The speed�?curvature power law of movements: a reappraisal

[Martin Taylor 2017.10.31.13.35]

Yes, but that includes your team, too. A long time ago I suggested a

start to seeking possible controlled variables in different
conditions. You said you would try some. Have you?
True.
So far as I am aware, only Rick’s bogus mathematics has led anyone
on CSGnet even close to saying such a thing.
Why, if none of the obvious tests have been done?
First, let’s define the challenge. You have a considerable body of
observations that relate some environmental states to a power-law
relationship between local curvature of a track followed by
(including produced by) organisms in motion and the tangential
velocity of movement along the track. You also have conditions under
which the relationship is not followed. What are the essential
differences among these conditions? Is the challenge for PCT to
predict/explain that? Or is it in general to explain why power laws
are observed sometimes and not other times? PCT does offer a generic
explanation for the observation of power laws, which Bill and Rick
used to explain the Stevens power law for perceived (reported)
sensory magnitudes. It is that a power law will result when a
perception is controlled of a relationship between two perceptions
that have a near-logarithmic relation to their relevant magnitudes.
In this case, maybe the challenge resolves into discovering the two
perceptions in question. Might that be true? Or is this particular
power law not an example of the generic case? Maybe that’s the
challenge.
If you are going to assert that PCT is “unable” to explain any data,
whatever the experiment, you first have to seek a controlled
variable. It is highly unlikely in any of the conditions of any of
the experiments that the mover controlled a perception either of
following a power law relation between speed and curvature, and even
if they did, that they were controlling for making the exponent take
on some particular value. So the first step is to propose some
plausible perception(s) that might be being controlled, and then try
to disturb them to include or exclude them from the plausible list.
If a perception of the power-law relationship and the particular
exponent is implausible, then the power-law itself is a side-effect
of control, and the problem becomes one of explaining what
environmental conditions affect the perception and the action
influence on whatever is being controlled.
A perceptual variable that is available to larvae and to humans
would naturally be more plausible than a requirement that different
species control different variables but wind up with the same
results. But it may prove that several different perceptual controls
working through similar environmental constraints would all give the
same power law. A power law is, after all, the result of subtracting
one logarithm from another, and since most perceptions do seem to
have a near logarithmic relation to the relevant environmental
variable (Weber-Fechner Law), such a result is not too far-fetched
to contemplate.
Whatever the controlled variables might be, difficulty in finding
them is not the same as proof that they do not exist, or that PCT is
a crumbling edifice. It helps if the search has been at least begun
without successful conclusion, but such searches sometimes take
thousands of years. Ptolemy’s laws explained the planetary motions
relative to the starts well enough not to be discarded for a
thousand years, within one conceptual frame – Earth-centred
Universe. Kepler and Newton provided a better explanation, and that
was good enough in a different conceptual frame – a Universe
conceptually known synoptically by an omniscient being. But it had
little niggles in it such as the advance of the perihelion of
Mercury. Einstein came up with a better explanation in a third
conceptual frame – “what you see is what you get” (relativity), but
it also has niggles in its incompatibility with quantum
chromodynamics, so I guess the next advance is a fourth conceptual
frame yet to be found.
PCT is, I think, in the relativistic conceptual frame – “what you
perceive is what you get”. Earlier theories that base behaviour
strictly on the environment are in the Newtonian conceptual frame
“You would know it all if you were God”. As with Ptolemy-Newton or
Newton-Einstein, the earlier and older theories explain the data
pretty well, because that’s what they are designed to do. In each
case, the newer theory explained a wider range of data and explained
it more accurately because it started from “why”, not “what”.
Newton’s “why” for the planetary motions was the gravitational law
that produced Kepler’s ellipses, which were a descriptive
improvement on Ptolemy’s epicycles. Einstein’s “why” for Newton’s
gravitational law was the distortion of space-time by mass-energy. I
suppose the next conceptual revolution in that area of physics will
be the finding of a “why” for space-time deformation that resolves
the problems with quantum theory. One “why” is simpler than a whole
lot of “whats” in the Occam’s Razor sense. PCT offers a relativity-level “why” for a whole mass of data that is
observed and for which many people have provided Ptolemy or
Newton-level “what” explanations. Maybe optimal control theory does,
too, but PCT has the advantage of not having to do complex
computations of such things as joint angles and of not having to
make special provision for the effects of unexpected external events
and forces, since dealing with them is built into the structure. I
am not aware of optimal control theory having been applied to
sociology, but I suppose it must have been. However that may be, I
suspect that another change of conceptual framing will someday
provide a “why” for the “whats” of PCT, further simplifying science
as a whole.
Enough philosophy of science. It would be nice to be able to figure
out what controlled perceptions in what environmental circumstances
lead to power laws, and with what exponents when power laws are
found. Incidentally, has anyone ever analyzed movies of a skater
doing school figures? It is my impression that their skates move
faster along the ice when the curvature is high (low radius of
curvature), but that may be an illusion.
Martin

