Useful opposition and emergent properties (1. Stiffness)

[Martin Taylor 2017.10.26.10.47]

For a moment I'd like to leave the world of single control loops and

arguments about whether there is anything really “out there” that we
can perceive. Instead, I want to talk about a couple of emergent
properties of clusters of control loops, perhaps hierarchically
arranged, both of which depend on conflict to enhance the strength
and resilience of complex control systems.

What is an "emergent property"? The Wikipedia article on "Emergence"

defines it thus: "In philosophy**, systems theory**, science* ,
and* art**, emergence * is a
phenomenon whereby larger entities arise through interactions
among smaller or simpler entities such that the larger entities
exhibit properties the smaller/simpler entities do not exhibit.* "
That is also the definition I use, according to which “control” is
an emergent property of a particular structure of some specific
basic functions (which we call perceptual, comparator, and output
functions).

In this message I will talk about an emergent property that in

living organisms is dependant on control, which I call “stiffness”.
In a later message, I will talk about another emergent property
commonly known as “tensegrity”. Tensegrity depends on stiffness.
Both stiffness and tensegrity can exist in non-living structures,
and I will refer to the non-living versions as guides to the
stiffness and tensegrity properties of complexes of control loops.
But this message is quite long enough dealing with stiffness, and
the tensegrity properties of control loop complexes are conceptually
trickier, so their discussion can be delayed.

**Stiffness and opposition**

Since the subject line of this message includes the word

“opposition”, that must be defined as it is used here. I use
opposition as a variant of the PCT definition of conflict, that it
exists when N >1 control units try to bring their perceptions of
M<N environmental properties to their individual different
reference values. The classic case demonstrated by Kent McClelland’s
presentation at CSG-93 is of two control systems trying to bring one
CEV to their two different reference values, the result being that
if the TCV is applied to the CEV, it seems to be being controlled to
an intermediate reference value by a controller with a gain that is
the sum of the gains of the conflicted control systems.

The conflict cannot be seen by a Tester doing the Test for the

controlled variable. To see the conflict requires a wider view that
compares what the control systems seem to be trying to do, as in the
case of someone observing a tug-of-war at a country fair. What the
tester sees is a strongly controlled property of the environment,
say the location of the handkerchief tied in the middle of the
tug-of-war rope.

Some time ago we had a thread about whether Bill's action to disturb

Dag’s control of the steering wheel angle constituted a conflict
between Bill and Dag, which according to the definition above it
does not. But Dag’s output force that countered Bill’s disturbance
is an opposition to Bill’s force. Together these forces bring the
steering wheel to an angle that keeps the car in the place in its
lane where Dag wants it to be.

Lost in this view of the situation is another property of the

handkerchief in the tug-of-war, its location perpendicular to the
axis along which the two teams are pulling. Let’s call their pulling
axis “X”, so that one team pulls in the +X direction while the other
pulls in the -X direction. If you apply a force to the handkerchief
in the Y direction or the Z direction, it will resist in the same
way as would a spring, snapping back to its original location when
the perpendicular force is removed. The stronger the two teams, the
stronger the apparent spring, and the more secure is the
handkerchief in the Y and Z directions, no matter who wins the
tug-of-war, provided the teams pull only along the X axis direction.
Think what has happened here. Control has been used to produce
stability in a property that is not controlled. This “stiffness” is
an emergent property of control conflict. It cannot exist without at
least two pulls in opposite directions.

Of course if the teams are standing on a platform that moves freely

in the Y direction, they, the rope, and the handkerchief all will
move in Y when a Y-direction force is applied to the handkerchief
and the spring-like effect will not be observed. But if the teams do
not move so easily in Y, the rope in tension will resist the Y-force
on the handkerchief, which will spring back when the force is
removed. [Aside: here we have a hint about tensegrity effects in
control. But that is for a later message.]

The pulls does not need to be caused by two control systems, since

the same thing happens when one pulls a rope attached to a rock, nor
does it need even one control system, since it would be true of a
cable staying the boom of a crane, or a vine that prevents a falling
tree from falling all the way to the ground. Stiffness is a purely
physical property that can exist in accidentally constructed
physical systems without control. Nevertheless, stiffness does
emerge from control opposition, and that opposition need not be in
just one dimension.

Think of a bunch of people holding a blanket to catch someone

jumping from a burning building. If they all pull moderately hard,
the person will probably be safe. If they pull too loosely, the
person will hit the ground almost as hard as if the blanket was not
there. If they pull too hard, the blanket will be as stiff as the
ground and the person again risks serious damage. The people are
pulling against each other in various directions in one
two-dimensional plane, and the stiffness in the direction
perpendicular to the plane is what protects the falling person by
its “spring-like” effects while the pulling people are anchored to
the fixed ground.

The pullers collectively control the X-Y location of the blanket so

that it will be under the falling person, so they all have the same
reference value for its location and they should not be in conflict.
However, the location isn’t the only thing that affects the survival
of the falling person, and the pullers are controlling for the
person to survive. For the person to survive, the blanket must be
stiff but not too stiff, which means that at some level the pullers
must control for sufficient opposition to exist among their
different pulls. They must therefore be able to perceive either the
opposition or something highly correlated with the opposition, such
as the blanket’s stiffness. Whether or not they perceive and control
the magnitude of the opposition, the opposition is necessary for
them to save the falling person.

