Linear Feedback Analysis.

[Bjorn Simonsen (2005.10.04,11:55 EST)]

I
visited the state hospital last week for a NCV (Nerve Condition Velocity Test)
and a EMG (Electromyography). It is nothing serious, just a routine to get a
diagnosis in my knees.

I
had a converse with the neurologist and I showed him the CSG-web. The starting point for doing that was our
discussion about the Tendon Reflex. I mentioned the feedback signal and the
Tendon Receptor. I think I said “a sensory cell” in the Tendon and he arrested
me and said that there are no neurons in the Tendon. I know the Golgi Tendon
Receptors are clustered near the Tendon, but I thought it also were on the
Tendon.

BCP
tells us page 83 that the Golgi cells are clustered on and near the Tendon. Is
this still correct? Then I will arrest the neurologist.

This
was a long story before my next question. I had to re-read BCP chapter 7 (the
new release is in the post to Norway) and I really understood the Tendon Reflex
better. Look also to http://www.kcl.ac.uk/teares/gktvc/vc/lt/mspindle/spinmain.htm
and then Dynamic Bag
1 Fibre Response.

Don’t
look at http://www.dushkin.com/connectext/psy/ch02/spinal.mhtml
because this is wrong.

Back
to my question. At the pages 84 and 85 we read: 1.) e = r – p 2.) p = ke
3.) p = k
r/(1+k).

Page
87: ………. The act so as to maintain the perceptual signal at nearly the same
magnitude as the reference signal. (this is OK, -my words) This result remains
essentially true despite a variety of changes which without the feedback to the
subtractor neuron, would drastically alter the sensory signal.

I
think I understand the last sentence, but I need a verification/denial. I read
it as: If the sensory signal did not go to the subtractor neuron, and we did
not have a feedback, the sensory signal would not change.

My
last question is from the same page.

We
have a feedback system. The constant of proportionality is 10 and p = 10*r/11.

If
we imagine that the cell is more sensitive and the constant of proportionality
is 20, p = 20*r/21.

20r/21
is about 5% greater than 10
r/11.

But
if k = 20, then p = ke = 20e, and the muscle tension would get a doubled
magnitude.

I
understand that we use a greater constant of proportionality (20) because this
muscle is more sensitive.

Let
us think upon the two muscles at the same time. (10 and 20)- Let us go backward
around the loop. We go from the sensory nerve over the muscle to the error, e.

If k= 10, then (1.) e = r- p) —
1.) e = r- 10e. 11e = r e = r/11

If k= 20, then 1.) e = r – 20e — 21e = r ----- e = r/21

If
k changes from 10 to 20, there is a drop in the error signal from r/11 to r/21.

Then
the muscle contraction should not be so intense, but the muscle is more
sensitive (20). Therefore it will contract more than if k = 10.

And
now, my uncertainty. The two last sentences in the section.

Am
I correct if I say. Think upon k = 10. The reference signal and the perceptual
signal are almost in balance. That is e is near zero. If k becomes 20, p = 20* e. This is a rise in the perceptual signal. But if e was near zero
and p becomes greater, than e becomes negative. And that doesn’t’ work.

I
know I am wrong, but I don’t know where.

bjorn

···

[From Bjorn Simonsen
(2005.10.04.22:30 EST)]

From Rick Marken (2005.10.03.1120)

Page 87: ……. The act so as
to maintain the perceptual signal at nearly the

same magnitude as the
reference signal. (this is OK, -my words) This result

remains essentially true
despite a variety of changes which without the

feedback to the subtractor
neuron, would drastically alter the sensory signal.

I think I understand the
last sentence, but I need a verification/denial. I

read it as: If the sensory
signal did not go to the subtractor neuron, and we

did not have a feedback,
the sensory signal would not change.

I think it means that without
feedback the sensory signal would change

drastically.

Yes I see you think what you see. But
I need help to point out where it stops for me. Let me take the sentence “This
result remains ….” Word for word.

This result (The result that
feedback maintains the perceptual signal nearly the same magnitude as the
reference signal) will we see again and
again (true) despite we study muscles with different sensitivity. Once again.
The perceptual signal becomes every time close to the reference signal, if we
have negative feedback. If negative feedback didn’t exist, we would have (as
you said an open loop) , we would only have a reference signal where the error
is and the reference signal would stimulate the muscle. My question is: “Which
qualities would make the reference signal alter. There is no perceptual signal in
the neighbourhood.”

