# Another Behavioral Illusion (was Re: the speed-curvature power law in humans and flies)

[Martin Taylor 2016.07.18.21.49]

``````So why has time mysteriously disappeared from equation 1? V =
``````

sqrt((dx/dt)^2 + (dy/dt^2)) is indeed a proper velocity. But Why should you expect to compute V from R or vice versa, since the
essence of the problem is to ask why control systems tend to slow
down around sharp curves, but less so if the organism is a larva or
a human moving in a viscous medium. Then the power-law relation
between linear velocity and R has an exponent nearer 0.25 than 0.33.
The geometry is the same. Why is the relation between V and R
different?
Martin

···

On 2016/07/18 6:17 PM, Richard Marken
wrote:

[From Rick Marken (2016.07.18.1515)]

Martin Taylor (2017.07.18.14.13)

``````                                Alex:
``````

you have simply numerically checked
a mathematical equality by writing
curvature as a function of speed.
Every single scientist working on
the power law has done that. But
they don’t believe it is such a big
achievement.

``````                        RM: If they know this then I don't
``````

understand why they still think that any
observed relationship between R and V would
tell them anything about how the curves are
produced. There is simply no way for them to
find any relationship between R and V other
than

``````                          V
``````

= |dXd2Y-d2XdY| 1/3 *R1/3
(1)

``````            MT: The question
``````

d(distance)/d(time). Your V is just a measure of local
curvature. There’s no time in it at all. Alex keeps
telling you as much. His original question was about why
people slow down at sharp curves, not about how you
describe curves in a Cartesian space.

``````            V(angular velocity) = (d(distance travelled)/d(time))/R
``````

for a portion of a circular arc of radius R.

``````          RM: In determining the power relationship between V and R,
``````

V (velocity) is measured as:

``````          where X.dot and Y.dot are Newton's notation for the
``````

time derivatives of X (dX/dt) and Y(dY/dt) respectively.
This measure of V is the variable that is actually
computed from the curved paths that are observed in the
velocity/curvature power law studies. This measure of
velocity is then related to the R measure of curvature,
which is computed as follows:

``````          RM: Equation 1 is found by solving the two equations
``````

above, for V and R, simultaneously. X and Y are, of
course, the coordinates of the curve (or path) that was
observed to have been produced by the organism under
study.

``````  V
``````

= |dXd2Y-d2XdY| 1/3 *R1/3 is not.
Something (a bunch of dt’s) got lost in the translation.

``````          RM: So whatever the merits of your equation for V might
``````

be (and one of its demerits is that it doesn’t specify how
to compute the value of the radius, which you call R) it
is not the V that they are talking about in the power law
research.

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

option A: we say it is an artifact, an illusion, from those who don’t understand pct.

option B: we demonstrate something new and interesting because we understand pct.

so far 95% of A and 5% of B

Re Another Behavioral Illusion2 (110 Bytes)

Re Another Behavioral Illusion3 (110 Bytes)

···

Martin Taylor (2017.07.18.14.13)

``````            MT: The question
``````

d(distance)/d(time). Your V is just a measure of local
curvature. There’s no time in it at all. Alex keeps
telling you as much. His original question was about why
people slow down at sharp curves, not about how you
describe curves in a Cartesian space.

``````            V(angular velocity) = (d(distance travelled)/d(time))/R
``````

for a portion of a circular arc of radius R.

``````          RM: In determining the power relationship between V and R,
``````

V (velocity) is measured as:

``````          where X.dot and Y.dot are Newton's notation for the
``````

time derivatives of X (dX/dt) and Y(dY/dt) respectively.
This measure of V is the variable that is actually
computed from the curved paths that are observed in the
velocity/curvature power law studies. This measure of
velocity is then related to the R measure of curvature,
which is computed as follows:

``````          RM: Equation 1 is found by solving the two equations
``````

above, for V and R, simultaneously. X and Y are, of
course, the coordinates of the curve (or path) that was
observed to have been produced by the organism under
study.

``````                                Alex:
``````

you have simply numerically checked
a mathematical equality by writing
curvature as a function of speed.
Every single scientist working on
the power law has done that. But
they don’t believe it is such a big
achievement.

``````                        RM: If they know this then I don't
``````

understand why they still think that any
observed relationship between R and V would
tell them anything about how the curves are
produced. There is simply no way for them to
find any relationship between R and V other
than

``````                          V
``````

= |dXd2Y-d2XdY| 1/3 *R1/3
(1)

``````          RM: So whatever the merits of your equation for V might
``````

be (and one of its demerits is that it doesn’t specify how
to compute the value of the radius, which you call R) it
is not the V that they are talking about in the power law
research.

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

[From Rick Marken (2016.07.19.1725)]

···

On Mon, Jul 18, 2016 at 5:12 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:
Â

AGM: First, Rick, your demo hardly proves anything because you inject ad hoc temporal dynamics in the references whose lawful (or unlawful) properties will simply be reflected by the control system, which does hardly more than integrating them.Â

RM: OK, let’s start from the beginning. The goal of this exercise is to develop a model that explains how people (and other organisms) produce curved paths that have the property that the velocity of movement while producing the path (V) is proportional (by a power function) to the curvature of the path at each instant. So my first step was to develop a control model of someone like an artist drawing a curved line. The model is diagrammed below:

RM: The phenomenon to be accounted for by the model is the curved pattern (squiggle) produced by the artist. The completed squiggle is shown at the bottom of the figure, in the environment where the squiggle is actually produced. The model has to produce this squiggle exactly as the artist produced it, by varying the position of the pen over time. According to PCT, the observed variations in pen position (qi.x and qi.y) are controlled results of variations in the reference specifications (r.x and r.y) for the perception of those positions (p.x and p.y). Therefore the model varies these references in a way that would produce the observed variations in qi.x and qi.y.Â

RM: r.x and r.y are the references that you object to, claiming that they contain ad hoc temporal dynamics. I question whether they do, but I agree that it looks trivial (and a lot like cheating) to put the desired end result (the squiggly movements of the qi.x and qi.y over time) into the model (in the form of the identical squiggly movements of r.x and r.y). But that is the way the PCT model works; controlled (intended) results are results that match specifications set autonomously by the organism itself.Â

RM: But the reference signals in the control model are not “cheating” any more than are the Â “command” signals in motor control models of behavior, like that of Gribble/Ostry, which is shown below. The commands in theÂ model are commands for output; forces that will produce movements of the pen that will result in the observed squiggle. In the PCT model, references, r.x and r.y, are commands for input; perception that match the reference specifications.