We use "stiffness" or the opposition associated with it in much more

mundane circumstances. imagine holding a small parade flag up with
one hand. If it is a calm day your arms will be quite relaxed,
tensors and extensors applying equal but small opposing forces. If
the wind starts getting stronger, all your muscles become tenser,
creating stronger opposition between tensors and extensors. If the
wind is gusty and in erratic directions, your muscle tensions
increase even more. You use that opposition to make the orientation
of the flagstaff stiffer, easing your control. As we will see, this
increased stiffness is associated with an automatic increase in the
effective gain of the flag orientation control unit. [Aside:
Increased gain can lead to oscillatory instability in a control
loop. Might this be the underlying cause of “intentional tremor”?]

Can stiffness due to conflict be used for internal purposes as well

as in the external environment? Perhaps, but whether it is useful is
another question. The Method of Levels is predicated on the idea
that all conflict is bad, and reducing or removing it is good. I
hazard a guess that this may overstate the case, and that some
opposition, which is easily confused with conflict, serves to
stabilize a personality. “Good” and “bad” being subjective
perceptions, I suggest that it may not be conflict or internal
opposition that is the problem, so much as that the person perceives
their situation to be “bad” (in error according to some reference
value for some perception they have of themselves. If that is so, a
resolution to the problem might be in a direction orthogonal to the
direction of the apparent conflict).

"Stiffness" is a property that we ascribe to some people, both in

their physical comportment and in their personality. We perceive a
person who appears easy and relaxed, while being effective in both
their interactions with the physical environment (e.g. sports, arts,
construction, etc.) and with other people (e.g. easy-going,
tolerant, down-to-earth, etc.) to be in some way “better” than
someone who is rigid, formal, rule-bound, intolerant of strangeness,
and so forth, in other words, “stiff”.

**Stiffness as negative tolerance**

I just used the word "tolerant" in a way that opposes it to "stiff".

The opposition is inherent in the requirement for neural firing
rates to be non-negative. I’m not going to recap the thread on that
topic of a few weeks ago. Suffice it to say that there must be two
separate comparator outputs, one for negative error and one for
positive error. These may be biased one way so that an error near
zero is treated as being zero, or the other way so that even a zero
error is treated as an error in the direction reported by that half
of the comparator. In the latter case, the error is simultaneously
reported as being both positive and negative. The diagram suggests
these different possibilities.

![TolerantAndStiffComparators.jpg|1544x1144](upload://uUGG1pSZUXJRxzVtsbr9WjHdzZ4.jpeg)

The six panels of this Figure show possible comparator functions.

The four in the left column show the output versus actual error
(reference - perception) taking into account the fact that the
neural firing rate cannot be negative. Of these four, the lower of
each pair shows the output that would be inhibitory downstream at
the output function, equivalent to a negative output. The right-hand
pair shows the equivalent virtual two-way comparator, the lower half
being the lower left panel flipped vertically. In each panel the
dashed curve (line) shows an unbiased comparator, while the solid
line shows the output for a biased comparator.

In the upper set of three panels, the bias is such that the

equivalent two-way comparator has a tolerance zone, a region near
zero error that is treated as though the error was truly zero. In
the lower set, the bias is in the other direction, so that both
one-way comparators produce output even when the perception is equal
to the reference. The equivalent two-way comparator never does that,
but it has a zone in which the equivalent output changes twice as
fast as a function of the true error. The output being non-zero for
both “half-comparators” in a region around zero actual error creates
an opposition between the output in one direction and the output in
the other direction, which produces a zone of stiffness around zero
error. Stiffness and tolerance are two sides of the same coin, and a
system can be smoothly changed from a tolerant one to a stiff one by
a continuous change of bias.

The stiffness-tolerance bias is not part of Powers's simple

hierarchy, but it is something we employ, at least at the muscular
level. I see no reason why it could not be a controllable
perception. After all, we do say to people things like “Let it go.
It’s OK as it is, so stop trying to make it better.”, which asks the
person to widen a tolerance zone. The opposite is less obvious, and
is seen usually more in interpersonal interaction than in dealing
with physical systems, though it is not unheard of to control to get
something near its reference level and then to stiffen up,
increasing the gain to get the almost right to become “just right”.

As noted above, the virtual gain increase that goes along with the

conflict in creating stiffness may not be the main value to the
organism of making something stiff. The value is likely to be in
stabilizing something in another dimension that is used by some
quite different control system, without attempting to control in
that other dimension, thus avoiding conflict with the system that
uses the stabilized but not controlled dimension. Kent McClelland
has talked about collective control providing systems of stable
properties of the environment, such as roads than enable quicker
travel between towns than would be possible through untamed jungle,
or administrative roles in an organization that allow other people
to use people in those roles for their own purposes, as a sales
assistant may make it easier for a high-school graduate to control
her perception of just what dress to buy for the Prom.

I think that's enough about stiffness for now. In the first draft of

this message I followed this with a longer section about tensegrity,
but I will leave that for a later message.

Martin

[Eetu Pikkarainen 2017-10-31-11:29]

[Martin Taylor 2017.10.26.10.47]

Martin, thanks, interesting.

