PCT Lament and conflict

CSGnet Archive CSG2012
21

[From Bill Powers (2012.09.23.1005 MDT)]

Rick Marken (2012.09.23.0850) --

RM: I think the dead zone has nothing to do with it; it think we rarely see conflicts in everyday life for the same reason that we don't see conflicts in your CROWD program; organisms are rarely controlling the same perception of the same physical variables at the same time.

BP: Conflicts also arise when the action I use to control my CV disturbs the CV you are controlling, which need not be the same as mine, and your action used to control your CV disturbs mine. The case where the CVs are the same is just one special example.

Best,

Bill P.

22

[From Rick Marken (2012.09.23.0945)

Bill Powers (2012.09.23.1005 MDT)--

Rick Marken (2012.09.23.0850) --

RM: I think the dead zone has nothing to do with it; it think we rarely
see conflicts in everyday life for the same reason that we don't see
conflicts in your CROWD program; organisms are rarely controlling the same
perception of the same physical variables at the same time.

BP: Conflicts also arise when the action I use to control my CV disturbs the
CV you are controlling, which need not be the same as mine, and your action
used to control your CV disturbs mine. The case where the CVs are the same
is just one special example.

You will have to show me how that works because it doesn't seem to me
that this would typically lead to conflict. I have built many models
using multiple control systems where the output (action) of one system
disturbs the CV of another (and vice versa) and there is no conflict.
For example, in my object interception models there are two control
systems -- one controlling vertical optical velocity (CV1) by moving
forward and back (A1) and the other controlling horizontal
displacement (CV2) by moving left and right (A2). A1 also affects CV2
and A2 affects CV1. But there is no conflict and both systems control
their controlled variables perfectly. The same happens in the CROWD
program, right. The movements of each follower as it controls it's
position is a disturbance to the variables controlled by the others.
But there is no conflict. I can imagine situations were mutual
disturbance could result in conflict (I set up such a situation in my
conflict demo at
Cost of Conflict) but this is a
very special case.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

23

[Martin Taylor 2012.09.23.13.49]

[From Rick Marken (2012.09.23.0945)

Bill Powers (2012.09.23.1005 MDT)--

Rick Marken (2012.09.23.0850) --

RM: I think the dead zone has nothing to do with it; it think we rarely
see conflicts in everyday life for the same reason that we don't see
conflicts in your CROWD program; organisms are rarely controlling the same
perception of the same physical variables at the same time.

BP: Conflicts also arise when the action I use to control my CV disturbs the
CV you are controlling, which need not be the same as mine, and your action
used to control your CV disturbs mine. The case where the CVs are the same
is just one special example.

You will have to show me how that works because it doesn't seem to me
that this would typically lead to conflict. I have built many models
using multiple control systems where the output (action) of one system
disturbs the CV of another (and vice versa) and there is no conflict.
For example, in my object interception models there are two control
systems -- one controlling vertical optical velocity (CV1) by moving
forward and back (A1) and the other controlling horizontal
displacement (CV2) by moving left and right (A2). A1 also affects CV2
and A2 affects CV1. But there is no conflict and both systems control
their controlled variables perfectly. The same happens in the CROWD
program, right. The movements of each follower as it controls it's
position is a disturbance to the variables controlled by the others.
But there is no conflict. I can imagine situations were mutual
disturbance could result in conflict (I set up such a situation in my
conflict demo at
Cost of Conflict) but this is a
very special case.

As I said before, we have to be careful when using the word "conflict". It has too many related meanings, even within PCT.

All we need to say is that if, in a system of control systems, there exists a loop involving at least one controlled perception in which the loop gain equals or exceeds +1.0, that perception is out of control. If the actions of one controller disturb another, the other will act to counter the effect of the disturbance. If that countering action disturbs the first in such a way as to lead to action in the same direction as the original disturbance, the feedback loop has positive gain. Will there be escalation? Yes, if the loop gain through both controllers is greater than 1.0. Does this mean that the two are "in conflict"? Yes, if you use the language that way; No, if you say "conflict" means the inability of two systems to control because of limited degrees of freedom.

When you have a lot of control systems interacting through a common environment with more than enough degrees of freedom to spare, there are quite likely to be many feedback loops through multiple control systems. Some of those feedback loops may have positive gain. Dead zones lessen the likelihood that all these loops will actually involve non-zero gain at any one moment, thus lessening the probability that loops of gain greater than +1.0 will exist in the complex. Those that do will probably be reorganized away in a learning environment, but it is much harder to reorganize effectively if every action you make disturbs a multiplicity of other control systems and their actions disturb your controlled variable, whatever the sign and magnitude of the various feedback loops.

Not every situation in which control systems act so as to disturb each other's controlled perceptions leads to escalation, but with more tolerance, escalation into conflict in the everyday sense becomes less probable.

Martin

24

[From Rick Marken (2012.09.24.1640)]

Martin Taylor (2012.09.23.13.49)--

MT: As I said before, we have to be careful when using the word "conflict". It
has too many related meanings, even within PCT.

All we need to say is that if, in a system of control systems, there exists
a loop involving at least one controlled perception in which the loop gain
equals or exceeds +1.0, that perception is out of control.

RM: But that is not necessarily a result of conflict. For example, in
my polarity reversal demo
(Levels of Control) the loop gain
goes positive when the relationship between the direction of mouse
movement and cursor movement is suddenly reversed. There is a sudden
loss of control but it is not a result of conflict. I think a conflict
exists when the efforts of one control system to bring a controlled
variable to a reference are _actively_ resisted by the efforts of
another control system. You know, like in a tug of war; when one team
increases its efforts to pull the flag to it's side the other team
increases its efforts to prevent that from happening -- and it does
this in order to get the flag to their side.

MT: If the actions of
one controller disturb another, the other will act to counter the effect of
the disturbance. If that countering action disturbs the first in such a way
as to lead to action in the same direction as the original disturbance, the
feedback loop has positive gain.

