[Martin Taylor 2016.09.14.14.07]
[From Rick Marken (2016.09.14.0845)]
I don't know what Alex is implying, but since I have demonstrated in
ways you ought to be able to understand that your so-called
“explanation” is no explanation at all, I don’t think “rhetoric”
applies. I would call your “explanation” non-existent.
No you haven't. You have produced a model that makes a cursor track
a target moving in two dimensions. You have not produced a model
that traces a reference trajectory, let alone one that does so while
moving its “cursor” at some velocity that has some relation to the
local curvature of the trajectory; you have not produced a model
that generates a trajectory in any of the situations faced by Alex’s
odour-seeking maggots. A model that tracks a moving target
inherently cannot “account for” a law that relates cursor velocity
to trajectory curvature.
I guess that all mathematics is "rhetoric", then, and therefore
irrelevant to serious analysis of problems of perceptual control.
Over the years, you have frequently implied that this is so, and I
guess you believe it. Most scientists don’t, whatever their research
interest.
It really DOES matter that your math is wrong in the same way that
the math of the “divided by zero” error is wrong. I see the below
your signature you quoted all of my kindergarten level explanation
of why it matters, but you have never said anything that would
suggest you understood even that. Bruce offered YAWTLAI (yet another
way to look at it). Your response to him continues the error without
attempting to show why he is wrong in saying (as I also show in my
“Sunday” exposition on the “divided by zero” error) that while the
“V” in Gribble and Ostry’s equation 9 CAN BE the same as the X in
equation 8, the only reason it would be is the pure convenience of
being able to use the same measures of time derivatives in both
equations. You cannot use equation 9 in ANY further use of the “V”
variable.
In the divide by zero syllogism
x/0 = infinity
3/0 = infinity
Therefore x = 3
x might actually BE 3 in some situation, but you can't use that
faint possibility to substitute 3 for x in further equations. That
is just what you are doing (falling prey to the mathematical error)
when you say [From Rick Marken (2016.09.14.1125)]
RM: These data -- the variables measured perequations 8 and 9 – are then analyzed, using linear regression
analysis
Back to the immediate message.
Why do you say that? It is unlike anything I remember seeing in any
of the curvature threads. What HAS been said is that when we observe
action, the PCT presumption is that some variable is being
controlled. What has also been said is that we see some consistency
in the observed action, that consistency might offer a clue as to
what variable is being controlled by the observed action.
According to a different contributor to CSGnet, also called Rick
Marken, the very first thing one should do in answering how PCT
applies to a specified situation is to seek the controlled
variable(s). I guess you really ought to set up a thread in which
you would argue the point with him.
...law, there's not much point in your continuing the pretence that
in the last two months you have said anything relevant to it. You
could stop the nonsense and begin contributing to answering Alex’s
original problem if you wanted, but I guess that isn’t something for
which you are controlling.
They have been posted and reposted and re-reposted on CSGnet ad
nauseam. Why do you want them posted elsewhere as well?
I'm leaving the "Sunday" kindergarten explanation below, so you
don’t have to look back to find it. If you find even something at
that elementary level incomprehensible, maybe you could point out
the specific place that you don’t understand, and perhaps we could
clear it up. Or you could do the same with Bruce’s post, which
illustrates the same problem from a different angle. Or you could
tell us if you have found anything wrong with any of the myriad
other explanations, dating back to Alex’s post within an hour of
your first mention of the so-called “behavioural illusion”.
Martin
···
On Wed, Sep 14, 2016 at 1:52 AM, Alex
Gomez-Marin agomezmarin@gmail.com
wrote:
AGM: In other words, joinme in the efforts of these newly created and much
needed ONG:
(RCP= Rhetoric Control Theory)
RM: I presume you are implying that my PCT explanation
of the power law is all “rhetoric”.
That strikes me as odd since I have produced a PCT
model, tested it against data and showed how it accounts
for the power law;
reference trajectory all the "non-rhetorical" PCT side
has produced is, well, rhetoric
(mainly having to do with how my math is wrong
and that the power law "suggests" the existence of some
unspecified controlled variable).
Until I see your PCT model that accounts for the
existence of the power
I think all that needs to be posted at the StopRCP
site is the arguments of the ostensibly non-rhetorical PCT
side of the discussion.
Best
Rick
–
On Wed, Sep 14, 2016 at
8:38 AM, Alex Gomez-Marin agomezmarin@gmail.com
wrote:
martin, the csgNet isnow a hybrid of a basic math accademy with an
entertainment program for writing and joking
with those who write back. stay tuned!On Wednesday, 14 September 2016, MartinTaylor <mmt-csg@mmtaylor.net >
wrote:[Martin Taylor 2016.09.13.22.49]
[From Rick Marken(2016.09.13.1610)]
If you actually read and thought aboutwhat you quote, I cannot read your
question as anything other than a not
too subtle joke, so I have to assume
that you either did not read it or the
maths, which I tried to explain at the
most basic level O could manage without
seeming to insult you (which I was
afraid I was doing anyway), was a bit
too deep for you.Isuggest you try again, concentratingon figuring out why this DOES explain
why you have been making the same kind
of mistake as the “divide by zero”
error. Perhaps I should repeat the last
lines: " When
we put all this together, we come to
the way this is a variant of the
“divide by zero” error. That error
depends on the fact that you can put
any variable at all in for “x” in “x/0
= infinity”. The – shall we call it
– the “curvature error” depends on
the fact that you can use anything at
all for V (including the measured
values), provided only that V is
defined as ds/dz where z is some
variable for which ds/dz exists
everywhere. You therefore cannot use
the curvature equation in any way to
determine V."I emphasize "IN ANY WAY". Since I maybe a little too subtle when I say
this, it simply says that your
equation V = D1/3*C1/3 means nothing
at all, because it is true when V is
any variable at all that satisfies a
very loose condition. If it is a
velocity it can be any velocity at
all, or it can be any value of any
variable (and here I will repeat
myself) that depends on any other
variable “z” whatever for which ds/dz
is everywhere calculable.