Stiffness is not only a possibly stable character of a person but often also a feature of action in strange context. Then it could be perhaps called also excitement.
When I was practicing to drive a car I tensed my muscles and at the same time pushed the wheel to the left by my right hand and to the right by my left hand when driving straight forward. That is very straining but more learning and experience makes the performance
more flexible and lighter. I think this can be partially generalized: a stiff personality possible feels the normal contexts strange. I agree that stiffness can be controlled but it is not always easy to affect it and it may require learning i.e. reorganization.

The lower right diagram panel makes me a little disconcerted. In the stiffness area the time rate of change is twice as much of elsewhere. Intuitively I would had said
that stiffness slows down the rate of change. I must think about this more.

Is stiffness in some way a side effect of control?

image00287.jpg

···

Eetu

Please, regard all my statements as questions,

no matter how they are formulated.

For a moment I’d like to leave the world of single control loops and arguments about whether there is anything really “out there” that we can perceive.
Instead, I want to talk about a couple of emergent properties of clusters of control loops, perhaps hierarchically arranged, both of which depend on conflict to enhance the strength and resilience of complex control systems.
What is an “emergent property”? The Wikipedia article on “Emergence” defines it thus: "In
philosophy,
systems theory,
science, and
art
, emergence is a phenomenon whereby larger entities arise through interactions among smaller or simpler entities such that the larger entities exhibit properties the smaller/simpler entities do not exhibit.
" That is also the definition I use,
according to which “control” is an emergent property of a particular structure of some specific basic functions (which we call perceptual, comparator, and output functions).
In this message I will talk about an emergent property that in living organisms is dependant on control, which I call “stiffness”. In a later message, I will talk about another emergent property commonly known as “tensegrity”. Tensegrity depends on stiffness.
Both stiffness and tensegrity can exist in non-living structures, and I will refer to the non-living versions as guides to the stiffness and tensegrity properties of complexes of control loops. But this message is quite long enough dealing with stiffness,
and the tensegrity properties of control loop complexes are conceptually trickier, so their discussion can be delayed.
Stiffness and opposition
Since the subject line of this message includes the word “opposition”, that must be defined as it is used here. I use opposition as a variant of the PCT definition of conflict, that it exists when N >1 control units try to bring their perceptions of M<N environmental
properties to their individual different reference values. The classic case demonstrated by Kent McClelland’s presentation at CSG-93 is of two control systems trying to bring one CEV to their two different reference values, the result being that if the TCV
is applied to the CEV, it seems to be being controlled to an intermediate reference value by a controller with a gain that is the sum of the gains of the conflicted control systems.
The conflict cannot be seen by a Tester doing the Test for the controlled variable. To see the conflict requires a wider view that compares what the control systems seem to be trying to do, as in the case of someone observing a tug-of-war at a country fair.
What the tester sees is a strongly controlled property of the environment, say the location of the handkerchief tied in the middle of the tug-of-war rope.
Some time ago we had a thread about whether Bill’s action to disturb Dag’s control of the steering wheel angle constituted a conflict between Bill and Dag, which according to the definition above it does not. But Dag’s output force that countered Bill’s disturbance
is an opposition to Bill’s force. Together these forces bring the steering wheel to an angle that keeps the car in the place in its lane where Dag wants it to be.
Lost in this view of the situation is another property of the handkerchief in the tug-of-war, its location perpendicular to the axis along which the two teams are pulling. Let’s call their pulling axis “X”, so that one team pulls in the +X direction while the
other pulls in the -X direction. If you apply a force to the handkerchief in the Y direction or the Z direction, it will resist in the same way as would a spring, snapping back to its original location when the perpendicular force is removed. The stronger
the two teams, the stronger the apparent spring, and the more secure is the handkerchief in the Y and Z directions, no matter who wins the tug-of-war, provided the teams pull only along the X axis direction. Think what has happened here. Control has been used
to produce stability in a property that is not controlled. This “stiffness” is an emergent property of control conflict. It cannot exist without at least two pulls in opposite directions.
Of course if the teams are standing on a platform that moves freely in the Y direction, they, the rope, and the handkerchief all will move in Y when a Y-direction force is applied to the handkerchief and the spring-like effect will not be observed. But if the
teams do not move so easily in Y, the rope in tension will resist the Y-force on the handkerchief, which will spring back when the force is removed. [Aside: here we have a hint about tensegrity effects in control. But that is for a later message.]
The pulls does not need to be caused by two control systems, since the same thing happens when one pulls a rope attached to a rock, nor does it need even one control system, since it would be true of a cable staying the boom of a crane, or a vine that prevents
a falling tree from falling all the way to the ground. Stiffness is a purely physical property that can exist in accidentally constructed physical systems without control. Nevertheless, stiffness does emerge from control opposition, and that opposition need
not be in just one dimension.
Think of a bunch of people holding a blanket to catch someone jumping from a burning building. If they all pull moderately hard, the person will probably be safe. If they pull too loosely, the person will hit the ground almost as hard as if the blanket was
not there. If they pull too hard, the blanket will be as stiff as the ground and the person again risks serious damage. The people are pulling against each other in various directions in one two-dimensional plane, and the stiffness in the direction perpendicular
to the plane is what protects the falling person by its “spring-like” effects while the pulling people are anchored to the fixed ground.
The pullers collectively control the X-Y location of the blanket so that it will be under the falling person, so they all have the same reference value for its location and they should not be in conflict. However, the location isn’t the only thing that affects
the survival of the falling person, and the pullers are controlling for the person to survive. For the person to survive, the blanket must be stiff but not too stiff, which means that at some level the pullers must control for sufficient opposition to exist
among their different pulls. They must therefore be able to perceive either the opposition or something highly correlated with the opposition, such as the blanket’s stiffness. Whether or not they perceive and control the magnitude of the opposition, the opposition
is necessary for them to save the falling person.
We use “stiffness” or the opposition associated with it in much more mundane circumstances. imagine holding a small parade flag up with one hand. If it is a calm day your arms will be quite relaxed, tensors and extensors applying equal but small opposing forces.
If the wind starts getting stronger, all your muscles become tenser, creating stronger opposition between tensors and extensors. If the wind is gusty and in erratic directions, your muscle tensions increase even more. You use that opposition to make the orientation
of the flagstaff stiffer, easing your control. As we will see, this increased stiffness is associated with an automatic increase in the effective gain of the flag orientation control unit. [Aside: Increased gain can lead to oscillatory instability in a control
loop. Might this be the underlying cause of “intentional tremor”?]
Can stiffness due to conflict be used for internal purposes as well as in the external environment? Perhaps, but whether it is useful is another question. The Method of Levels is predicated on the idea that all conflict is bad, and reducing or removing it is
good. I hazard a guess that this may overstate the case, and that some opposition, which is easily confused with conflict, serves to stabilize a personality. “Good” and “bad” being subjective perceptions, I suggest that it may not be conflict or internal opposition
that is the problem, so much as that the person perceives their situation to be “bad” (in error according to some reference value for some perception they have of themselves. If that is so, a resolution to the problem might be in a direction orthogonal to
the direction of the apparent conflict).
“Stiffness” is a property that we ascribe to some people, both in their physical comportment and in their personality. We perceive a person who appears easy and relaxed, while being effective in both their interactions with the physical environment (e.g. sports,
arts, construction, etc.) and with other people (e.g. easy-going, tolerant, down-to-earth, etc.) to be in some way “better” than someone who is rigid, formal, rule-bound, intolerant of strangeness, and so forth, in other words, “stiff”.
Stiffness as negative tolerance