RM:Â So both models have to use internal commands in order to produce the observed result (squiggle). The difference is that the commands in the PCT model “look like” the observed result; the commands in the Gribble/Ostry don’t necessarily “look like” the result produced. But in both cases the commands have to be carefully crafted to produce the correct result. So the possibility of introducing “ad hoc temporal dynamics” is present in both models. But the PCT model can do something that the Gribble/Ostry cannot do: it can control. That is, it can produce the intended squiggle in the face of disturbances.Â

RM: Although the variations in the references (r.x, Â r.y) in the PCT model correspond to the squiggle that is produced (qi.x, qi.y) , I didn’t expect this simple model to produce a squiggle with a power function relationship between angular velocity (V) and curvature (R). I assumed, like you, that the power law relationship was either 1) a controlled result in itself (the person controlling for speeding up through tighter turns), which would require a whole extra control organization in the model or 2) the result of complex dynamic characteristics of muscle force production (the functions of e.x and e.y in the control model diagram above) and/or of the feedback function connecting force output to pen movement input (k.f in that diagram).Â

RM: So I was very surprised to find that the squiggle produced by this simple control model showed a power relationship between V and R . And when the squiggle was an ellipse the coefficient of the power function was about the same (~.31) as that found by Gribble/Ostry for their ellipse production model Â – a model with a far more dynamically complex method of generating the ellipse than my control model. That’s when I realized that the observed relationship between V and R might be a mathematical property of all curved lines. And, indeed, it turns out that it is. The relationship between V and R, which can be found using kindergarten math, isÂ

V = Â |dXd2Y-d2XdY|Â 1/3Â *R1/3Â Â Â

RM: Â Note that the termÂ Â |dXd2Y-d2XdY|, which I called D, implying that it was a constant, is a variable. So the value of V for any curve is proportional (exactly) to the 1/3 power ofÂ |dXd2Y-d2XdY| and the 1/3 power of R.Â Â I was as surprised by this as as anyone. So I wanted to make sure it was true so I did the multiple regression analysis using log (Â |dXd2Y-d2XdY| ) and log (R) as predictors of log (V) for many different “squiggles” and always found that all the variance in log (V) was accounted for by an equation of the form:

log (V) = .33* log (|dXd2Y-d2XdY|) +.33* log(R)Â

AGM: Second, you are stubbornly confused about the difference between a mathematical relation (that allows to re-express curvature as a function of speed, plus another non-constant term that you insist in ignoring and treating like a constant),

RM: I hope you see now that I do not treat the variableÂ Â |dXd2Y-d2XdY| Â as a constant. The mathematical relationship is as flawless as my kindergarten math teacher;)

Â

between a physical realization (the fact that one can in principle draw the same curved line at infinitely different speeds),

RM: Actually, I understand that the same curved line (squiggle) can be produced at an infinity of different speeds and by an infinity of different means (different variations in o.x and o.y producing the same squiggle, qi.x, qi.y).Â The same relationship between V and R holds regardless of the speed with which the squiggle is produced and and the means used to produce it. The relationship between V and R is always:Â

log (V) = .33* log (|dXd2Y-d2XdY|) +.33* log(R)Â

RM: This same relationship between V and R even holds for all the different squiggly patterns made by o.x and o.y to Â produce the same squiggly pattern --qi.x, qi.y.Â

AGM: and between a biological fact (that out of all possible combinations of speed and curvature, living beings are, for yet some unknown reason —but there are tens if not hundreds of papers making proposalsââ€” constrained following the power law,

RM: But now we know the reason. It’s a result of the fact that the relationship between V and R for any curved line is

V = Â |dXd2Y-d2XdY|Â 1/3Â *R1/3Â Â Â

RM: There is no way to draw a curved line so that this equation does not hold. So there is no biological constraint that creates the observed power law; it’s a mathematical constraint.Â

RM: The reason people have found different power coefficients for the relationship between V and R is because they have left the variableÂ Â |dXd2Y-d2XdY| Â out of the analysis. When you leaveÂ Â |dXd2Y-d2XdY| Â out of the analysis, variations in that variable can lead to different estimates of the power coefficient of R. The amount by which the value of the power coefficient of R is affected by leavingÂ Â |dXd2Y-d2XdY| Â out of the analysis depends on the shape of the squiggle thatÂ is drawn. LeavingÂ Â |dXd2Y-d2XdY| out of the analysis of the V/R relationship for an ellipse affects the actual power coefficient of R (.33) very little, so the value obtained is around .31 (see Gribble and Ostry, Table 1). Other squiggles can bring the power coefficient of R down as low as .2.Â

RM: On that note, Martin Taylor noted that the power coefficient for R, which is around .33 for a curved figure drawn in the air, is closer to .25 when the same figure is drawn Â in a viscous medium (like water). It turns out that this can be explained in terms of a difference in the feedback function (k.f in the diagram) in the two cases.Â

RM: In the PCT model, the feedback function is a simple, linear coefficient. When the model traces out an ellipse with a feedback function of k.f = 1.0, the power coefficient of R is .32; when the feedback function is changed to k.f = .5 – equivalent to trying to move a pen through a more resistive medium – theÂ power coefficient of R is .26. This happens simply because the ellipse drawn in the resistive medium is a little sloppier than the one drawn in the air. The change in feedback function changes the loop gain of the control system.Â

AGM: But you will now reply for the n-th time saying that everybody that has ever worked on the power-law misses the point of control systems and that your toy demo proves they don’t get it.

RM: Yes. But they have been fooled by a rather convincing illusion. It’s hard not to see the observed relationship between V and R as a situation where the agent purposefully changes speed through curves (the power law actually suggests that agents increase their speed as the curve increases, but this increase in speed decreases as curvature increases; it does not suggest that control systems tend to slow down around sharp curves).

RM: So I agree that it is very surprising (and, perhaps, disappointing) that the relationship between V and R tells us nothing about how people draw curves. But that doesn’t mean that research on how people (and other organisms) produce curved paths should come to an end. To the contrary, it opens up new and fruitful questions about exactly how this is done. For example, the integral output function that I use in the existing model is obviously an over simplification. Something like theÂ Â Gribble/Ostry model pictured above is probably a closed approximation. A clever experimenter should be able to design behavioral (and/or physiological) studies to determine what the best model of the output function is.Â

RM: Going “up a level” (so to speak) research could also be aimed at determining how what are presumably higher level control systems set the references for the x,y coordinates of the figure being drawn (assuming that the figure is a controlled result and not a side effect of controlling other variables, as in the CROWD demo).Â

RM: So there is really a lot of very important and challenging research to be done in order to understand how people draw figures. But this research must be based on an understanding of the fact that the figure drawn is a controlled variable – an intended result. And so any research aimed at understanding how figures are drawn must be based on an understanding of how control works.Â

AGM: But, again, you gloss over serious flaws interpreting the difference between mathematical equations, physical conditions and biological constraints as facts, and you magnify the relevance of a toy demos that, I wish could shed new light, but so far don’t shed much new to the problem.

RM: I hope this post helps. I don’t believe I have glossed over flaws. But if there are substantive flaws please point them out. As I said above, if my analysis is correct that doesn’t mean all is lost. Indeed, I think it actually opens up many new and very productive possibilities for research.Â

Best regards

Rick

So I encourage you (and everyone still reading these email exchanges) to say something new and relevant, because I still believe that asking what is being perceived and what is being controlled is worth-while in figuring out why speed and curvature are constrained they way they are.

