the external
environment.

                                              These two sentences

are the behavioral
illusion doctrine.
Please refer to the
last paragraph of page
9 of Bill’s paper
(1978):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.

                                                The

Behavioural Illusion
is in someone’s
perception that the
the form of f(AB)
reflects something
about f^-1 (AB).

                                                                                    No. There's

no illusion there. It’s
just a simple fact.
Whether you call it a fact
of physics or of
mathematics is up to you,
but it is not an illusion.

                                                The term

f(AB) reflects how
the distal stimulus
determines the form
of the output.

                                      Yes.

                                                Â The term,

f^-1 (AB),
reflects how the
internal processes
determine the form
of the output.Â

                                                                                    If you

replace “how” with “that”,
you have a description of
the Behavioural Illusion
in someone’s mind. Another
way of putting it is “The
term f^-1 (AB)
determines what the
internal processes must do
in order for control to be
effective, given that the
environmental function is
f(AB). If a person
perceives that the
internal processes produce
f-¹⁽ AB) and
assumes that they do it
autonomously,
independently of the
external environment, that
is the Behavioural
Illusion.”

                                              Martin

                                              On

Sat, Mar 10, 2018 at
2:41 PM, Martin Taylor
mmt-csg@mmtaylor.net
wrote:

[Martin Taylor
2018.03.10.17.23]

                                                      On

2018/03/10
4:45 PM,
PHILIP JERAIR
YERANOSIAN
wrote:

                                                      The

behavioral
illusion
doctrine
states that an
experimenter cannot use an observed relationship between the output and
the disturbance to describe a dependence between the input and the
output. Nor
can this
observed
relationship
between output
and
disturbance be
used to
describe a
dependence
between the
input and
disturbance.
The purpose of
this doctrine
is to prevent
an
experimenter
from using a
shown
dependence to
reveal
something
about the
mechanisms
that produce
the output.

                                                   Actually,

this isn’t
correct, and there
is no “doctrine”
involved. It’s a
simple requirement
of control loops.
The behavioural
illusion is based
on a fundamental
fact about
negative feedback
loops that
stabilize their
variables, and
therefore about
control loops that
control well. If
there is a
functional
relation f(AB)
between the
variation at point
A and the
variation at point
B going one way
around the loop,
the functional
relation f(BA)
going the rest of
the way around the
loop is the
inverse function:
f(BA) = f-¹⁽AB).

                                                  If "A" is the

output, and “B”
the CEV, the
environmental
variable that
corresponds to the
controlled
perceptual
variable, and if a
change in the CEV
is taken to be a
“stimulus”, then
the response
(output) is
determined by the
properties of the
environmental link
between A and B.
Those properties,
which produce
f(AB), are
observable, in
principle, and are
not influenced by
whatever happens
inside the
organism. The
internal
mechanisms are not
observable, but
they must be such
as to produce
f(BA) of a
specific form,
that form being f^-1 (AB).

                                                  The modelling done

in simulations to
analyze the
mechanisms that
produce the output
relies on this
fact (and on the
discrepancy from f^-1 (AB)
that occurs
because of
imperfect
control). The
Behavioural
Illusion is in
someone’s
perception that
the internal
processes
determine the form
of the output in a
situation for
which control is
good.

                                                      Martin

Virus-free.
www.avast.com

                                                      On

Fri, Mar 9,
2018 at 3:04
PM, Richard
Marken rsmarken@gmail.com
wrote:

                                                      [Rick

Marken
2018-03-09_15:03:56]

                                                      [philip

2018.03.09]Â

                                                      PY: The

behavioral
illusion
refers to the
fact that the
behavior
[where the
behavior is
the observable
event we are
referring to]
does not
correlate to
the controlled
variable
[where the
controlled
variable is
the perception
which is
influenced by
the
behavior].Â
Instead, the
behavior
correlates
with the
disturbance
[where the
disturbance is
an event that
is influencing
the controlled
variable
independent of
the
behavior].Â

Â

                                                      RM: I

prefer the
definition
given in our
reply paper:Â Â “…the
behavioral
illusion
occurs when an
observed
relationship
between
variables is
seen
as revealing
something
about the
mechanisms
that produce a
behavior when,
in fact, it
does not. For
example,
the behavioral
illusion
occurs when
“reinforcementâ€?
is seen as
“selectingâ€?
the behavior
that produced
it (Marken
and Powers
1989; Yin
2013, pp.
342–343) or
when a tap
on the
patellar
tendon is seen
as the cause
of the
knee-jerk
response
(Marken 2014b,
p. 123). The
illusion
occurs when
the behavior
under study is
assumed to be
that of
an open-loop,
cause–efffect
system when it
is actually
that of a
closed-loop
control system
(Powers
1978)”.

Best

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
 --Antoine de
Saint-Exupery

                                                      --

[rsmarken]

[Rick Marken 2018-03-14_14:41:42]

[Martin Taylor 2018.03.11.17.39]

MT: I explained why Philip's explanation of the Behavioural Illusion was wrong. Would you care to explain why mine was wrong?

RM: Â The main problem for both of you is that you give the impression there is just one Behavioral Illusion -- the S-R illusion discussed by Powers' (1978). And you get even that one wrong when you describe it thus:
Â

MT: If "A" is the output, and "B" the CEV, the environmental variable that corresponds to the controlled perceptual variable, and if a change in the CEV is taken to be a "stimulus", then the response (output) is determined by the properties of the environmental link between A and B...

RM: The S-R illusion is seeing the disturbance to a controlled variable (what you call a CEV) as a stimulus that is the cause, via the organism, of the output (response) that protects the controlled variable from the effects of the disturbance. The illusion occurs, according to Powers (1978), because psychological scientists have been unaware of (or in denial about) the fact that organisms are control (purposeful) systems -- that they control -- and, therefore, these scientists are unaware of the existence or role of controlled variables in behavior. So these scientists would never take a change in the controlled variable to be a stimulus that causes a response since they don't know that such a variable even exists. Â
RM: In general, a behavioral illusion occurs when some aspect of the controlling done by an organism is taken to reflect the operation of cause-effect mechanisms. That is, the behavioral illusion occurs when the behavior of a control (N-) system is taken to be that of a cause-effect (Z-) system. And the illusion is always based on failure to notice the existence of a controlled variable or variables. So one is experiencing a behavioral illusion when a tap on the knee is seen as the cause of the knee jerk, not noticing that the controlled variable is tension on the patellar tendon; one is also experiencing a behavioral illusion when food pellets are seen as "selecting" lever press responses, not noticing that the controlled variable is the amount (and rate) of food being received; and one is experiencing a behavioral illusion when the egg rolling behavior of the grey lag goose is seen as a "fixed action pattern" (caused output), not noticing that the controlled variable is pressure on the back of the bill (<http://www.mindreadings.com/ControlDemo/Goose.html&gt;http://www.mindreadings.com/ControlDemo/Goose.html\).Â

MT: It is possible that your explanation might help to explain why you think you have shown why the results of velocity-curvature experiments are behavioural illusions as opposed to simple side-effects of control. That would be nice.

RM: The power law relationship between movement velocity and curvature is, indeed, a simple side effect of control. The illusion is that this side-effect tells us something about the processes that produce the movement. And the illusion results from not noticing that the controlled variable is the movement itself. I explained this at the beginning of the our original paper and demonstrated it in our rebuttal to the rebuttals using the ellipse drawing experiment, the results of which are presented in Figure 1. Another example of a side-effect of control that is a behavioral illusion is the invariant "velocity profile" described by Atkeson & Hollerback (1985) J. Neuroscience, 5, 2318-2330. Again the illusion results from taking the profile to be telling something about the processes that produce movement, not noticing that the controlled variable is the movement itself.
RM: So the fact that the power law is an example of a behavioral illusion can be seen without any need for mathematics. All you have to know is that movements are controlled results of muscle forces and therefore observation of characteristics of the movements themselves -- such as the power law relationship between velocity and curvature -- can tell you nothing about how the movement was produced. Thinking that it can is succumbing to the behavioral illusion.Â
RM: The mathematical analysis of the power law was done to show why a 1/3 or 2/3 power relationship between velocity and curvature is so consistently found, since it is this consistency that has seduced researchers into thinking that the power relationship between velocity and curvature says something important about the processes that produce the movement. So the complaints about our math being wrong are really irrelevant to the question of whether or not the power law is an example of a behavioral illusion.Â
RM: But our math isn't wrong, which I think we made pretty clear in our rebuttal to the rebuttals. Nevertheless, there are still complaints, like this one from  Bruce Abbott (2018.03.08.1905 EST):

BA: I’ve only quickly skimmed your rebuttal thus far, but wish to note a couple places I’ve noticed where straw men are raised.
Â
BA: One is where you cite other researchers’ use or approval of the Gribble and Ostry equations for computing tangential velocity and curvature. Â

