Point attractors and other strange creatures

CSGnet Archive CSG2018
1

[From Bruce Abbott (2018.02.23.1020 EST)]

[From Rupert Young (2018.02.22 16.05)]

(Rick Marken 2018-02-19_09:48:29]

Rupert Young (2018.02.18 18.15)–

RY: With Vehicle 1 (http://www.bcp.psych.ualberta.ca/~mike/Pearl_Street/Margin/Vehicles/Vehicle.1.html) the output speed is proportional to the sensory input (in this case temperature). How does the effect of the output reduce the effect of the input?

RM: It depends on the direction of rotation of the wheel. If the wheel turns clockwise with the sensor to the right of the axle then movement of the wheel will move the sensor toward the heat source, increasing the heat at the sensor. So the effect of output on input is to increase the input effect on the output; there is positive feedback and the car will accelerate toward the heat source. No control:

RY: Yes, exactly (Eetu also raised this) (though I think it’s just a matter of whether the motor goes forwards or backwards). Whether the input reduces or increases is entirely dependent upon the environment, not the architecture (design) of the system. So, could this be said to be a control system?

RM: It’s a control system as long as increases in sensory input (heat) above zero cause increases in wheel velocity that move the vehicle away from the cause of the sensory input (the heat source) and decreases in sensory input below zero cause increases in wheel movement that move the vehicle toward the cause of the sensory input. With proper adjustment of gain and slowing this system will be stable and control sensed heat, keeping it at a perceptual level that corresponds to zero perceptual signal.

This system would run straight into a heat source (if it were straight ahead), so does that mean it is not a control system?

RY: Braitenberg’s other vehicles were more complex dynamical systems, but I think rather than controlling a specific perception they would settle on various attractor points. If disturbed they may settle on a different attractor point. A perceptual control system would always act to return to the same point.

RM: I think the people who build these vehicles are just being politically correct when they talk about “attractor points”. Since these vehicles are control systems the reference state of the the variables they control are not attractor points (like the resting state of a pendulum or a mass on a spring); they are the reference states of controlled variables. The concept of attractor points is the politically correct way to refer to controlled (purposefully produced) results because it implies that these results can be produced by ordinary cause-effect processes.

I agree, partially. Controlled results are attractor points within dynamical systems. But not all attractor points within dynamical systems are controlled results. For example, the predator/prey relationship between penguins and seals may stabilise at a certain value. It is an attractor point within a dynamical system, but it is not a controlled result. Add a disturbance with a bunch of polar bears to the environment and the relationship between penguins and seals would probably stabilise at a different value; i.e. a different attractor point. I think this is what Braitenberg’s vehicles are like, rather than a perceptual control system, which would oppose disturbances to return to the same “attractor point”.

Exactly so, Rupert. But let’s examine what attractor points and their cousins in phase space actually are for. (I strongly disagree with Rick that “the concept of attractor points is the politically correct way to refer to controlled results,� and that it is used “because it implies that these results can be produced by ordinary cause-effect processes.�)

Phase-space diagrams plot the dynamic variables of a system against one another as those variables change over time. For example, a phase portrait of the behavior of a pendulum plots the pendulum bob’s angular position against its angular velocity. (The two variables act 180 degrees out of phase, with maximum position at zero velocity and minimum position at maximum velocity.)

Attractor points and associated curves in phase space simply describe the behavior over time of the points of a dynamic system, plotted from various starting points (representing different initial conditions). The graphs do not explain that behavior, they simply exhibit it. It is up to theory to provide an explanation.

For attractor points, the lines converge over time to a single point in n-dimensional space (e.g., a single X,Y value for a two-dimensional space, or a single X,Y,Z point in three-dimensional space. But there are other possibilities. For example, the points may converge, not to a single point, but to a closed loop – a â“limit cycle.â€? In this case, once the points reach the limit cycle they cycle around the same sets of values. Another example is the “strangeâ€? attractor, in which the points keep cycling around the same area but never repeat the same path exactly – thhe hallmark of chaos.

A pendulum with friction will eventually converge to a single point at which the position and velocity of the pendulum are both zero. A frictionless pendulum will continue to swing back and forth forever, describing a limit cycle in phase space. A double pendulum (one with a pivot connecting two segments) may generate chaotic behavior, which shows up in phase space as a strange attractor.

A control system that stabilizes to a single value after disturbance or during a constant disturbance produces a point attractor. An “underdamped� control system goes into perpetual oscillation and generates a limit cycle in phase space. And I suppose there are conditions under which certain control-system architectures would behave chaotically and show a strange attractor in phase space.

Phase-space diagrams are simply tools used to reveal the nature of the behavior of a dynamic system under specified conditions; having discovered that a system behaves, say, chaotically, it is up to the system analyst to discover what is causing it to behave this way. Such a diagram is a purely descriptive tool to help the analyst understand how the system behaves over time; it in no way provides an explanation for that behavior and therefore is not a substitute for an explanatory model. As such it certainly does not imply “that these results are produced by ordinary cause-effect processes,� as Rick incorrectly asserts.

Bruce

···

On 17/02/2018 19:56, Richard Marken wrote:

2

[Rick Marken 2018-02-24_10:26:48]

···

Bruce Abbott (2018.02.23.1020 EST)–

Â

RY: I agree, partially. Controlled results are attractor points within dynamical systems…

BA: Exactly so, Rupert. But let’s examine what attractor points and their cousins in phase space actually are for. (I strongly disagree with Rick that “the concept of attractor points is the politically correct way to refer to controlled results,� and that it is used “because it implies that these results can be produced by ordinary cause-effect processes.�)

RM: Yes, I should have said "
the concept of attractor points is the politically correct way to refer to physical phenomena that appear to be purposeful (goal directed) and are, thus, seen as a way to use cause-effect rather than control models to explain controlling (purposeful behavior)".

BA: Attractor points and associated curves in phase space simply describe the behavior over time of the points of a dynamic system, plotted from various starting points (representing different initial conditions). The graphs do not explain that behavior, they simply exhibit it. It is up to theory to provide an explanation.

RM: Yes, and the theory that explains this behavior is Newton’s laws.

BA: A control system that stabilizes to a single value after disturbance or during a constant disturbance produces a point attractor. An “underdamped� control system goes into perpetual oscillation and generates a limit cycle in phase space. And I suppose there are conditions under which certain control-system architectures would behave chaotically and show a strange attractor in phase space.

RM: There are ways to distinguish the behavior of a causal system from that of a control system. But you don’t really care for research aimed at testing for controlled variables, do you?Â

BA: Phase-space diagrams are simply tools used to reveal the nature of the behavior of a dynamic system under specified conditions; having discovered that a system behaves, say, chaotically, it is up to the system analyst to discover what is causing it to behave this way. Such a diagram is a purely descriptive tool to help the analyst understand how the system behaves over time; it in no way provides an explanation for that behavior and therefore is not a substitute for an explanatory model. As such it certainly does not imply “that these results are produced by ordinary cause-effect processes,� as Rick incorrectly asserts.