···

On 2017/10/31 12:01 PM, Alex
Gomez-Marin wrote:

      regardless of your helicopter data and RCT

mantras, it would be good if someone from CSGnet took
seriously the challenge to PCT that the speed-curvature power
law entails.Â

      any figure panel of our paper proves rick's

mathematical claims wrong: the PL is not a must and when it
takes place it is not trivial and can have different
exponents.

      now, how can "control of perception" explain

that phenomenon? claiming it is an illusion because it does
not fit in the dogma is like creationists insisting that dino
fossils are bogus.

      so, as adam and myself take this job seriously,

and given how many optimal control and nonPCT theories explain
the data, I think Bill would really find his edifice
crumbling, or at least unable.

      so, take your best shot at it and really

challenge your “revolutionary paradigm changing” theory of
behavior.

On Sun, 29 Oct 2017 at 02:48, Richard Marken <rsmarken@gmail.com >
wrote:

[From Rick Marken (2017.10.28.1745)

              On Sat, Oct 28, 2017 at 3:34

PM, Alex Gomez-Marin agomezmarin@gmail.com
wrote:

attachedÂ

            RM: Finally! Thank you, Alex. I hope the journal gives

us an opportunity to respond. But for now I have only
one word for you: helicopter movements. Oh, that’s two
words But you know how bad I am at math;-)

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

    Alex

Gomez-Marin

    [behavior-of-organisms.org](http://behavior-of-organisms.org)

[From Bruce Abbott (2017.11.01.0945 EDT)]

Â

···

[From Rick Marken (2017.10.31.2215)]

Â

            On Tue, Oct 31, 2017 at 9:01 AM, Alex

Gomez-Marin <agomezmarin@gmail.com >
wrote:

                  AGM: regardless of your

helicopter data and RCT mantras, it would be good
if someone from CSGnet took seriously the
challenge to PCT that the speed-curvature power
law entails.Â

Â

              RM: What challenge? PCT explains it

quite nicely as a mathematical property of curved
trajectories. This fact explains why it appears as a
side effect of intentionally produced curved
movement… But apparently no one else on CSGNet sees
it that way so your paper has demonstrated to me that
no one on CSGNet (no one who posts, anyway)
understands PCT. At least, they don’t understand it
the way I do. This has convinced me that I must
withdraw my Preface to LCS IV because I can’t in good
conscience say that the papers in that book will be
based on Powers’ theory and, thus, honor his legacy.

Â

              BA: You can resolve this

controversy yourself quite easily. Next time you are
on campus, stop by the Mathematics Department and ask
a faculty member who is competent in analytical
geometry to review the mathematical basis of your
paper. Be sure to give this person both your disputed
paper and the Gribble and Ostry (1998) paper from
which you get the equations you rely on.

Â

Â

              BA: So again, I encourage you –

indeed implore you – to submit your analyssis
(and its context) to a mathematician on campus for
review. You may not be happy with the result, but at
least you will learn why so many of us on CSGnet have
been asserting that your mathematical analysis of the
power law is unsound. What have you got to lose?

Â

[Martin Taylor 2017.11.01.23.16]

[From Rick Marken (2017.11.01.1720)]

So far, so good.