RM: This is not a straw man. It is a demonstration of the hypocrisy of our critics who hurl the cry of "mathematical error" at our work. The main "other researchers" to whom we refer are Maoz et al who derived the equations shown as 5 and 6 in our report. These equations are precisely equivalent to the corresponding equations we derived (1 and 3), save for the fact that the variable we called D they called alpha and their curvature measure was 1/R rather than R (as we noted) so the coefficient of curvature for them is -1/3 rather than 1/3. Yet our critics had no problem with the Maoz et al math but our identical math was said to be in error. This is hypocrisy that rivals that of the reigning champions of hypocrisy -- the christian right in teh US.Â
RM: Anyway, I think I read a post from Alex where he said he was going to try to show what's wrong with our analysis of the experiment we present at the beginning of our rebuttal -- the one whose results are presented in Figure 1. If so, then our papers have had the desired effect, which was to get people to start testing PCT. So I suggest that we continue the discussion of the power law after we get some results from Alex's (and any other) labs.Â
Best
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

[wmansell]

Hi Rick,

Is the movement really the controlled variable? Or in a two level hierarchy couldn’t the movement be a means to control a one or more higher level variables such as to (a) draw a specific shape and (b) to complete this drawing quickly? It seems that we all get very used to asking what is the CV, but within a hierarchical control system one is controlling multiple CVs simultaneously with the CVs of the lower level systems often changing over the period that the higher level CVs remain relatively more constant.

So what we consider to be a CV often depends on the time frame we are working from.

How does that sound to you?

Warren

···

[Rick Marken 2018-03-14_14:41:42]

[Martin Taylor 2018.03.11.17.39]

MT: I explained why Philip's explanation of the Behavioural Illusion was

wrong. Would you care to explain why mine was wrong?

RM: The main problem for both of you is that you give the impression there is just one Behavioral Illusion – the S-R illusion discussed by Powers’ (1978). And you get even that one wrong when you describe it thus:

MT:
If “A” is the output, and “B” the CEV, the environmental variable that corresponds to the controlled perceptual variable, and if a change in the CEV is taken to be a “stimulus”, then the response (output) is determined by the properties of the environmental link between A and B…

RM: The S-R illusion is seeing the disturbance to a controlled variable
(what you call a CEV)

as a stimulus that is the cause, via the organism, of the output (response) that protects the controlled variable from the effects of the disturbance. The illusion occurs, according to Powers (1978), because psychological scientists have been unaware of (or in denial about) the fact that organisms are control (purposeful) systems – that they control – and, therefore, these scientists are unaware of the existence or role of controlled variables in behavior. So these scientists would never take a change in the controlled variable to be a stimulus that causes a response since they don’t know that such a variable even exists.

RM: In general, a behavioral illusion occurs when some aspect of the controlling done by an organism is taken to reflect the operation of cause-effect mechanisms. That is, the behavioral illusion occurs when the behavior of a control (N-) system is taken to be that of a cause-effect (Z-) system. And the illusion is always based on failure to notice the existence of a controlled variable or variables. So one is experiencing a behavioral illusion when a tap on the knee is seen as the cause of the knee jerk, not noticing that the controlled variable is tension on the patellar tendon; one is also experiencing a behavioral illusion when food pellets are seen as “selecting” lever press responses, not noticing that the controlled variable is the amount (and rate) of food being received; and one is experiencing a behavioral illusion when the egg rolling behavior of the grey lag goose is seen as a “fixed action pattern” (caused output), not noticing that the controlled variable is pressure on the back of the bill (http://www.mindreadings.com/ControlDemo/Goose.html).

MT: It is possible that your explanation might help to explain why you

think you have shown why the results of velocity-curvature
experiments are behavioural illusions as opposed to simple
side-effects of control. That would be nice.

RM: The power law relationship between movement velocity and curvature is, indeed, a simple side effect of control. The illusion is that this side-effect tells us something about the processes that produce the movement. And the illusion results from not noticing that the controlled variable is the movement itself. I explained this at the beginning of the our original paper and demonstrated it in our rebuttal to the rebuttals using the ellipse drawing experiment, the results of which are presented in Figure 1. Another example of a side-effect of control that is a behavioral illusion is the invariant “velocity profile” described by Atkeson & Hollerback (1985) J. Neuroscience, 5, 2318-2330. Again the illusion results from taking the profile to be telling something about the processes that produce movement, not noticing that the controlled variable is the movement itself.

RM: So the fact that the power law is an example of a behavioral illusion can be seen without any need for mathematics. All you have to know is that movements are controlled results of muscle forces and therefore observation of characteristics of the movements themselves – such as the power law relationship between velocity and curvature – can tell you nothing about how the movement was produced. Thinking that it can is succumbing to the behavioral illusion.

RM: The mathematical analysis of the power law was done to show why a 1/3 or 2/3 power relationship between velocity and curvature is so consistently found, since it is this consistency that has seduced researchers into thinking that the power relationship between velocity and curvature says something important about the processes that produce the movement. So the complaints about our math being wrong are really irrelevant to the question of whether or not the power law is an example of a behavioral illusion.

RM: But our math isn’t wrong, which I think we made pretty clear in our rebuttal to the rebuttals. Nevertheless, there are still complaints, like this one from Bruce Abbott (2018.03.08.1905 EST):

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

BA: One is where you cite other researchers’ use or approval of the Gribble and Ostry equations for computing tangential velocity and curvature.

RM: This is not a straw man. It is a demonstration of the hypocrisy of our critics who hurl the cry of “mathematical error” at our work. The main “other researchers” to whom we refer are Maoz et al who derived the equations shown as 5 and 6 in our report. These equations are precisely equivalent to the corresponding equations we derived (1 and 3), save for the fact that the variable we called D they called alpha and their curvature measure was 1/R rather than R (as we noted) so the coefficient of curvature for them is -1/3 rather than 1/3. Yet our critics had no problem with the Maoz et al math but our identical math was said to be in error. This is hypocrisy that rivals that of the reigning champions of hypocrisy – the christian right in teh US.

RM: Anyway, I think I read a post from Alex where he said he was going to try to show what’s wrong with our analysis of the experiment we present at the beginning of our rebuttal – the one whose results are presented in Figure 1. If so, then our papers have had the desired effect, which was to get people to start testing PCT. So I suggest that we continue the discussion of the power law after we get some results from Alex’s (and any other) labs.

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

[rsmarken]

[Rick Marken 2018-03-14_19:20:51]

WM: Is the movement really the controlled variable?

RM: Good question. My little demo shows only that the position of the cursor is controlled relative to reference states that vary over time.These changing reference states trace out an approximately elliptical path that can also be considered to be controlled; the path would not have been elliptical if the disturbance to the position of the cursor had not been resisted in just the right way at each reference position. So this implies that one aspect of cursor movement that was being controlled is the curvature of the movement at each instant.
RM: The velocity of the movement was surely also being controlled and as we noted in our rebuttal to the rebuttal it is most likely that the velocity being controlled is affine rather than tangential or angular. It might be possible to figure out which velocity is being controlled using just the disturbances to position since it's possible that the disturbance differentially affects these different variables. But all these questions would be good grist for PCT research, the goal of which would be to determine what perceptual aspects of the cursor trajectory are being controlled when a person draws an ellipse "free hand".Â

WM: Or in a two level hierarchy couldn’t the movement be a means to control a one or more higher level variables such as to (a) draw a specific shape and (b) to complete this drawing quickly?

RM: Very likely; a multi-level model will probably be necessary to account for the behavior in free hand movement tasks.
Â

WM: It seems that we all get very used to asking what is the CV, but within a hierarchical control system one is controlling multiple CVs simultaneously with the CVs of the lower level systems often changing over the period that the higher level CVs remain relatively more constant.Â

RM: There is no question that people are controlling many hierarchically related CVs, all of them being controlled simultaneously relative to continuously varying reference specifications. But that doesn't make it impossible to determine what these variables are. If it did, then research based on PCT would be impossible and PCT would be an untestable theory. As it is, we have plenty of evidence that we can test to determine what variables are being controlled when the variable being tested is being controlled relative to varying references set by higher level systems that are using variations in that variable to achieve their own goals. This is what is being done, for example, in the Test for the Controlled Variable (Mind Reading) demo (<http://www.mindreadings.com/ControlDemo/Mindread.html&gt;http://www.mindreadings.com/ControlDemo/Mindread.html\).Â

Â
WM: So what we consider to be a CV often depends on the time frame we are working from.

RM: What we consider a CV is a variable that is maintained in a fixed or variable reference state, protected from disturbance. We test to see whether or not any variable is controlled by applying disturbances that should have an effect on the variable if it is not controlled and seeing whether or not the disturbance has the expected effect. We can do this with variables that are controlled on a fast time scale (like the position of the avatars in the Mind Reading demo) or with variables that are controlled on a very slow time scale (like the program in the program control demo, <http://www.mindreadings.com/ControlDemo/ProgramControl.html&gt;http://www.mindreadings.com/ControlDemo/ProgramControl.html\).Â
BestÂ
Rick

How does that sound to you?