I just used the word “tolerant” in a way that opposes it to “stiff”. The opposition is inherent in the requirement for neural firing rates to be non-negative. I’m not going to recap the thread on that topic of a few weeks ago. Suffice it to say that there must
be two separate comparator outputs, one for negative error and one for positive error. These may be biased one way so that an error near zero is treated as being zero, or the other way so that even a zero error is treated as an error in the direction reported
by that half of the comparator. In the latter case, the error is simultaneously reported as being both positive and negative. The diagram suggests these different possibilities.

The six panels of this Figure show possible comparator functions. The four in the left column show the output versus actual error (reference - perception) taking into account the fact that the neural firing rate cannot be negative. Of these four, the lower
of each pair shows the output that would be inhibitory downstream at the output function, equivalent to a negative output. The right-hand pair shows the equivalent virtual two-way comparator, the lower half being the lower left panel flipped vertically. In
each panel the dashed curve (line) shows an unbiased comparator, while the solid line shows the output for a biased comparator.

In the upper set of three panels, the bias is such that the equivalent two-way comparator has a tolerance zone, a region near zero error that is treated as though the error was truly zero. In the lower set, the bias is in the other direction, so that both one-way
comparators produce output even when the perception is equal to the reference. The equivalent two-way comparator never does that, but it has a zone in which the equivalent output changes twice as fast as a function of the true error. The output being non-zero
for both “half-comparators” in a region around zero actual error creates an opposition between the output in one direction and the output in the other direction, which produces a zone of stiffness around zero error. Stiffness and tolerance are two sides of
the same coin, and a system can be smoothly changed from a tolerant one to a stiff one by a continuous change of bias.

The stiffness-tolerance bias is not part of Powers’s simple hierarchy, but it is something we employ, at least at the muscular level. I see no reason why it could not be a controllable perception. After all, we do say to people things like “Let it go. It’s
OK as it is, so stop trying to make it better.”, which asks the person to widen a tolerance zone. The opposite is less obvious, and is seen usually more in interpersonal interaction than in dealing with physical systems, though it is not unheard of to control
to get something near its reference level and then to stiffen up, increasing the gain to get the almost right to become “just right”.

As noted above, the virtual gain increase that goes along with the conflict in creating stiffness may not be the main value to the organism of making something stiff. The value is likely to be in stabilizing something in another dimension that is used by some
quite different control system, without attempting to control in that other dimension, thus avoiding conflict with the system that uses the stabilized but not controlled dimension. Kent McClelland has talked about collective control providing systems of stable
properties of the environment, such as roads than enable quicker travel between towns than would be possible through untamed jungle, or administrative roles in an organization that allow other people to use people in those roles for their own purposes, as
a sales assistant may make it easier for a high-school graduate to control her perception of just what dress to buy for the Prom.

I think that’s enough about stiffness for now. In the first draft of this message I followed this with a longer section about tensegrity, but I will leave that for a later message.

Martin

[Eetu
Pikkarainen 2017-10-31-11:29]

[Martin Taylor 2017.10.26.10.47]

Martin, thanks, interesting.