But really, appeals to authority don't work, so perhaps Bruce was

barking up the wrong tree to suggest you might consider getting yet
another opinion. I’m sure you are as aware as the rest of us how
much effort most publication reviewers put into checking every
equation, and how easily things pass their notice, both in accepting
and in rejecting papers.

More important is your ability to deal with the central argument

against your analysis, an analysis based largely on the equation

V = R<sup>1/3</sup>D<sup>1/3</sup>

R is the radius of curvature, while D is what you call a

“correction” factor that makes the 1/3 power law exact for all
curves. I think you will agree that the expression for D resolves to
V3 times an expression in x, y, and distance along the
curve, s. In other words, D = V3 *f(x, y, s). Or at least
I hope you will, because I showed you many times over the last year
how that is proved, and Zago et al. showed it in a peer reviewed
published paper, which is apparently your Gold Standard for
correctness.

Your equation therefore is

V = R<sup>1/3</sup>*V*(f(x, y, s))<sup>1/3</sup>

which says only that R*f(x,y,s)=1, or f(x,y,s) = 1/R = C

(curvature). Your equation is therefore

V = V*R<sup>1/3</sup>*C<sup>1/3</sup>.

I don't think you can disagree with any of that, but where does it

leave this “correction factor” D? D is the only place in the R1/3D1/3
expression where velocity comes in (as V3 /R), but the
experiments show a near power-law relation between V and R, even
without the “correction factor” D, with a power that ranges,
according to Zago et al. Fig 2c) between 1/6 and 2/5, depending
apparently on the complexity of the curve. Even if your equation
meant something interesting, it would still leave this D-less fact
to be explained.

You said you were going to spend time looking for a PCT explanation

of that fact and the other observational facts associated with
velocities and curvature (such as, I guess, the difference between
the timing of velocity change between going from less curved to more
curved as opposed to the opposite change of curvature). I hope you
succeed. I don’t think it is easy, but I have faith (and at this
point it’s no more than faith) that such an explanation is indeed
possible.

Martin
···
                Bruce Abbott (2017.11.01.0945

EDT)–

                          RM: What challenge? PCT

explains it quite nicely as a mathematical
property of curved trajectories. This fact
explains why it appears as a side effect
of intentionally produced curved
movement… But apparently no one else on
CSGNet sees it that way so your paper has
demonstrated to me that no one on CSGNet
(no one who posts, anyway) understands
PCT. At least, they don’t understand it
the way I do. This has convinced me that I
must withdraw my Preface to LCS IV
because I can’t in good conscience say
that the papers in that book will be
based on Powers’ theory and, thus, honor
his legacy.

                        BA: You can resolve this

controversy yourself quite easily. Next
time you are on campus, stop by the
Mathematics Department and ask a faculty
member who is competent in analytical
geometry to review the mathematical basis of
your paper. Be sure to give this person
both your disputed paper and the Gribble and
Ostry (1998) paper from which you get the
equations you rely on.

          RM: I wrote the power law paper and submitted it for

publication in EBR because I felt that my
mathematical/statistical analysis was correct and the
criticisms I was getting on the net in our net discussion
over a year ago were wrong. I thought that if the paper
were accepted in a peer reviewed journal – the very
journal where much of the research on the power law is
published – that might convince you that your criticisms
of my analysis were themselves wrong. And the paper was
reviewed and accepted for publication and the result was
that the criticisms became even more earnest. So I don’t
think that getting my paper reviewed by someone in the
Math department is going to help. But I actually did have
a senior researcher from RAND review it and he thought it
was just fine. But I’m sure this will carry no weight
with you even if I tell you that he is got his PhD in
applied math from Harvard under Nobel Prize winner Kenneth
Arrow. You’ll just say he was the wrong kind of
mathematician.

                        BA: The dispute is not

with PCT, it is about the soundness of your
mathematical analysis.

          RM: So you say. But, in fact, the dispute is all about

PCT because the fact that the power law is an example of a
behavioral illusion is not based on the math; it’s based
on the fact that an intentionally produced curved movement
is a controlled result produced by variable means.