BestÂ
Rick

···

On Wed, Mar 14, 2018 at 4:59 PM, Warren Mansell <<mailto:wmansell@gmail.com>wmansell@gmail.com> wrote:

Warren

On 14 Mar 2018, at 21:41, Richard Marken <<mailto:rsmarken@gmail.com>rsmarken@gmail.com> wrote:

[Rick Marken 2018-03-14_14:41:42]

[Martin Taylor 2018.03.11.17.39]

MT: I explained why Philip's explanation of the Behavioural Illusion was wrong. Would you care to explain why mine was wrong?

RM: Â The main problem for both of you is that you give the impression there is just one Behavioral Illusion -- the S-R illusion discussed by Powers' (1978). And you get even that one wrong when you describe it thus:
Â

MT: If "A" is the output, and "B" the CEV, the environmental variable that corresponds to the controlled perceptual variable, and if a change in the CEV is taken to be a "stimulus", then the response (output) is determined by the properties of the environmental link between A and B...

RM: The S-R illusion is seeing the disturbance to a controlled variable (what you call a CEV) as a stimulus that is the cause, via the organism, of the output (response) that protects the controlled variable from the effects of the disturbance. The illusion occurs, according to Powers (1978), because psychological scientists have been unaware of (or in denial about) the fact that organisms are control (purposeful) systems -- that they control -- and, therefore, these scientists are unaware of the existence or role of controlled variables in behavior. So these scientists would never take a change in the controlled variable to be a stimulus that causes a response since they don't know that such a variable even exists. Â
RM: In general, a behavioral illusion occurs when some aspect of the controlling done by an organism is taken to reflect the operation of cause-effect mechanisms. That is, the behavioral illusion occurs when the behavior of a control (N-) system is taken to be that of a cause-effect (Z-) system. And the illusion is always based on failure to notice the existence of a controlled variable or variables. So one is experiencing a behavioral illusion when a tap on the knee is seen as the cause of the knee jerk, not noticing that the controlled variable is tension on the patellar tendon; one is also experiencing a behavioral illusion when food pellets are seen as "selecting" lever press responses, not noticing that the controlled variable is the amount (and rate) of food being received; and one is experiencing a behavioral illusion when the egg rolling behavior of the grey lag goose is seen as a "fixed action pattern" (caused output), not noticing that the controlled variable is pressure on the back of the bill (<http://www.mindreadings.com/ControlDemo/Goose.html&gt;http://www.mindreadings.com/ControlDemo/Goose.html\).Â

MT: It is possible that your explanation might help to explain why you think you have shown why the results of velocity-curvature experiments are behavioural illusions as opposed to simple side-effects of control. That would be nice.

RM: The power law relationship between movement velocity and curvature is, indeed, a simple side effect of control. The illusion is that this side-effect tells us something about the processes that produce the movement. And the illusion results from not noticing that the controlled variable is the movement itself. I explained this at the beginning of the our original paper and demonstrated it in our rebuttal to the rebuttals using the ellipse drawing experiment, the results of which are presented in Figure 1. Another example of a side-effect of control that is a behavioral illusion is the invariant "velocity profile" described by Atkeson & Hollerback (1985) J. Neuroscience, 5, 2318-2330. Again the illusion results from taking the profile to be telling something about the processes that produce movement, not noticing that the controlled variable is the movement itself.
RM: So the fact that the power law is an example of a behavioral illusion can be seen without any need for mathematics. All you have to know is that movements are controlled results of muscle forces and therefore observation of characteristics of the movements themselves -- such as the power law relationship between velocity and curvature -- can tell you nothing about how the movement was produced. Thinking that it can is succumbing to the behavioral illusion.Â
RM: The mathematical analysis of the power law was done to show why a 1/3 or 2/3 power relationship between velocity and curvature is so consistently found, since it is this consistency that has seduced researchers into thinking that the power relationship between velocity and curvature says something important about the processes that produce the movement. So the complaints about our math being wrong are really irrelevant to the question of whether or not the power law is an example of a behavioral illusion.Â
RM: But our math isn't wrong, which I think we made pretty clear in our rebuttal to the rebuttals. Nevertheless, there are still complaints, like this one from  Bruce Abbott (2018.03.08.1905 EST):

BA: I’ve only quickly skimmed your rebuttal thus far, but wish to note a couple places I’ve noticed where straw men are raised.
Â
BA: One is where you cite other researchers’ use or approval of the Gribble and Ostry equations for computing tangential velocity and curvature. Â

RM: This is not a straw man. It is a demonstration of the hypocrisy of our critics who hurl the cry of "mathematical error" at our work. The main "other researchers" to whom we refer are Maoz et al who derived the equations shown as 5 and 6 in our report. These equations are precisely equivalent to the corresponding equations we derived (1 and 3), save for the fact that the variable we called D they called alpha and their curvature measure was 1/R rather than R (as we noted) so the coefficient of curvature for them is -1/3 rather than 1/3. Yet our critics had no problem with the Maoz et al math but our identical math was said to be in error. This is hypocrisy that rivals that of the reigning champions of hypocrisy -- the christian right in teh US.Â
RM: Anyway, I think I read a post from Alex where he said he was going to try to show what's wrong with our analysis of the experiment we present at the beginning of our rebuttal -- the one whose results are presented in Figure 1. If so, then our papers have had the desired effect, which was to get people to start testing PCT. So I suggest that we continue the discussion of the power law after we get some results from Alex's (and any other) labs.Â
Best
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

--
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

[MartinT]

[Martin Taylor 2018.03.14.18.01]

Yes.

Yes. But how does any of what you wrote contradict what I said in my

explanation (of which you quoted only a sentence that paraphrases
the last part of your second paragraph)? In what way was my
explanation (I didn’t offer a description) wrong? I ask again.

Martin

···

[Rick Marken 2018-03-14_14:41:42]

[Martin Taylor 2018.03.11.17.39]

              MT: I explained why Philip's explanation of the

Behavioural Illusion was wrong. Would you care to
explain why mine was wrong?

            RM:  The main

problem for both of you is that you give the impression
there is just one Behavioral Illusion – the S-R
illusion discussed by Powers’ (1978). And you get even
that one wrong when you describe it thus:

                MT:
                  If

“A” is the output, and “B” the CEV, the
environmental variable that corresponds to the
controlled perceptual variable, and if a change in
the CEV is taken to be a “stimulus”, then the
response (output) is determined by the properties
of the environmental link between A and B…

              RM: The S-R illusion is seeing the disturbance to a

controlled variable
(what
you call a CEV) as a stimulus that is the
cause, via the organism, of the output (response) that
protects the controlled variable from the effects of
the disturbance.

                The

illusion occurs, according to Powers (1978), because
psychological scientists have been unaware of (or in
denial about) the fact that organisms are control
(purposeful) systems – that they control – and,
therefore, these scientists are unaware of the
existence or role of controlled variables in
behavior. So these scientists would never take a change
in the controlled variable to be a stimulus that
causes a response since they don’t know that such
a variable even exists.

                                          RM:

In general, a behavioral illusion occurs when
some aspect of the controlling done by an
organism is taken to reflect the operation of
cause-effect mechanisms. That is, the behavioral
illusion occurs when the behavior of a control
(N-) system is taken to be that of a
cause-effect (Z-) system. And the illusion is
always based on failure to notice the existence
of a controlled variable or variables. So one is
experiencing a behavioral illusion when a tap on
the knee is seen as the cause of the knee jerk,
not noticing that the controlled variable is
tension on the patellar tendon; one is also
experiencing a behavioral illusion when food
pellets are seen as “selecting” lever press
responses, not noticing that the controlled
variable is the amount (and rate) of food being
received; and one is experiencing a behavioral
illusion when the egg rolling behavior of the
grey lag goose is seen as a “fixed action
pattern” (caused output), not noticing that the
controlled variable is pressure on the back of
the bill (http://www.mindreadings.com/ControlDemo/Goose.html ).

[wmansell]

Thanks Rick, Warren

···

[Rick Marken 2018-03-14_19:20:51]

On Wed, Mar 14, 2018 at 4:59 PM, Warren Mansell wmansell@gmail.com wrote:

WM: Is the movement really the controlled variable?

RM: Good question. My little demo shows only that the position of the cursor is controlled relative to reference states that vary over time.These changing reference states trace out an approximately elliptical path that can also be considered to be controlled; the path would not have been elliptical if the disturbance to the position of the cursor had not been resisted in just the right way at each reference position. So this implies that one aspect of cursor movement that was being controlled is the curvature of the movement at each instant.

