···
[Rick Marken 2018-07-17_10:31:31]
[Martin Taylor 2018.07.16.15.12]
MT: As well you have known for a very long time, I have insufficient
hubris to attempt a model of observed behaviour before trying the
TCV to figure out what variable(s) might be being controlled during
the task. I have no means to do the TCV needed, so I refrain from
suggesting a model. You are not so inhibited.
RM: You have to have had some idea of what the controlled variable might be when people make curved movements or you wouldn’t know that the power law is “almost certainly a side-effect in any of the experiments that find velocity to have a near power-law relationship to the radius of curvature”, as you note in your rebuttal. In PCT, a “side-effect” is a relationship between variables that exists because a variable is under control but this relationship not part of the process that results in control of that variable. For example, the relationship between disturbance and output in a tracking task is a side effect of controlling the position of the cursor but is not part of the process that results in control of cursor position. In order to know that the power law is, indeed, a side-effect, you had to have an idea of what variable is under control when people make curved movements as well as having an idea of how the instantaneous curvature and velocity of these movements are related to this variable. This should have been enough to let you develop a first approximation to a model of curved movements that would demonstrate why the instantaneous curvature and velocity of these movements is a side effect of controlling this variable. The model itself would have been a basis for the TCV; it would be a test of the correctness of your hypothesis regarding the variable under control. So it would not have been hubris to model the behavior before doing the TCV since you presumably had to have had the essential components of the model in mind when you said that the power law is almost certainly a side effect.Â
MT: For the record, here are just eight of the falsehoods you
incorporated in your rebuttal of my comment on the Marken and
Shaffer paper (copied from [Martin Taylor 2018.03.08.23.07]).
Despite having been made aware of their falsity, yet you continue to
repeat some of them on CSGnet. Why do you do that?
RM: Because they are not “falsehoods” but the best we could do to understand your criticisms.
Â
----------begin quote (replacing references to "you" with references
to “they”, and added numbering)-------
* MT: (1) In the very first paragraph you claim that my reason for
writing a critique was that the idea that the power law might be a
behavioural illusion caused “consternation”, whereas I made
explicit that nothing in my critique had any bearing on that
issue. Indeed, I finished my critique with the statement that
perhaps the power law is indeed a behavioural illusion, though
M&S sheds no light on that issue.*
RM: Since, as I noted above, you came up with no hypothesis about what variable might be controlled, I dismissed your claims of accepting that the power law is a behavioral illusion because you gave no evidence of understanding what a behavioral illusion is.
Â
Ostry’s equations is based on my belief that those equations are
wrong or misleading, whereas I pointed out that they are well
known and universally accepted equations for using observed data
to measure the velocity (equation 1) and curvature (equation 2)
profiles observed in an experiment. Neither Gribble and Ostry nor
(so far as I know) anyone other than Marken and Shaffer ever
claimed that the observed velocity was the only velocity that
could be used to get the correct curvature from the equation for
R.*
RM: No, we said that your critique was based on our misunderstanding of those equations. Specifically that the derivatives in the curvature equation were different from those in the velocity equation. Your claim that these derivatives are different is simply wrong and, thus, invalidates your mathematical critique from the get go.
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MT: (3) I never said that the derivation of V = R*1/3D1/3** was wrong. I said that since the formula for D was velocity (V)
times a constant in spatial variables, the equation is not an
equation from which one can determine V. The M&S claim that it
is an equation from which one can determine V is the core of my
critique.*
RM: And we never said that you said that the derivation of
V = R*1/3D1/3**Â *was wrong. We said that what you said about it not being an equation that can be used to predict V using linear regression is wrong. Which it is.Â
been obvious that X-dot and Y-dot are derivatives with respect to
time in the expression for V, whereas they are derivatives with
respect to space in the expression for R (p. 5)". On the contrary,
I devote the first couple of pages of my critique to showing why,
despite the radius of curvature being a spatial property,
nevertheless it is quite proper to use time derivatives in the
formula for R.*
RM: But that’s what you argued, right here:Â
RM: What you are saying is that we made the mistake of taking the dot derivatives in the two Gribble/Ostry equations as being time derivatives. But that was not mistake. The mistake is all yours.
transformed Viviani and Stucchi’s expression for R using spatial
derivatives into one using time derivatives (a derivation with
which I started my comment), therefore they were correct to say
that ONLY the velocity found in an experiment can be substituted
into the numerator of the expression for R, whereas both my
derivation and that of Viviani and Stucchi (essentially the same)
makes it crystal clear that this is not true.*
RM: Well, that would be news to all the power law researchers who computed velocity and curvature the way I did in my analyses, using time derivatives.
Â
of paragraphs to show why the V = R**1/3D1/3** equation is correct, implying that my comment claimed it to be
wrong. Early in my comment, however, I wrote: “They then write
their key Eq (6) [V = R**1/3D1/3** ],
which is true for any value of V whatever…” Any implication that
my comment claimed the equation to be incorrect is false.*
RM: What we showed is that that equation has been used by others to show what we showed in our paper – that using only R (curvature) as the predictor in a regression on V (speed) – will result in an estimate of the power coefficient of R that deviates from 1/3 by an amount proportional to the correlation between R and D (radial velocity).Â
Â
finding predicted and reported by M&S was actually a tautology
having no relation to experimental findings, which will always
produce the result claimed by M&S to be an experimental
result. M&S in the paper and in the rebuttal treat it as a
discovery that can be made only by careful statistical analysis,
and do not acknowledge the tautology criticism at all.*
RM: Your demonstration that our findings are a “tautology” made no sense to us. You made this claim based on your derivation of an equation for V of the form V = V. But this is true for any equation. If X = f(Y) then you can substitute X for the right side of the equation and write the equation X = X. That’s not a tautology; that’s just an irrelevant observation.
Z/M and Taylor is the assumption that the power law is a result of
a direct causal connection between curvature and speed of movement
or between these variables and the physiological mechanisms that
produce them." I have no idea how this astonishing statement can
be derived from my exposition of the mathematical and logical
flaws in their paper. My comment is designed to refute exactly
M&S’s claim of my motivation. The comment shows that there is
NO necessary relationship, causal connection or otherwise, between
curvature and speed of movement.*
RM: You were apparently trying to show, mathematically, that the curvature and velocity of a curved movement are physically independent, like the disturbance and output in a tracking task. Since you didn’t speculate about the controlled variable that might be simultaneously affected by these two variables I assumed that you were dong this to justify the assumptions of power law researchers that these two variables are either causally related or simultaneously caused by a third variable.Â
Â
--------end quote-------
MT: I repeat from my last message: " What’s the advantage to you
of refusing to deal with scientific points people bring up about
your work?"
RM: We dealt with your confusing rebuttal as best we could. There was nothing scientific about it inasmuch as it was purely mathematical.
Best
Rick
Â
Well, I guess predictions aren't always wrong, and I am indeed not
surprised.
Martin
–
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery
Best
Rick
Â
What's the
advantage to you of refusing to deal with scientific
points people bring up about your work? In what
perception you control would it create error if you
were to accept normal mathematics or physics as
being valid? When your work is good, it’s good, but
when you make a mistake, why does it seem so
difficult for you to correct it? In the curvature
paper none of the criticisms were relevant to a PCT
interpretation, but you make out that all of them
were intended to refute a “correct PCT analysis” of
the experimental findings. Why?
I don't expect an answer to a question raised, but I
wouldn’t be surprised at an answer to something
completely different.