RM: I think a better way to say this is: if the disturbance increases
or decreases in proportion to increases or decreases in the countering
action then there is probably a conflict. For example, if, as you
increase your efforts to open a sticky door you feel proportional
increases in the resistance to those efforts, then it's likely that
there is someone on the other side trying to keep the door closed.
If, on the other hand, your increased efforts to open the door
eventually lead to the door opening, then your efforts to control for
opening the door were just good old disturbance resistance.

MT: When you have a lot of control systems interacting through a common
environment with more than enough degrees of freedom to spare, there are
quite likely to be many feedback loops through multiple control systems.
Some of those feedback loops may have positive gain. Dead zones lessen the
likelihood that all these loops will actually involve non-zero gain at any
one moment, thus lessening the probability that loops of gain greater than
+1.0 will exist in the complex.

RM: So you are saying that dead zones lessen the probability of
conflict? I'll believe it when I see it demonstrated in a working
model. Right now I still think dead zones have nothing to do with
conflict.

MT: Not every situation in which control systems act so as to disturb each
other's controlled perceptions leads to escalation, but with more tolerance,
escalation into conflict in the everyday sense becomes less probable.

RM: I agree, when "tolerance" is defined as "lowering system gain". I
have run conflict models where the conflict is reduced (in the sense
of an asymptote in the outputs of the systems involved in the
conflict) through reduction of the gains of the systems involved. I
have never seen a reduction in conflict due to a dead zone
computation.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

25

[Martin Taylor 2012.09.25.11.03]

[From Rick Marken (2012.09.24.1640)]

Martin Taylor (2012.09.23.13.49)--
MT: As I said before, we have to be careful when using the word "conflict". It
has too many related meanings, even within PCT.

All we need to say is that if, in a system of control systems, there exists
a loop involving at least one controlled perception in which the loop gain
equals or exceeds +1.0, that perception is out of control.

RM: But that is not necessarily a result of conflict.

Yes. See the first paragraph of what you quoted, and then the second.

MT: If the actions of
one controller disturb another, the other will act to counter the effect of
the disturbance. If that countering action disturbs the first in such a way
as to lead to action in the same direction as the original disturbance, the
feedback loop has positive gain.
RM: I think a better way to say this is: if the disturbance increases
or decreases in proportion to increases or decreases in the countering
action then there is probably a conflict.

There may indeed be a conflict, but we can't say that there certainly is. All we can say is that there is a feedback loop with positive gain.

MT: When you have a lot of control systems interacting through a common
environment with more than enough degrees of freedom to spare, there are
quite likely to be many feedback loops through multiple control systems.
Some of those feedback loops may have positive gain. Dead zones lessen the
likelihood that all these loops will actually involve non-zero gain at any
one moment, thus lessening the probability that loops of gain greater than
+1.0 will exist in the complex.

RM: So you are saying that dead zones lessen the probability of
conflict? I'll believe it when I see it demonstrated in a working
model. Right now I still think dead zones have nothing to do with
conflict.

When you say "have nothing to do with" do you mean that the same degree of output escalation would happen whether or not there was a dead zone in the feedback path dynamics? Or do you mean that if there is an escalating conflict, then none of the control systems involved are at that moment in a dead zone? Or if neither of these, then what DO you mean?

It is obvious that if the perception of any control system that forms part of a feedback loop is in a dead zone, the feedback loop gain is zero. You can't get escalation from a feedback loop with zero gain.

MT: Not every situation in which control systems act so as to disturb each
other's controlled perceptions leads to escalation, but with more tolerance,
escalation into conflict in the everyday sense becomes less probable.

RM: I agree, when "tolerance" is defined as "lowering system gain".

Or if the gain is zero, as it is when the perception signal value is in a dead zone.

   I
have run conflict models where the conflict is reduced (in the sense
of an asymptote in the outputs of the systems involved in the
conflict) through reduction of the gains of the systems involved. I
have never seen a reduction in conflict due to a dead zone
computation.

How many different dead-zone configurations and parameter variations have you tried?

In your personal life, have you never said to yourself "I would prefer it if that fellow was not doing what he is doing, but it's not worth bothering about, so I will let it pass"? Do you try to correct every little grammar mistake you notice when conversing with someone? Do you never think: "She's opening the window though I would kind of like it better closed, but she wants it open, so let it be open?"

What would be likely to happen in that kind of circumstance if you acted to bring your perception to its reference value (the fellow stopping what he was doing, the grammar mistake corrected, the window closed)? Do you not think that at least sometimes you might get into an escalating conflict that you avoided by incorporating a dead zone?

Martin

26

[From Rick Marken (2012.09.25.0930)]

Martin Taylor (2012.09.25.11.03)--

RM: So you are saying that dead zones lessen the probability of
conflict? I'll believe it when I see it demonstrated in a working
model. Right now I still think dead zones have nothing to do with
conflict.

MT: When you say "have nothing to do with" do you mean that the same degree of
output escalation would happen whether or not there was a dead zone in the
feedback path dynamics? Or do you mean that if there is an escalating
conflict, then none of the control systems involved are at that moment in a
dead zone? Or if neither of these, then what DO you mean?

RM: What I mean is that the dead zone seems to me to be a theoretical
concept in search of a phenomenon to explain. What, in other words, is
it about observed conflicts that is explained by the dead zone? For
example, you can participate in a conflict by doing my demo at
Cost of Conflict. The reason for
the conflict is explained in the "What it's about" section of the
write up. The data is the x, y movements of the mouse. I have found
that these data are accounted for pretty well by two simple control
systems, one of which is controlling the target in the x dimension and
the other of which is controlling it in the y dimension. It is
possible that adding a dead zone will improve the fit of the model to
the data. If it does then I will see the relevance of the dead zone to
conflict behavior. That's all; I just like to see how theories relate
to what I observe.

MT: In your personal life, have you never said to yourself "I would prefer it if
that fellow was not doing what he is doing, but it's not worth bothering
about, so I will let it pass"?