If k changes from 10 to
20, there is a drop in the error signal from r/11 to

r/21.

Then the muscle
contraction should not be so intense, but the muscle is more

sensitive (20). Therefore
it will contract more than if k = 10.

And now, my uncertainty. The
two last sentences in the section.

Am I correct if I say. Think
upon k = 10. The reference signal and the

perceptual signal are
almost in balance. That is e is near zero. If k becomes

20, p = 20* e.

That’s what p would be if there
were no feedback. With feedback, p =

(20/21)*r, making it even
closer to r than it was when k = 10.

Of course. Stupid me.

The rest is OK. Thank you.

Bjorn

···

[From Rick Marken (2005.10.05.0830)]

Bjorn Simonsen (2005.10.04.22:30 EST)--

Yes I see you think what you see. But I need help to point out where it stops
for me. Let me take the sentence �This result remains �.� Word for word.

This result (The result that feedback maintains the perceptual signal nearly
the same magnitude as the reference signal)� will we see again and again
(true) despite we study muscles with different sensitivity. Once again. The
perceptual signal becomes every time close to the reference signal, if we have
negative feedback. If negative feedback didn�t exist, we would have (as you
said an open loop) , we would only have a reference signal where the error is
and the reference signal would stimulate the muscle. My question is: �Which
qualities would make the reference signal alter. There is no perceptual signal
in the neighbourhood.�

I guess I don't quite understand what you are asking. If we are dealing with
an open-loop situation then, as you say, there is no perceptual signal going
into a comparator and the output is driven directly by the reference signal,
not the error signal (as you note, when you say that the reference signal
would stimulate the muscle). I don't know what qualities would make the
reference signal alter, other than whatever is driving the reference signal
in the model.

I guess the days are getting quickly shorter over there now. Hope you're
well stocked up on Aquavit.

Best regards

Rick

···

--
Richard S. Marken
MindReadings.com
Home: 310 474 0313
Cell: 310 729 1400

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[Martin Taylor 2005.10.05.18.44]

[From Rick Marken (2005.10.05.0830)]

Bjorn Simonsen (2005.10.04.22:30 EST)--

Yes I see you think what you see. But I need help to point out where it stops
for me. Let me take the sentence "This result remains �." Word for word.

This result (The result that feedback maintains the perceptual signal nearly
the same magnitude as the reference signal) will we see again and again
(true) despite we study muscles with different sensitivity. Once again. The
perceptual signal becomes every time close to the reference signal, if we
have
negative feedback. If negative feedback didn't exist, we would have (as you
said an open loop) , we would only have a reference signal where the error is
and the reference signal would stimulate the muscle. My question is: "Which
qualities would make the reference signal alter. There is no perceptual
signal in the neighbourhood."

I guess I don't quite understand what you are asking. If we are dealing with
an open-loop situation then, as you say, there is no perceptual signal going
into a comparator and the output is driven directly by the reference signal,

That's not necessarily right. Open-loop means that the loop is broken somewhere, not that the perceptual signal doesn't exist. It could mean that the action has no influence on the perception. The perception could, for example, be generated by imagination, or the action might be inappropriate to affect a perception based on sensory data. Probably it would be better to say that the fluctuations in the perceptual sigal aren't influenced by fluctuations in the error signal.

not the error signal (as you note, when you say that the reference signal
would stimulate the muscle). I don't know what qualities would make the
reference signal alter, other than whatever is driving the reference signal
in the model.

Well, that reference signal might be the output of a higher-level control system that includes among its inputs the perception that is presently uninfluenced by the output of the "open-loop" system. The higher-level perception might well be under control, while the lower-level (open-loop) one is simply the result of imagination.

I guess the days are getting quickly shorter over there now. Hope you're
well stocked up on Aquavit.

Why, don't they get shorter in La-La Land? Sure do, here (same latitude as Northern California).