RM: The velocity of the movement was surely also being controlled and as we noted in our rebuttal to the rebuttal it is most likely that the velocity being controlled is affine rather than tangential or angular. It might be possible to figure out which velocity is being controlled using just the disturbances to position since it’s possible that the disturbance differentially affects these different variables. But all these questions would be good grist for PCT research, the goal of which would be to determine what perceptual aspects of the cursor trajectory are being controlled when a person draws an ellipse “free hand”.

WM: Or in a two level hierarchy couldn’t the movement be a means to control a one or more higher level variables such as to (a) draw a specific shape and (b) to complete this drawing quickly?

RM: Very likely; a multi-level model will probably be necessary to account for the behavior in free hand movement tasks.

WM: It seems that we all get very used to asking what is the CV, but within a hierarchical control system one is controlling multiple CVs simultaneously with the CVs of the lower level systems often changing over the period that the higher level CVs remain relatively more constant.

RM: There is no question that people are controlling many hierarchically related CVs, all of them being controlled simultaneously relative to continuously varying reference specifications. But that doesn’t make it impossible to determine what these variables are. If it did, then research based on PCT would be impossible and PCT would be an untestable theory. As it is, we have plenty of evidence that we can test to determine what variables are being controlled when the variable being tested is being controlled relative to varying references set by higher level systems that are using variations in that variable to achieve their own goals. This is what is being done, for example, in the Test for the Controlled Variable (Mind Reading) demo (http://www.mindreadings.com/ControlDemo/Mindread.html).

WM: So what we consider to be a CV often depends on the time frame we are working from.

RM: What we consider a CV is a variable that is maintained in a fixed or variable reference state, protected from disturbance. We test to see whether or not any variable is controlled by applying disturbances that should have an effect on the variable if it is not controlled and seeing whether or not the disturbance has the expected effect. We can do this with variables that are controlled on a fast time scale (like the position of the avatars in the Mind Reading demo) or with variables that are controlled on a very slow time scale (like the program in the program control demo, http://www.mindreadings.com/ControlDemo/ProgramControl.html).

Best

Rick

How does that sound to you?
Best

Rick

Warren

On 14 Mar 2018, at 21:41, Richard Marken rsmarken@gmail.com wrote:

–
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

[Rick Marken 2018-03-14_14:41:42]

[Martin Taylor 2018.03.11.17.39]

MT: I explained why Philip's explanation of the Behavioural Illusion was

wrong. Would you care to explain why mine was wrong?

RM: The main problem for both of you is that you give the impression there is just one Behavioral Illusion – the S-R illusion discussed by Powers’ (1978). And you get even that one wrong when you describe it thus:

MT:
If “A” is the output, and “B” the CEV, the environmental variable that corresponds to the controlled perceptual variable, and if a change in the CEV is taken to be a “stimulus”, then the response (output) is determined by the properties of the environmental link between A and B…

RM: The S-R illusion is seeing the disturbance to a controlled variable
(what you call a CEV)

as a stimulus that is the cause, via the organism, of the output (response) that protects the controlled variable from the effects of the disturbance. The illusion occurs, according to Powers (1978), because psychological scientists have been unaware of (or in denial about) the fact that organisms are control (purposeful) systems – that they control – and, therefore, these scientists are unaware of the existence or role of controlled variables in behavior. So these scientists would never take a change in the controlled variable to be a stimulus that causes a response since they don’t know that such a variable even exists.

RM: In general, a behavioral illusion occurs when some aspect of the controlling done by an organism is taken to reflect the operation of cause-effect mechanisms. That is, the behavioral illusion occurs when the behavior of a control (N-) system is taken to be that of a cause-effect (Z-) system. And the illusion is always based on failure to notice the existence of a controlled variable or variables. So one is experiencing a behavioral illusion when a tap on the knee is seen as the cause of the knee jerk, not noticing that the controlled variable is tension on the patellar tendon; one is also experiencing a behavioral illusion when food pellets are seen as “selecting” lever press responses, not noticing that the controlled variable is the amount (and rate) of food being received; and one is experiencing a behavioral illusion when the egg rolling behavior of the grey lag goose is seen as a “fixed action pattern” (caused output), not noticing that the controlled variable is pressure on the back of the bill (http://www.mindreadings.com/ControlDemo/Goose.html).

MT: It is possible that your explanation might help to explain why you

think you have shown why the results of velocity-curvature
experiments are behavioural illusions as opposed to simple
side-effects of control. That would be nice.

RM: The power law relationship between movement velocity and curvature is, indeed, a simple side effect of control. The illusion is that this side-effect tells us something about the processes that produce the movement. And the illusion results from not noticing that the controlled variable is the movement itself. I explained this at the beginning of the our original paper and demonstrated it in our rebuttal to the rebuttals using the ellipse drawing experiment, the results of which are presented in Figure 1. Another example of a side-effect of control that is a behavioral illusion is the invariant “velocity profile” described by Atkeson & Hollerback (1985) J. Neuroscience, 5, 2318-2330. Again the illusion results from taking the profile to be telling something about the processes that produce movement, not noticing that the controlled variable is the movement itself.

RM: So the fact that the power law is an example of a behavioral illusion can be seen without any need for mathematics. All you have to know is that movements are controlled results of muscle forces and therefore observation of characteristics of the movements themselves – such as the power law relationship between velocity and curvature – can tell you nothing about how the movement was produced. Thinking that it can is succumbing to the behavioral illusion.

RM: The mathematical analysis of the power law was done to show why a 1/3 or 2/3 power relationship between velocity and curvature is so consistently found, since it is this consistency that has seduced researchers into thinking that the power relationship between velocity and curvature says something important about the processes that produce the movement. So the complaints about our math being wrong are really irrelevant to the question of whether or not the power law is an example of a behavioral illusion.

RM: But our math isn’t wrong, which I think we made pretty clear in our rebuttal to the rebuttals. Nevertheless, there are still complaints, like this one from Bruce Abbott (2018.03.08.1905 EST):

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

BA: One is where you cite other researchers’ use or approval of the Gribble and Ostry equations for computing tangential velocity and curvature.

RM: This is not a straw man. It is a demonstration of the hypocrisy of our critics who hurl the cry of “mathematical error” at our work. The main “other researchers” to whom we refer are Maoz et al who derived the equations shown as 5 and 6 in our report. These equations are precisely equivalent to the corresponding equations we derived (1 and 3), save for the fact that the variable we called D they called alpha and their curvature measure was 1/R rather than R (as we noted) so the coefficient of curvature for them is -1/3 rather than 1/3. Yet our critics had no problem with the Maoz et al math but our identical math was said to be in error. This is hypocrisy that rivals that of the reigning champions of hypocrisy – the christian right in teh US.

RM: Anyway, I think I read a post from Alex where he said he was going to try to show what’s wrong with our analysis of the experiment we present at the beginning of our rebuttal – the one whose results are presented in Figure 1. If so, then our papers have had the desired effect, which was to get people to start testing PCT. So I suggest that we continue the discussion of the power law after we get some results from Alex’s (and any other) labs.

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

[MartinT]

[Martin Taylor 2018.03.15.11.20]

I must confess to ignorance, here, so would you mind explaining

“affine velocity”. I realize that you don’t want to respond to the
criticisms made in my comment on your curvature paper, but I’m not
criticizing here.

I think I understand a few concepts of affine geometry, but affine

velocity is not among them, and I could find nothing about it in
Wikipedia among all the articles about affine spaces. Since
(according to Wikipedia) affine geometry is "what remains of Euclidean geometry * when
not using (mathematicians often say “when forgetting”) the* metric notions of distance and angle ", I
don’t understand how an affine velocity can be calculated.

My notion of velocity is the distance covered in a unit of time, but

if affine geometry has no concept of distance, I don’t understand
how to translate the concept of velocity into “affine velocity”. I
suppose it has some relation to four-dimensional affine geometry,
but I don’t understand what to do with the imaginary value of time
in that space. An explanation would be most welcome.

Martin

···

[Rick Marken 2018-03-14_19:20:51]

…

          RM: The velocity of the movement was surely also being

controlled and as we noted in our rebuttal to the rebuttal
it is most likely that the velocity being controlled is
affine rather than tangential or angular.

[rsmarken]

[Rick Marken 2018-03-16_12:16:39]

[Martin Taylor 2018.03.14.18.01]

RM: Â The main problem for both of you is that you give the impression there is just one Behavioral Illusion -- the S-R illusion discussed by Powers' (1978)...

MT: Yes. But how does any of what you wrote contradict what I said in my explanation (of which you quoted only a sentence that paraphrases the last part of your second paragraph)? In what way was my explanation (I didn't offer a description) wrong? I ask again.

RM: I'll reply to your entire explanation.Â

MT: Actually, this isn't correct, and there is no "doctrine" involved.

RM: This statement is correct; the "behavioral illusion" is not a doctrine but a description of a phenomenon: seeing the behavior of a control system as that of a cause-effect system.
Â

MT: It's a simple requirement of control loops. The behavioural illusion is based on a fundamental fact about negative feedback loops that stabilize their variables, and therefore about control loops that control well. If there is a functional relation f(AB) between the variation at point A and the variation at point B going one way around the loop, the functional relation f(BA) going the rest of the way around the loop is the inverse function: f(BA) = f-1(AB).