        Stiffness is not only a possibly stable

character of a person but often also a feature of action in
strange context. Then it could be perhaps called also
excitement. When I was practicing to drive a car I tensed my
muscles and at the same time pushed the wheel to the left by
my right hand and to the right by my left hand when driving
straight forward. That is very straining but more learning
and experience makes the performance more flexible and
lighter.

image00287.jpg

···

Eetu

          Please, regard all my statements as

questions,

no matter how they are formulated.

        For a moment I'd like to leave the world of single control

loops and arguments about whether there is anything really
“out there” that we can perceive.
Instead, I want to talk about a couple of emergent
properties of clusters of control loops, perhaps
hierarchically arranged, both of which depend on conflict to
enhance the strength and resilience of complex control
systems.

      What is an "emergent property"? The Wikipedia article on

“Emergence” defines it thus: "* In
philosophy ,
systems
theory
,
science, and
art
, emergence is a phenomenon whereby larger
entities arise through interactions among smaller or simpler
entities such that the larger entities exhibit properties
the smaller/simpler entities do not exhibit.* " That is
also the definition I use, according to which “control” is an
emergent property of a particular structure of some specific
basic functions (which we call perceptual, comparator, and
output functions).

      In this message I will talk about an emergent property that in

living organisms is dependant on control, which I call
“stiffness”. In a later message, I will talk about another
emergent property commonly known as “tensegrity”. Tensegrity
depends on stiffness. Both stiffness and tensegrity can exist
in non-living structures, and I will refer to the non-living
versions as guides to the stiffness and tensegrity properties
of complexes of control loops. But this message is quite long
enough dealing with stiffness, and the tensegrity properties
of control loop complexes are conceptually trickier, so their
discussion can be delayed.

      **Stiffness and opposition**

      Since the subject line of this message includes the word

“opposition”, that must be defined as it is used here. I use
opposition as a variant of the PCT definition of conflict,
that it exists when N >1 control units try to bring their
perceptions of M<N environmental properties to their
individual different reference values. The classic case
demonstrated by Kent McClelland’s presentation at CSG-93 is of
two control systems trying to bring one CEV to their two
different reference values, the result being that if the TCV
is applied to the CEV, it seems to be being controlled to an
intermediate reference value by a controller with a gain that
is the sum of the gains of the conflicted control systems.

      The conflict cannot be seen by a Tester doing the Test for the

controlled variable. To see the conflict requires a wider view
that compares what the control systems seem to be trying to
do, as in the case of someone observing a tug-of-war at a
country fair. What the tester sees is a strongly controlled
property of the environment, say the location of the
handkerchief tied in the middle of the tug-of-war rope.

      Some time ago we had a thread about whether Bill's action to

disturb Dag’s control of the steering wheel angle constituted
a conflict between Bill and Dag, which according to the
definition above it does not. But Dag’s output force that
countered Bill’s disturbance is an opposition to Bill’s force.
Together these forces bring the steering wheel to an angle
that keeps the car in the place in its lane where Dag wants it
to be.

      Lost in this view of the situation is another property of the

handkerchief in the tug-of-war, its location perpendicular to
the axis along which the two teams are pulling. Let’s call
their pulling axis “X”, so that one team pulls in the +X
direction while the other pulls in the -X direction. If you
apply a force to the handkerchief in the Y direction or the Z
direction, it will resist in the same way as would a spring,
snapping back to its original location when the perpendicular
force is removed. The stronger the two teams, the stronger the
apparent spring, and the more secure is the handkerchief in
the Y and Z directions, no matter who wins the tug-of-war,
provided the teams pull only along the X axis direction. Think
what has happened here. Control has been used to produce
stability in a property that is not controlled. This
“stiffness” is an emergent property of control conflict. It
cannot exist without at least two pulls in opposite
directions.

      Of course if the teams are standing on a platform that moves

freely in the Y direction, they, the rope, and the
handkerchief all will move in Y when a Y-direction force is
applied to the handkerchief and the spring-like effect will
not be observed. But if the teams do not move so easily in Y,
the rope in tension will resist the Y-force on the
handkerchief, which will spring back when the force is
removed. [Aside: here we have a hint about tensegrity effects
in control. But that is for a later message.]

      The pulls does not need to be caused by two control systems,

since the same thing happens when one pulls a rope attached to
a rock, nor does it need even one control system, since it
would be true of a cable staying the boom of a crane, or a
vine that prevents a falling tree from falling all the way to
the ground. Stiffness is a purely physical property that can
exist in accidentally constructed physical systems without
control. Nevertheless, stiffness does emerge from control
opposition, and that opposition need not be in just one
dimension.

      Think of a bunch of people holding a blanket to catch someone

jumping from a burning building. If they all pull moderately
hard, the person will probably be safe. If they pull too
loosely, the person will hit the ground almost as hard as if
the blanket was not there. If they pull too hard, the blanket
will be as stiff as the ground and the person again risks
serious damage. The people are pulling against each other in
various directions in one two-dimensional plane, and the
stiffness in the direction perpendicular to the plane is what
protects the falling person by its “spring-like” effects while
the pulling people are anchored to the fixed ground.

      The pullers collectively control the X-Y location of the

blanket so that it will be under the falling person, so they
all have the same reference value for its location and they
should not be in conflict. However, the location isn’t the
only thing that affects the survival of the falling person,
and the pullers are controlling for the person to survive. For
the person to survive, the blanket must be stiff but not too
stiff, which means that at some level the pullers must control
for sufficient opposition to exist among their different
pulls. They must therefore be able to perceive either the
opposition or something highly correlated with the opposition,
such as the blanket’s stiffness. Whether or not they perceive
and control the magnitude of the opposition, the opposition is
necessary for them to save the falling person.