          The math just shows why researchers have consistently

found a power law relationship between two measures –
velocity and curvature – of the time varying state of
this controlled result.

[Martin Taylor 2017.11.03.17.35]

[Martin Taylor 2017.11.01.23.16]
In my comments eaarlier, I assumed that the implications of D = V3 *f(x,y,s)
for the Marken Shaffer paper on the power law relation between
curvature and the velocity with which living organisms trace the
curve would be self-evident. However, on reflection, maybe they
aren’t, so here’s a postscript to that message.

Throughout the Marken-Shaffer paper, D<sup>1/3</sup> = Velocity*(a

function of spatial variables) is used to “correct” an observed
relationship between the physical curvature of a path in space and
the velocity with which that path is travelled. In a section on
“Omitted Variable” analysis, they show that the observed
relationship is “predictable” by including D, which means simply
that it is predictable by including V to explain V.

Following that, they purport to provide a PCT model that explains

the power law, though the model they provide shows no relation to
the power law at all. All it does is show a possible PCT model for
how a person controls for following a toy helicopter. That has no
implications whatever for the power law. Nevertheless, they find
that both helicopter and human move in a manner that exhibits the
power law between velocity and curvature, which they then predict
with amazing accuracy by using V (as D1/3) to predict V.

In spite of the fact that the PCT model they provide for how humans

follow toy helicopters has absolutely no implications for the power
law, and in spite of the fact that the wrongness of the use of V to
predict V has been explained many times over the last year and more,
Marken [From Rick Marken (2017.10.28.1745)] still uses the
helicopter model as though it provided a PCT explanation of the
power law, and treats criticism of his paper as denial of PCT.

That the paper is actually total garbage is irrelevant to the beauty

and power of PCT. What is not irrelevant to the potential
propagation of PCT to the wider world of science is the fact that
the paper has not been withdrawn, and worse, that Rick continues to
refer to it outside the semi-closed society of CSGnet readers as
though it was some kind of triumph of PCT thought rather than a
simple pollution of the literature. To any mathematically literate
reader who takes the time to work through the formulae, the thought
that Rick might be a typical proponent of PCT as a science, and is
yet capable of seriously publishing such nonsense, must be very
off-putting when it comes to the possibility of looking more deeply
into PCT to see if it has anything to offer.

I just hope that someone is able to figure out just what perceptions

are being controlled when living organisms move fast but smoothly
(which seems to be the condition under which the power law is
observed), and why control of those perceptions leads to a power law
with a particular power, whether the power be as low as 1/6 or as
high as 2/5. If that can be done, we can put this whole disgraceful
episode behind us.

Martin
···

[Martin Taylor 2017.11.01.23.16]

[From Rick Marken (2017.11.01.1720)]

                  Bruce Abbott (2017.11.01.0945

EDT)–

                            RM: What challenge?

PCT explains it quite nicely as a
mathematical property of curved
trajectories. This fact explains why it
appears as a side effect of
intentionally produced curved movement…
But apparently no one else on CSGNet
sees it that way so your paper has
demonstrated to me that no one on CSGNet
(no one who posts, anyway) understands
PCT. At least, they don’t understand it
the way I do. This has convinced me that
I must withdraw my Preface to LCS IV
because I can’t in good conscience say
that the papers in that book will be
based on Powers’ theory and, thus, honor
his legacy.

                          BA: You can resolve

this controversy yourself quite easily.
Next time you are on campus, stop by the
Mathematics Department and ask a faculty
member who is competent in analytical
geometry to review the mathematical basis
of your paper. Be sure to give this
person both your disputed paper and the
Gribble and Ostry (1998) paper from which
you get the equations you rely on.

