Thanks Rick, yes, that's coming really close to how I was thinking about it. Putting aside whether it is closed loop for a moment, I think it is interesting that they choose length and rate of change of length as what we could call the controlled perceptual references and they don't have force as a sensed or controlled variable. This is what our joystick paradigm is doing at the moment and getting good results. Just like Bill's inverted pendulum model, I am predicting that controlling position at an upper level in a hierarchy to set the reference rate of change in position will lead to a more accurate model. This is because if the limb is already moving at a fast enough rate to the reference position but not got there yet, then no error will be detected and if it is too fast it will be slowed down, helping it not to overshoot its target reference position. I know the Latash people don't understand it this way, but the physiological data they have used can help us focus on what the controlled variables are likely to be and our PCT model is consistent with other findings and known physiological constraints. Given that PCT is such a broad theory I think we need domain-specific information to build the models. That said, most of the threshold model is not original and based on physiology that was understood by Bill prior to 1973... So it is a hard political game to play...
Sent from my iPhone
On 31 Dec 2013, at 20:31, Richard Marken <rsmarken@GMAIL.COM> wrote:
[From Rick Marken (2013.12.31.1230)]
Bruce Abbott (2013.12.30.1930 EST)--
RM: So the lambda model is what I thought it was in the first place; an
output generation mode, not a control model. It will fail miserably as soon
as you include disturbances to the apparently controlled variable.
BA: If you examine the larger portion of Figure 3 (showing a representation
of the skull and jaw at right, you will see an arrow labeled "muscle lengths
and rate of change in muscle lengths" running back to the muscles. These
changes alter the outputs of the muscle spindles, contributing to motor
neuron depolarization thresholds, so that a lengthening muscle generates a
feedback signal that opposes the lengthening. Any disturbance that began to
stretch the muscle beyond the "equilibrium point" established by the lambda
control inputs generates this opposing force.
RM: You're right. If I read the arrows as representing neural signal
paths and the boxes as comparators (points of synapse), then the
central command (lambda) is a reference signal and "length" and "rate
of change in length" are perceptual signals entering a comparator
function called "Length Dependent". The comparator is presumably what
carries out the calculation of the muscle activation signal per
equation 1 (or 3, which takes neural delays into account). Actually
the output of the comparator (A in equations 1 and 3) goes through a
series of subsequent functions (called "Time Dependent " and Velocity
Dependent") but eventually the output signal produces a force, which
has feedback effects on the "length" and "rate of change in length"
So if I'm reading this right this is precisely a PCT model of control
of a perception of a combination of muscle length and rate of change
in muscle length. This perception is being controlled relative to
lambda, the reference input. Their diagram does leave out some of the
nice functional labels that we would include in a PCT model,
particularly the "length" and "rate of change in length" perceptual
functions; it also leaves out disturbances to the controlled variable.
Disturbances are forces that affect the muscle length/rate of change
perception that are independent of the forces produced by the control
system. So those forces would enter from outside the "Force generating
mechanisms" box and join with the forces generated by the control
system at the circle containing the plus sign, adding to the forces
that have an affect on the controlled variable (muscle length/rate of
change). Maybe this is what Bill Powers saw as their model being
similar to PCT.
So I would have to agree that this model is not only similar to PCT;
it is exactly PCT. At least, that's true of the diagram. So it's not
an equilibrium model; it's a closed loop control model, just like PCT.
It's a muscle length control model, like the one Bill implemented in
the little man, except that it adds the derivative of muscle length
into the percpetion for some reason.
From my point of view I see nothing PCT has to learn from this model;
but I see a lot (in terms of clarity) that the people who developed
this model could learn from PCT.
I've just downloaded their more "detailed" presentation of the model
--Laboissiere , Ostry and Feldman ( in press ) -- because the math
that they show in the Appendix to the subject paper doesn't seem to
match the model shown in the diagram. The main problem is that the
math doesn't describe the closed loop that is implied by the diagram.
Because there is no feedback equation showing the dependence of
length/rate of change in length on the output of the system the
length/rate of change perception can be treated as though it were an
independent (rather than a controlled) variable. I suspect that this
is what is going on because the behavior that they show in figure 5
could be produced by a filtered version of the "command signal" and
the series of functions they show in the diagram in Figure 3 looks a
lot like a cascade of filters.
I've scanned the detailed model paper and I can't find any feedback
function stuff in their either.
I guess I'm at the point where I can't tell what the heck this paper
shows. The diagram suggests that they have a control model of muscle
length (with the addition of the derivative of muscle length into the
perception). Their math suggests that they have an output generation
model, where the output generated by the lambda command signal is
filtered by the processes that turn the difference between lambda and
length/rate of change in length into the forces that change length. If
it's a PCT model, then the main question would be whether they got the
controlled variable right; is it really length/rate of change in
length that is controlled or just length? This should be easily
testable. It it's an output generation model then it is completely
different than PCT and it should be easy to show that it fails where
So I suggest that, rather than arguing about whether these equilibrium
theory folks have anything to teach (or learn from) us, we should just
implement their model as a computer program. Once we agree that we've
got their model right we can go on to see what we can learn from it. A
computer model would (I think) go a long way to helping me see how
their model works and what it does.
I can tell you one thing their model does for me; it makes me long for
the clarity and simplicity of PCT.
Richard S. Marken PhD
The only thing that will redeem mankind is cooperation.
-- Bertrand Russell