RM: The the behavior of the dynamical systems you’ve been talking about – mass spring, pendulum, etc – does not involve control and their behavior is perfectly well explained by the open-loop cause-effect laws of physics. If the phase space diagram is that of the behavior of the (poorly) controlled variable of a control system then its behavior would have to be explained by the closed-loop causal laws of control theory.Â

RM: Control theory explains control. So you have to know whether the behavior you are dealing with involves control before you start applying closed-loop control models to explain the behavior. If what appears to be an “attractor point” is actually the reference state of a controlled variable then control theory is required to explain why that variable remains in the reference state. The attractor points of the dynamical systems you have been talking about are easily shown to not be the reference states of controlled variables (using the test for controlled variables) so control theory is not needed to explain their behavior. And vice versa: the physical theories that explain attractor points that are not the reference states of controlled variables cannot explain the existence of attractor points that are.

Â

BestÂ

Rick

–
Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

3

[Martin Taylor 2018.02.25.13.32]

[Rick Marken 2018-02-24_10:26:48]

So far, so good.

The only reasonable comment on this is "So what". The phase diagram

itself is indistinguishable, since the attractor in a phase diagram
is relevant only to an isolated system, which makes nonsense of

  The attractor points of the dynamical

systems you have been talking about are easily shown to not
be the reference states of controlled variables (using the test
for controlled variables)

The phase diagram simply shows what happens it the system is started

in some initial state (location and momentum or velocity) and is
thereafter left alone. To determine what the phase diagram will show
depends entirely on the physics of the structure that affects the
variable whose behaviour is described by the phase diagram. When the
system is isolated from subsequent external influences and allowed
to evolve, there’s no way to tell whether the attractor point or
cycle is the result of control or of a system that stores and
releases energy like a spring. If there’s no energy dissipation, a
limit cycle or a strange attractor is possible in either case. If
there is energy dissipation, then the attractor will be a point and
the orbit will be either an inward spiral or a straight line.

You certainly can describe arbitrary waveforms, such as you would

get when you use “The Test” to disturb a controlled variable, using
phase plots, but they tell you nothing about the system that
generates the waveform, and since the system being described is not
isolated from external influences, it has no attractor.

A phase diagram does nothing to help one distinguish between a

spring-like energy storage system and a control loop. It’s just
another way to describe in compact form the waveform of a variable
that is undisturbed after being set going in some initial state.

Martin

PS. Bruce, I may be wrong, but I think a strange attractor is

possible if the system response is as nonlinear as a square law.
Since control tends to linearize nonlinearities in the components,
maybe it is unlikely to occur in a phase diagram for a variable in a
control loop. I think the possibility is likely to be academic
anyway, since the system is dissipative. In a control loop, the
energy supplied by the disturbance is dissipated to the external
environment in the energy flow that powers the entropy-reduction
induced by the output’s compensation for the disturbance. In a
non-control “springy” system, frictional looses are inevitable, too.
The end result is, I think, always a point attractor.

··· 
                  Bruce

Abbott (2018.02.23.1020 EST)–

Â

                RY:

I agree, partially. Controlled results are attractor
points within dynamical systems…

                  BA: Exactly so, Rupert.Â

But let’s examine what attractor points and their
cousins in phase space actually are for. (I
strongly disagree with Rick that “the concept of
attractor points is the politically correct way
to refer to controlled results,� and that it is
used “because it implies that these results can be
produced by ordinary cause-effect processes.�)

          RM: Yes, I should have said "
            the

concept of attractor points is the politically correct
way to refer to physical phenomena that appear to be
purposeful (goal directed) and are, thus, seen as a way
to use cause-effect rather than control models to
explain controlling (purposeful behavior)".

…
RM: The the behavior of the dynamical systems you’ve
been talking about – mass spring, pendulum, etc – does
not involve control and their behavior is perfectly well
explained by the open-loop cause-effect laws of physics.
If the phase space diagram is that of the behavior of the
(poorly) controlled variable of a control system then its
behavior would have to be explained by the closed-loop
causal laws of control theory.

          RM: Control theory explains control. So you have to

know whether the behavior you are dealing with involves
control before you start applying closed-loop control
models to explain the behavior. If what appears to be an
“attractor point” is actually the reference state of a
controlled variable then control theory is required to
explain why that variable remains in the reference state.
The attractor points of the dynamical systems you have
been talking about are easily shown to not be the
reference states of controlled variables (using the test
for controlled variables) so control theory is not needed
to explain their behavior. And vice versa: the physical
theories that explain attractor points that are not
the reference states of controlled variables cannot
explain the existence of attractor points that are.

4

[Rick Marken 2018-02-24_16:05:47]

[Martin Taylor 2018.02.25.13.32]

RM: Control theory explains control. So you have to know whether the behavior you are dealing with involves control before you start applying closed-loop control models to explain the behavior. If what appears to be an "attractor point" is actually the reference state of a controlled variable then control theory is required to explain why that variable remains in the reference state. The attractor points of the dynamical systems you have been talking about are easily shown to not be the reference states of controlled variables (using the test for controlled variables) so control theory is not needed to explain their behavior. And vice versa: the physical theories that explain attractor points that are not the reference states of controlled variables cannot explain the existence of attractor points that are.

MT: The only reasonable comment on this is "So what".

RM: Well, at least that's better than bullshit. But I'm having some difficulty understanding what this attractor stuff has to do with perceptual control theory. Maybe you could give those of us who are not as mathematically adroit as you are (as evidenced by that brilliant comment on our paper in EBR) maybe you could give us the idiot's guide to what dynamic attractors contribute to our understanding of the behavior of living systems.Â
BestÂ
Rick

Â

···

The phase diagram itself is indistinguishable, since the attractor in a phase diagram is relevant only to an isolated system, which makes nonsense of

The attractor points of the dynamical systems you have been talking about are easily shown to not be the reference states of controlled variables (using the test for controlled variables)

The phase diagram simply shows what happens it the system is started in some initial state (location and momentum or velocity) and is thereafter left alone. To determine what the phase diagram will show depends entirely on the physics of the structure that affects the variable whose behaviour is described by the phase diagram. When the system is isolated from subsequent external influences and allowed to evolve, there's no way to tell whether the attractor point or cycle is the result of control or of a system that stores and releases energy like a spring. If there's no energy dissipation, a limit cycle or a strange attractor is possible in either case. If there is energy dissipation, then the attractor will be a point and the orbit will be either an inward spiral or a straight line.

You certainly can describe arbitrary waveforms, such as you would get when you use "The Test" to disturb a controlled variable, using phase plots, but they tell you nothing about the system that generates the waveform, and since the system being described is not isolated from external influences, it has no attractor.

A phase diagram does nothing to help one distinguish between a spring-like energy storage system and a control loop. It's just another way to describe in compact form the waveform of a variable that is undisturbed after being set going in some initial state.

Martin

PS. Bruce, I may be wrong, but I think a strange attractor is possible if the system response is as nonlinear as a square law. Since control tends to linearize nonlinearities in the components, maybe it is unlikely to occur in a phase diagram for a variable in a control loop. I think the possibility is likely to be academic anyway, since the system is dissipative. In a control loop, the energy supplied by the disturbance is dissipated to the external environment in the energy flow that powers the entropy-reduction induced by the output's compensation for the disturbance. In a non-control "springy" system, frictional looses are inevitable, too. The end result is, I think, always a point attractor.