RM: Sure. But I don't see how that would be explained by a "dead
zone". A dead zone means zero error in that zone. So how would I even
know that what the fellow was doing was something I didn't like
(something that creates an error)? It's not creating any error if
there is a dead zone. I think this kind of experience is better
explained as "lowering the gain"; the system controlling for zero
amount of what the fellow is doing is experiencing error that would
lead to action but another system sees that such action might have
unwanted consequences (escalating conflict) and turns down the gain on
the system experiencing the error; you still experience the error (I
don't like what that fellow is doing") but I do nothing about it
because the gain of the system has been turn down to zero, say.

MT: What would be likely to happen in that kind of circumstance if you acted to
bring your perception to its reference value (the fellow stopping what he
was doing, the grammar mistake corrected, the window closed)? Do you not
think that at least sometimes you might get into an escalating conflict that
you avoided by incorporating a dead zone?

RM: My sense is that I avoid escalating conflict because I have
systems that lower the gain on the systems that would act to escalate
the conflict. I don't think a dead zone accounts for this experience
for the reasons I said above -- I still experience the error (which
would not exist if there were a dead zone) I just don't do anything to
reduce the error (gain goes to zero).

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

27

[Martin Taylor 2012.09.25.15.26]

[From Rick Marken (2012.09.25.0930)]

Martin Taylor (2012.09.25.11.03)--

RM: So you are saying that dead zones lessen the probability of
conflict? I'll believe it when I see it demonstrated in a working
model. Right now I still think dead zones have nothing to do with
conflict.

MT: When you say "have nothing to do with" do you mean that the same degree of
output escalation would happen whether or not there was a dead zone in the
feedback path dynamics? Or do you mean that if there is an escalating
conflict, then none of the control systems involved are at that moment in a
dead zone? Or if neither of these, then what DO you mean?

RM: What I mean is that the dead zone seems to me to be a theoretical
concept in search of a phenomenon to explain. What, in other words, is
it about observed conflicts that is explained by the dead zone?

Their absence, mainly.

MT: In your personal life, have you never said to yourself "I would prefer it if
that fellow was not doing what he is doing, but it's not worth bothering
about, so I will let it pass"?

RM: Sure. But I don't see how that would be explained by a "dead
zone". A dead zone means zero error in that zone. So how would I even
know that what the fellow was doing was something I didn't like
(something that creates an error)? It's not creating any error if
there is a dead zone.

Consciously, we certainly do perceive (r-p). But in the standard PCT hierarchy there is no perceptual signal that corresponds to the value of an error signal, whether the signal be (r-p) or the output of a comparator. To perceive error, you have to have a perceptual input function that takes as at least one of its inputs the error in some other control system. The reorganization system is supposed to do this, but the simple HPCT control hierarchy does not. Your comment applies equally to the zero-gain control as to the dead-zone. To perceive an error signal or to perceive (r-p) requires an amendment to the simple hierarchy. (So does a control that would allow you to set the gain of a control system to zero or to some high value).

  I think this kind of experience is better
explained as "lowering the gain"; the system controlling for zero
amount of what the fellow is doing is experiencing error that would
lead to action but another system sees that such action might have
unwanted consequences (escalating conflict) and turns down the gain on
the system experiencing the error; you still experience the error (I
don't like what that fellow is doing") but I do nothing about it
because the gain of the system has been turn down to zero, say.

Yep, that would work. Do you have experimental evidence that this is what happens? Subjectively, I usually act to correct an error when (r-p) is sufficiently annoying to make it worthwhile dealing with that problem rather than controlling something else. If your gain is set to zero, you wouldn't behave that way, but with a dead-zone functin you would.

Personally, I think, without experimental evidence, that both effects are likely. Setting the gain to zero is what would be accomplished by paying no attention to the perception at issue. Using a dead zone comparator would account for the fact that you can tolerate a certain amount of background noise when you are trying to relax, but if the noise gets loud enough you get up and see if you can stop it.

MT: What would be likely to happen in that kind of circumstance if you acted to
bring your perception to its reference value (the fellow stopping what he
was doing, the grammar mistake corrected, the window closed)? Do you not
think that at least sometimes you might get into an escalating conflict that
you avoided by incorporating a dead zone?

RM: My sense is that I avoid escalating conflict because I have
systems that lower the gain on the systems that would act to escalate
the conflict. I don't think a dead zone accounts for this experience
for the reasons I said above -- I still experience the error (which
would not exist if there were a dead zone) I just don't do anything to
reduce the error (gain goes to zero).

And I believe you do as you say, but also don't treat small values of (r-p) as error at all. The point about perceiving the error does not distinguish these two effects, because HPCT has to be modified in almost the same way if the error signal is to be perceived as it must if (r-p) is to be perceived.

Martin

28

[From Rick Marken (2012.09.26.1810)]

Martin Taylor (2012.09.25.15.26)--

RM: What I mean is that the dead zone seems to me to be a theoretical
concept in search of a phenomenon to explain. What, in other words, is
it about observed conflicts that is explained by the dead zone?

MT: Their absence, mainly.

RM: This would require a rather wide dead zone, wouldn't it? If I want
X=10 and you want X=20 then there will be no conflict only if our
respective dead zones have a width that encompasses all values of X
between 10 and 20, in which case the disturbances to X which push X
towards 10 or 20 will result in no error on the part of you or me and
there will be no push back from either of us and, thus, no error; X
can vary around between 10 and 20 all it wants and there will be no
conflict -- or control. I think people generally control much better
than a fixed dead zone approach to conflict avoidance would imply. But
if the dead zone could be varied in the same way as I assume gain can
be varied -- the dead zone being made wider when a conflict is sensed
-- then it can probably work for conflict avoidance just as well as
gain variation.

RM: I think this kind of experience [of conflict reduction] is better
explained as "lowering the gain" zero, say.

MT: Yep, that would work. Do you have experimental evidence that this is what
happens?

RM: Sort of. In my conflict demo I am apparently able to adjust the
gain of my x and y dimension control systems so that the gains are
approximately equal and not too high so that the systems are in
detente throughout the experiment. The smooth output curves that I get
suggests that there is no dead zone involved; it's just two control
systems of equal strength (gain) pushing against each other with equal
force and not continuously escalating (gain < 1 but >0).