Â

Alex

Richard S. MarkenÂ

“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

[Martin Taylor 2016.07.20.00.15]

[From Rick Marken (2016.07.19.1725)]

``````That is as I understand the problem. It's about a relation between
``````

speed and curvature. Why do people slow down by a precisely
predictable amount when they could choose to do the whole path at a
constant slow speed at which they could navigate the sharpest
curves.

``````That is NOT as I understand the problem. This statement ignores
``````

speed altogether.

``````Your two statements of the problem are completely different, in fact
``````

almost unrelated to each other. This second statement talks about
how a control system could reproduce the shape, a problem with many
solutions, whereas the other (I believe correctly) talked about the
speed with which the parts of the shape are drawn. Why do people
slow down when going around sharp curves when there is no mechanical
reason for them to do so? Does your control system model? Unless I
missed it, you haven’t told us.

``````The slowdown for sharp curves may not be so hard to understand
``````

intuitively, but the real question is whether your or any other
candidate control system slows down in exactly the same way around
the sharp curves. If yours did, you haven’t yet said so, because all
you have talked about is how the geometry of the reproduced pattern
has a geometric property characteristic of all squiggles, including
I find easier to think of in terms of the relationship between
along-path linear speed and the radius of curvature. The exponent
for that power law is 1-Beta, where Beta is the exponent when you
compare angular direction change per second with curvature

``````The real question goes beyond asking why the power law for your
``````

first statement of the problem is the same as the geometric power
law that relates angular direction change per unit path length with
curvature. That’s a non-trivial problem, as Alex has been trying to
point out. But for me the deeper question is why the power law
exponent changes when the medium is viscous or when the mover is a
larva. In linear-velocity to radius-of-curvature terms, the exponent
is reduced from about 1/3 to about 1/4. In other words, curvature
has less effect on speed under those conditions. Why? And if the
limit cases really are so simple as 1/3 and 1/4, that’s something
that might have some deep explanation – or it might turn out to be
trivial once the initial problem is solved. Is there a difference
between plane curves and space curves, or do the 1/3 1/4 values
apply equally to both?

``````As for an experimental task, it seems to me that Grand Prix race
``````

drivers finding the best line through curves have a similar problem
when they aren’t limited by the g-force breaking the tire adhesion
to the track. A possible experiment might be to set up something
similar for people to trace, either a wide track or a set of slalom
gates. Does the ability to see where you are about to go affect the
exponent? You could window the track so as to limit their look-ahead
possibility, to see whether being able to see the geometry matters
(when they draw a random squiggle of their choice, they can look
ahead in imagination as far as they want).

``````Does the ability to see the geometry affect the exponent or do they
``````

just slow down when they can’t look ahead? If the task uses slalom
gates, the lookahead is defined in number of gates. Is one enough,
do you need more for straight or sharply curved portions of track?
Do people take wide fast curves or cut corners? If the task is
presented as trying to keep to the centre of the track or as staying
somewhere within bounds, does that affect the exponent? Etc. Etc. I
imagine all these experiments have been done, and it would be nice
to know the effects of such manipulations, because that’s what a
good control model must reproduce.

``````Martin
``````
···

On Mon, Jul 18, 2016 at 5:12 PM, Alex
Gomez-Marin agomezmarin@gmail.com
wrote:

``````              AGM:
``````

First, Rick, your demo hardly proves anything
because you inject ad hoc temporal dynamics in the
references whose lawful (or unlawful) properties will
simply be reflected by the control system, which does
hardly more than integrating them.

``````          RM: OK, let's start from the beginning. The goal of
``````

this exercise is to develop a model that explains how
people (and other organisms) produce curved paths that
have the property that the velocity of movement while
producing the path (V) is proportional (by a power
function) to the curvature of the path at each instant.

``````          So my first step was to develop a control model of
``````

someone like an artist drawing a curved line. The model is
diagrammed below:

``````          RM: The phenomenon to be accounted for by the model is
``````

the curved pattern (squiggle) produced by the artist.

Martin, I like your set of proposed experiments. For a long time I have wanted to obtain racing data, specially MotoGP, but they don’t post it on their website. Another interesting situation is that of robots, for instance, would the Braitenberg vehicles comply with the power law or not? Animats, like animals, behave in the real world and are subject to physical constraints too, but the biological constraint on speed and curvature may not be at work there. A third place to look, as has been suggested, is in computer simulations of behavior (collective behavior, or others), and I anticipate that in most of those the speed-curvature constraint is not met, since most simulations are not trying to account for the real way in which trajectories are generated, but other high level phenomena, and so the rules that determine progression and reorientation are simplistic.

So, while Rick clarifies to us what he actually showed and didn’t show, we may explore other alternatives such as generative PCT models that control for smoothness (via keeping jerk at minimum) and generate the law, and other generative situations (like robots or simulations) where biology is not at work and the law is violated. In either case, we may learn something. Thanks, guys, for the train of thoughts.

Alex

···

On Wed, Jul 20, 2016 at 7:06 AM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.07.20.00.15]

[From Rick Marken (2016.07.19.1725)]

``````That is as I understand the problem. It's about a relation between
``````

speed and curvature. Why do people slow down by a precisely
predictable amount when they could choose to do the whole path at a
constant slow speed at which they could navigate the sharpest
curves.

``````That is NOT as I understand the problem. This statement ignores
``````

speed altogether.

``````Your two statements of the problem are completely different, in fact
``````

almost unrelated to each other. This second statement talks about
how a control system could reproduce the shape, a problem with many
solutions, whereas the other (I believe correctly) talked about the
speed with which the parts of the shape are drawn. Why do people
slow down when going around sharp curves when there is no mechanical
reason for them to do so? Does your control system model? Unless I
missed it, you haven’t told us.

``````The slowdown for sharp curves may not be so hard to understand
``````

intuitively, but the real question is whether your or any other
candidate control system slows down in exactly the same way around
the sharp curves. If yours did, you haven’t yet said so, because all
you have talked about is how the geometry of the reproduced pattern
has a geometric property characteristic of all squiggles, including
I find easier to think of in terms of the relationship between
along-path linear speed and the radius of curvature. The exponent
for that power law is 1-Beta, where Beta is the exponent when you
compare angular direction change per second with curvature

``````The real question goes beyond asking why the power law for your
``````

first statement of the problem is the same as the geometric power
law that relates angular direction change per unit path length with
curvature. That’s a non-trivial problem, as Alex has been trying to
point out. But for me the deeper question is why the power law
exponent changes when the medium is viscous or when the mover is a
larva. In linear-velocity to radius-of-curvature terms, the exponent
is reduced from about 1/3 to about 1/4. In other words, curvature
has less effect on speed under those conditions. Why? And if the
limit cases really are so simple as 1/3 and 1/4, that’s something
that might have some deep explanation – or it might turn out to be
trivial once the initial problem is solved. Is there a difference
between plane curves and space curves, or do the 1/3 1/4 values
apply equally to both?

``````As for an experimental task, it seems to me that Grand Prix race
``````