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

5

[Martin Taylor 2018.02.24.23.20]

Remember, I wasn't the one who brought the attractor idea up. I

believe that what I said in the message to which you are responding
could be summarized as “.”
But you seemed to go along with Bruce in dealing with it as though
it did, in some way with which you disagreed, and you made a
specific false statement that assumed that it did: "
That last was what prompted my intervention, because it was untrue,
whereas what Bruce had been saying was not (so far as I remember
without going back and re-reading his messages). Attractor dynamics
are, in my opinion, irrelevant to the question of distinguishing
equilibrium systems from control systems. So far as I can see, the
only reliable difference between them is, as Kennaway said (and with
which you disagreed), that the control system opposes the
disturbance by using energy from a separate source. I explained why
this has to be a distinguishing feature (but presumably not the only
distinguishing feature) in [Martin Taylor 2018.02.17.23.29].
Martin

···

[Rick Marken 2018-02-24_16:05:47]

[Martin Taylor 2018.02.25.13.32]

                        RM: Control theory explains control. So

you have to know whether the behavior you
are dealing with involves control before you
start applying closed-loop control models to
explain the behavior. If what appears to be
an “attractor point” is actually the
reference state of a controlled variable
then control theory is required to explain
why that variable remains in the reference
state. The attractor points of the dynamical
systems you have been talking about are
easily shown to not be the reference
states of controlled variables (using the
test for controlled variables) so control
theory is not needed to explain their
behavior. And vice versa: the physical
theories that explain attractor points that
are not the reference states of
controlled variables cannot explain the
existence of attractor points that are.

            MT: The only reasonable comment on this is "So

what".

          RM: Well, at least that's better than bullshit.  But

I’m having some difficulty understanding what this
attractor stuff has to do with perceptual control theory.

  •  I'm having some difficulty understanding

what this attractor stuff has to do with perceptual control theory*

  •  The attractor

points of the dynamical systems you have been talking about are
easily shown to* not * be the reference states of
controlled variables (using the test for controlled variables)".*

6

[From Bruce Abbott (2018.02.25.1400 EST)]

[Rick Marken 2018-02-24_10:26:48]

Bruce Abbott (2018.02.23.1020 EST)–

RY: I agree, partially. Controlled results are attractor points within dynamical systems…

BA: Exactly so, Rupert. But let’s examine what attractor points and their cousins in phase space actually are for. (I strongly disagree with Rick that “the concept of attractor points is the politically correct way to refer to controlled results,� and that it is used “because it implies that these results can be produced by ordinary cause-effect processes.�)

RM: Yes, I should have said " the concept of attractor points is the politically correct way to refer to physical phenomena that appear to be purposeful (goal directed) and are, thus, seen as a way to use cause-effect rather than control models to explain controlling (purposeful behavior)".

That’s no better. Phase portraits graphicly depict the behavior of a dynamic system over time, starting from given initial conditions. An attractor point is just a single point on the graph at which the system comes to rest.  It is not a cause-effect model; in fact it’s not a model at all. To see how silly your statement is, consider the following parallel statement:

“ The concept of the point to which qi converges on a time-series plot of tracking data is the politically correct way to refer to physical phenomena that appear to be purposeful (goal directed) and are, thus, seen as a way to use cause-effect rather than control models to explain controlling (purposeful behavior).�

I would also note your use of the passive voice in your assertion: “is seen�. By whom? Unnamed boogey-men plotting against PCT? Evidently by you, but I rather doubt that anyone else  does.

BA: Attractor points and associated curves in phase space simply describe the behavior over time of the points of a dynamic system, plotted from various starting points (representing different initial conditions). The graphs do not explain that behavior, they simply exhibit it. It is up to theory to provide an explanation.

RM: Yes, and the theory that explains this behavior is Newton’s laws.

Or, perhaps, control theory, if the behavior being exhibited on the phase plot is that of a control system. It depends on what kind of dynamic system is producing the behavior.

BA: A control system that stabilizes to a single value after disturbance or during a constant disturbance produces a point attractor. An “underdamped� control system goes into perpetual oscillation and generates a limit cycle in phase space. And I suppose there are conditions under which certain control-system architectures would behave chaotically and show a strange attractor in phase space.

RM: There are ways to distinguish the behavior of a causal system from that of a control system. But you don’t really care for research aimed at testing for controlled variables, do you?

Control systems are causal systems, so there is no way to distinguish the behavior of a causal system from that of a control system. Equilibrium systems are also causal systems. Equilibrium systems and control systems both entail negative feedback, but they can be distinguished with proper tests. Both can be distinguished from open-loop (non-feedback) systems and from systems with positive feedback.

As for whether I “really care for research aimed at testing for controlled variables,� that depends on whether the information gained is likely help us understand observed behavior or can be put to practical (or theoretical) use. I don’t need a test for the controlled variable to know that, when driving, I am controlling my car’s position on the road, its speed, acceleration rate, lateral acceleration, minimum distance from other vehicles, braking rate, the car’s fuel mileage, and the route it takes to get me where I am trying to go (and probably more). Your fielder-related research, on the other hand, is worthwhile, because it demonstrates that the fielder’s behavior when pursuing and catching a ball can be explained rather simply in terms of controlling the optical velocity of the ball, as opposed to other much more complex models. But I’m mainly interested in contributing to further development of PCT, which as it stands has a number of unsolved problems. I start and stop controlling thousands of variables every day, depending on what I am trying to accomplish and the conditions under which I act. Developing an exhaustive catalog of what those variables are doesn’t seem very useful to me. But give me a behavior whose genesis is unclear and I’d be interested in learning not only what is being controlled, but what the system’s architecture is and, if possible, how it developed.

BA: Phase-space diagrams are simply tools used to reveal the nature of the behavior of a dynamic system under specified conditions; having discovered that a system behaves, say, chaotically, it is up to the system analyst to discover what is causing it to behave this way. Such a diagram is a purely descriptive tool to help the analyst understand how the system behaves over time; it in no way provides an explanation for that behavior and therefore is not a substitute for an explanatory model. As such it certainly does not imply “that these results are produced by ordinary cause-effect processes,� as Rick incorrectly asserts.

RM: The the behavior of the dynamical systems you’ve been talking about – mass spring, pendulum, etc – does not involve control and their behavior is perfectly well explained by the open-loop cause-effect laws of physics. If the phase space diagram is that of the behavior of the (poorly) controlled variable of a control system then its behavior would have to be explained by the closed-loop causal laws of control theory.

Why would you think that the phase portrait would have to be that of a POORLY controlled variable? A poorly controlled variable would not generate a point attractor in phase space. For example, if the system went into undamped, stable oscillations it would generate a limit cycle.

RM: Control theory explains control. So you have to know whether the behavior you are dealing with involves control before you start applying closed-loop control models to explain the behavior. If what appears to be an “attractor point” is actually the reference state of a controlled variable then control theory is required to explain why that variable remains in the reference state. The attractor points of the dynamical systems you have been talking about are easily shown to not be the reference states of controlled variables (using the test for controlled variables) so control theory is not needed to explain their behavior. And vice versa: the physical theories that explain attractor points that are not the reference states of controlled variables cannot explain the existence of attractor points that are.