RM: This is incorrect. There is no version of the behavioral illusion that is this based on the "fundamental fact" about negative feedback loops that you describe here. >

MT: If "A" is the output, and "B" the CEV, the environmental variable that corresponds to the controlled perceptual variable, and if a change in the CEV is taken to be a "stimulus", then the response (output) is determined by the properties of the environmental link between A and B. Those properties, which produce f(AB), are observable, in principle, and are not influenced by whatever happens inside the organism. The internal mechanisms are not observable, but they must be such as to produce f(BA) of a specific form, that form being f-1(AB).Â

RM: This is incorrect. The CEV would never be taken to be the "stimulus" because it is not an independent variable, one that can be manipulated by an experimenter. An experimenter can't manipulate the CEV because it is under control. The behavioral illusion you are talking about occurs when an experimenter observes a relationship between stimulus and response variables and reasonably concludes that this relationship reveals something about the functional characteristics of the organism, f(), that turn variations in the stimulus into variations in the response:
Â
response =Â Â f(stimulus)Â Â Â Â Â Â Â Â Â (1)

RM: Powers (1978) showed that, if the organism under study is actually a control system, then the observed relationship between stimulus and response depends (inversely) on the feedback function, g(), that relates variations in the response to variations in what you call the CEV.
response = g-1(stimulus)Â Â Â Â Â Â Â (2)
RM: So the illusion is that the observed relationship between stimulus and response reveals something about the functional characteristics of the organism, f(), when in fact it reveals only something about the nature of the environmental feedback connection between response and CEV.Â
RM: Powers (1978) proved that an observed relationship between stimulus and response is described by Eq. 2 rather than Eq. 1 when the behavior you are observing is that of a control (N) rather than a cause-effect (Z) system. In that proof, the stimulus variable is the disturbance variable, d, the response variable is the output variable, q.o, and the CEV is the controlled variable, q.i.  The proof was done by solving the simultaneous equations that describe the behavior of a control system for the relationship between stimulus (disturbance) and response (output); it had nothing to do with the "fundamental fact" about negative feedback loops that you describe above.Â
RM: Powers (1978) also explains why psychological scientists have succumbed to the behavioral illusion. It's because they assume that organisms are cause-effect (Z) systems; the observation that variations in a stimulus variable are fairly consistently related to variations in a response variable is perfectly compatible with this assumption. This is because the behavior of a control system looks like that of a cause-effect system as long as one ignores the fact that responses (outputs) are countering the effects of the stimulus (disturbances) on a controlled variable, q.i. Thus, the illusion of a causal relationship between stimulus and response variables can be dispelled using the Test for the Controlled Variable (also described in Powers, 1978) to determine both that a variable is being controlled and what that variable is.Â
RM: There are other behavioral illusions besides the stimulus-response illusion described in Powers (1978) that results from assuming, incorrectly, that the system being observed is a cause-effect rather than a control system. The illusions are described in my "Blind Men and the Elephant" paper in my book More Mind Readings. In that paper I call the different illusion different "views" of control; there is the stimulus-response view (covered above), the reinforcement view and the cognitive view. These different views correspond to the three dominant "schools' of scientific psychology. PCT shows that all three are based on an illusion that results from the fact that the behavior of a control system can look like that of a cause-effect system.Â
Best
Rick

···

On Wed, Mar 14, 2018 at 8:43 PM, Martin Taylor <<mailto:mmt-csg@mmtaylor.net>mmt-csg@mmtaylor.net> wrote:
--
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

[rsmarken]

···

[Rick Marken 2018-03-16_12:38:01]

[Martin Taylor 2018.03.15.11.20]

MT: I must confess to ignorance, here, so would you mind explaining

“affine velocity”. I realize that you don’t want to respond to the
criticisms made in my comment on your curvature paper, but I’m not
criticizing here.

RM: According to Moaz et al affine velocity is defined as

which, of course, is our “cross-product” variable D (as mentioned in our rebuttal to you rebuttal). A more detailed explanation of affine velocity is given in Pollack and Sapiro (1997), which is available here:Â

https://www.sciencedirect.com/science/article/pii/S0042698996001162

Â

BestÂ

Rick

I think I understand a few concepts of affine geometry, but affine

velocity is not among them, and I could find nothing about it in
Wikipedia among all the articles about affine spaces. Since
(according to Wikipedia) affine geometry is "what remains of Euclidean geometry * when
not using (mathematicians often say “when forgetting”) the* metric notions of distance and angle ", I
don’t understand how an affine velocity can be calculated.

My notion of velocity is the distance covered in a unit of time, but

if affine geometry has no concept of distance, I don’t understand
how to translate the concept of velocity into “affine velocity”. I
suppose it has some relation to four-dimensional affine geometry,
but I don’t understand what to do with the imaginary value of time
in that space. An explanation would be most welcome.

Martin

–

          RM: The velocity of the movement was surely also being

controlled and as we noted in our rebuttal to the rebuttal
it is most likely that the velocity being controlled is
affine rather than tangential or angular.

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

[MartinT]

[Martin Taylor 2018.03.16.17.58]

OK,

Perhaps you could suggest one that isn't?  I remain ready to be

corrected by an effective explanation of a counter-example (not, as
at the end of your message, different schools of psychology that
concentrate on different things entirely).

Yes, you are quite right. I should have said the experimenter-caused

change in the disturbance is the stimulus, not just the change in
the CEV due to the change in the disturbance. But the rest of what I
said is OK, because the part of the loop that forces the form of the
“response” is the environmental feedback path between the output
observed by the experimenter and the CEV, not the internal processes
part of the loop, as you agree in the second half of your comment.

Yes, that was exactly what I said, wasn't it? But I think I put it a

bit more clearly.

The part of your paragraph up to "it had nothing..." is exactly what

I said. I had no need to prove it for two reasons. One is that it is
self-evident that even if you have a loop, each variable in it has
only one value at a time whether you traverse the loop forward or
backward, while the other is that, as you note, Powers proved it to
those few for whom it might not have been self-evident. Your last
clause “it had nothing…” directly contradicts the rest of your
paragraph.

Yes.

No. The behaviour of a control system IS (not looks like) that of a

cause-effect system as long as the reference value is constant .
The circuitry is the same, exactly. The experimenter’s
interpretation of how the loop works is the illusion, not the actual
operation of the loop.

No. A suitable S-R system -- one in which the S-R function is the

inverse of the function between the observable output and the CEV –
will behave in exactly the same way as a control loop if the
stimulus keeps changing, as it will if there is a feedback
connection through the CEV, provided the reference value stays the
same. The illusion is entirely in the mind of the experimenter, that
the form of the response is determined by consistent internal
processes, whereas the internal processes are actually constrained
to produce what they do by the form of the environmental feedback
function. Since the signal paths are fixed, the TCV cannot
distinguish between S-R and control, because control works only when
the stimulus-response function does closely match the inverse of the
environmental feedback function.

The problem is that the straw S-R theorist thinks that this

stimulus-response function would be the same if you offered the same
stimulus but had a different environmental feedback path. I wonder
how many of those there are, or ever were. My first summer job 60
years ago when I was first learning what psychology was involved
changing the feedback path for a gun sight, by changing the gearing
ratios – I don’t remember of what part of the mechanism, but they
were part of the environmental feedback path. To me, coming out of
undergraduate Engineering Physics (and being in an Operations
Research Master’s program) it was a simple engineering issue of what
happened in the feedback loop, and my boss did not disagree, so far
as I remember.

However, these are not different "behavioural illusions". They are

coherent schools of thought about aspects of psychology that PCT
treats differently. Reinforcement is a school of thought that deals
with learning. Cognitive psychology is interpretable in PCT as that
the reference values up and down the hierarchy are set autonomously,
an approach that leads to enormous complexity in the computation of
what to do in different situations. Neither has any relationship to
the behavioural illusion.

You simply can't decide that all other psychological theories are

behavioural illusions, simply because they differ from PCT and don’t
recognize the primacy of control. They may be illusory, but
centuries from now, scientists with the advantage of ideas and data
we don’t have may well see PCT as an illusion, too. But PCT will
even then not be a “behavioural illusion” and in the present time
neither are other schools of thought in psychology.

Martin

···

[Rick Marken 2018-03-16_12:16:39]

        On Wed, Mar 14, 2018 at 8:43 PM,

Martin Taylor mmt-csg@mmtaylor.net
wrote:

[Martin Taylor 2018.03.14.18.01]

            MT: Yes. But how does any of what you wrote

contradict what I said in my explanation (of which you
quoted only a sentence that paraphrases the last part of
your second paragraph)? In what way was my explanation
(I didn’t offer a description) wrong? I ask again.

RM: I’ll reply to your entire explanation.