G+O showed the correct formulas, and Isaid so. You did the correct FORMAL
algebra. Your math error was and
apparently continues to be the
equivalent of the “divide by zero”
error, which also depends on doing the
algebra correctly. The “divide by zero”
or its “curvature error” equivalent is a
math error if ever there was one. It
could be and should be easily
correctable, but apparently it isn’t. I
don’t know why.Martin
RM: Oh, I see. It's
contained in this:
MT:Now we have to see how
they came to equation
(9). That’s a bit more
complicated, so please
bear with me.MT:They presumably either
used someone else’s
derivation or made their
own, starting from one
of several equivalent
measures of curvature,
one of which is C = 1/R
where R is the radius of
the osculating circle at
the point of concern.
Another one is developed
using vector calculus,
which I have no
intention of introducing
into this discussion. It
is C = dx/dsd2y/ds2 -
dy/ds * d2x/ds2 ,
where s is distance
along the curve from
some arbitrary starting
point.
For
G+O this formula was not
very convenient, because
they would have had to
measure these first and
second derivatives of x
and y with respect to
distance along the curve
fairly accurately. But
they had a trick
available, in the “chain
rule” of
differentiation:
dx/dydy/dz = dx/dz. The
"dy"s cancel out just
like ordinary variables.
Using the chain rule on
the first derivative
gives you the rule for
the second derivative,
and so on. For the
second derivative the
rule is (d2x/dy2)(dy/dz)2 =
d2x/dz2.
Using
the chain rule, G+O
could multiply the
formula for C by (ds/dz}3/(ds/dz)3 =
1, for any variable z
that allowed the
differentiation, to get
C = ((dx/ds)(ds/dz)(d2y/ds2)(ds/dz)2)(ds/dz)3 -
(dy/ds)(ds/dz)(d2x/ds2)__(ds/dz)__3)/(ds/dz)3 .
This formula is true
(allowing for typos) for
variable “z” whatever
(as with the divide by
zero example), but it
wouldn’t have helped G+O
very much, had it not
been that for one
particular variable they
already had measures
they could use. Those
measures were the ds/dt
velocity and the derived
d2s/dt2 values
they had obtained from
their observations of
movement. Using those
measures, they could
set “z” = t (time),
making dx/dt =
dx/ds*ds/dt. They could
then take advantage of
their measured
velocities to substitute
for ds/dt, and writeC= (dx/dtd2y/dt2)/V3 -
(dy/dtd2y/dt2)/V3Ohgoody! We don’t have to
measure anything new to
get our curvatures. We
can use the values of
dx/dt and dy/dt that we
got before! Very handy.
… But also very
confusing, because it
made the published
equations look as though
the V3/V3 multiplier
was special to the
velocities they
measured, whereas it was
simply a convenient
choice from a literally
infinite variety of
choices they could have
made. G+O made it even
more confusing in the
publication by using the
Newton dotty notation,
which made it look as
though there was
something necessary
about the time
differentiation in the
curvature equation.Whenwe put all this
together, we come to the
way this is a variant of
the “divide by zero”
error. That error
depends on the fact that
you can put any variable
at all in for “x” in
“x/0 = infinity”. The –
shall we call it – the
“curvature error”
depends on the fact that
you can use anything at
all for V (including the
measured values),
provided only that V is
defined as ds/dz where z
is some variable for
which ds/dz exists
everywhere. You
therefore cannot use the
curvature equation in
any way to determine V.Doesthis "Sunday "
explanation help?
RM: Not really. Are you
saying that G+O used the
wrong formulas for V and
R? Or that the formulas
they published are not
actually the ones they
used to compute V and R?
Or that there is no way to
compute R since we can’t
measure ds? Either way,
you can’t say I made a
math error since I did the
math correctly on the
formulas I was given.
(And, as I mentioned, the
results came out exactly
right).
MT:but the critical
point of my
suggestion that
you read my
earlier message is
contained in this:
RM: Contained in
what?
RM: Rather than saying
that I was making a math
error, it would have
helped if you had just
said: “these are the
correct formulas for
computing V and R” and
showed me the formulas.
That would have saved
a lot of trouble. So how
about it; what are the
correct formulas for
computing V and R?
Best
Rick
–
Richard
S. Marken
"The
childhood of
the human race
is far from
over. We have
a long way to
go before most
people will
understand
that what they
do for others
is just as
important to
their
well-being as
what they do
for
themselves."
– William T.
Powers
–
Richard
S. Marken
"The
childhood of
the human race
is far from
over. We have
a long way to
go before most
people will
understand
that what they
do for others
is just as
important to
their
well-being as
what they do
for
themselves."
– William T.
Powers
Richard S. Marken
"The childhood of the human
race is far from over. We
have a long way to go before
most people will understand that
what they do for
others is just as important to
their well-being as what they do
for
themselves." – William T.
Powers
