[Martin Taylor 2018.03.08.23.07]
[Rick Marken 2018-03-08_11:24:06]
RM: Our reply to the comments of Taylor and Zago et al on
our power law paper have been published in the on-line edition
of Experimental Brain Research. The abstract is available at:
https://doi.org/10.1007/s00221-018-5208-4
RM: For those of you who are interested, the full article
is available at:
https://www.dropbox.com/s/3m51ko4vs1xdult/MarkenShafferReappraisal.pdf?dl=0
Best
I realize there's no point in re-arguing the mathematical and
logical points of why your paper was utter nonsense. You know all
these.
But I wonder why you felt it necessary to rebut imaginary criticisms
that were not made rather than those that were made, and why you
imputed motives for the criticisms that you knew to be false? I will
not speak to Alex’s critique. He can do that if he wishes. Nor do I
wish to rewrite mine, but I would like to know why in your rebuttal
you do not address the issues I raised, but instead chose to show
that criticisms not made would have been wrong had they been made.
A few examples:
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.
M&S say that my critique of your use of Gribble and Ostry's
equations is based on my belief that those equations are wrong or
misleading, whereas I pointed out that they are well known and
universally accepted equations for using observed data to measure
the velocity (equation 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.
I never said that the derivation of V = R<sup>1/3</sup>D<sup>1/3</sup>
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.
M&S falsely claim that I argue that "it should have been obvious
that X-dot and Y-dot are derivatives with respect to time in the
expression for V, whereas they are derivatives with respect to space
in the expression for R (p. 5)". On the contrary, I devote the first
couple of pages of my critique to showing why, despite the radius of
curvature being a spatial property, nevertheless it is quite proper
to use time derivatives in the formula for R.
M&S say that because Gribble and Ostry correctly transformed
Viviani and Stucchi’s expression for R using spatial derivatives
into one using time derivatives (a derivation with which I started
my comment), therefore you 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.
M&S follow this astounding assertion with an couple of
paragraphs to show why the V = R1/3D1/3
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 = R1/3D1/3 ], which is true for
any value of V whatever…” Any implication that my comment claimed
the equation to be incorrect is false.
Omitted Variable Bias: My comment demonstrated that the finding
predicted and reported by M&S was actually a tautology having no
relation to experimental findings, which will always produce the
result claimed by M&S to be an experimental result. M&S in
the paper and in the rebuttal treat it as a discovery that can be
made only by careful statistical analysis, and do not acknowledge
the tautology criticism at all.
M&S: "At the heart of the criticisms of our paper by Z/M and
Taylor is the assumption that the power law is a result of a direct
causal connection between curvature and speed of movement or between
these variables and the physiological mechanisms that produce them."
I have no idea how this astonishing statement can be derived from my
exposition of the mathematical and logical flaws in their paper. My
comment is designed to refute exactly M&S’s claim of my
motivation. The comment shows that there is NO necessary
relationships, causal connection or otherwise, between curvature and
speed of movement.
Nothing of M&S's so-called "re appraisal" after that will load
from the link Rick provided, so I cannot show any later examples of
mis-statements of the criticisms made, and rebuttals of criticisms
not made. Maybe later in their reappraisal M&S do comment on a
criticism that was actually made in my comment, I can’t tell. But I
think this should be enough to raise some significant questions as
to the scientific legitimacy of both the original paper and the
rebuttal comment.
I just wonder why the rebuttal was written, if it was not going to
address the criticisms made, but had to invent imaginary ones that
were not made or that were actually opposite to ones that were made.
Martin