                          RM: Â The main

problem for both of you is that you give
the impression there is just one
Behavioral Illusion – the S-R illusion
discussed by Powers’ (1978)…

              MT:

Actually, this isn’t correct, and there is no
“doctrine” involved.

            RM: This statement is correct; the "behavioral

illusion" is not a doctrine but a description of a
phenomenon: seeing the behavior of a control system as
that of a cause-effect system.

Â

              MT:

It’s a simple requirement of control loops. The
behavioural illusion is based on a fundamental fact
about negative feedback loops that stabilize their
variables, and therefore about control loops that
control well. If there is a functional relation f(AB)
between the variation at point A and the variation at
point B going one way around the loop, the functional
relation f(BA) going the rest of the way around the
loop is the inverse function: f(BA) = f-¹⁽AB).

            RM: This is incorrect. There is no version of the

behavioral illusion that is this based on the
“fundamental fact” about negative feedback loops that
you describe here.

                              MT:
                If

“A” is the output, and “B” the CEV, the
environmental variable that corresponds to the
controlled perceptual variable, and if a change in
the CEV is taken to be a “stimulus”, then the
response (output) is determined by the properties of
the environmental link between A and B. Those
properties, which produce f(AB), are observable, in
principle, and are not influenced by whatever
happens inside the organism. The internal mechanisms
are not observable, but they must be such as to
produce f(BA) of a specific form, that form being f^-1(AB).Â

            RM: This is incorrect. The CEV would never be taken

to be the “stimulus” because it is not an independent
variable, one that can be manipulated by an
experimenter. An experimenter can’t manipulate the CEV
because it is under control. The behavioral illusion you
are talking about occurs when an experimenter observes a
relationship between stimulus and response variables and
reasonably concludes that this relationship reveals
something about the functional characteristics of the
organism ,
f(), that turn variations in the
stimulus into variations in the response:

Â

              response

=Â Â f(stimulus)Â Â
       (1)

            RM: Powers (1978) showed that, if the organism under

study is actually a control system, then the observed
relationship between stimulus and response depends
(inversely) on the feedback function, g(), that relates
variations in the response to variations in what you
call the CEV.

response = g^-1 (stimulus)Â
      (2)

            RM: So the illusion is that the observed relationship

between stimulus and response reveals something about
the functional characteristics of the organism, f(),
when in fact it reveals only something about the nature
of the environmental feedback connection between
response and CEV.

            RM: Powers (1978) proved that an observed

relationship between stimulus and response is described
by Eq. 2 rather than Eq. 1 when the behavior you are
observing is that of a control (N) rather than a
cause-effect (Z) system. In that proof, the stimulus
variable is the disturbance variable, d, the response
variable is the output variable, q.o, and the CEV is the
controlled variable, q.i.  The proof was done by
solving the simultaneous equations that describe the
behavior of a control system for the relationship
between stimulus (disturbance) and response (output);
it had nothing to do with the “fundamental fact” about
negative feedback loops that you describe above.

          RM: Powers (1978) also explains why psychological

scientists have succumbed to the behavioral illusion. It’s
because they assume that organisms are cause-effect (Z)
systems; the observation that variations in a stimulus
variable are fairly consistently related to variations in
a response variable is perfectly compatible with this
assumption.

          This is because the behavior of a control system looks

like that of a cause-effect system as long as one ignores
the fact that responses (outputs) are countering the
effects of the stimulus (disturbances) on a controlled
variable, q.i.

          Thus, the illusion of a causal relationship between

stimulus and response variables can be dispelled using the
Test for the Controlled Variable (also described in
Powers, 1978) to determine both that a variable is being
controlled and what that variable is.

          RM: There are other behavioral illusions besides the

stimulus-response illusion described in Powers (1978) that
results from assuming, incorrectly, that the system being
observed is a cause-effect rather than a control system.
The illusions are described in my “Blind Men and the
Elephant” paper in my book More Mind Readings . In
that paper I call the different illusion different “views”
of control; there is the stimulus-response view (covered
above), the reinforcement view and the cognitive view.
These different views correspond to the three dominant
"schools’ of scientific psychology. PCT shows that all
three are based on an illusion that results from the fact
that the behavior of a control system can look like that
of a cause-effect system.

Best

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
–Antoine de Saint-Exupery

[rsmarken]

[Rick Marken 2018-03-17_15:44:58]

[Martin Taylor 2018.03.16.17.58]

MT: It's a simple requirement of control loops. The behavioural illusion is based on a fundamental fact about negative feedback loops that stabilize their variables, and therefore about control loops that control well. If there is a functional relation f(AB) between the variation at point A and the variation at point B going one way around the loop, the functional relation f(BA) going the rest of the way around the loop is the inverse function: f(BA) = f-1(AB).

RM: This is incorrect. There is no version of the behavioral illusion that is this based on the "fundamental fact" about negative feedback loops that you describe here.Â

MT: Perhaps you could suggest one that isn't? Â

RM: As I said, none of them are based on this "fundamental fact". But the illusion that is most obviously not based on it is the S-R illusion -- the illusion that stimuli cause responses via the organism. The problem is that your analysis assumes that A and B are points in a control loop. The S-R illusion is seeing a variable outside the loop -- the stimulus (or disturbance) variable -- as the cause of the system's responses when it is not.Â

MT: If "A" is the output, and "B" the CEV, the environmental variable that corresponds to the controlled perceptual variable, and if a change in the CEV is taken to be a "stimulus", then the response (output) is determined by the properties of the environmental link between A and B. ...

RM: This is incorrect. The CEV would never be taken to be the "stimulus" because it is not an independent variable...

MT: Yes, you are quite right. I should have said the experimenter-caused change in the disturbance is the stimulus, not just the change in the CEV due to the change in the disturbance. But the rest of what I said is OK, because the part of the loop that forces the form of the "response" is the environmental feedback path between the output observed by the experimenter and the CEV, not the internal processes part of the loop, as you agree in the second half of your comment.

RM. No, the rest of what you say is not OK because your analysis assumes that the relationship between CEV (controlled variable) and response is the observed relationship that is being misinterpreted as the "organism function". Scientific psychologists don't observe this relationship because they are unaware of the existence of controlled variables. Scientific psychologists observe the relationship between stimuli (independent variables) and responses (dependent variables). If the system under study is a control system, these stimuli are disturbances to controlled variables and the responses are outputs that compensate for these disturbances. The illusion described in Powers (1978) turns on the fact that, for an N system. the observed relationship between stimuli (disturbances) and responses (output) depends on characteristics of the feedback connection between output and controlled variable, not on characteristics of the system itself.
Â

RM:Â Â response =Â Â f(stimulus)Â Â Â Â Â Â Â Â Â (1)
RM: Powers (1978) showed that, if the organism under study is actually a control system, then the observed relationship between stimulus and response depends (inversely) on the feedback function, g(), that relates variations in the response to variations in what you call the CEV.
R: response = g-1(stimulus)Â Â Â Â Â Â Â (2)
RM: So the illusion is that the observed relationship between stimulus and response reveals something about the functional characteristics of the organism, f(), when in fact it reveals only something about the nature of the environmental feedback connection between response and CEV.

MT: Yes, that was exactly what I said, wasn't it? But I think I put it a bit more clearly.

RM: It is what you said, if what you call the stimulus is the disturbance to the controlled variable. But I got the impression that you were implying that the stimulus is the controlled variable itself, or a change thereof, , in which case what you said is quite different than what I said.Â

RM: Powers (1978) proved that an observed relationship between stimulus and response is described by Eq. 2 rather than Eq. 1 when the behavior you are observing is that of a control (N) rather than a cause-effect (Z) system. In that proof, the stimulus variable is the disturbance variable, d, the response variable is the output variable, q.o, and the CEV is the controlled variable, q.i.  The proof was done by solving the simultaneous equations that describe the behavior of a control system for the relationship between stimulus (disturbance) and response (output); it had nothing to do with the "fundamental fact" about negative feedback loops that you describe above.Â

MT: The part of your paragraph up to "it had nothing..." is exactly what I said. I had no need to prove it for two reasons. One is that it is self-evident that even if you have a loop, each variable in it has only one value at a time whether you traverse the loop forward or backward, while the other is that, as you note, Powers proved it to those few for whom it might not have been self-evident. Your last clause "it had nothing..." directly contradicts the rest of your paragraph.

RM: As I said above, Powers (1978) was not proving something about variables in the loop; he was proving that a variable outside the loop -- an independent variable -- can appear to be the cause of system outputs if this variable is a disturbance to variables controlled by a control system.Â
Â

RM: Powers (1978) also explains why psychological scientists have succumbed to the behavioral illusion. It's because they assume that organisms are cause-effect (Z) systems; the observation that variations in a stimulus variable are fairly consistently related to variations in a response variable is perfectly compatible with this assumption.

MT: Yes.