Again, you are laboring under the mistaken belief that attractor points can only be explained by “physical theories,â€? which I take you to mean theories that explain the behavior of an object (such as a pendulum) purely in terms of physics. Control systems are just as physical as any other system – do not the human ones havee physical neural signals traversing physical neurons to physical synapses, and so on, not to mention their interaction with physical environmental variables? Both exhibit behaviors that can be depicted on a phase diagram, sometimes revealing attractors of various kinds.

Bruce

7

[Rick Marken 2018-02-25_13:07:19]

Martin Taylor (2018.02.24.23.20)--

MT:Â Attractor dynamics are, in my opinion, irrelevant to the question of distinguishing equilibrium systems from control systems. So far as I can see, the only reliable difference between them is, as Kennaway said (and with which you disagreed), that the control system opposes the disturbance by using energy from a separate source. I explained why this has to be a distinguishing feature (but presumably not the only distinguishing feature) in [Martin Taylor 2018.02.17.23.29].

RM: This assumes that equilibrium systems oppose disturbances. But this is easily shown not to be the case. So I think the way to distinguish equilibrium systems from control systems is the way you distinguish any Z - system from an N - system: using the test for the controlled variable.
BestÂ
Rick

···

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

8

[Martin Taylor 2018.02.25.16.40]

I don't suppose that suggesting you read what you criticise would be

any more use now than it has been in the past, so I won’t suggest
it. I will just respond:

S--i--g---h.......!

Martin
···

[Rick Marken 2018-02-25_13:07:19]

Martin Taylor (2018.02.24.23.20)–

            MT:  Attractor dynamics are, in my opinion, irrelevant

to the question of distinguishing equilibrium systems
from control systems. So far as I can see, the only
reliable difference between them is, as Kennaway said
(and with which you disagreed), that the control system
opposes the disturbance by using energy from a separate
source. I explained why this has to be a distinguishing
feature (but presumably not the only distinguishing
feature) in [Martin Taylor 2018.02.17.23.29].

      RM: This assumes that equilibrium systems oppose disturbances.

But this is easily shown not to be the case. So I think the
way to distinguish equilibrium systems from control systems is
the way you distinguish any Z - system from an N - system:
using the test for the controlled variable.

9

[From Bruce Abbott (2018.02.25.1655 EST)]

[Rick Marken 2018-02-25_13:07:19]

Martin Taylor (2018.02.24.23.20)–

MT: Attractor dynamics are, in my opinion, irrelevant to the question of distinguishing equilibrium systems from control systems. So far as I can see, the only reliable difference between them is, as Kennaway said (and with which you disagreed), that the control system opposes the disturbance by using energy from a separate source. I explained why this has to be a distinguishing feature (but presumably not the only distinguishing feature) in [Martin Taylor 2018.02.17.23.29].

RM: This assumes that equilibrium systems oppose disturbances. But this is easily shown not to be the case. So I think the way to distinguish equilibrium systems from control systems is the way you distinguish any Z - system from an N - system: using the test for the controlled variable.

Of COURSE equilibrium systems oppose disturbances. Try pushing your hand through a table top. Do you feel any opposition to your efforts or does the table top just let your hand slide through, unopposed?

(Hint: Equilibrium systems are N-systems, too!)

Bruce

10

[Rick Marken 2018-02-25_14:31:46]

Bruce Abbott (2018.02.25.1400 EST)]

BA: Attractor points and associated curves in phase space simply describe the behavior over time of the points of a dynamic system, plotted from various starting points (representing different initial conditions). The graphs do not explain that behavior, they simply exhibit it. It is up to theory to provide an explanation.

RM: Yes, and the theory that explains this behavior is Newton's laws.

Â

BA: Or, perhaps, control theory, if the behavior being exhibited on the phase plot is that of a control system. It depends on what kind of dynamic system is producing the behavior.

RM: True. If the behavior of the variable in the phase plot is produced by a Z-system (like a pendulum or a ball rolling down the side of a bowl) then there will be no disturbance resistance. If it was produced by an N- system (like a person) there will disturbance resistance.Â
 >

BA: A control system that stabilizes to a single value after disturbance or during a constant disturbance produces a point attractor. An “underdamped� control system goes into perpetual oscillation and generates a limit cycle in phase space. And I suppose there are conditions under which certain control-system architectures would behave chaotically and show a strange attractor in phase space.

RM: There are ways to distinguish the behavior of a causal system from that of a control system. But you don't really care for research aimed at testing for controlled variables, do you?Â

Â

BA: Control systems are causal systems, so there is no way to distinguish the behavior of a causal system from that of a control system.Â

RM: When I say causal (or cause-effect) systems I am referring to what Powers called Z (for Zero feedback) system; and when I say control system I am referring to what Powers called an N (for Negative feedback). Both involve casual components; they differ in terms of how these components are organized. When I say there is a way to distinguish the behavior of a causal system from that of a control system I mean that there is a way to distinguish the behavior of a Z from that of an N system. Equilibrium systems are Z systems so they can be easily distinguished from control () systems using the test for the controlled variable.
Â

BA: Equilibrium systems are also causal systems. Equilibrium systems and control systems both entail negative feedback, but they can be distinguished with proper tests. Both can be distinguished from open-loop (non-feedback) systems and from systems with positive feedback.

RM: If equilibrium systems are N-systems then they could be distinguished from Z- systems by testing to see if there was evidence that these systems are controlling some variable. I don't think you can provide such evidence. The effect of force disturbances to the position of a pendulum bob, for example, are precisely what is predicted by the laws of physics that apply to Z systems. If the position of the bob were being controlled, even very poorly (very low gain) there would be evidence that a force applied to the bob has less effect on the bob's position than what is predicted by physical law.Â
 >

 BA: As for whether I “really care for research aimed at testing for controlled variables,â€? that depends on whether the information gained is likely help us understand observed behavior or can be put to practical (or theoretical) use.Â

RM: How can it not help us understand observed behavior? What other way is there to understand observed behavior once you know you are dealing with an N system?

BA: I don’t need a test for the controlled variable to know that, when driving, I am controlling my car’s position on the road, its speed, acceleration rate, lateral acceleration, minimum distance from other vehicles, braking rate, the car’s fuel mileage, and the route it takes to get me where I am trying to go (and probably more).Â

RM: OK, so you don't need no stinkin' test for the controlled variable. So what kind of research do you do instead?
Â

BA: Your fielder-related research, on the other hand, is worthwhile, because it demonstrates that the fielder’s behavior when pursuing and catching a ball can be explained rather simply in terms of controlling the optical velocity of the ball, as opposed to other much more complex models. But I’m mainly interested in contributing to further development of PCT, which as it stands has a number of unsolved problems. I start and stop controlling thousands of variables every day, depending on what I am trying to accomplish and the conditions under which I act. Developing an exhaustive catalog of what those variables are doesn’t seem very useful to me. But give me a behavior whose genesis is unclear and I’d be interested in learning not only what is being controlled, but what the system’s architecture is and, if possible, how it developed.