MT: Personally, I think, without experimental evidence, that both effects are
likely.

RM: I completely agree. Let's leave it at that and hope someone does
do the experiment to test this.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

29

[From Bill Powers (2012.09.28.0945 MDT)]

Rick Marken (2012.09.26.1810) --

RM: This would require a rather wide dead zone, wouldn't it? If I want
X=10 and you want X=20 then there will be no conflict only if our
respective dead zones have a width that encompasses all values of X
between 10 and 20, in which case the disturbances to X which push X
towards 10 or 20 will result in no error on the part of you or me and
there will be no push back from either of us and, thus, no error; X
can vary around between 10 and 20 all it wants and there will be no
conflict -- or control.

BP: Excellent point. In that case the mutual disturbances would be far larger than any practical dead zone, so the dead zone would make almost no difference.

Where the dead zone is used in most control applications, it is meant to prevent the control system's reacting to very small errors, particularly system noise. In a high-gain, highly-accurate single control system, the accuracy is achieved by high amplification of the error signal so that even small errors will result in strong opposing actions. This works well unless there is some noise level in the system that makes the comparator think there is always some kind of disturbance acting. Just add some noise to the output of the comparator in a model and you'll see what happens. The output will continuously fluctuate, keeping the error signal small but causing large actual errors and wasting a lot of output effort.

The case of conflict in which a dead zone is appropriate for independent actors is one in which the systems are actually intending to cooperate in achieving very precise control of the same CV relative to the same reference level. If they start reacting to every tiny error, or if the perceptions and reference levels are just a small amount different, the strong reactions against the random errors will become large disturbances to the other person, who will resist, and so on.

We see this all the time on CSGnet. We are all supposed to be proponents of PCT, right? But what happens if you get a little careless and say that a control system "responds" to a disturbance? Someone who is trying to be strictly correct all the time will instantly pounce on the technical error, and will be accused in turn of acting like a policeman, and so on. Big argument over little disagreements. That's what happens when you have only a tiny dead zone. Lack of a dead zone ends up with people who are trying to cooperate going into conflict with each other instead. It is not easy to cooperate with others, and the more important the goal the harder it is.

As you say, lowering the gain will make the squabbling less harmful -- but it will also make the cooperative control sloppy and inaccurate. For a given size of error, the action will have to be sluggish and weak, to avoid instability.

If you want to be able to generate large actions to oppose large disturbances, the output function had to have high gain, but without a dead zone that will generate endless output fluctutations when there are small random errors.
A dead zone will take care of disturbances that are actually irrelevant and impossible to resist, like those caused by fast random disturbances or internally-generated system noise.

In your proposed case, where the controlled variables are very different or the reference levels very far apart, the dead zone will not make any practical difference. The main difference will be seen near the condition of zero error in both systems. There is a tradeoff between how much the systems can cooperate without conflict, and how much control can be improved when one controller tries to "help" another one control something.

Best,

Bill P.

···

  I think people generally control much better
than a fixed dead zone approach to conflict avoidance would imply. But
if the dead zone could be varied in the same way as I assume gain can
be varied -- the dead zone being made wider when a conflict is sensed
-- then it can probably work for conflict avoidance just as well as
gain variation.

>> RM: I think this kind of experience [of conflict reduction] is better
>> explained as "lowering the gain" zero, say.
>
> MT: Yep, that would work. Do you have experimental evidence that this is what
> happens?

RM: Sort of. In my conflict demo I am apparently able to adjust the
gain of my x and y dimension control systems so that the gains are
approximately equal and not too high so that the systems are in
detente throughout the experiment. The smooth output curves that I get
suggests that there is no dead zone involved; it's just two control
systems of equal strength (gain) pushing against each other with equal
force and not continuously escalating (gain < 1 but >0).

> MT: Personally, I think, without experimental evidence, that both effects are
> likely.

RM: I completely agree. Let's leave it at that and hope someone does
do the experiment to test this.

Best

Rick

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

30

[From Rick Marken (2012.09.28.1100)]

Bill Powers (2012.09.28.0945 MDT)--

Where the dead zone is used in most control applications, it is meant to
prevent the control system's reacting to very small errors, particularly
system noise. In a high-gain, highly-accurate single control system, the
accuracy is achieved by high amplification of the error signal so that even
small errors will result in strong opposing actions. This works well unless
there is some noise level in the system that makes the comparator think
there is always some kind of disturbance acting. Just add some noise to the
output of the comparator in a model and you'll see what happens. The output
will continuously fluctuate, keeping the error signal small but causing
large actual errors and wasting a lot of output effort.

I have added noise to my simulations and found that it had more effect
on the input than on the output, but really not too much effect on
either.. As you demonstrated to me (or, actually, had me demonstrate
to myself) an integral control system acts like a linear low-pass
filter, smoothing the output (and the input -- controlled variable)
compared to what would result if the same noise were added to an
equivalent open loop (and unfiltered) system. I can see that a narrow
dead zone might be necessary for a high gain proportional control
system but it seems like it wouldn't improve things much for an
integral control system. I guess I can test this using simulation but
just for the sake of simplicity it seems like the filtering
characteristics of closed loop (integral) control would have made it
unnecessary for the neurons to have developed a dead zone
characteristic. Is there any evidence that neurons do have a dead zone
(in terms of firing rate)?

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

31

[Martin Taylor 2012.09.28.15.27]

[From Rick Marken (2012.09.26.1810)]

Martin Taylor (2012.09.25.15.26)--

RM: What I mean is that the dead zone seems to me to be a theoretical
concept in search of a phenomenon to explain. What, in other words, is
it about observed conflicts that is explained by the dead zone?

MT: Their absence, mainly.

RM: This would require a rather wide dead zone, wouldn't it?

Depends on the circumstances.