RM: This is because the behavior of a control system looks like that of a cause-effect system as long as one ignores the fact that responses (outputs) are countering the effects of the stimulus (disturbances) on a controlled variable, q.i.Â

MT: No. The behaviour of a control system IS (not looks like) that of a cause-effect system as long as the reference value is constant. The circuitry is the same, exactly. The experimenter's interpretation of how the loop works is the illusion, not the actual operation of the loop.

RM: Powers (1978) uses the term "Z system" to refer to a cause-effect system, one that has no feedback connection from effect (output) back to cause (input); he uses the term "N system" is refer to a control system where there is feedback from effect to cause. Powers (1978) proved that there is a behavioral illusion that occurs when an observed relationship between a stimulus and response is seen as the behavior of Z system when it is actually that of an N system.Â
RM: The illusion does involve a misinterpretation on the part of the experimenter, but it is not a misinterpretation of how the loop works - the experimenter has not observed a loop; rather, it is a misinterpretation of how the observed stimulus-response relationship works. The illusion exists when the experimenter interprets the observed S-R relationship as working because the stimulus causes the response via the organism. If the system were a Z system, this interpretation would be correct. But since the system is an N system, this interpretation is incorrect; the observed S-R relationship works because the system is acting to keep a controlled variable in a constant or variable reference state, protected from the effects of disturbances. The controlled variable is a crucial part of this correct interpretation; this is why failure to see that organisms control -- that they are controlling variables -- is at the heart of this (and all) behavioral illusions.Â
Â

RM: Thus, the illusion of a causal relationship between stimulus and response variables can be dispelled using the Test for the Controlled Variable (also described in Powers, 1978) to determine both that a variable is being controlled and what that variable is.Â

MT: No. A suitable S-R system -- one in which the S-R function is the inverse of the function between the observable output and the CEV -- will behave in exactly the same way as a control loop if the stimulus keeps changing, as it will if there is a feedback connection through the CEV, provided the reference value stays the same.

RM: This is demonstrably false, even if we go with your definition of the stimulus as a change in the CEV. But it is such an important misunderstanding of the behavioral illusion that I will deal with it in a separate post when I get a chance.

RM: There are other behavioral illusions besides the stimulus-response illusion described in Powers (1978) that results from assuming, incorrectly, that the system being observed is a cause-effect rather than a control system. The illusions are described in my "Blind Men and the Elephant" paper in my book More Mind Readings. In that paper I call the different illusion different "views" of control; there is the stimulus-response view (covered above), the reinforcement view and the cognitive view. These different views correspond to the three dominant "schools' of scientific psychology. PCT shows that all three are based on an illusion that results from the fact that the behavior of a control system can look like that of a cause-effect system.

MT: However, these are not different "behavioural illusions". They are coherent schools of thought about aspects of psychology that PCT treats differently. Reinforcement is a school of thought that deals with learning.

RM: Reinforcement theory also deals with steady state behavior. And in either case the theory is based on the illusion that consequences select behavior (rather than vice versa).Â

MT: Cognitive psychology is interpretable in PCT as that the reference values up and down the hierarchy are set autonomously, an approach that leads to enormous complexity in the computation of what to do in different situations. Neither has any relationship to the behavioural illusion.

RM: Cognitive psychology is based on the illusion that behavior is caused output. >

MT: You simply can't decide that all other psychological theories are behavioural illusions, simply because they differ from PCT and don't recognize the primacy of control.

RM: Why not? The problem with these theories is not that they don't recognize the primacy of control; the problem is that they don't recognize the fact of control.

MT: They may be illusory, but centuries from now, scientists with the advantage of ideas and data we don't have may well see PCT as an illusion, too. But PCT will even then not be a "behavioural illusion" and in the present time neither are other schools of thought in psychology.

RM: It's not the theories that are illusions; it's the interpretations of the observations that are the illusion. Future scientists may find PCT to have been fundamentally flawed. But I don't see why that possibility requires present day scientists to stay silent about the fact that S-R, reinforcement and cognitive theories are certainly wrong.
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.�
                --Antoine de Saint-Exupery

[MartinT]

[Martin Taylor 2018.03.17.23.19]

I'm getting bored with threads in which my contributions are said to

be wrong, and when I ask in what way they are wrong, I am told
“this” is correct, and “this” turns out to be a paraphrase of what I
said initially. Or that Bill P. said “that”, when what I said had
been a paraphrase of “that”. So I am not going to respond to this
simply for the purpose of keeping up the volume of messages on
CSGnet.

Martin

···

[Rick Marken 2018-03-17_15:44:58]

[Martin Taylor 2018.03.16.17.58]

MT: Perhaps you could suggest one that isn’t? Â

          RM: As I said, none of them are based on this

“fundamental fact”. But the illusion that is most
obviously not based on it is the S-R illusion – the
illusion that stimuli cause responses via the organism.
The problem is that your analysis assumes that A and B are
points in a control loop . The S-R illusion is
seeing a variable outside the loop – the stimulus
(or disturbance) variable – as the cause of the system’s
responses when it is not.Â

            MT: Yes, you are quite right. I should have said

the experimenter-caused change in the disturbance is the
stimulus, not just the change in the CEV due to the
change in the disturbance. But the rest of what I said
is OK, because the part of the loop that forces the form
of the “response” is the environmental feedback path
between the output observed by the experimenter and the
CEV, not the internal processes part of the loop, as you
agree in the second half of your comment.

          RM. No, the rest of what you say is not OK because your

analysis assumes that the relationship between CEV
(controlled variable) and response is the observed
relationship that is being misinterpreted as the “organism
function”. Scientific psychologists don’t observe this
relationship because they are unaware of the existence of
controlled variables. Scientific psychologists observe the
relationship between stimuli (independent variables) and
responses (dependent variables). If the system under study
is a control system, these stimuli are disturbances to
controlled variables and the responses are outputs that
compensate for these disturbances. The illusion described
in Powers (1978) turns on the fact that, for an N system.
the observed relationship between stimuli
(disturbances) and responses (output) depends on
characteristics of the feedback connection between output
and controlled variable, not on characteristics of the
system itself.

Â

            MT: Yes, that was exactly what I said, wasn't it?

But I think I put it a bit more clearly.

          RM: It is what you said, if what you call the stimulus

is the disturbance to the controlled variable. But I got
the impression that you were implying that the stimulus is
the controlled variable itself, or a change thereof, , in
which case what you said is quite different than what I
said.Â

            MT: The part of your paragraph up to "it had

nothing…" is exactly what I said. I had no need to
prove it for two reasons. One is that it is self-evident
that even if you have a loop, each variable in it has
only one value at a time whether you traverse the loop
forward or backward, while the other is that, as you
note, Powers proved it to those few for whom it might
not have been self-evident. Your last clause “it had
nothing…” directly contradicts the rest of your
paragraph.

          RM: As I said above, Powers (1978) was not proving

something about variables in the loo p; he was
proving that a variable outside the loop – an
independent variable – can appear to be the cause of
system outputs if this variable is a disturbance to
variables controlled by a control system.Â

Â

MT: Yes.

            MT: No. The behaviour of a control system IS (not

looks like) that of a cause-effect system * as long as
the reference value is constant* . The circuitry is
the same, exactly. The experimenter’s interpretation of
how the loop works is the illusion, not the actual
operation of the loop.

          RM: Powers (1978) uses the term "Z system" to refer to

a cause-effect system, one that has no feedback connection
from effect (output) back to cause (input); he uses the
term “N system” is refer to a control system where there
is feedback from effect to cause. Powers (1978) proved
that there is a behavioral illusion that occurs when an
observed relationship between a stimulus and response is
seen as the behavior of Z system when it is actually that
of an N system.Â

          RM: The illusion does involve a misinterpretation on

the part of the experimenter, but it is not a
misinterpretation of how the loop works - the experimenter
has not observed a loop; rather, it is a misinterpretation
of how the observed stimulus-response relationship works.
The illusion exists when the experimenter interprets the
observed S-R relationship as working because the stimulus
causes the response via the organism. If the system were a
Z system, this interpretation would be correct. But since
the system is an N system, this interpretation is
incorrect; the observed S-R relationship works because the
system is acting to keep a controlled variable in a
constant or variable reference state, protected from the
effects of disturbances. The controlled variable is a
crucial part of this correct interpretation; this is why
failure to see that organisms control – that they are
controlling variables – is at the heart of this (and all)
behavioral illusions.Â

Â

            MT: No. A suitable S-R system -- one in which the

S-R function is the inverse of the function between the
observable output and the CEV – will behave in exactly
the same way as a control loop if the stimulus keeps
changing, as it will if there is a feedback connection
through the CEV, provided the reference value stays the
same.

          RM: This is demonstrably false, even if we go with your

definition of the stimulus as a change in the CEV. But it
is such an important misunderstanding of the behavioral
illusion that I will deal with it in a separate post when
I get a chance.