BA: Well, since you haven't yet hit on to any behaviors whose genesis is unclear to you I suppose we can continue to count on you to continue not doing any PCT research.>

Â

RM: The the behavior of the dynamical systems you've been talking about -- mass spring, pendulum, etc -- does not involve control and their behavior is perfectly well explained by the open-loop cause-effect laws of physics. If the phase space diagram is that of the behavior of the (poorly) controlled variable of a control system then its behavior would have to be explained by the closed-loop causal laws of control theory.Â

BA: Again, you are laboring under the mistaken belief that attractor points can only be explained by “physical theories,� which I take you to mean theories that explain the behavior of an object (such as a pendulum) purely in terms of physics. Control systems are just as physical as any other system – do not the human ones have physical neural signals traversing physical neurons to physical synapses, and so on, not to mention their interaction with physical environmental variables? Both exhibit behaviors that can be depicted on a phase diagram, sometimes revealing attractors of various kinds.

RM: It's how the causality in the system is organized that matters. The main organizational difference is that between a Z (open loop) and N (closed loop) systems. Both can be called causal because they both have causal components. But the difference in organization of these systems results in very different behavior: N-systems control; Z-systems don't. You claim that an equilibrium system is an N-system. If this is true then an equilibrium system must be controlling some variable, even if it's doing it with very low gain. So we should be able to detect this controlling using the test for the controlled variable. I don't believe that you can do this. But I'm kind of tired of arguing about this; if you want to study equilibrium systems as examples of N systems then go ahead (as though you needed my permission;-)
Best
Rick

···

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

11

[Rick Marken 2018-02-25_14:40:22]

···

Bruce Abbott (2018.02.25.1655 EST)–

Â

RM: This assumes that equilibrium systems oppose disturbances. But this is easily shown not to be the case. So I think the way to distinguish equilibrium systems from control systems is the way you distinguish any Z - system from an N - system: using the test for the controlled variable.

Â

BA: Of COURSE equilibrium systems oppose disturbances. Try pushing your hand through a table top. Do you feel any opposition to your efforts or does the table top just let your hand slide through, unopposed?

Â

BA: (Hint: Equilibrium systems are N-systems, too!)

RM: Wow, so tables are control systems too? Is there anything that’s not a control system?

BestÂ

Rick

–

Richard S. MarkenÂ

"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

12

[From Bruce Abbott (2018.02.25.1835 EST)]

[Rick Marken 2018-02-25_14:40:22]

Bruce Abbott (2018.02.25.1655 EST)–

RM: This assumes that equilibrium systems oppose disturbances. But this is easily shown not to be the case. So I think the way to distinguish equilibrium systems from control systems is the way you distinguish any Z - system from an N - system: using the test for the controlled variable.

BA: Of COURSE equilibrium systems oppose disturbances. Try pushing your hand through a table top. Do you feel any opposition to your efforts or does the table top just let your hand slide through, unopposed?

BA: (Hint: Equilibrium systems are N-systems, too!)

RM: Wow, so tables are control systems too? Is there anything that’s not a control system?

I know you’re an intelligent guy, Rick, so why play dumb?  I started the paragraph by saying that of course equilibrium systems oppose disturbances. Then I gave an example of an equilibrium system that opposes disturbances. So you come back with “wow, so tables are control systems too?� Apparently you would rather look stupid than conceive the point. So, paraphrasing the immortal words of James Carville, “It’s an equilibrium system, stupid!� NOW do you understand? Sheesh!

Bruce

13

[Rick Marken 2018-02-25_16:24:43]

Bruce Abbott (2018.02.25.1835 EST)

BA: Of COURSE equilibrium systems oppose disturbances. Try pushing your hand through a table top. Do you feel any opposition to your efforts or does the table top just let your hand slide through, unopposed?

Â

BA: (Hint: Equilibrium systems are N-systems, too!)

RM: Wow, so tables are control systems too? Is there anything that's not a control system?

Â

BA: I know you’re an intelligent guy, Rick, so why play dumb?

RM: I'm not playing; this is the real thing.Â
Â

BA: I started the paragraph by saying that of course equilibrium systems oppose disturbances. Then I gave an example of an equilibrium system that opposes disturbances. So you come back with “wow, so tables are control systems too?� Apparently you would rather look stupid than conceive the point. So, paraphrasing the immortal words of James Carville, “It’s an equilibrium system, stupid!� NOW do you understand? Sheesh!

RM:Â I don't understand what I got wrong? You said that a table top opposes disturbances. Only control systems oppose disturbances. So you were saying that a table top is a control system. If you want to call the table top an equilibrium system that's up to you. But if it opposes disturbances, it's a control system. I don't think it does oppose disturbances. So a table top is not a control system of an equilibrium system if the latter is a system that opposes disturbances (an N-system).
BestÂ
Rick

···

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

14

[From Bruce Abbott (2018.02.26.1155 EST)]

[Rick Marken 2018-02-25_16:24:43]

Bruce Abbott (2018.02.25.1835 EST)

BA: Of COURSE equilibrium systems oppose disturbances. Try pushing your hand through a table top. Do you feel any opposition to your efforts or does the table top just let your hand slide through, unopposed?

BA: (Hint: Equilibrium systems are N-systems, too!)

RM: Wow, so tables are control systems too? Is there anything that’s not a control system?

BA: I know you’re an intelligent guy, Rick, so why play dumb?

RM: I’m not playing; this is the real thing.

BA: I started the paragraph by saying that of course equilibrium systems oppose disturbances. Then I gave an example of an equilibrium system that opposes disturbances. So you come back with “wow, so tables are control systems too?� Apparently you would rather look stupid than conceive the point. So, paraphrasing the immortal words of James Carville, “It’s an equilibrium system, stupid!� NOW do you understand? Sheesh!

RM: I don’t understand what I got wrong? You said that a table top opposes disturbances. Only control systems oppose disturbances. So you were saying that a table top is a control system. If you want to call the table top an equilibrium system that’s up to you. But if it opposes disturbances, it’s a control system. I don’t think it does oppose disturbances. So a table top is not a control system of an equiliare brium system if the latter is a system that opposes disturbances (an N-system).

The part you got wrong is “only control systems oppose disturbances.â€? The fact that you can’t just push your hand through a table top proves that equilibrium systems oppose disturbances, too. The downward force that you exert on the table top is resisted by the counterforce that develops as your downward force compresses the table at the area of contact with your hand. Think of the table top as a very stiff spring that is being compressed. Unless your force is sufficient to break the table, the counterforce will grow until it equals the downward force compressing the table top, and there your hand will be stopped – disturbance resisted.

As Richard Kennaway, Martin Taylor, and I have been saying, negative feedback is present in both control systems and equilibrium systems; the important difference lies in the source of the counteracting output. In the case of the equilibrium system it comes from the disturbance itself (e.g., hand compressing table, building up spring counterforce). In the case of the control system it comes from a source independent of the disturbance. A control system in which the gain is such that the counterforce it generates equals the force of the disturbance will act like an equilibrium system. But control systems usually are supplied with a source that can generate more counterforce than the disturbance can supply. Consequently, they are able to overcome to a large degree the effect of the disturbance on their controlled variables, how much being determined by the loop gain.