  If I want
  X=10 and you want X=20 then there will be no conflict only if our
respective dead zones have a width that encompasses all values of X
between 10 and 20,

One of us, not both. If you really, really want it to be 20 +- .01, and I can live with 10<X<30, there will be no conflict. You will maintain X against disturbances very near 20, and I will do nothing about it. If a sudden disturbance pushes X momentarily up to 40, we both will combine to bring it down again, but I will stop helping you when X gets to 30. It's then up to you to get X back to 20.

This seems to me to be just how things work in the real world.

... I think people generally control much better
than a fixed dead zone approach to conflict avoidance would imply. But
if the dead zone could be varied in the same way as I assume gain can
be varied -- the dead zone being made wider when a conflict is sensed
-- then it can probably work for conflict avoidance just as well as
gain variation.

I'm not clear why you added the word "fixed" in front of "dead zone". If I ever implied that any dead zone was fixed, I must have been in a delirious fit. The second part of this quote is about right, though I do not include a "conflict sensor" as part of the control loop. That perception occurs elsewhere, if it occurs at all (as is also true of the perception of r-p and of the error signal).

What I can tolerate at any moment may well depend on what higher-level perceptions this one contributes to, and whether I can control those higher-level perceptions by other means without engendering escalating conflict. Without sensing conflict, if I suddenly decided that X=20 was actually causing me a problem in control of something else, I probably would narrow my dead zone for X control to a region over which I would then find tolerable. We would get into an escalating conflict which we would eventually settle one way or another.

In respect of the use of a dead zone for reducing the effect of noise, the effective zone can be very small. As I mentioned a few days ago, I remember getting a best fit with a sub-pixel dead zone in a pursuit tracking task with a smoothly varying disturbance. In respect of varying the dead zone, if the whole positive and negative control curve is obtained from neurons that cannot have a negative firing rate, neurons that fire for a positive r-p must balance those that fire with a negative r-p. Shifting their biases shifts the dead zone or widens and narrows it.

Martin

32

[From Bill Powers (2012.09.29.0830 MDT)]

Rick Marken (2012.09.28.1100) --

I have added noise to my simulations and found that it had more effect
on the input than on the output, but really not too much effect on
either.. As you demonstrated to me (or, actually, had me demonstrate
to myself) an integral control system acts like a linear low-pass
filter, smoothing the output (and the input -- controlled variable)
compared to what would result if the same noise were added to an
equivalent open loop (and unfiltered) system.

BP: Most human control systems have leaky integrator outputs; the leak reduces the high-pass filtering. Also, if you add low-frequency noise (say 1 Hz bandwidth) to the comparator or input function, so it is in the same range as the bandwidth of good control, you will see even more effect on the output. The latter would be like driving in a gusty crosswind or steering a small motorboat through choppy seas, or an airplane through turbulent air. My first student takeoff in an airplane was through extremely gusty air and I was working very hard to keep the wings level (you've heard this story, I think). My instructor Ernie finally asked, "Bill, what are you doing?". I explained that the turbulence was pretty bad. "No, it isn't," he said. "Relax." I relaxed and the airplane steadied right down. Was that too much gain or not enough dead zone? Or as Kent McClelland has suggested, a nonlinear blend of the two?

RM: I can see that a narrow dead zone might be necessary for a high gain proportional control system but it seems like it wouldn't improve things much for an
integral control system.

BP: You're right in general, except for the effects of low-frequency disturbances.

RM: I guess I can test this using simulation but
just for the sake of simplicity it seems like the filtering
characteristics of closed loop (integral) control would have made it
unnecessary for the neurons to have developed a dead zone
characteristic.

BP: That all depends on the bandwidth of noise or disturbances.

RM: Is there any evidence that neurons do have a dead zone
(in terms of firing rate)?

BP: Yes. All neurons do. A single excitatory impulse entering a synapse raises the membrane potential by a small amount partway toward the threshold for producing an action potential, but in a few milliseconds it has decayed back toward the resting potential being maintained by the ion pumps in the membrane. At a very low rate of incoming impulses, that is all that happens for each incoming impulse and the neuron never fires. As the rate of incoming impulses increases, the decay back to resting potential becomes incomplete and the peak changes in potential start accumulating and becoming larger, until finally the peaks just cross the threshold potential for generating an output impulse or action potential from the neuron. The neuron then begins firing at a low rate which increases as the input rate increases still further. Each time the neuron fires, the membrane potential is reset to a low value (high negative value) and has to build up again over some number of input impulses (if they occur fast enough) until it reaches the action potential threshold again. That is why the output rate of firing is zero until the incoming rate rises above the dead zone.

Some "electrical" neurons have a resting potential that is not far below the threshold for firing of the neuron. In these, a single input impulse can produce an output impulse. These neurons do not have a dead zone. They are not common.

Some neurotransmitters, like dopamine, affect the sensitivity of synapses to other neurotransmitters. This effectively changes the gain at the synapse. Henry Yin has been studying this effect for some time, in connection with the basal ganglia and their role in Parkinson's disease. Chloride ions released by other neurotransmitters subtract fron the postsynaptic potential (or drive it more negative), increasing the size of the dead zone for all excitatory inputs. So both gain and dead zone are adjustable by neural signals just about everywhere in the brain.

An adjustable dead zone is a result of the inhibitory effect of some inputs. Inhibitory signals make the membrane potential even more negative than the resting potential. When the neuron is firing at some rate, the inhibitory input impulses just subtract from that rate. But since rates can't be less than zero, enough inhibition creates a dead zone that has to be overcome by excitation before further increases in excitation can cause any output impulses at all.

Best,

Bill P.

33

[From Rick Marken (2012.09.29.1645)]

Bill Powers (2012.09.29.0830 MDT)

RM: I can see that a narrow dead zone might be necessary for a high gain
proportional control system but it seems like it wouldn't improve things
much for an
integral control system.

BP: You're right in general, except for the effects of low-frequency
disturbances.