drivers finding the best line through curves have a similar problem
when they aren’t limited by the g-force breaking the tire adhesion
to the track. A possible experiment might be to set up something
similar for people to trace, either a wide track or a set of slalom
gates. Does the ability to see where you are about to go affect the
exponent? You could window the track so as to limit their look-ahead
possibility, to see whether being able to see the geometry matters
(when they draw a random squiggle of their choice, they can look
ahead in imagination as far as they want).

``````Does the ability to see the geometry affect the exponent or do they
``````

just slow down when they can’t look ahead? If the task uses slalom
gates, the lookahead is defined in number of gates. Is one enough,
do you need more for straight or sharply curved portions of track?
Do people take wide fast curves or cut corners? If the task is
presented as trying to keep to the centre of the track or as staying
somewhere within bounds, does that affect the exponent? Etc. Etc. I
imagine all these experiments have been done, and it would be nice
to know the effects of such manipulations, because that’s what a
good control model must reproduce.

``````Martin
``````
``````        On Mon, Jul 18, 2016 at 5:12 PM, Alex
``````

Gomez-Marin agomezmarin@gmail.com
wrote:

``````              AGM:
``````

First, Rick, your demo hardly proves anything
because you inject ad hoc temporal dynamics in the
references whose lawful (or unlawful) properties will
simply be reflected by the control system, which does
hardly more than integrating them.

``````          RM: OK, let's start from the beginning. The goal of
``````

this exercise is to develop a model that explains how
people (and other organisms) produce curved paths that
have the property that the velocity of movement while
producing the path (V) is proportional (by a power
function) to the curvature of the path at each instant.

``````          So my first step was to develop a control model of
``````

someone like an artist drawing a curved line. The model is
diagrammed below:

``````          RM: The phenomenon to be accounted for by the model is
``````

the curved pattern (squiggle) produced by the artist.

[From Rick Marken (2016.07.20.1130)]

···

[Martin Taylor 2016.07.20.00.15]

[From Rick Marken (2016.07.19.1725)]

``````MT: That is as I understand the problem. It's about a relation between
``````

speed and curvature. Why do people slow down by a precisely
predictable amount when they could choose to do the whole path at a
constant slow speed at which they could navigate the sharpest
curves.

RM: The power law implies that speed increases as curvature increases. Here’s a graph of V = R^(1/3):

RM: So speed is increasing, but by a decreasing amount, as curvature increases. Whether or not people are choosing to do this (I presume you mean controlling for doing this) cannot be determined from the data. You would have to see if this relationship between R and V is maintained against disturbance.

``````MT That is NOT as I understand the problem. This statement ignores
``````

speed altogether.

RM: The statement may ignore the speed with which the curved pattern is produced but the model doesn’t ignore it. You should have been able to see this from the equations used to compute V and R. The equations for both require the computation of derivatives, which are measures of speed and acceleration in the X and Y direction.

``````MT: Why do people
``````

slow down when going around sharp curves when there is no mechanical
reason for them to do so?

RM: The power law (above) shows that they speed up when going around sharp curves. And the reason why is because this is the mathematical relationship between speed (as measured by V) and curvature (as measured by R).

``````MT: Does your control system model [take speed into account]? Unless I
``````

missed it, you haven’t told us.

RM: As I noted above, it does indeed take speed into account. But the ability of the model to replicate the power law is no accomplishment. The main thing I found is that anything that can produce a curved pattern over time – model, organism, equation, robot, whatever – will produce a power law relationship between V and R.

``````MT: The slowdown for sharp curves may not be so hard to understand
``````

intuitively,

RM: But you don’t need to understand it because it doesn’t happen! Unless I’m crazy (a distinct possibility) the graph of the power law relationship between curvature (R) and speed (V) shows that speed increases (at a decreasing rate) as curvature increases.

``````MT: but the real question is whether your or any other
``````

candidate control system slows down in exactly the same way around
the sharp curves.

RM: My control system doesn’t slow down around sharp curves and neither do people drawing figures. Like people (and, as I said, virtually anything else that produces curves over time), the control system draws curves that follow the power law: V = KR^B where the value of B depends on the nature of the curve drawn. If the complete equation relating V to R is used to estimate B (an equation where K is actually the variable |dXd2Y-d2X*dY| raised to the B power) B will always be precisely .33.

``````MT: If yours did, you haven't yet said so, because all
``````

you have talked about is how the geometry of the reproduced pattern
has a geometric property characteristic of all squiggles, including
the reference squiggle.

RM: The model draws the figures over time. I get the same results – a power law relationship between V and R – regardless of the speed with which the figure is produced. The resulting geometry of the figure – ellipse, squiggle, etc - affects the estimated value of B when you regress log (R) on log (V). If you include log (|dXd2Y-d2XdY| ) as a predictor variable then the estimate of B is always .33 regardless of the shape of the figure produced.

``````MT: But for me the deeper question is why the power law
``````

exponent changes when the medium is viscous or when the mover is a
larva. In linear-velocity to radius-of-curvature terms, the exponent
is reduced from about 1/3 to about 1/4. In other words, curvature
has less effect on speed under those conditions. Why?

RM: In my previous post I showed that this could be explained as the result of a change in the feedback function, a decrease in the feedback coefficient resulting in a somewhat sloppier version of the curve being drawn.

``````MT: And if the
``````

limit cases really are so simple as 1/3 and 1/4, that’s something
that might have some deep explanation – or it might turn out to be
trivial once the initial problem is solved. Is there a difference
between plane curves and space curves, or do the 1/3 1/4 values
apply equally to both?

RM: I think this is a job for Richard Kennaway. I agree that there should be a way to show how the difference in the shape of the curves that are produced results in differences in the computed value of B when only R is included as a predictor of V. I’m sure it has something to do with how different curves affect the value of the variable |dXd2Y-d2XdY|.

``````MT: As for an experimental task, it seems to me that Grand Prix race
``````

drivers finding the best line through curves have a similar problem
when they aren’t limited by the g-force breaking the tire adhesion
to the track.

RM: Except for the fact that the power law suggests the opposite for curve drawing, this would be a good way to study controlling through curves. In order to get an idea of what the drivers are controlling you wold have to look at the relationship between the expected and actual direction of movement of the car at each instant. Expected direction would be the car’s direction if the driver were doing nothing (or just randomly turning the steering wheel). It would also be nice to get a measure of the driver’s steering wheel position to see how well the driver is compensating for the disturbances (g forces) that would result in movement in an undesired direction.

RM: What my results show is that if you analyzed the path of a race car (position over time) you would find a power law relationship between V and R. Indeed, if you analyzed the curved paths traced out by anything you will find a power law relationship between V and R. So looking at the relationship between V and R is not the way to figure out how curved paths are produced by race drivers.

``````MT: A possible experiment might be to set up something
``````

similar for people to trace, either a wide track or a set of slalom
gates.