I take the term “controlâ€? to involve more than just opposing disturbances to a particular variable, but actively opposing them – ddrawing energy from a source other than the disturbance, generating an opposing effect that is greater than that of the disturbance. Equilibrium systems resist the effects of disturbances, but they do so passively, drawing their opposing action from effects of the disturbances themselves. This action is therefore necessarily weaker than that typically produced by a control system.

Given this way of defining “control,� one can indeed say that “only control systems control.� But for a some purposes an equilibrium system may be the better choice. You can hold a bowling ball in your outstretched hand and will be doing so by using control systems to tense your arm muscles so as to oppose the effect of gravity, which pulls down on the ball.  After a while your arm will get sore and eventually your muscles will give out. Or you can set the bowling ball on the floor and let the floor’s stiff springiness prevent the ball from falling below the floor’s level. Either way, gravity’s disturbing force is opposed.

Bruce

15

[Rick Marken 2018-02-26_22:06:21]

Bruce Abbott (2018.02.26.1155 EST)

Â

RM:Â I don't understand what I got wrong? You said that a table top opposes disturbances. Only control systems oppose disturbances. So you were saying that a table top is a control system. If you want to call the table top an equilibrium system that's up to you. But if it opposes disturbances, it's a control system. I don't think it does oppose disturbances. So a table top is not a control system of an equiliare brium system if the latter is a system that opposes disturbances (an N-system).

Â

BA: The part you got wrong is “only control systems oppose disturbances.â€? The fact that you can’t just push your hand through a table top proves that equilibrium systems oppose disturbances, too.Â

RM: In PCT the term disturbance has a technical meaning:an effect on a controlled variable that is independent of the control system's effect on that variable. So when you say that equilibrium systems oppose disturbance the implication is that these systems are controlling some variable. But according to you and Martin an equilibrium system is not a control system, implying that there is novariable being controlled; not controlled variable. So the best I can make of this discussion of equilibrium systems is that they are negative feedback systems that don't control but, nevertheless, oppose disturbances to a controlled variable.Â

BA: As Richard Kennaway, Martin Taylor, and I have been saying, negative feedback is present in both control systems and equilibrium systems; the important difference lies in the source of the counteracting output.Â

RM: Yes, now I can see why this would be what distinguishes control from equilibrium systems. Control systems could be distinguished from equilibrium systems by noting that control systems control and equilibrium systems don't (which is my simple minded way of looking at it). But apparently equilibrium systems do something a lot like controlling in the sense that they oppose disturbances but, unlike control systems, this disturbance opposition doesn't keep a controlled variable in a reference state because these systems can't control so there can't be a controlled variable involved. So the only way to distinguish control from equilibrium systems is in the source of energy for the disturbance opposition.Â
RM: If this is the aspect of control theory that interests you then, mazel tov. But I'll stick with PCT.
Best
Rick

Â

···

In the case of the equilibrium system it comes from the disturbance itself (e.g., hand compressing table, building up spring counterforce). In the case of the control system it comes from a source independent of the disturbance. A control system in which the gain is such that the counterforce it generates equals the force of the disturbance will act like an equilibrium system. But control systems usually are supplied with a source that can generate more counterforce than the disturbance can supply. Consequently, they are able to overcome to a large degree the effect of the disturbance on their controlled variables, how much being determined by the loop gain.

Â

I take the term “controlâ€? to involve more than just opposing disturbances to a particular variable, but actively opposing them – drawing energy froom a source other than the disturbance, generating an opposing effect that is greater than that of the disturbance. Equilibrium systems resist the effects of disturbances, but they do so passively, drawing their opposing action from effects of the disturbances themselves. This action is therefore necessarily weaker than that typically produced by a control system.

Â

Given this way of defining “control,â€? one can indeed say that “only control systems control.â€? But for a some purposes an equilibrium system may be the better choice. You can hold a bowling ball in your outstretched hand and will be doing so by using control systems to tense your arm muscles so as to oppose the effect of gravity, which pulls down on the ball. After a while your arm will get sore and eventually your muscles will give out. Or you can set the bowling ball on the floor and let the floor’s stiff springiness prevent the ball from falling below the floor’s level. Either way, gravity’s disturbing force is opposed.

Â

Bruce

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

16

[From Bruce Abbott (2018.02.27.1025 EST)]

[Rick Marken 2018-02-26_22:06:21]

Bruce Abbott (2018.02.26.1155 EST)

RM: I don’t understand what I got wrong? You said that a table top opposes disturbances. Only control systems oppose disturbances. So you were saying that a table top is a control system. If you want to call the table top an equilibrium system that’s up to you. But if it opposes disturbances, it’s a control system. I don’t think it does oppose disturbances. So a table top is not a control system of an equiliare brium system if the latter is a system that opposes disturbances (an N-system).

BA: The part you got wrong is “only control systems oppose disturbances.� The fact that you can’t just push your hand through a table top proves that equilibrium systems oppose disturbances, too

RM: In PCT the term disturbance has a technical meaning:an effect on a controlled variable that is independent of the control system’s effect on that variable. So when you say that equilibrium systems oppose disturbance the implication is that these systems are controlling some variable. But according to you and Martin an equilibrium system is not a control system, implying that there is novariable being controlled; not controlled variable. So the best I can make of this discussion of equilibrium systems is that they are negative feedback systems that don’t control but, nevertheless, oppose disturbances to a controlled variable.

Your �PCT� definition of “disturbance� is fine if only applied to a control system, but is overly restrictive.  In physics and engineering, “disturbance� means the same thing whether the variable being disturbed is a controlled quantity or one that, in the absence of disturbance, would settle to an equilibrium value. Indeed, the controlled quantity of a control system settles to an equilibrium value in the absence of disturbance, so long as the reference is steady.

It is important to recognize that equilibrium systems have their own stabilizing effects that can either augment or interfere with control. I have already given one example of the former: dropping a weight into an outstretched hand. The spring-like qualities of muscle and tendon limit the degree of sag of the arm as the weight is added, even if there is no change in the neural output to the muscles. A control system acting in parallel may reduce the sag by increasing the neural output to the muscles, but at some delay owing to the time involved in conducting neural impulses around the control loop.  The equilibrium system’s springiness begins to oppose the disturbance immediately, thus helping to stabilize the arm even before the control system can act.

Equilibrium systems may also oppose the attempts of a control system to alter the value of a controlled variable, making controlling that variable more difficult. Physicians sometimes run into this problem when to treat a disorder they need to change the level of a physiological variable like body temperature or blood glucose level and must overcome the homeostatic mechanism that is keeping the temperature or glucose level too high (or too low).

RM: If this is the aspect of control theory that interests you then, mazel tov. But I’ll stick with PCT.

If “sticking with PCT� means sticking your head in the sand and ignoring potentially important influences on control, then I would strongly recommend not taking that approach. PCT is an application of the principles of system dynamics, not an independent science that stands apart from it. The PCT theorist would be well advised to become familiar with system dynamics, which provides the tools for analyzing complex dynamic systems, including control systems, equilibrium systems, positive feedback systems, open-loop systems, and various combinations of these.