I set up a simulation finally to see what's going on. I tested the
effect of dead zone width and gain on the variability of the
controlled variable when the frequency of a sine wave disturbance is
varied. The preliminary results seem to be this:

Increasing gain lowers the variability of the controlled variable
(increases control) about the same for both high and low frequency
disturbances -- slightly more improvement for the low frequency
disturbance. Increasing the width of the dead zone increases the
variability of the controlled variable (reduces control) and this
increase is much greater for low than for high frequency disturbances.

I guess this is what you want from a dead zone -- a lowered ability to
control with increasing width of the dead zone. By I'm kind of
surprised that this decreased ability to control (which would lessen
conflict) is greatest when disturbances are low frequency.

RM: I guess I can test this using simulation but
just for the sake of simplicity it seems like the filtering
characteristics of closed loop (integral) control would have made it
unnecessary for the neurons to have developed a dead zone
characteristic.

BP: That all depends on the bandwidth of noise or disturbances.

Indeed, though the effect of dead zone width as function of bandwidth
(frequency) is not what I expected. The dead zone seems to insert high
frequency noise rather than eliminate it.

Best

Rick

···

RM: Is there any evidence that neurons do have a dead zone

(in terms of firing rate)?

BP: Yes. All neurons do. A single excitatory impulse entering a synapse
raises the membrane potential by a small amount partway toward the threshold
for producing an action potential, but in a few milliseconds it has decayed
back toward the resting potential being maintained by the ion pumps in the
membrane. At a very low rate of incoming impulses, that is all that happens
for each incoming impulse and the neuron never fires. As the rate of
incoming impulses increases, the decay back to resting potential becomes
incomplete and the peak changes in potential start accumulating and becoming
larger, until finally the peaks just cross the threshold potential for
generating an output impulse or action potential from the neuron. The neuron
then begins firing at a low rate which increases as the input rate increases
still further. Each time the neuron fires, the membrane potential is reset
to a low value (high negative value) and has to build up again over some
number of input impulses (if they occur fast enough) until it reaches the
action potential threshold again. That is why the output rate of firing is
zero until the incoming rate rises above the dead zone.

Some "electrical" neurons have a resting potential that is not far below the
threshold for firing of the neuron. In these, a single input impulse can
produce an output impulse. These neurons do not have a dead zone. They are
not common.

Some neurotransmitters, like dopamine, affect the sensitivity of synapses to
other neurotransmitters. This effectively changes the gain at the synapse.
Henry Yin has been studying this effect for some time, in connection with
the basal ganglia and their role in Parkinson's disease. Chloride ions
released by other neurotransmitters subtract fron the postsynaptic potential
(or drive it more negative), increasing the size of the dead zone for all
excitatory inputs. So both gain and dead zone are adjustable by neural
signals just about everywhere in the brain.

An adjustable dead zone is a result of the inhibitory effect of some inputs.
Inhibitory signals make the membrane potential even more negative than the
resting potential. When the neuron is firing at some rate, the inhibitory
input impulses just subtract from that rate. But since rates can't be less
than zero, enough inhibition creates a dead zone that has to be overcome by
excitation before further increases in excitation can cause any output
impulses at all.

Best,

Bill P.

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

34

[From Bill Powers (2012.10.01.0822 MDT)]

Rick Marken (2012.09.29.1645) –

RM: I guess this is what you
want from a dead zone – a lowered ability to

control with increasing width of the dead zone. By I’m kind of

surprised that this decreased ability to control (which would lessen

conflict) is greatest when disturbances are low
frequency.

BP:

We’re approaching this subject bass ackward. The first thing to do is set
up a tracking task in which there are fast disturbances which you can
handle two ways: (1) try very hard to correct every little error caused
by the fast disturbances, and (2) just correct the average disturbance at
a more relaxed level of effort. I think you will find that the second way
is what we normally do. You will probably say that the latter shows lower
gain, but I claim that normally you don’t even try to correct the fastest
errors which are clearly too fast to oppose. Yet you keep the average
error as small as ever, showing that the steady-state gain is as high as
ever. I think this is evidence for a dead zone.

···

=======================================================

New subject, and you had better keep Linda with you while you explore it
because you are going to fall in love.

Here is an except from a post I sent to Alice this morning:
Google on “Stephanie Trick: Rising Star of Jazz (Don
Wolff)”. This will get you an interview well worth watching, and on
the right side a lot of links to other performances.
The “Stephanie Trick at Aborsjazz” link has the “I
ain’t got nobody” that I raved about. All the others are worth at
least a listen. Also select or Google “Stephanie Trick on State of
the Arts” to get three good ones, the first being her version of St.
Louis Blues that includes a part patterned after Earl Father Hines boogie
on the SLB that I used to play. She learned most of her boogie by
listening to records the same way I did – no transcriptions available.
The Death Ray Boogie by Pete Johnson, next, is also a fast one I learned,
and it’s very interesting to hear the differences in how she and I
remember it. I can hear the parts where she put in her own riffs. I may
send her some short clips of my version, just to back up her memory with
mine.
This girl makes me tear up with joy.And this is an excerpt from a post to Alice yesterday:
Watching and listening to Stephanie Trick playing makes me remember
my high-school playing as the fumbling of a person with brain damage. I
wouldn’t dare touch a key where she might hear it. Her classical training
shows all over the place, from the fingering to the knowledge of chord
progressions to the way she handles dynamics. Total mastery. And I would
hate to get any sensitive body part between those steel fingers and the
keyboard. She has to be incredibly strong to maintain that fast stride
and right hand for three or four minutes at a time, and sometimes much
longer.
But the best part of every piece she does alone is when it ends and
she turns to the audience with that delighted sharing grin. “Wasn’t
that just GREAT?” she is saying, and she means the music, not
herself. Every now and then you can see that same expression starting to
form while she’s playing something and it’s sounding just perfect. She’s
an audience at the same time she’s a performer. I remember feeling
exactly that way, for a lot less reason.