            RM: I wrote the power law paper and submitted it for

publication in EBR because I felt that my
mathematical/statistical analysis was correct and the
criticisms I was getting on the net in our net
discussion over a year ago were wrong. I thought that if
the paper were accepted in a peer reviewed journal –
the very journal where much of the research on the power
law is published – that might convince you that your
criticisms of my analysis were themselves wrong. And the
paper was reviewed and accepted for publication and the
result was that the criticisms became even more earnest.
So I don’t think that getting my paper reviewed by
someone in the Math department is going to help. But I
actually did have a senior researcher from RAND review
it and he thought it was just fine. But I’m sure this
will carry no weight with you even if I tell you that he
is got his PhD in applied math from Harvard under Nobel
Prize winner Kenneth Arrow. You’ll just say he was the
wrong kind of mathematician.

                          BA: The dispute is not

with PCT, it is about the soundness of
your mathematical analysis.

            RM: So you say. But, in fact, the dispute is all

about PCT because the fact that the power law is an
example of a behavioral illusion is not based on the
math; it’s based on the fact that an intentionally
produced curved movement is a controlled result produced
by variable means.

  So far, so good.
            The math just shows why researchers have

consistently found a power law relationship between two
measures – velocity and curvature – of the time
varying state of this controlled result.

  But really, appeals to authority don't work, so perhaps Bruce was

barking up the wrong tree to suggest you might consider getting
yet another opinion. I’m sure you are as aware as the rest of us
how much effort most publication reviewers put into checking every
equation, and how easily things pass their notice, both in
accepting and in rejecting papers.

  More important is your ability to deal with the central argument

against your analysis, an analysis based largely on the equation

  V = R<sup>1/3</sup>D<sup>1/3</sup>



  R is the radius of curvature, while D is what you call a

“correction” factor that makes the 1/3 power law exact for all
curves. I think you will agree that the expression for D resolves
to V3 times an expression in x, y, and distance along
the curve, s. In other words, D = V3 *f(x, y, s). Or at
least I hope you will, because I showed you many times over the
last year how that is proved, and Zago et al. showed it in a peer
reviewed published paper, which is apparently your Gold Standard
for correctness.

  Your equation therefore is



  V = R<sup>1/3</sup>*V*(f(x, y, s))<sup>1/3</sup>



  which says only that R*f(x,y,s)=1, or f(x,y,s) = 1/R = C

(curvature). Your equation is therefore

  V = V*R<sup>1/3</sup>*C<sup>1/3</sup>.



  I don't think you can disagree with any of that, but where does it

leave this “correction factor” D? D is the only place in the R1/3D1/3
expression where velocity comes in (as V3 /R), but the
experiments show a near power-law relation between V and R, even
without the “correction factor” D, with a power that ranges,
according to Zago et al. Fig 2c) between 1/6 and 2/5, depending
apparently on the complexity of the curve. Even if your equation
meant something interesting, it would still leave this D-less fact
to be explained.

  You said you were going to spend time looking for a PCT

explanation of that fact and the other observational facts
associated with velocities and curvature (such as, I guess, the
difference between the timing of velocity change between going
from less curved to more curved as opposed to the opposite change
of curvature). I hope you succeed. I don’t think it is easy, but I
have faith (and at this point it’s no more than faith) that such
an explanation is indeed possible.

  Martin

[Martin Taylor 2017.11.05.23.03]

[Bruce Nevin (2017.11.05.19:56 ET)]

      I've been trying unsuccessfully to track this discussion,

without being able to focus on it. I may be wildly off base,
but this is my take after looking through the two papers this
evening.

Rick Marken (2017.11.05.1220) –

      What we showed is that the curved paths taken by both

pursuers and a PCT model of those pursuers (a model that
accounts for on average 93% of the variance in the curved
paths taken by pursuers on 41 different trials ) exhibits a
power law relationship between speed and curvature. This is
evidence that the power law is a side-effect of the outputs
that produced the curved paths as the means of controlling for
intercepting

Sounds to me like this is the central finding…

      We know that that negative-feedback control systems that

use movements to control their input do not calculate the path
geometry or kinematics of those movements, though the
movements in the cases considered here can be described with
path geometry and kinematics. Indeed, that is the final point
of the Marken & Shaffer paper. The problem appears to be
that the brief mention of this experimental finding at the end
of the paper is dwarfed and obscured by the protracted
critique that precedes it and which has every appearance of
being presented as the main point of the paper.