Bruce

17

[Martin Taylor 2018.02.27.14.17]

An interesting application of R-logic (R-Math Axiom 1) here.

A force is applied to a variable. The force is resisted and the

variable is influenced less than it would have been without the
resistance. We want to know whether the cause of the resistance is
that the variable is the environmental correlate of a controlled
perception. In R-logic, this is easy. If the force is a disturbance,
the answer is “Yes”. If it is not a disturbance, the answer is “no”.
That’s a variant on the all-powerful Test for the Controlled
Variable of which I was previously unaware. But then, sadly, I am
constrained to using only publicly available mathematics and logic.
I suppose there is also an R-linguistics that determines whether the
force is a disturbance, so that this Test can be applied?
Martin

···

[Rick Marken 2018-02-25_16:24:43]

Bruce Abbott (2018.02.25.1835 EST)

            BA: I started the paragraph by saying

that of course equilibrium systems oppose disturbances.Â
Then I gave an example of an equilibrium system that
opposes disturbances. So you come back with “wow, so
tables are control systems too?� Apparently you would
rather look stupid than conceive the point. So,
paraphrasing the immortal words of James Carville, “It’s
an equilibrium system, stupid!â€? NOW do you understand?Â
Sheesh!

    RM:Â  I don't understand what I got wrong? You said that a

table top opposes disturbances. Only control systems oppose
disturbances. So you were saying that a table top is a control
system.

18

[Rick Marken 2018-02-27_13:33:51]

 Bruce Abbott (2018.02.27.1025 EST)--

BA: Your â€?PCTâ€? definition of “disturbanceâ€? is fine if only applied to a control system, but is overly restrictive. In physics and engineering, “disturbanceâ€? means the same thing whether the variable being disturbed is a controlled quantity or one that, in the absence of disturbance, would settle to an equilibrium value. Indeed, the controlled quantity of a control system settles to an equilibrium value in the absence of disturbance, so long as the reference is steady.

RM: You say that the only way to distinguish control from equilibrium systems is in terms of the source of energy for the disturbance opposition. This implies that you need some way to distinguish these system because the system you are dealing with could be either one. I would like to know why this is necessary. Why would you think that what is actually an equilibrium system might be a control system, and vice versa? What is it, for example, about the behavior of a mass spring system that would lead me to think that it could be an equilibrium or a control system so that I would need to look for the source of its energy for disturbance resistance in order to know which it is? Or, alternatively, what is it about the behavior of a living organism that would lead me to think that it could be an equilibrium or a control system so that I would need to look for the source of its energy for disturbance resistance in order to know which it is?Â

Â

BA: It is important to recognize that equilibrium systems have their own stabilizing effects that can either augment or interfere with control. I have already given one example of the former: dropping a weight into an outstretched hand. The spring-like qualities of muscle and tendon limit the degree of sag of the arm as the weight is added, even if there is no change in the neural output to the muscles. A control system acting in parallel may reduce the sag by increasing the neural output to the muscles, but at some delay owing to the time involved in conducting neural impulses around the control loop. The equilibrium system’s springiness begins to oppose the disturbance immediately, thus helping to stabilize the arm even before the control system can act.

RM: I think this means that you have to take into account the properties of the feedback connection between output and input when you are trying to understand the behavior of a control system. You are describing the behavior of a control system with a springy rather than a rigid feedback connection between input and output. >

Â

BA: Equilibrium systems may also oppose the attempts of a control system to alter the value of a controlled variable, making controlling that variable more difficult. Physicians sometimes run into this problem when to treat a disorder they need to change the level of a physiological variable like body temperature or blood glucose level and must overcome the homeostatic mechanism that is keeping the temperature or glucose level too high (or too low).

RM: Body temperature and glucose level are controlled variables. The problem you describe is one of conflict between control systems.>

Â

RM: If this is the aspect of control theory that interests you then, mazel tov. But I'll stick with PCT.

Â

BA: If “sticking with PCTâ€? means sticking your head in the sand and ignoring potentially important influences on control, then I would strongly recommend not taking that approach. PCT is an application of the principles of system dynamics, not an independent science that stands apart from it.

RM: PCT is an application of control theory to understanding the behavior of organisms.
Â

BA: The PCT theorist would be well advised to become familiar with system dynamics, which provides the tools for analyzing complex dynamic systems, including control systems, equilibrium systems, positive feedback systems, open-loop systems, and various combinations of these.

RM: I think PCT provides all the tools you need -- the tools of control theory -- to understand the purposive behavior of organisms. There is nothing wrong with learning the tools of systems dynamics but it seems to me that the important thing is to know about these tools is when to use them. I think it's pretty clear that these tools have been profoundly misused (for example, by the likes of A.. Feldman) to show that control phenomena can be explained in terms of equilibrium (rather than control) theory.Â
RM: I am also suspicious of the usefulness of the tools of system dynamics because they deal only with the equilibriating done by systems controlling a very simple variable: position;the pendulum equilibriates the position of the bob; a mass-spring system equilibriates the position of the mass; the bowl equilibriates the position of the ball; etc.  So all that the tools of system dynamics could possibly contribute to our understanding of the behavior of organisms is something about the dynamics of control of what are called "intensity" variables in PCT -- variables which are very important for control of more complex variables (like programs) but are only a very small subset of the many different kinds of variables that organisms control.Â
RM: But the biggest problem with systems dynamics tools is their misapplication to the study of purposive behavior. Indeed, I think that so far they have only been misapplied. Maybe you can do it right. But it seems to me that the right way to apply the tools of system dynamics to the behavior of organisms is as a model of the physical characteristics of the feedback connection in some control loops (such as control of the position of the limbs by variation in muscle forces) .But I think that's just part of PCT modeling, since you have to properly model the feedback function in order to get a proper model of the controlling that is observed.
Best
Rick

···

Â

Bruce

Â

Â

Â

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

19

[Rick Marken 2018-02-27_14:03:57]

Martin Taylor (2018.02.27.14.17)--

MT: An interesting application of R-logic (R-Math Axiom 1) here.>>

RM:Â I don't understand what I got wrong? You said that a table top opposes disturbances. Only control systems oppose disturbances. So you were saying that a table top is a control system.

MT: A force is applied to a variable. The force is resisted and the variable is influenced less than it would have been without the resistance.

RM: How do you know how much the variable would have been influenced without the resistance? For example, I push on a pendulum and its position is changed by an amount X. How do I know how much the position would have been changed if there hadn't been resistance to the push? Indeed, how do I know that there was any resistance to the push?
Â

MT: We want to know whether the cause of the resistance is that the variable is the environmental correlate of a controlled perception. In R-logic, this is easy. If the force is a disturbance, the answer is "Yes". If it is not a disturbance, the answer is "no".

RM: No, Martin. First you look up the equations that tell how much a force of F newtons is expected to displace a pendulum bob of mass M suspended from a string of length L. Solving this equation you find that the expected displacement is X centimeters. You then apply force F to the bob and observe how much it is actually displaced. If it is displaced X centimeters, the pendulum is not a control system. If it is displaced slightly less than X centimeters it could be a control system operating with low gain. But if it is displaced by an amount that is much less than X then it's almost certainly a control system. >

MT: That's a variant on the all-powerful Test for the Controlled Variable of which I was previously unaware.