      We use "stiffness" or the opposition associated with it in

much more mundane circumstances. imagine holding a small
parade flag up with one hand. If it is a calm day your arms
will be quite relaxed, tensors and extensors applying equal
but small opposing forces. If the wind starts getting
stronger, all your muscles become tenser, creating stronger
opposition between tensors and extensors. If the wind is gusty
and in erratic directions, your muscle tensions increase even
more. You use that opposition to make the orientation of the
flagstaff stiffer, easing your control. As we will see, this
increased stiffness is associated with an automatic increase
in the effective gain of the flag orientation control unit.
[Aside: Increased gain can lead to oscillatory instability in
a control loop. Might this be the underlying cause of
“intentional tremor”?]

      Can stiffness due to conflict be used for internal purposes as

well as in the external environment? Perhaps, but whether it
is useful is another question. The Method of Levels is
predicated on the idea that all conflict is bad, and reducing
or removing it is good. I hazard a guess that this may
overstate the case, and that some opposition, which is easily
confused with conflict, serves to stabilize a personality.
“Good” and “bad” being subjective perceptions, I suggest that
it may not be conflict or internal opposition that is the
problem, so much as that the person perceives their situation
to be “bad” (in error according to some reference value for
some perception they have of themselves. If that is so, a
resolution to the problem might be in a direction orthogonal
to the direction of the apparent conflict).

      "Stiffness" is a property that we ascribe to some people, both

in their physical comportment and in their personality. We
perceive a person who appears easy and relaxed, while being
effective in both their interactions with the physical
environment (e.g. sports, arts, construction, etc.) and with
other people (e.g. easy-going, tolerant, down-to-earth, etc.)
to be in some way “better” than someone who is rigid, formal,
rule-bound, intolerant of strangeness, and so forth, in other
words, “stiff”.

      **Stiffness as negative tolerance**

      I just used the word "tolerant" in a way that opposes it to

“stiff”. The opposition is inherent in the requirement for
neural firing rates to be non-negative. I’m not going to recap
the thread on that topic of a few weeks ago. Suffice it to say
that there must be two separate comparator outputs, one for
negative error and one for positive error. These may be biased
one way so that an error near zero is treated as being zero,
or the other way so that even a zero error is treated as an
error in the direction reported by that half of the
comparator. In the latter case, the error is simultaneously
reported as being both positive and negative. The diagram
suggests these different possibilities.

      The six panels of this Figure show possible comparator

functions. The four in the left column show the output versus
actual error (reference - perception) taking into account the
fact that the neural firing rate cannot be negative. Of these
four, the lower of each pair shows the output that would be
inhibitory downstream at the output function, equivalent to a
negative output. The right-hand pair shows the equivalent
virtual two-way comparator, the lower half being the lower
left panel flipped vertically. In each panel the dashed curve
(line) shows an unbiased comparator, while the solid line
shows the output for a biased comparator.

      In the upper set of three panels, the bias is such that the

equivalent two-way comparator has a tolerance zone, a region
near zero error that is treated as though the error was truly
zero. In the lower set, the bias is in the other direction, so
that both one-way comparators produce output even when the
perception is equal to the reference. The equivalent two-way
comparator never does that, but it has a zone in which the
equivalent output changes twice as fast as a function of the
true error. The output being non-zero for both
“half-comparators” in a region around zero actual error
creates an opposition between the output in one direction and
the output in the other direction, which produces a zone of
stiffness around zero error. Stiffness and tolerance are two
sides of the same coin, and a system can be smoothly changed
from a tolerant one to a stiff one by a continuous change of
bias.

      The stiffness-tolerance bias is not part of Powers's simple

hierarchy, but it is something we employ, at least at the
muscular level. I see no reason why it could not be a
controllable perception. After all, we do say to people things
like “Let it go. It’s OK as it is, so stop trying to make it
better.”, which asks the person to widen a tolerance zone. The
opposite is less obvious, and is seen usually more in
interpersonal interaction than in dealing with physical
systems, though it is not unheard of to control to get
something near its reference level and then to stiffen up,
increasing the gain to get the almost right to become “just
right”.

      As noted above, the virtual gain increase that goes along with

the conflict in creating stiffness may not be the main value
to the organism of making something stiff. The value is likely
to be in stabilizing something in another dimension that is
used by some quite different control system, without
attempting to control in that other dimension, thus avoiding
conflict with the system that uses the stabilized but not
controlled dimension. Kent McClelland has talked about
collective control providing systems of stable properties of
the environment, such as roads than enable quicker travel
between towns than would be possible through untamed jungle,
or administrative roles in an organization that allow other
people to use people in those roles for their own purposes, as
a sales assistant may make it easier for a high-school
graduate to control her perception of just what dress to buy
for the Prom.

      I think that's enough about stiffness for now. In the first

draft of this message I followed this with a longer section
about tensegrity, but I will leave that for a later message.

      Martin

[From Rick Marken (2017.10.31.1225)]

TolerantAndStiffComparators.jpg

···

Martin Taylor (2017.10.26.10.47)–

MT: The conflict cannot be seen by a Tester doing the Test for the

controlled variable.