Martin

[From Rick Marken (2005.10.05.1607)]

Martin Taylor 2005.10.05.18.44

Rick Marken (2005.10.05.0830)--

I guess I don't quite understand what you are asking. If we are dealing with
an open-loop situation then, as you say, there is no perceptual signal going
into a comparator and the output is driven directly by the reference signal,

That's not necessarily right. Open-loop means
that the loop is broken somewhere, not that the
perceptual signal doesn't exist. It could mean
that the action has no influence on the
perception. The perception could, for example, be
generated by imagination, or the action might be
inappropriate to affect a perception based on
sensory data. Probably it would be better to say
that the fluctuations in the perceptual sigal
aren't influenced by fluctuations in the error
signal.

Good point!

I guess the days are getting quickly shorter over there now. Hope you're
well stocked up on Aquavit.

Why, don't they get shorter in La-La Land? Sure
do, here (same latitude as Northern California).

They sure do get shorter here, too, but the rate of shortening is not as
precipitous (which is why, I presume, Aquavit was invented up there in the
far Northern latitudes).

Best

Rick

···

---
Richard S. Marken
MindReadings.com
Home: 310 474 0313
Cell: 310 729 1400

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[From
Bjorn Simonsen (2005.10.06.08:50 EST)]

From Rick
Marken (2005.10.05.0830)

I
guess I don’t quite understand what you are asking. If we are dealing with

an
open-loop situation then, as you say, there is no perceptual signal going

into
a comparator and the output is driven directly by the reference signal,

not
the error signal (as you note, when you say that the reference signal

would stimulate the muscle). I don’t know what qualities would make the

reference
signal alter, other than whatever is driving the reference signal

in
the model.

I am
sorry. I did read BCP as Old Nick read the Bible. It is neither the polar night
nor the Aquavit.

BCP says:
“The
act so as to maintain the perceptual signal at nearly the same magnitude as the
reference signal. This result remains essentially true despite a variety of
changes which without the feedback to the subtractor neuron, would drastically
alter the sensory signal”. I did read “….would drastically alter the reference signal”.

I now see that
without feedback, the perceptual signal would have the value near the
disturbance (k=1). That is drastically altered relative to a nearly zero value
(with feedback). I now also see the difference between PCT with negative
feedback and the behaviorist theory without feedback.

I
guess the days are getting quickly shorter over there now. Hope you’re

well
stocked up on Aquavit.

I will
tell you story about me. I don’t drink every day, but I appreciate a good drink
now and then. I have some rituals. One of them is as follows. My wife and I
have a cabin in the mountain. Our family goes there for Christmas, Eastern and weekends.
I am going there today and will return on Sunday evening. It is not far away
from the road, but we must go (skiing in the winter) some hundred yards. Beside
the entrance I have a birdcage. It is closed for birds, but it holds half a bottle
of Aquavit and two glasses. The first we do when we arrive the cabin, I open
the birdcage and pour into the two glasses. Then we sit down at the steps, say nothing, drink the Aquavit and enjoy the silence.
In this afternoon, when I arrive, I will think upon you.

I wish all
of you a nice weekend.

[From Rick Marken (2005.10.06.1630)]

Bjorn Simonsen (2005.10.06.08:50 EST)--

I now see that without feedback, the perceptual signal would have the
value near the disturbance (k=1). That is drastically altered relative
to a nearly zero value (with feedback). I now also see the difference
between PCT with negative feedback and the behaviorist theory without
feedback.

Excellent.

I will tell you story about me. I don�t drink every day, but I appreciate a
good drink now and then. I have some rituals. One of them is as follows. My
wife and I have a cabin in the mountain. Our family goes there for Christmas,
Eastern and weekends. I am going there today and will return on Sunday
evening. It is not far away from the road, but we must go (skiing in the
winter) some hundred yards. Beside the entrance I have a birdcage. It is
closed for birds, but it holds half a bottle of Aquavit and two glasses. The
first we do when we arrive the cabin, I open the birdcage and pour into the
two glasses. Then we sit down at the steps, _say nothing, drink the Aquavit
and enjoy the silence_. In this afternoon, when I arrive, I will think upon
you.

And you can be sure I'll be wishing I was there. Sounds lovely!

I wish all of you a nice weekend.

Same to you.

Best

Rick

···

--
Richard S. Marken
MindReadings.com
Home: 310 474 0313
Cell: 310 729 1400

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This email message is for the sole use of the intended recipient(s) and
may contain privileged information. Any unauthorized review, use,
disclosure or distribution is prohibited. If you are not the intended
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