Just look at the model itself, and ask yourself in what way does it

even try to suggest how the power-law side effect is produced? So
far as I can see, the model is thrown in simply to say that this
paper is related to PCT. Neither the diagram nor the text makes any
claim as to how the power-law relation between curvature and
velocity is brought about. The spurious introduction of their "D1/3 "
correction factor simply allows them to say “V=V, so that proves we
are right.”

If M&S simply wanted to suggest that the same kind of

perceptions are controlled when chasing the helicopter as are
involved in catching a ball, they could have written that paper, and
I don’t suppose anybody would have bothered to complain. To pretend
that it has something to do with demonstrating the correctness of
their nonsensical illogic, well, that is something else.

Martin

[Martin Taylor 2017.11.05.23.26]

[From Rick Marken (2017.11.05.1220)]

Since "D" (the cross-product variable) is V<sup>3</sup>    *f(x,y,s), (f

is a function of purely spatial variables), your equation (5)

V = D1/3*R1/3

is actually

V= V•f(x,y,s)<sup>1/3</sup>*R<sup>1/3</sup>

which I think most people would say uses V to predict V.

Other people would simply divide both sides by V and say that it

shows that f(x, y, s) = 1/R = C.

What D is NOT is a "omitted variable" in the determination of the

power of the power function. Using it simply eliminates V from
consideration.

But I and others have pointed this out to you many, many, times, so

I don’t suppose you will take any notice this time, either.

Martin
···

Martin Taylor (2017.11.03.17.35)–

          RM: I shouldn't respond to this but I can't seem to

focus on other things until I do.Â

Â

            RM: Throughout the Marken-Shaffer

paper, D1/3 = Velocity*(a function of spatial
variables) is used to “correct” an observed relationship
between the physical curvature of a path in space and
the velocity with which that path is travelled. In a
section on “Omitted Variable” analysis, they show that
the observed relationship is “predictable” by including
D, which means simply that it is predictable by
including V to explain V.

          RM: This is not what we show. What we show is that

leaving D (the cross product variable) out of the
regression analysis (D being the “omitted variable”)
results in a biased estimate of the coefficient of the
actual mathematical power function (1/3 or 2/3
depending on how velocity and curvature are measured)
relating velocity to curvature in curved movements.

[Martin Taylor 2017.11.06.15.16]

[From Adam Matic 2017.11.6]

BN: I wonder if a more fruitful approach might be: Given the characteristics of control systems, and a presumption of least output to maintain control (an efficiency assumption, if you will), what constraints on output behavior are imposed by inertial forces and other physiological and environmental factors?

.... There were attempts with minimization of torque and similar effort-related variables, but the jerk minimization seems most successful. How these trajectories emerge in the end is still an open question.

Adam

The PCT question then would be whether jerk is perceived and is controlled. The difference between moving in a viscous environment and in a free one is that in a viscous environment f=ma does not hold, and increases in force do not translate directly into increases in acceleration. Jerk in a high-viscosity environment is always very low, and yet the power law is observed for a given task in free and (with a different power) in viscous environments. My guess is that jerk is not a controlled perception, but it would need some testing to discover whether the guess is right or wrong.

At least for me, one of the takeaways from long interaction with Powers and reading his writings is that maximization or minimization is rarely the reference value of a controlled perception. It is usually a side-effect of something, possibly just that the reference value is higher or lower than the system can attain, but often that some other variable is controlled and the environment produces a side-effect that maximizes or minimizes the observed variable.

Finding what perception(s) is (are) controlled should be the basis for figuring out how the power-law side-effect is produced by environmental constraints. Maybe it is jerk, maybe it is lateral deviation from a reference path, maybe lateral deviation of the reference curve from straight ahead for a fixed lead time around the curve, maybe something else entirely. One could hypothesize endlessly, always fruitlessly until the TCV is used. Is the hypothesized variable actually perceived, and is it directly influenced? When you disturb it, is the disturbance resisted?