[earlier comment by me to Alice]
Get this one, “I ain’t got nobody”. Particularly catch the
incredibly coy little ending of the descending glissando at 3:25.
[This is in the Trephanie Trick at Aborsjazz link]In some of the performances she is 23 years old; she was 25 in 2012.
A pretty young girl with a wonderful smile, you think. A commentator on
one YouTube page said that this pretty young girl can hit those keys like
a 300-pound black bear. Others said things like “This is the best
piano-playing of any kind I have EVER heard.”

Enjoy.

Bill P.

35

[From Rick Marken (2012.10.02.1400)]

Bill Powers (2012.10.01.0822 MDT) --

RM: I guess this is what you want from a dead zone -- a lowered ability to
control with increasing width of the dead zone...

BP:
We're approaching this subject bass ackward. The first thing to do is set up
a tracking task in which there are fast disturbances which you can handle
two ways: (1) try very hard to correct every little error caused by the fast
disturbances, and (2) just correct the average disturbance at a more relaxed
level of effort. I think you will find that the second way is what we
normally do. You will probably say that the latter shows lower gain, but I
claim that normally you don't even try to correct the fastest errors which
are clearly too fast to oppose. Yet you keep the average error as small as
ever, showing that the steady-state gain is as high as ever. I think this is
evidence for a dead zone.

RM: Well,in my continuing efforts to do things bass ackwards I took
some tracking data using fast disturbances and analyzed it using the
plain vanilla control model with adjustable gain and the same control
model with the addition of a dead zone of adjustable width. (The data
comes from the "Difficult" condition described in my paper WHEN
CAUSALITY DOES NOT IMPLY CORRELATION: MORE SPADEWORK AT THE
FOUNDATIONS OF SCIENTIFIC PSYCHOLOGY). In a typical run, the plain
vanilla model accounts for 95% of the variance in mouse movements and
93% of the variance in cursor movements. The RMS deviation of model
from actual mouse movements was 44 pixels, about 6% of the range of
mouse movements; the RMS deviation of model from actual cursor
movements was 39 pixels, about 7% of the range of mouse movements.
Adding a dead zone actually decreases the fit of model to data. The
decrease in fit is very small until the dead zone gets pretty large:
with a dead done of 50 pixels the fit to mouse movements changes
hardly at ll but the fit to cursor movements decreases: the proportion
of variance accounted for goes from 93% to 82% and RMS error goes from
39 to 46 pixels (7 to 9%).

So while your subjective experiment may suggest to you that a dead
zone is involved in tracking, my much more crude and medieval model
testing approach suggests that it's not. So who you gonna trust, me or
your lyin' eyes;-)

BP: New subject, and you had better keep Linda with you while you explore it
because you are going to fall in love.

RM: She's great but Linda has nothing to worry about (and she's not
even watching me type this;-)

Best

Rick

···

Here is an except from a post I sent to Alice this morning: Google on
"Stephanie Trick: Rising Star of Jazz (Don Wolff)". This will get you an
interview well worth watching, and on the right side a lot of links to other
performances.
The "Stephanie Trick at Aborsjazz" link has the "I ain't got nobody" that I
raved about. All the others are worth at least a listen. Also select or
Google "Stephanie Trick on State of the Arts" to get three good ones, the
first being her version of St. Louis Blues that includes a part patterned
after Earl Father Hines boogie on the SLB that I used to play. She learned
most of her boogie by listening to records the same way I did -- no
transcriptions available. The Death Ray Boogie by Pete Johnson, next, is
also a fast one I learned, and it's very interesting to hear the differences
in how she and I remember it. I can hear the parts where she put in her own
riffs. I may send her some short clips of my version, just to back up her
memory with mine.
This girl makes me tear up with joy. And this is an excerpt from a post to
Alice yesterday: Watching and listening to Stephanie Trick playing makes me
remember my high-school playing as the fumbling of a person with brain
damage. I wouldn't dare touch a key where she might hear it. Her classical
training shows all over the place, from the fingering to the knowledge of
chord progressions to the way she handles dynamics. Total mastery. And I
would hate to get any sensitive body part between those steel fingers and
the keyboard. She has to be incredibly strong to maintain that fast stride
and right hand for three or four minutes at a time, and sometimes much
longer.
But the best part of every piece she does alone is when it ends and she
turns to the audience with that delighted sharing grin. "Wasn't that just
GREAT?" she is saying, and she means the music, not herself. Every now and
then you can see that same expression starting to form while she's playing
something and it's sounding just perfect. She's an audience at the same time
she's a performer. I remember feeling exactly that way, for a lot less
reason.

[earlier comment by me to Alice] Get this one, "I ain't got nobody".
Particularly catch the incredibly coy little ending of the descending
glissando at 3:25. [This is in the Trephanie Trick at Aborsjazz link] In
some of the performances she is 23 years old; she was 25 in 2012. A pretty
young girl with a wonderful smile, you think. A commentator on one YouTube
page said that this pretty young girl can hit those keys like a 300-pound
black bear. Others said things like "This is the best piano-playing of any
kind I have EVER heard."

Enjoy.

Bill P.

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

36

I have heard her and talked with her personally. She is from St Louis. Her dad is retired from tech support at Principia HS in St Louis. She gave a concert at our local Ethical Society last year. She is endearing, but that jazz she puts out is mean. I think I also remember her doing some great stride work.
Glad to share another common uncommon love.

Lloyd

“Stephanie Trick: Rising Star of Jazz (Don Wolff)”. This will get you an interview well worth watching, and on the right side a lot of links to other performances.
The “Stephanie Trick at Aborsjazz”

Dr. Lloyd Klinedinst
10 Dover Lane
Villa Ridge, MO 63089-2001
HomeVoice: (636) 451-3232

Lloyd Mobile: (314)-609-5571
email: lloydk@klinedinst.com

website: http://www.klinedinst.com

···

On Oct 1, 2012, at 10:01 AM, Bill Powers wrote:

37

[Martin Taylor 2012.10.03.16.01]

[From Rick Marken (2012.10.02.1400)]

...In a typical run, the plain vanilla model accounts for 95% of the variance in mouse movements and 93% of the variance in cursor movements. The RMS deviation of model from actual mouse movements was 44 pixels, about 6% of the range of mouse movements; the RMS deviation of model from actual cursor movements was 39 pixels, about 7% of the range of mouse movements. Adding a dead zone actually decreases the fit of model to data. The decrease in fit is very small until the dead zone gets pretty large: with a dead done of 50 pixels the fit to mouse movements changes hardly at ll but the fit to cursor movements decreases: the proportion of variance accounted for goes from 93% to 82% and RMS error goes from 39 to 46 pixels (7 to 9%).