RM: You are unaware of the variant of TCV that you describe because there is no such variant.This is what you get from never doing the TCV.
Â

MT: But then, sadly, I am constrained to using only publicly available mathematics and logic. I suppose there is also an R-linguistics that determines whether the force is a disturbance, so that this Test can be applied?

RM:Â Your problem, Martin, is not with your math but but with your facts. Though your math could use some work too.
BestÂ

···

Martin

--
Richard S. MarkenÂ
"Perfection is achieved not when you have nothing more to add, but when you
have nothing left to take away.�
                --Antoine de Saint-Exupery

20

[From Bruce Abbott (2018.02.27.1900 EST)]

[Rick Marken 2018-02-27_13:33:51]

Bruce Abbott (2018.02.27.1025 EST)–

BA: Your �PCT� definition of “disturbance� is fine if only applied to a control system, but is overly restrictive. In physics and engineering, “disturbance� means the same thing whether the variable being disturbed is a controlled quantity or one that, in the absence of disturbance, would settle to an equilibrium value. Indeed, the controlled quantity of a control system settles to an equilibrium value in the absence of disturbance, so long as the reference is steady.

RM: You say that the only way to distinguish control from equilibrium systems is in terms of the source of energy for the disturbance opposition. This implies that you need some way to distinguish these system because the system you are dealing with could be either one. I would like to know why this is necessary. Why would you think that what is actually an equilibrium system might be a control system, and vice versa? What is it, for example, about the behavior of a mass spring system that would lead me to think that it could be an equilibrium or a control system so that I would need to look for the source of its energy for disturbance resistance in order to know which it is? Or, alternatively, what is it about the behavior of a living organism that would lead me to think that it could be an equilibrium or a control system so that I would need to look for the source of its energy for disturbance resistance in order to know which it is?

No, I never claimed that the only way to distinguish control from equilibrium systems is in terms of the source of energy for the disturbance opposition. I said that it is one way. Control systems can also be distinguished from control systems in that only a control system can have a loop gain greater than one (because it draws on a source of energy other than the disturbance itself to produce the opposing action). And only control systems have references, comparators, and error signals (although these can be implied, or combined in ways that make their presence less than obvious).

You ask why one would want to know if a system one is investigating is an equilibrium system or a control system. Well, I’d say that if I want to thoroughly understand what processes are at work, then whether an equilibrium system is involved (instead of or alongside a control system) is an important part of the explanation.

BA: It is important to recognize that equilibrium systems have their own stabilizing effects that can either augment or interfere with control. I have already given one example of the former: dropping a weight into an outstretched hand. The spring-like qualities of muscle and tendon limit the degree of sag of the arm as the weight is added, even if there is no change in the neural output to the muscles. A control system acting in parallel may reduce the sag by increasing the neural output to the muscles, but at some delay owing to the time involved in conducting neural impulses around the control loop. The equilibrium system’s springiness begins to oppose the disturbance immediately, thus helping to stabilize the arm even before the control system can act.

RM: I think this means that you have to take into account the properties of the feedback connection between output and input when you are trying to understand the behavior of a control system. You are describing the behavior of a control system with a springy rather than a rigid feedback connection between input and output.

Yes. But consider this: Some physiologists have suggested that skeletal movement is achieved by changing the equilibrium position toward which opposing muscles drive the joint position, achieved by altering the effective spring constants of the opposing muscles.  So are we dealing with an adjustable equilibrium position and/or a control system? If you wish to understand how we move our joints, wouldn’t you like to know? Or shall we just ignore the possible influences of equilibrium systems on behavior?

BA: Equilibrium systems may also oppose the attempts of a control system to alter the value of a controlled variable, making controlling that variable more difficult. Physicians sometimes run into this problem when to treat a disorder they need to change the level of a physiological variable like body temperature or blood glucose level and must overcome the homeostatic mechanism that is keeping the temperature or glucose level too high (or too low).

RM: Body temperature and glucose level are controlled variables. The problem you describe is one of conflict between control systems.

Actually their regulation involves both. For example, blood concentration of glucose drives a reaction in the liver that converts glucose to glycogen when glucose levels are high, thus removing excess levels from the bloodstream.  When glucose levels fall the reaction reverses and glucose is released back into the bloodstream. In either case the system is seeking an equilibrium. But there are also control systems that produce an input of more nutrients (via the digestive system) via control of several variables; we experience errors in these variables as hunger.

RM: If this is the aspect of control theory that interests you then, mazel tov. But I’ll stick with PCT.

BA: If “sticking with PCT� means sticking your head in the sand and ignoring potentially important influences on control, then I would strongly recommend not taking that approach. PCT is an application of the principles of system dynamics, not an independent science that stands apart from it.

RM: PCT is an application of control theory to understanding the behavior of organisms.

And control theory is an application of system dynamics.Â

BA: The PCT theorist would be well advised to become familiar with system dynamics, which provides the tools for analyzing complex dynamic systems, including control systems, equilibrium systems, positive feedback systems, open-loop systems, and various combinations of these

RM: I think PCT provides all the tools you need – the tools of control theory – to understand the purposive behavior of organisms. There is nothing wrong with learning the tools of systems dynamics but it seems to me that the important thing is to know about these tools is when to use them. I think it’s pretty clear that these tools have been profoundly misused (for example, by the likes of A… Feldman) to show that control phenomena can be explained in terms of equilibrium (rather than control) theory.

RM: I am also suspicious of the usefulness of the tools of system dynamics because they deal only with the equilibriating done by systems controlling a very simple variable: position;the pendulum equilibriates the position of the bob; a mass-spring system equilibriates the position of the mass; the bowl equilibriates the position of the ball; etc.

Where, oh where do you come up with these ideas? The tools of system dynamics do not only deal with such things, they deal with the whole spectrum of possible system dynamics, including control.

So all that the tools of system dynamics could possibly contribute to our understanding of the behavior of organisms is something about the dynamics of control of what are called “intensity” variables in PCT – variables which are very important for control of more complex variables (like programs) but are only a very small subset of the many different kinds of variables that organisms control.

Nonsense.

RM: But the biggest problem with systems dynamics tools is their misapplication to the study of purposive behavior. Indeed, I think that so far they have only been misapplied.

Vague charges again:Â by whom, and in what way? But granting this, some have misapplied control theory, so according to your logic, we should avoid it?

Maybe you can do it right. But it seems to me that the right way to apply the tools of system dynamics to the behavior of organisms is as a model of the physical characteristics of the feedback connection in some control loops (such as control of the position of the limbs by variation in muscle forces) .But I think that’s just part of PCT modeling, since you have to properly model the feedback function in order to get a proper model of the controlling that is observed.

Because control systems are dynamic systems, they fall within the purview of system dynamics, and the tools provided, including the development and testing of generative models, are legitimately applied to the elucidation of system organization and dynamics. A scientist should be permitted to use whatever tools may prove useful in the design and analysis of such systems.

Bruce