            MT: However, these are not different "behavioural

illusions". They are coherent schools of thought about
aspects of psychology that PCT treats differently.
Reinforcement is a school of thought that deals with
learning.

          RM: Reinforcement theory also deals with steady state

behavior. And in either case the theory is based on the
illusion that consequences select behavior (rather than
vice versa).Â

            MT: Cognitive psychology is

interpretable in PCT as that the reference values up and
down the hierarchy are set autonomously, an approach
that leads to enormous complexity in the computation of
what to do in different situations. Neither has any
relationship to the behavioural illusion.

          RM: Cognitive psychology is based on the illusion that

behavior is caused output.Â

            MT: You simply can't decide that all other psychological

theories are behavioural illusions, simply because they
differ from PCT and don’t recognize the primacy of
control.

          RM: Why not? The problem with these theories is not

that they don’t recognize the primacy of control; the
problem is that they don’t recognize the * fact of
control*.

            MT: They may be illusory, but

centuries from now, scientists with the advantage of
ideas and data we don’t have may well see PCT as an
illusion, too. But PCT will even then not be a
“behavioural illusion” and in the present time neither
are other schools of thought in psychology.

          RM: It's not the theories that are illusions; it's the

interpretations of the observations that are the illusion.
Future scientists may find PCT to have been fundamentally
flawed. But I don’t see why that possibility requires
present day scientists to stay silent about the fact that
S-R, reinforcement and cognitive theories are certainly
wrong.

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
–Antoine de Saint-Exupery

                            MT:

It’s a simple requirement of control
loops. The behavioural illusion is based
on a fundamental fact about negative
feedback loops that stabilize their
variables, and therefore about control
loops that control well. If there is a
functional relation f(AB) between the
variation at point A and the variation
at point B going one way around the
loop, the functional relation f(BA)
going the rest of the way around the
loop is the inverse function: f(BA) = f-¹⁽AB).

                          RM: This is incorrect. There is no

version of the behavioral illusion that is
this based on the “fundamental fact” about
negative feedback loops that you describe
here.Â

                            MT:
                              If

“A” is the output, and “B” the CEV,
the environmental variable that
corresponds to the controlled
perceptual variable, and if a change
in the CEV is taken to be a
“stimulus”, then the response (output)
is determined by the properties of the
environmental link between A and B.
…

                          RM: This is incorrect. The CEV would

never be taken to be the “stimulus”
because it is not an independent
variable…

RM:Â Â response
=Â Â f(stimulus) Â Â
       (1)

                          RM: Powers (1978) showed that, if the

organism under study is actually a control
system, then the observed relationship
between stimulus and response depends
(inversely) on the feedback function,
g(), that relates variations in the
response to variations in what you call
the CEV.

R: response = g^-1 (stimulus)Â
      (2)

                          RM: So the illusion is that the

observed relationship between stimulus and
response reveals something about the
functional characteristics of the
organism, f(), when in fact it reveals
only something about the nature of the
environmental feedback connection between
response and CEV.

                          RM: Powers (1978) proved that an

observed relationship between stimulus and
response is described by Eq. 2 rather than
Eq. 1 when the behavior you are observing
is that of a control (N) rather than a
cause-effect (Z) system. In that proof,
the stimulus variable is the disturbance
variable, d, the response variable is the
output variable, q.o, and the CEV is the
controlled variable, q.i.  The proof was
done by
solving the simultaneous equations that
describe the behavior of a control
system for the relationship between
stimulus (disturbance) and response
(output); it had nothing to do with the
“fundamental fact” about negative
feedback loops that you describe above.Â

                        RM: Powers (1978) also explains why

psychological scientists have succumbed to
the behavioral illusion. It’s because they
assume that organisms are cause-effect (Z)
systems; the observation that variations in
a stimulus variable are fairly consistently
related to variations in a response variable
is perfectly compatible with this
assumption.

                        RM: This is because the behavior of a

control system looks like that of a
cause-effect system as long as one ignores
the fact that responses (outputs) are
countering the effects of the stimulus
(disturbances) on a controlled variable,
q.i.Â

                        RM: Thus, the illusion of a causal

relationship between stimulus and response
variables can be dispelled using the Test
for the Controlled Variable (also described
in Powers, 1978) to determine both that a
variable is being controlled and what that
variable is.Â

                        RM: There are other behavioral illusions

besides the stimulus-response illusion
described in Powers (1978) that results from
assuming, incorrectly, that the system being
observed is a cause-effect rather than a
control system. The illusions are described
in my “Blind Men and the Elephant” paper in
my book More Mind Readings . In that
paper I call the different illusion
different “views” of control; there is the
stimulus-response view (covered above), the
reinforcement view and the cognitive view.
These different views correspond to the
three dominant "schools’ of scientific
psychology. PCT shows that all three are
based on an illusion that results from the
fact that the behavior of a control system
can look like that of a cause-effect system.

[rsmarken]

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[amatic]

(From A. Matic 19.3.2018)

RM: It means that you can't tell anything about the organism by looking at
observed relationships between stimuli and responses. Which is the conclusion
of our original paper and our reappraisal of the reappraisal paper on the
power law; you can't tell the nature of the organismic processes that produce
a movement by simply looking at the relationship between variables that you
take to be an S (curvature) and an R (velocity).

···

----

AM:
Well, no one is taking curvature and velocity to be stimulus and response.
Both C&V are calculated from the response trajectory, and are properties of
the response. Stimuli could be a shape on a piece of paper and some indication
of average speed. Everything is calculated from the response trajectory.

You can find things like "maximum velocity" as a property of the response and
conclude something about the organism producing it. For example, if you know
the mass, you could find the maximum force that the organism can exert. Same
with the power law.

[rsmarken]

[Rick Marken 2018-03-19_11:51:06]

···

(From A. Matic 19.3.2018)

RM: It means that you can’t tell anything about the organism by looking at

observed relationships between stimuli and responses. Which is the conclusion

of our original paper and our reappraisal of the reappraisal paper on the

power law; you can’t tell the nature of the organismic processes that produce

a movement by simply looking at the relationship between variables that you

take to be an S (curvature) and an R (velocity).

---

AM:Well, no one is taking curvature and velocity to be stimulus and response.

RM: It’s hard to pin down my critics on this. For example, when you say in your “reappraisal” that “muscle forces will not be consistently related to the curvature and velocity of the movementâ€? you seem to acknowledge that curvature and velocity are not stimulus and response but, rather, simultaneously caused by muscle forces, which is correct. But later in the same paper you say that the power law involves a “…causal relationshipp between curvature and speed…â€?. So you are kind of a moving target on that.Â

RM: But as I have noted before, the power law is a different kind of behavioral illusion than the S-R version of the illusion described in Powers(1978). It’s more like the illusion described in our “Control Blindness” paper: Willett, A. B. S., Marken, R. S.,
Parker, M. G. & Mansell, W. (2017) Control Blindness: Why
People Can Make Incorrect Inferences about the Intentions of Others, Attention, Perception & Performance,
doi:10.3758/s13414-016-1268-3. The illusion is that a side-effect of control is what the organism is “doing” (controlling for). In the Control Blindness paper, the phenomenon is seen in people taking the picture traced out by the actions that compensate for disturbances as what another person is doing. Another example of this kind of illusion is the "invariant velocity profile" described in  Atkeson, C. G. and Hollerback,
J.M.(1985); Kinematic features of unrestrained vertical arm movements.
The Journal of Neuroscience, 5, 2318-2330. These are all behavioral illusions in the sense that they are observable side-effects of control that seem to tell you something about how the organism functions when, in fact, they don’t.Â

Â

AM: Both C&V are calculated from the response trajectory, and are properties of the response.
Stimuli could be a shape on a piece of paper and some indication of average speed. Everything is calculated from the response trajectory.

RM: Yes, that’s right. Indeed, it’s an important part of my demonstration of why the power law tells you nothing about the mechanisms that produce a movement. But not all of my critics agree that curvature (R or C) and velocity (V or A) are calculated from the response trajectory… Indeed, Taylor says that one reason for my purported mathematical error was thinking that they are. In his rebuttal Taylor says that velocity, V, is calculated from the response trajectory but curvature, R, is not because, in the equation for R, the derivatives of X and Y "…are arbitrary parameters, corresponding to any velocity. â€? It’s hard to deal with critics who say I’m wrong for reasons that contradict each other.

Â

AM: You can find things like “maximum velocity” as a property of the response and conclude something about the organism producing it. For example, if you know the mass, you could find the maximum force that the organism can exert. Same with the power law.

RM: This is certainly true of Z systems but not of N systems. The maximum velocity of movement that you observe in an organism is not necessarily the maximum velocity that could be produced by the muscle forces. The velocity with which a limb is moved affects other variables that are being controlled by the organism, such as the attachment of tendons to bone. I doubt that muscles ever produce the maximum velocity of which they are capable, at least not in an intact organism.Â

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.�
                --Antoine de Saint-Exupery