That's a HUGE dead zone for such a tracking task. How precisely did you vary the dead zone for fitting at the small end? As I remember my optimizations using a dead zone, 0.6 pixels sticks as being pretty typical. And no, it didn't make much difference, but it made some.

Martin

38

[From Rick Marken (2012.10.03.1750)]

Martin Taylor (2012.10.03.16.01)

Rick Marken (2012.10.02.1400)

RM:…In a typical run, the plain vanilla model accounts for 95% of the variance in mouse movements and 93% of the variance in cursor movements. The RMS deviation of model from actual mouse movements was 44 pixels, about 6% of the range of mouse movements; the RMS deviation of model from actual cursor movements was 39 pixels, about 7% of the range of mouse movements. Adding a dead zone actually decreases the fit of model to data. The decrease in fit is very small until the dead zone gets pretty large: with a dead done of 50 pixels the fit to mouse movements changes hardly at ll but the fit to cursor movements decreases: the proportion of variance accounted for goes from 93% to 82% and RMS error goes from 39 to 46 pixels (7 to 9%).

MT: That’s a HUGE dead zone for such a tracking task. How precisely did you vary the dead zone for fitting at the small end? As I remember my optimizations using a dead zone, 0.6 pixels sticks as being pretty typical. And no, it didn’t make much difference, but it made some.

I did start at a small dead zone value (1.0) and then worked up. A dead zone of 1 compared to one of 0 made some difference, but in the fourth decimal place. As I increased the dead zone width (I just tried starting from .6 as you suggest) the model sometimes improved (by .00001, say) and sometimes did worse (by the same amount). Only when the dead zone got up to the very large values I report could one see a definite effect on the fit of the model to the data. Maybe the problem is in how I computed the dead zone. Here’s my code:

p = o + d
sign = Sgn(p)
If Abs(p) <= dz Then
e = 0
Else
e = -(sign * Abs(p - dz))
End If

This assumes that r = 0 and that e=p-r = p so p is the error signal.

Or it could be because the data I use – compensatory tracking with a fast disturbance – doesn’t show the effects of the dead zone as well as your data.

Best

Rick

···

–
Richard S. Marken PhD

rsmarken@gmail.com
www.mindreadings.com

39

[Martin Taylor 2012.10.03.22.56]

[From Rick Marken (2012.10.03.1750)]

      Martin

Taylor (2012.10.03.16.01)

      As I

remember my optimizations using a dead zone, 0.6 pixels sticks
as being pretty typical. And no, it didn’t make much
difference, but it made some.

      I did start at a small dead zone value (1.0) and then worked

up. A dead zone of 1 compared to one of 0 made some
difference, but in the fourth decimal place. As I increased
the dead zone width (I just tried starting from .6 as you
suggest) the model sometimes improved (by .00001, say) and
sometimes did worse (by the same amount). Only when the dead
zone got up to the very large values I report could one see a
definite effect on the fit of the model to the data. Maybe the
problem is in how I computed the dead zone. Here’s my code:

      p = o + d

      sign = Sgn(p)

      If Abs(p) <= dz Then

        e = 0

      Else

       e = -(sign * Abs(p - dz))

      End If

  This assumes that r = 0 and that e=p-r  = p so p is the error

signal.

  Or it could be because the data I use -- compensatory tracking

with a fast disturbance – doesn’t show the effects of the dead
zone as well as your data.

Your code looks right to my eye.

I would be quite surprised if the effectiveness of the dead zone did

not vary with the specific task. Your viewing conditions are
probably different from mine. One possible variation is to separate
the target and the cursor so that it becomes a bit more difficult to
see when they are properly aligned. Also, I agree with you that the
effect on the fit is small. It’s small, but I remember it as being
consistent.

The problem is that most of the time changes in the control function

get swamped by the averaging effect of having error that vary over a
fairly wide range. I tried, with no success, to find a difference
among different kinds on nonlinear control curve, of which the dead
zone is one extreme example. I don’t remember what variants I tried,
but an example that I might or might not have done would be a
two-sided square-law (based on your code).

p = o + d

sign = Sgn(r-p)

e = a*(r-p) +(1-a)*sign * (r-p)*(r-p)      // (a is a parameter

between 0 and 1)

I thought that changing the severity of the nonlinearity might make

an appreciable difference to the fit, but I couldn’t find it, and
the explanation I came up with is that there is really very little
difference averaged over one peak-to-peak excursion of the
disturbance between such a nonlinear control curve and a straight
line through the origin, if the line has an appropriate slope for
the degree of difficulty of the task. Remember, the output stage
integrates, so we never get to see the effect of the momentary
error.

I suppose the point is rather whether one wants a fit that is very

good to be good enough (your personal tolerance – dead-- zone), or
whether one wants to tease out from its little imperfections
something further about what actually is going on in the control
system under study. If the latter, then maybe the simple existence
of an optimum value for the dead zone says more than the very small
degree of improvement of the optimum over having no dead zone.

Martin
40

[From Rupert Young (2012.10.04.1300 BST)]

[From Rick Marken (2012.09.28.1100)]
RM: As you demonstrated to me (or, actually, had me demonstrate
to myself) an integral control system acts like a linear low-pass
filter, smoothing the output (and the input -- controlled variable)

RY: I am interested in this particular point. How is the output smoothed in an integral function? Changing the values of gain and slow seems to change the magnitude of the output, but not the smoothness. To get a smoother output from the output function of a control system I am smoothing the input to the perceptual signal function.

I am using this for the intergral function, output += slow * (gain * error - output);

Thanks,
Rupert