RM: Yes, a two dimensional tracking task might be just the ticket!

``````MT: Does the ability to see where you are about to go affect the
``````

exponent?

RM: The only thing that will affect the exponent is the shape of the curve that is traced. I think the two dimensional tracking task will be a good way to demonstrate this.

Best

Rick

``````You could window the track so as to limit their look-ahead
``````

possibility, to see whether being able to see the geometry matters
(when they draw a random squiggle of their choice, they can look
ahead in imagination as far as they want).

``````Does the ability to see the geometry affect the exponent or do they
``````

just slow down when they can’t look ahead? If the task uses slalom
gates, the lookahead is defined in number of gates. Is one enough,
do you need more for straight or sharply curved portions of track?
Do people take wide fast curves or cut corners? If the task is
presented as trying to keep to the centre of the track or as staying
somewhere within bounds, does that affect the exponent? Etc. Etc. I
imagine all these experiments have been done, and it would be nice
to know the effects of such manipulations, because that’s what a
good control model must reproduce.

``````Martin
``````

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

``````          RM: OK, let's start from the beginning. The goal of
``````

this exercise is to develop a model that explains how
people (and other organisms) produce curved paths that
have the property that the velocity of movement while
producing the path (V) is proportional (by a power
function) to the curvature of the path at each instant.

``````          RM: The phenomenon to be accounted for by the model is
``````

the curved pattern (squiggle) produced by the artist.

[Martin Taylor 2016.07.20.16.37]

[From Rick Marken (2016.07.20.1130)]

``````Your V is still not the velocity that is of interest, and never has
``````

been. Your V is angular velocity *** provided that the
along-track velocity is held constant at a defined value of 1.0*** .
It really has nothing to do with the problem posed by Alex. Of
course the angular velocity increases with the sharpness of a curve
if the along-track velocity stays the same! The unit along-track
speed is used in the Wikipedia article on “Curvature” for ease of
explanation, but in the real world of interest, the along track
speed is anything but constant.

``````Alex has provided lots of references to studies showing that
``````

along-track velocity varies with a power-law relationship to the
local curvature, when there is absolutely no physical constraint
that enforces that relationship. Indeed, if I drive at the speed
limit, I go around curves at the same speed as I go along the
straights (if the curve isn’t too tight). So I am distinctly able to
not conform to the power law. The issue is that in the cited
experiments people (and larvae) do conform to the power law but with
different exponents under different environmental conditions.

``````Martin
``````
···

[Martin Taylor 2016.07.20.00.15]

[From Rick Marken
(2016.07.19.1725)]

``````            MT: That is as I understand the problem. It's
``````

about a relation between speed and curvature. Why do
people slow down by a precisely predictable amount when
they could choose to do the whole path at a constant
slow speed at which they could navigate the sharpest
curves.

``````          RM: The power law implies that speed increases as
``````

curvature increases. Here’s a graph of V = R^(1/3):

``````                        RM: OK, let's start from the beginning.
``````

The goal of this exercise is to develop a
model that explains how people (and other
organisms) produce curved paths that have
the property that the velocity of movement
while producing the path (V) is proportional
(by a power function) to the curvature of
the path at each instant.

[From Rick Marken (2016.07.20.1425)}

···

Martin Taylor (2016.07.20.16.37)–

``````MT: Your V is still not the velocity that is of interest, and never has
``````

been. Your V is angular velocity *** provided that the
along-track velocity is held constant at a defined value of 1.0***…

``````MT: Alex has provided lots of references to studies showing that
``````

along-track velocity varies with a power-law relationship to the
local curvature, when there is absolutely no physical constraint
that enforces that relationship.

RM: Yes, and in all those studies V is computed exactly as I am computing it. For example, here is V as defined by Vivianni and Stucchi (1992) JEP, 18, 603-623.

and here it is in Gribble and Ostry (1996) J Neurophysiology, 76, 2853-2860:

RM: I have a dream that one day I will wake up, open an email from a presumed “expert” on PCT and it will say “What a nice observation, Rick. Now here’s where we might go with it”.

RM: Don’t get me wrong, though. I don’t really mind being the only one who believes that the power law is an example of the behavioral illusion. It’s kind of fun trying to figure out whether I’m a genius or a crank (my wife says she knows which it is but won’t tell because it doesn’t matter to her;-). I guess that’s why that celebratory email will continue to be as much of a dream as MLK’s dream of the end of racism.

Best

Rick

``````          RM: The power law implies that speed increases as
``````

curvature increases. Here’s a graph of V = R^(1/3):

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

Really, Rick, I don’t get it. Why all this?

RM: The power law (above) shows that they speed up when going around sharp curves. And the reason why is because this is the mathematical relationship between speed (as measured by V) and curvature (as measured by R).

Alex: That’s wrong. (speed V is different than angular velocity A=V/R, and curvature is not R but 1/R) and most importantly speed does not go up, but down, around sharp curves. And most important of all: given a curved trajectory, being able to go faster or slow is NOT due to the mathematical formula for curvature, but a physical fact. That is precisely the main point about studying how speed and curvature are constrained: that the first one is a kinematic measure, and the second one a geometric. Geometry is static!

RM: As I noted above, it does indeed take speed into account. But the ability of the model to replicate the power law is no accomplishment. The main thing I found is that anything that can produce a curved pattern over time – model, organism, equation, robot, whatever – will produce a power law relationship between V and R.

Alex: That’s wrong. Not anything that can produce a curved pattern will produce a power law. Robots don’t have to. Equations and models have been shown in the literature not to conform to the power low. And before testing it in flies, I tested in in fish and mice and they don’t follow it. And, if you look at my fly data, there are some individual flies that are outliers. So, again, Rick, are you just making a claim about how the Universe behaves from one simple demo simulation??

RM: But you don’t need to understand it because it doesn’t happen! Unless I’m crazy (a distinct possibility) the graph of the power law relationship between curvature (R) and speed (V) shows that speed increases (at a decreasing rate) as curvature increases.

Alex: That’s wrong. Stop thinking about “your results” and think about what experience tells you: how fast you move, namely, speed, does not increases as curvature increases. It decreases. That is why in motorbike races, pilots need to break down before the curve arrives.

RM: My control system doesn’t slow down around sharp curves and neither do people drawing figures.

Alex: That’s wrong. People of course do, whatever you say.

RM: What my results show is that if you analyzed the path of a race car (position over time) you would find a power law relationship between V and R.

Alex: That’s wrong. You results don’t say anything of that because your results are essentially a simple demo for a family of sinusoidal curves. There is no prediction there, apart from ad hoc inference.

RM: Indeed, if you analyzed the curved paths traced out by anything you will find a power law relationship between V and R.

Alex: That’s wrong. I can simulate curve paths that do not comply with the power law. And, again, fish don’t, and some flies don’t. And models sometimes don’t either.