RM: Part of the test for the controlled variable involves determining what system (or systems) output (or outputs) are affecting the variable that seems to be under control. So it’s not necessarily true that a Tester doing the Test would not see that there a conflict is involved. Testing involves careful observation so any reasonably competent Tester would see that a conflict exists, if a conflict does exist. So if there was a conflict over the state of a controlled variable the Tester would know that the apparent reference state of that variable was “virtual”.Â

MT: Some time ago we had a thread about whether Bill's action to disturb

Dag’s control of the steering wheel angle constituted a conflict
between Bill and Dag, which according to the definition above it
does not. But Dag’s output force that countered Bill’s disturbance
is an opposition to Bill’s force. Together these forces bring the
steering wheel to an angle that keeps the car in the place in its
lane where Dag wants it to be.

RM: This is true only if Bill quickly changes his reference for steering wheel position, which he does. If Bill had persisted in pushing the steering wheel to the position he wanted it in in order to create the disturbance then, assuming Bill and Dag are of of approximately equal strength, their combined forces would have caused the wheel to wind up in a virtual reference state between where Bill and Dag wanted it, making neither of them particularly happy.

MT: Can stiffness due to conflict be used for internal purposes as well

as in the external environment? Perhaps, but whether it is useful is
another question. The Method of Levels is predicated on the idea
that all conflict is bad, and reducing or removing it is good. I
hazard a guess that this may overstate the case, and that some
opposition, which is easily confused with conflict, serves to
stabilize a personality.

RM: I don’t know about conflict stabilizing personality but it turns out that a mild interpersonal conflict – a conflict between two control systems where one system is much weaker (lower gain) than the other – can indeed be a good thing. I showed this back when the CSGNet was just beginning. I was doing a little study of conflict using a tracking task where the disturbance was the output of a computer simulation of a control system that was also controlling the cursor, but relative to a slightly different reference position. I assumed that any degree of conflict would degrade my tracking performance but I found that a very mild conflict – where the opposing control system was very low gain – actually improved it. I was startled by this result and thought it might be inconsistent with PCT. But I simulated the conflict using control models and a mild conflict did, indeed, improve the performance of the stronger control system when that system included a transport lag and the opposing, weaker system didn’t. So it turns out that this is a real control phenomenon and I blushingly recall that Bill dubbed it “The Marken Effect”. You can find it in the CSGNet archives. A nice post on this turns up from 1994 if you search on “From: powers” and “Header: marken effect”

Best

Rick

Â

"Good" and "bad" being subjective

perceptions, I suggest that it may not be conflict or internal
opposition that is the problem, so much as that the person perceives
their situation to be “bad” (in error according to some reference
value for some perception they have of themselves. If that is so, a
resolution to the problem might be in a direction orthogonal to the
direction of the apparent conflict).

"Stiffness" is a property that we ascribe to some people, both in

their physical comportment and in their personality. We perceive a
person who appears easy and relaxed, while being effective in both
their interactions with the physical environment (e.g. sports, arts,
construction, etc.) and with other people (e.g. easy-going,
tolerant, down-to-earth, etc.) to be in some way “better” than
someone who is rigid, formal, rule-bound, intolerant of strangeness,
and so forth, in other words, “stiff”.

**Stiffness as negative tolerance**



I just used the word "tolerant" in a way that opposes it to "stiff".

The opposition is inherent in the requirement for neural firing
rates to be non-negative. I’m not going to recap the thread on that
topic of a few weeks ago. Suffice it to say that there must be two
separate comparator outputs, one for negative error and one for
positive error. These may be biased one way so that an error near
zero is treated as being zero, or the other way so that even a zero
error is treated as an error in the direction reported by that half
of the comparator. In the latter case, the error is simultaneously
reported as being both positive and negative. The diagram suggests
these different possibilities.

The six panels of this Figure show possible comparator functions.

The four in the left column show the output versus actual error
(reference - perception) taking into account the fact that the
neural firing rate cannot be negative. Of these four, the lower of
each pair shows the output that would be inhibitory downstream at
the output function, equivalent to a negative output. The right-hand
pair shows the equivalent virtual two-way comparator, the lower half
being the lower left panel flipped vertically. In each panel the
dashed curve (line) shows an unbiased comparator, while the solid
line shows the output for a biased comparator.

In the upper set of three panels, the bias is such that the

equivalent two-way comparator has a tolerance zone, a region near
zero error that is treated as though the error was truly zero. In
the lower set, the bias is in the other direction, so that both
one-way comparators produce output even when the perception is equal
to the reference. The equivalent two-way comparator never does that,
but it has a zone in which the equivalent output changes twice as
fast as a function of the true error. The output being non-zero for
both “half-comparators” in a region around zero actual error creates
an opposition between the output in one direction and the output in
the other direction, which produces a zone of stiffness around zero
error. Stiffness and tolerance are two sides of the same coin, and a
system can be smoothly changed from a tolerant one to a stiff one by
a continuous change of bias.

The stiffness-tolerance bias is not part of Powers's simple

hierarchy, but it is something we employ, at least at the muscular
level. I see no reason why it could not be a controllable
perception. After all, we do say to people things like “Let it go.
It’s OK as it is, so stop trying to make it better.”, which asks the
person to widen a tolerance zone. The opposite is less obvious, and
is seen usually more in interpersonal interaction than in dealing
with physical systems, though it is not unheard of to control to get
something near its reference level and then to stiffen up,
increasing the gain to get the almost right to become “just right”.