Martin

[Martin Taylor 2017.11.07.16.03]

What would be required of such a functional diagram? What hypothesis

would it test? Would it test whether the “minimum jerk” observation
was a direct result of jerk being controlled (a possibility) or a
side-effect of controlling something else, which then leads to the
power-law side-effect? One can’t draw a functional diagram without
having at least a hypothesis about what perception(s) is/are being
controlled. It can’t be “jerk” with a reference value of zero,
because that is most closely achieved by an actor that takes an
infinite time to trace the curve, whereas the actors in the various
experiments are much quicker, tracing curves that have quite
appreciable jerk.
Jerk is a strange quantity, the third derivative of position,
velocity being the first and acceleration the second. The first two
have direct relations to applied force under different environmental
conditions. Velocity is proportional to force in a viscous medium,
whereas acceleration is proportional to force in a non-viscous
medium (including frictional effects along with viscosity). Jerk is
rate of change of acceleration, which in a non-viscous medium is
proportional to rate of change of force, or in a viscous medium to
the rate of change of the rate of change of force. It’s a quantity
unlikely to be controlled directly (though not impossible), so its
appearance in observed data is likely to be a side-effect of
something else.
Should we assume that under conditions where the power law is
observed, the organisms are trying to move as fast as possible,
either to some target (fly larvae seeking food, Marken’s helicopter
chaser)? Probably not, unless “as fast as possible” refers to either
some environmental limit on speed as a function of curvature or to
some conflict with another controlled variable that occurs only
after some threshold velocity is achieved. In PCT, the words “as
possible” refer to an unachievable reference value for the
controlled perception in question.
When one is driving a car in the normal way to get somewhere rather
than for sightseeing, one does not go “as fast as possible” around
curves or even on a straight (even in, places with no speed limit).
But different people will take a curve of a specific radius of
curvature at different speeds, a race driver in a race much faster
than a senior who drives to the shopping mall with great
deliberation. Neither is constrained by the power of the engine, so
one must presume they control for something other than going “as
fast as possible” that either sets a reference value for velocity or
sets up a conflict. What might that “something other” be, and is the limiting factor
conflict or reference setting (which would mean that the driver
controls for something else, such as perceived safety)? Clearly the
fly larva doesn’t control for perceived safety. Nor, I assume does a
person tracing a drawn curve or someone actually scribbling
randomly. But if “minimum jerk” describes their performance well,
for what might they be controlling, and is it the same in all the
conditions where the power-law relationship is found? If there’s a
reasonable hypothesis about that, then one could devise a functional
diagram. and having that diagram (or maybe even without it) one
might be able to use the TCV to test whether the hypothesis is
tenable.
Sorry to sound so negative, but I think it is not a trivial problem.
Martin

···

On 2017/11/7 3:31 PM, Alex Gomez-Marin
wrote:

      i am saying not all can be compressed in a

simple (or complex) pct diagram, let alone complex maths. one
does not substitute the other. nevertheless, one should try.

On Tue, 7 Nov 2017 at 20:28, Bruce Nevin <bnhpct@gmail.com >
wrote:

[From Bruce Nevin (2017.11.07.14:27 ET)]

            Alex, are you saying that it is not possible for you

to draw a functional diagram of the negative-feedback
control loops that constitute the jerk-minimization
system which the mathematical expressions describe?

[Martin Taylor 2017.11.10.15.10]

Over the last few weeks, each of the three section editors who read my
original letter to them about the Marken-Shaffer paper has separately
and at widely different times asked me to submit my critique for
publication. Rick also asked me to do that.

Alberto suggested that the original letter should be published, but
nothing apparently came of that. A few days ago it was Goodale's turn to
ask me to publish, probably following his reading of the Zago et al.
critique. Lacquaniti made his request when he sent me the preprint of
the Zago et al. critique (the same as what Alex circulated to CSGnet).
So I have finally succumbed to the pressure and written a draft of what
I propose to submit to the journal.

I now ask CSGnet readers for comments before I do submit the attached.

Martin

MarkenShafferComment_v2.pdf (251 KB)