RM: The only thing that will affect the exponent is the shape of the curve that is traced.

Alex: That’s wrong. Wrong! Wrong! And not even wrong: ad hoc hand-waving! What has been rigorously shown is that humans drawing in air versus in water is what changes the exponent.

RM: Don’t get me wrong, though. I don’t really mind being the only one who believes that the power law is an example of the behavioral illusion. It’s kind of fun trying to figure out whether I’m a genius or a crank (my wife says she knows which it is but won’t tell because it doesn’t matter to her;-).

**Alex: At some point, in order to be able to have a sensible productive scientific discussion, it is quite annoying both that you are a crank or a genius, or that you believe you are both. Because you constantly magnify claims based on weak, particular and often wrong results. Please, step back and think. I can’t believe you are really insisting on this points over and over. You obsession for claiming that the power law is another behavioral illusion has become your own self-delusion. **

···

On Wed, Jul 20, 2016 at 10:46 PM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.07.20.16.37]

[From Rick Marken (2016.07.20.1130)]

``````Your V is still not the velocity that is of interest, and never has
``````

been. Your V is angular velocity *** provided that the
along-track velocity is held constant at a defined value of 1.0*** .
It really has nothing to do with the problem posed by Alex. Of
course the angular velocity increases with the sharpness of a curve
if the along-track velocity stays the same! The unit along-track
speed is used in the Wikipedia article on “Curvature” for ease of
explanation, but in the real world of interest, the along track
speed is anything but constant.

``````Alex has provided lots of references to studies showing that
``````

along-track velocity varies with a power-law relationship to the
local curvature, when there is absolutely no physical constraint
that enforces that relationship. Indeed, if I drive at the speed
limit, I go around curves at the same speed as I go along the
straights (if the curve isn’t too tight). So I am distinctly able to
not conform to the power law. The issue is that in the cited
experiments people (and larvae) do conform to the power law but with
different exponents under different environmental conditions.

``````Martin
``````

[Martin Taylor 2016.07.20.00.15]

[From Rick Marken
(2016.07.19.1725)]

``````            MT: That is as I understand the problem. It's
``````

about a relation between speed and curvature. Why do
people slow down by a precisely predictable amount when
they could choose to do the whole path at a constant
slow speed at which they could navigate the sharpest
curves.

``````          RM: The power law implies that speed increases as
``````

curvature increases. Here’s a graph of V = R^(1/3):

``````                        RM: OK, let's start from the beginning.
``````

The goal of this exercise is to develop a
model that explains how people (and other
organisms) produce curved paths that have
the property that the velocity of movement
while producing the path (V) is proportional
(by a power function) to the curvature of
the path at each instant.

[From Rick Marken (2016.07.20.1525)]

···

On Wed, Jul 20, 2016 at 2:36 PM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

AGM: Really, Rick, I don’t get it. Why all this?

RM: Fair question. It’s because I think the “power law” exposes a fundamental flaw in the view of behavior as output rather than control.

RM: The power law (above) shows that they speed up when going around sharp curves. And the reason why is because this is the mathematical relationship between speed (as measured by V) and curvature (as measured by R).

Alex: That’s wrong. (speed V is different than angular velocity A=V/R, and curvature is not R but 1/R) and most importantly speed does not go up, but down, around sharp curves.

RM: But the relationship between angular velocity (A) and curvature (C) is also a power function:

A = |dXd2Y-d2XdY| 1/3 *C2/3

This suggests that angular velocity (like velocity) also increases (at a decreasing rate) as the sharpness of the curve increases.

AGM: And most important of all: given a curved trajectory, being able to go faster or slow is NOT due to the mathematical formula for curvature, but a physical fact. That is precisely the main point about studying how speed and curvature are constrained: that the first one is a kinematic measure, and the second one a geometric. Geometry is static!

RM: The math doesn’t know whether the curve was produced by a physical process or an equation. I’ve analyzed curves produced by both and the results are the same; V is always a power function of R with an exponent of exactly 1/3 and A is always a power function of C with an exponent of exactly 2/3; this is true in both cases only when the |dXd2Y-d2XdY| variable is included in the regression; when it’s not the regression coefficients vary a bit around those values, depending on the shape of the path traced out.

RM: As I noted above, it does indeed take speed into account. But the ability of the model to replicate the power law is no accomplishment. The main thing I found is that anything that can produce a curved pattern over time – model, organism, equation, robot, whatever – will produce a power law relationship between V and R.

Alex: That’s wrong. Not anything that can produce a curved pattern will produce a power law. Robots don’t have to. Equations and models have been shown in the literature not to conform to the power low. And before testing it in flies, I tested in in fish and mice and they don’t follow it.

RM: Well, that’s interesting. I don’t suppose you could send me the curved path taken by the mice so I could check it out. If in fact those paths don’t follow a power law that would definitely be a disproof of my claim!

AGM: And, if you look at my fly data, there are some individual flies that are outliers. So, again, Rick, are you just making a claim about how the Universe behaves from one simple demo simulation??

RM: Yes, but it is a claim that can be rejected by data. That’s why I would really like to see your fish or mouse path data. If you have curved paths traced out that don’t follow

A = |dXd2Y-d2XdY| 1/3 *C2/3

then I will definitely have to concede that I am wrong about the power law.

RM: But you don’t need to understand it because it doesn’t happen! Unless I’m crazy (a distinct possibility) the graph of the power law relationship between curvature (R) and speed (V) shows that speed increases (at a decreasing rate) as curvature increases.

Alex: That’s wrong. Stop thinking about “your results” and think about what experience tells you: how fast you move, namely, speed, does not increases as curvature increases. It decreases. That is why in motorbike races, pilots need to break down before the curve arrives.

RM: That is indeed true. But I am saying that you wouldn’t see that slowing if you just analyzed the path taken by the motor bike. Although you may be able to prove me wrong about that. Just send me the paths of the fish or mice that don’t fit a power law and, if they really don’t, I’ll shut up about it;-)

RM: My control system doesn’t slow down around sharp curves and neither do people drawing figures.

Alex: That’s wrong. People of course do, whatever you say.

RM: I know they do; I do it all the time.

RM: What my results show is that if you analyzed the path of a race car (position over time) you would find a power law relationship between V and R.

Alex: That’s wrong. You results don’t say anything of that because your results are essentially a simple demo for a family of sinusoidal curves. There is no prediction there, apart from ad hoc inference.

RM: Maybe you’re right. Send me the path of a motorbike and let me see if doesn’t follow the power law.

RM: Indeed, if you analyzed the curved paths traced out by anything you will find a power law relationship between V and R.

Alex: That’s wrong. I can simulate curve paths that do not comply with the power law. And, again, fish don’t, and some flies don’t. And models sometimes don’t either.

RM: Please send me those paths!! If those paths really don’t comply with the power law (and they are not straight lines) then that will definitely shut me up.