As noted above, the virtual gain increase that goes along with the

conflict in creating stiffness may not be the main value to the
organism of making something stiff. The value is likely to be in
stabilizing something in another dimension that is used by some
quite different control system, without attempting to control in
that other dimension, thus avoiding conflict with the system that
uses the stabilized but not controlled dimension. Kent McClelland
has talked about collective control providing systems of stable
properties of the environment, such as roads than enable quicker
travel between towns than would be possible through untamed jungle,
or administrative roles in an organization that allow other people
to use people in those roles for their own purposes, as a sales
assistant may make it easier for a high-school graduate to control
her perception of just what dress to buy for the Prom.

I think that's enough about stiffness for now. In the first draft of

this message I followed this with a longer section about tensegrity,
but I will leave that for a later message.

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

[Martin Taylor 2017.10.31.17.28]

[From Rick Marken (2017.10.31.1225)]

Yes, but that's not really the point, is it? When the conflicted

control systems are the two one-way halves of a two-way control
system, the tester can’t see the two sources of influence. Not that
it matters, one way or the other.

Bill never had a reference value for the steering wheel position, as

we discussed not too long ago. He did have a reference for the force
he would apply, increasing gently and slowly, but eventually quite
strongly.

That would have been true, had Bill indeed controlled his perception

of the steering wheel position, but he never did, so the comment is
irrelevant to the point that the total applied force can be the sum
of opposing forces.

That’s interesting. Do you happen to know which month in 1994?

Martin
···
            Martin Taylor

(2017.10.26.10.47)–

            MT: The conflict cannot be seen by a Tester doing the

Test for the controlled variable.

          RM: Part of the test for the controlled variable

involves determining what system (or systems) output (or
outputs) are affecting the variable that seems to be under
control. So it’s not necessarily true that a Tester doing
the Test would not see that there a conflict is involved.
Testing involves careful observation so any
reasonably competent Tester would see that a conflict
exists, if a conflict does exist. So if there was a
conflict over the state of a controlled variable the
Tester would know that the apparent reference state of
that variable was “virtual”.

            MT: Some time ago we

had a thread about whether Bill’s action to disturb
Dag’s control of the steering wheel angle constituted a
conflict between Bill and Dag, which according to the
definition above it does not. But Dag’s output force
that countered Bill’s disturbance is an opposition to
Bill’s force. Together these forces bring the steering
wheel to an angle that keeps the car in the place in its
lane where Dag wants it to be.

          RM: This is true only if Bill quickly changes his

reference for steering wheel position, which he does.

          If Bill had persisted in pushing the steering wheel to

the position he wanted it in in order to create the
disturbance then, assuming Bill and Dag are of of
approximately equal strength, their combined forces would
have caused the wheel to wind up in a virtual reference
state between where Bill and Dag wanted it, making neither
of them particularly happy.

            MT: Can stiffness

due to conflict be used for internal purposes as well as
in the external environment? Perhaps, but whether it is
useful is another question. The Method of Levels is
predicated on the idea that all conflict is bad, and
reducing or removing it is good. I hazard a guess that
this may overstate the case, and that some opposition,
which is easily confused with conflict, serves to
stabilize a personality.

          RM: I don't know about conflict stabilizing personality

but it turns out that a mild interpersonal
conflict – a conflict between two control systems where
one system is much weaker (lower gain) than the other –
can indeed be a good thing. I showed this back when the
CSGNet was just beginning. I was doing a little study of
conflict using a tracking task where the disturbance was
the output of a computer simulation of a control system
that was also controlling the cursor, but relative to a
slightly different reference position. I assumed that any
degree of conflict would degrade my tracking performance
but I found that a very mild conflict – where the
opposing control system was very low gain – actually
improved it. I was startled by this result and thought it
might be inconsistent with PCT. But I simulated the
conflict using control models and a mild conflict did,
indeed, improve the performance of the stronger control
system when that system included a transport lag and the
opposing, weaker system didn’t. So it turns out that this
is a real control phenomenon and I blushingly recall that
Bill dubbed it “The Marken Effect”. You can find it in the
CSGNet archives. A nice post on this turns up from 1994 if
you search on “From: powers” and “Header: marken effect”

[From Dag Forssell (2017.10.31.15:50 PDT)]

[Rick Marken (2017.10.31.1225)]

<snip>

RM: This is true only if Bill quickly changes his reference for steering wheel position, which he does. If Bill had persisted in pushing the steering wheel to the position he wanted it in in order to create the disturbance then, assuming Bill and Dag are of of approximately equal strength, their combined forces would have caused the wheel to wind up in a virtual reference state between where Bill and Dag wanted it, making neither of them particularly happy.

DF: For the life of me I don't understand why you persist with this nonsense.

Preceding his test, Bill asked something like: "would you like to see a strong control system?"

All Bill wanted, and all Bill did, was to gently apply a force to my steering wheel, slow enough that I could counter it.

Clearly, Bill did not have a reference for actually moving the steering wheel.

You too, are perfectly able to apply a force to something by tensing your muscles, without any intention of moving that something.

Best, Dag