RM: The only thing that will affect the exponent is the shape of the curve that is traced.

Alex: That’s wrong. Wrong! Wrong! And not even wrong: ad hoc hand-waving! What has been rigorously shown is that humans drawing in air versus in water is what changes the exponent.

RM: I was just proposing a possible explanation of why the exponent changes when humans draw in water rather than air.Maybe it’s wrong; maybe not. It’s a theory. There are definitely ways to test it. Could you point me to a paper on it; I’d love to see what they found!

RM: Don’t get me wrong, though. I don’t really mind being the only one who believes that the power law is an example of the behavioral illusion. It’s kind of fun trying to figure out whether I’m a genius or a crank (my wife says she knows which it is but won’t tell because it doesn’t matter to her;-).

**Alex: At some point, in order to be able to have a sensible productive scientific discussion, it is quite annoying both that you are a crank or a genius, or that you believe you are both. Because you constantly magnify claims based on weak, particular and often wrong results. Please, step back and think. I can’t believe you are really insisting on this points over and over. You obsession for claiming that the power law is another behavioral illusion has become your own self-delusion. **

RM: Yes, I do want to avoid self delusion. And I believe the only way I can decide whether or not this is a delusion is through empirical evidence. I say every curved trace, no matter how it’s produced, witl show a power function relationship between V and R (or A and C) and the coefficient of that power function will be exactly .33 (for R) or .66 (for C) if the variable |dXd2Y-d2XdY| is taken into account.

RM: So send me that data that doesn’t follow a power function and if it pans out I’ll go work on something else.

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

On Wed, Jul 20, 2016 at 10:46 PM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[Martin Taylor 2016.07.20.16.37]

[From Rick Marken (2016.07.20.1130)]

``````Your V is still not the velocity that is of interest, and never has
``````

been. Your V is angular velocity *** provided that the
along-track velocity is held constant at a defined value of 1.0*** .
It really has nothing to do with the problem posed by Alex. Of
course the angular velocity increases with the sharpness of a curve
if the along-track velocity stays the same! The unit along-track
speed is used in the Wikipedia article on “Curvature” for ease of
explanation, but in the real world of interest, the along track
speed is anything but constant.

``````Alex has provided lots of references to studies showing that
``````

along-track velocity varies with a power-law relationship to the
local curvature, when there is absolutely no physical constraint
that enforces that relationship. Indeed, if I drive at the speed
limit, I go around curves at the same speed as I go along the
straights (if the curve isn’t too tight). So I am distinctly able to
not conform to the power law. The issue is that in the cited
experiments people (and larvae) do conform to the power law but with
different exponents under different environmental conditions.

``````Martin
``````

[Martin Taylor 2016.07.20.00.15]

[From Rick Marken
(2016.07.19.1725)]

``````            MT: That is as I understand the problem. It's
``````

about a relation between speed and curvature. Why do
people slow down by a precisely predictable amount when
they could choose to do the whole path at a constant
slow speed at which they could navigate the sharpest
curves.

``````          RM: The power law implies that speed increases as
``````

curvature increases. Here’s a graph of V = R^(1/3):

``````                        RM: OK, let's start from the beginning.
``````

The goal of this exercise is to develop a
model that explains how people (and other
organisms) produce curved paths that have
the property that the velocity of movement
while producing the path (V) is proportional
(by a power function) to the curvature of
the path at each instant.

[Martin Taylor 16.07.20.21.08]

[From Rick Marken (2016.07.20.1425)}

``````I doubt anyone would quibble with these. Both of them have the right
``````

dimension, Distance/Time. The second one is the liner along-track
velocity that I find easiest to work with. I’m not sure of the
other, because of the “phi” subscripts. Why not use them in your
analyses instead of the erroneous one you also called V in your
“kindergarten math”?

``````Martin
``````

Re Another Behavioral Illusion4 (110 Bytes)

Re Another Behavioral Illusion5 (110 Bytes)

···

Martin Taylor (2016.07.20.16.37)–

``````            MT: Your V is still not the velocity that is of
``````

interest, and never has been. Your V is angular velocity
*** provided that the along-track velocity is held
constant at a defined value of 1.0***…

``````            MT: Alex has provided lots of references to studies
``````

showing that along-track velocity varies with a
power-law relationship to the local curvature, when
there is absolutely no physical constraint that enforces
that relationship.

``````          RM: Yes, and in all those studies V is computed exactly
``````

as I am computing it. For example, here is V as defined by
Vivianni and Stucchi (1992) JEP, 18, 603-623.

``````          and here it is in Gribble and Ostry (1996) J
``````

Neurophysiology, 76, 2853-2860:

``````                        RM: The power law implies that speed
``````

increases as curvature increases. Here’s a
graph of V = R^(1/3):

[From Rick Marken (2016.07.20.1915)]

Re Another Behavioral Illusion6 (110 Bytes)

Re Another Behavioral Illusion7 (110 Bytes)

···

Martin Taylor (16.07.20.21.08)–

``````MT: I doubt anyone would quibble with these. Both of them have the right
``````

dimension, Distance/Time. The second one is the liner along-track
velocity that I find easiest to work with. I’m not sure of the
other, because of the “phi” subscripts. Why not use them in your
analyses instead of the erroneous one you also called V in your
“kindergarten math”?

RM: I do use them in my analysis. I compute V using the above formula and R using this formula:

RM: I think you don’t understand what my analysis was – it’s the same as the analysis used in all the papers on the power law – so I think I’ll have to write up an explanation.

RM: By the way, “kindergarten math” is the term Alex used to describe my finding that you could combine the equations for V and R to get the relationship:

V = |dXd2Y-d2XdY| 1/3 *R1/3

RM: I think it really took 8th or 9th grade math but I was pretty thrilled that I could do it (with a little help from my son the math teacher;-).

RM: I’ll get back to you with a description of my analysis asap.

Best regards

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

``````            MT: Alex has provided lots of references to studies
``````

showing that along-track velocity varies with a
power-law relationship to the local curvature, when
there is absolutely no physical constraint that enforces
that relationship.

``````          RM: Yes, and in all those studies V is computed exactly
``````

as I am computing it. For example, here is V as defined by
Vivianni and Stucchi (1992) JEP, 18, 603-623.

``````          and here it is in Gribble and Ostry (1996) J
``````

Neurophysiology, 76, 2853-2860:

Frankfurt starts his short interview like this:

âI was disturbed by the lack of respect and concern for the truth that I seem to observe in much of the speech and writing that was being producedâ?

Short wonderful interview here:

http://press.princeton.edu/titles/7929.html

Some more excerpts that exactly transcribe what is in my mind after such an exhausting exchange of emails:

Bullshit is a lack of concern for the difference between truth and falsity.

**The motivitation of the bullshiter is not to say things that are true or even to say things that are false; but he is serving some other purpose; and the question of whether what he says is true and false is irrevelant to his pursuit of that ambition. The bullshiter does not necessary need to be a liar. He may not think that what he says is false.Â **

**Bullshit is a more insidious threath to the value of truth, than lying. The liar wants you to say away from the truth, he wants to substitute for the truth, so the difference between truth and flasehood is very important for the liar. The bullshitter does not care at all.Â ****The liar has a constraint, he is limited to inserting a false for the true one.Â **The bullshitter, can say whatever he wants.

Why are we so tolerant of bullshit, whereas we are not tolerant to the liar?

**The increase in the amount of bullshit in contemporary life is because of the intensity of the marketing motive: selling products, candidates, people, ideas, books, programs, etc.Â **Once you settle that your object is to sell something, then your object is not to tell the truth about it but to make people believe what you want them to believe about it.

The tendency to bullshit is encouraged and promoted by the view that the responsible citizen (or scientist) must have an opinion about everything.

Highly educated people have the gifts that enable them to create bullshit. A lot of highly educated people acquire a kind of arrogance that encourages the production of bullshit.

Despite not being actively promoted, bullshit is protected.

()

If anyone wants to have a serious, careful and not showing-off discussion about the speed-curvature power law, from now on I am available atÂ agomezmarin@gmail.com

Have a hopefully non-bullshit day,

Alex

Re Another Behavioral Illusion8 (110 Bytes)

Re Another Behavioral Illusion9 (110 Bytes)

···

On Thu, Jul 21, 2016 at 4:15 AM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.07.20.1915)]

Martin Taylor Â (16.07.20.21.08)–

``````MT: I doubt anyone would quibble with these. Both of them have the right
``````

dimension, Distance/Time. The second one is the liner along-track
velocity that I find easiest to work with. I’m not sure of the
other, because of the “phi” subscripts. Why not use them in your
analyses instead of the erroneous one you also called V in your
“kindergarten math”?

Â RM: I do use them in my analysis. I compute V using the above formula and R using this formula:

RM: I think you don’t understand what my analysis was – it’s the same as the analysis used in all the papers on the power law – so I think I’ll have to write up an explanation.Â

RM: By the way, Â “kindergarten math” is the term Alex used to describe my finding that you could combine the equations for V and R to get the relationship:Â

V = Â |dXd2Y-d2XdY|Â 1/3Â *R1/3

RM: I think it really took 8th or 9th grade math but I was pretty thrilled that I could do it (with a little help from my son the math teacher;-).Â

RM: I’ll get back to you with a description of my analysis asap.Â

Best regards

Rick

Richard S. MarkenÂ

“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

``````            MT: Alex has provided lots of references to studies
``````

showing that along-track velocity varies with a
power-law relationship to the local curvature, when
there is absolutely no physical constraint that enforces
that relationship.

``````          RM: Yes, and in all those studies V is computed exactly
``````

as I am computing it. For example, here is V as defined by
Vivianni and Stucchi (1992) JEP, 18, 603-623.

``````          and here it is in Gribble and Ostry (1996) J
``````

Neurophysiology, 76, 2853-2860:

Is Rick talking about angular velocity while Alex is talking about the velocity of the tip of the pen?

···

On Thu, Jul 21, 2016 at 1:32 AM, Alex Gomez-Marin agomezmarin@gmail.com wrote:

Frankfurt starts his short interview like this:

âI was disturbed by the lack of respect and concern for the truth that I seem to observe in much of the speech and writing that was being producedâ?

Short wonderful interview here:

http://press.princeton.edu/titles/7929.html

Some more excerpts that exactly transcribe what is in my mind after such an exhausting exchange of emails:

Bullshit is a lack of concern for the difference between truth and falsity.

**The motivitation of the bullshiter is not to say things that are true or even to say things that are false; but he is serving some other purpose; and the question of whether what he says is true and false is irrevelant to his pursuit of that ambition. The bullshiter does not necessary need to be a liar. He may not think that what he says is false.Â **

**Bullshit is a more insidious threath to the value of truth, than lying. The liar wants you to say away from the truth, he wants to substitute for the truth, so the difference between truth and flasehood is very important for the liar. The bullshitter does not care at all.Â ****The liar has a constraint, he is limited to inserting a false for the true one.Â **The bullshitter, can say whatever he wants.

Why are we so tolerant of bullshit, whereas we are not tolerant to the liar?

**The increase in the amount of bullshit in contemporary life is because of the intensity of the marketing motive: selling products, candidates, people, ideas, books, programs, etc.Â **Once you settle that your object is to sell something, then your object is not to tell the truth about it but to make people believe what you want them to believe about it.

The tendency to bullshit is encouraged and promoted by the view that the responsible citizen (or scientist) must have an opinion about everything.

Highly educated people have the gifts that enable them to create bullshit. A lot of highly educated people acquire a kind of arrogance that encourages the production of bullshit.

Despite not being actively promoted, bullshit is protected.

()

If anyone wants to have a serious, careful and not showing-off discussion about the speed-curvature power law, from now on I am available atÂ agomezmarin@gmail.com

Have a hopefully non-bullshit day,

Alex

On Thu, Jul 21, 2016 at 4:15 AM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2016.07.20.1915)]

Martin Taylor Â (16.07.20.21.08)–

``````MT: I doubt anyone would quibble with these. Both of them have the right
``````

dimension, Distance/Time. The second one is the liner along-track
velocity that I find easiest to work with. I’m not sure of the
other, because of the “phi” subscripts. Why not use them in your
analyses instead of the erroneous one you also called V in your
“kindergarten math”?

Â RM: I do use them in my analysis. I compute V using the above formula and R using this formula:

RM: I think you don’t understand what my analysis was – it’s the same as the analysis used in all the papers on the power law – so I think I’ll have to write up an explanation.Â

RM: By the way, Â “kindergarten math” is the term Alex used to describe my finding that you could combine the equations for V and R to get the relationship:Â

V = Â |dXd2Y-d2XdY|Â 1/3Â *R1/3

RM: I think it really took 8th or 9th grade math but I was pretty thrilled that I could do it (with a little help from my son the math teacher;-).Â

RM: I’ll get back to you with a description of my analysis asap.Â

Best regards

Rick

Richard S. MarkenÂ

“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

``````            MT: Alex has provided lots of references to studies
``````

showing that along-track velocity varies with a
power-law relationship to the local curvature, when
there is absolutely no physical constraint that enforces
that relationship.

``````          RM: Yes, and in all those studies V is computed exactly
``````

as I am computing it. For example, here is V as defined by
Vivianni and Stucchi (1992) JEP, 18, 603-623.

``````          and here it is in Gribble and Ostry (1996) J
``````

Neurophysiology, 76, 2853-2860:

[Martin Taylor 2018.07.20.09.29]

``````No.
``````

Martin

···

On 2018/07/19 1:36 PM, PHILIP JERAIR
YERANOSIAN ( via csgnet Mailing List) wrote:

pyeranos@ucla.edu

``````    Is Rick talking about angular velocity while Alex
``````

is talking about the velocity of the tip of the pen?