[From Rick Marken (980625.0930)]

I've just added a cell (labeled d) that let's you enter
a disturbance to the controlled variable (q or q'). By varying
the value that you type into this cell (_any_ value, since
system outputs are not limited) you can see that the coercer
keeps his perception (p) of q under control (at the reference
r) whether the coercee is present or not.

Best

Rick

Coercion1 (58 Bytes)

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[From Bill Powers (980625.1447 MDT)]

Bruce Nevin (980625.1538 EDT)--

Here's a diagram of what [Rick's] spreadsheet is doing:
r
>
p --> C -->
> >(*s) Coercer
----------------------------
d --> q <--------o
/ \
/ ------
o' |
----------------------------
(*s')| p' Victim
> >
<---|C'|<--
>
r'

In this model, the coercer has no perception of the victim's output o'. All
the coercer perceives is the state of q.

In this diagram, as Bill's bracketed note says, the coercer is controlling
a perception of qo'. (I assume you mean qo' when you say o' in your
to do that, but realized I will have trouble on other fronts if I do; maybe
I'll be able to, maybe someone else will.

Rick has used 'q' to indicate a variable that is simultaneously the input
quantity of the coercer and the input quantity of the coercee. But since
the coercee's input quantity isn't separately shown, the diagram is
ambiguous. If we put in an explicit environmental feedback function (even
if it's just a unity multiplier) the relations become clearer. Using [eff]
for the environmental feedback function, we have either this diagram

r
>
p --> C ----
> > (*s) Coercer
------------|-----------|---
d --> q <--[eff]--o [q = qo' = qi]
/ \
/ ---[eff']--qi'
/ |
--------|----------------|-----
(*s')| p' Victim
> >
<----|C'|<------
>
r'

or this diagram

r
>
p --> C ----
> > (*s) Coercer
------------|-----------|---
d --> q o [q = qi = qi']
/ \ /
/ \ [eff]
> \ /
[eff'] \ /
> \ /
> X
> / \
o'<----- ----
> >
---------|--------------|---
(*s')| p' Victim
> >
<---|C'|<-----
>
r'

These are the cases we have been discussing. Obviously, there are more
cases, one of which is

r
>
p --> C ----
> > (*s) Coercer
------------|-----------|---
d --> q <--[eff]--o [q = qi = qi']
/ |
> >
[k1] [k2]
^ |
> v
o'---[eff']-->q'
----------|-------------|---
(*s')| p' Victim
> >
<---|C'|<----
>
r'

Each case introduces subtle differences in the interaction, the last case
bringing in two more constants to be considered. I doubt that informal
language has words for all possible cases.

Glad to see everyone climbing on the modeling bandwagon. It's the only way
to go if you want to be explicit about what you mean.

Best,

Bill P.

[From Rick Marken (980625.1400)]

Bruce Nevin (980625.1538 EDT) --

Nice work on the spreadsheet! Now we're getin' somewhere!

In this diagram, as Bill's bracketed note says, the coercer is
controlling a perception of qo'...This model could be demonstrated

Done! I'm returning an augmentation of your version of the
spreadsheet that allows you to have the coercer control either
qi (the coercee's controlled variable) or qo (the coercee's
output variable). Just enter "yes" in the cell next to "Control qi"
to have the coercer control qi; enter "no" in that cell to have
the coercer control qo.

Me:

What I can ask now is "does my model of coercion give an accurate
representation of the relationship between RTP teacher and
students (assuming more than one coercee in the model) in the
RTP classroom"?

Bruce:

Depends. Are the teacher and the students controlling the same
environment variable q (where q != o' the student's output), or is
the teacher controlling the student's output?

I agree. And now it can be either one in the model. I think the
teacher is controlling qi if she is controlling, say, the noise
level in the room. Noise level is an environmental variable and it
is affected (as it is in the model) by the outputs of both teacher
and student. But the teacher typically controls this variable, not
by compensating for the actions of the kids (like by piping phase
shifted noise into the room;-)); she does it by controlling the
kid's outputs (like by moving the source of the kid's contribution
to the noise -- his mouth -- out of the room; of course, this
usually involves moving the kid out too). So I guess the control
of qo model is probably most like what the RTP teacher does. Does
this sound right?

Best

Rick

Coercion3.xls (62 Bytes)

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[From Bruce Nevin (980625.1538 EDT)]

Rick Marken (980625.0930)--

Coercer : : Coerced
: :
r=50 : : r'=1
p=q : : p'=q
s=0.9 : : s'=0.01 d System
................: :......................................
o=o+s*(r-p) o'=o'+s'*(r'-p') Environment
d=10
q=o+o'+d

r
>
p --> C -->

Coercion2.xls (62 Bytes)

···

>(*s) Coercer

----------------------------
d --> q <--------o
/ \
/ ------
o' |
----------------------------
(*s')| p' Victim
> >
<---|C'|<--
>
r'

In this model, the coercer has no perception of the victim's output o'. All
the coercer perceives is the state of q.

Here's Bill's (980624.0145 MDT) diagram:

r
>
p --> C -->
> > Coercer
>s> >o>
----------------------------
qi -<---qo
(=)| / [coercer controls perception of qo']
qo'-------> qi'
> >
----------------------------
>o'| |s'| Coerced
> >
<---|C'|<--
>
r'

In this diagram, as Bill's bracketed note says, the coercer is controlling
a perception of qo'. (I assume you mean qo' when you say o' in your
to do that, but realized I will have trouble on other fronts if I do; maybe
I'll be able to, maybe someone else will.

These are two different models that have the same effect, that is, the
coercer is able to control despite the victim's attempts to control, and
the victim is unable to control because the coercer is controlling.
However, what they are controlling is different. In Bill's model, qi IS the
victim's outputs qo', and the victim is attempting to control something
else, qi'. In your spreadsheet, both are attempting to control the same
variable q.

Rick Marken (980625.1100)--

What I can ask now is "does
my model of coercion give an accurate representation of the
relationship between RTP teacher and students (assuming more
than one coercee in the model) in the RTP classroom"?

Depends. Are the teacher and the students controlling the same environment
variable q (where q != o' the student's output), or is the teacher
controlling the student's output? Might be other varieties of coercion too.
The word is ambiguous; the models are not.

Attached is a modification of your spreadsheet that can be used to
demonstrate the continuum between conflict and coercion by varying the
values of s and s', the relative strengths of the two control systems.

Bruce Nevin

[From Rick Marken (980625.2210)]

Bruce Nevin (980625.2023 EDT)

I don't understand the "else" value for qo'

if qi qo'=o'
else qo'=s'+o

This is my mistake; the "else" should be qo'=o'+o

I made a typo in the cell; the cell that contains this formula
should have a D7 rather than a D6. You should make that change in
your nicely revised version. This mistake didn't make much
difference to the performance of the model because the coercer's
output (o) completely overwhelms the coercee's output (o'); so
using s' (a small constant) as the coercee's output allows the
coercee to have about as much effect on his controlled perception
as does using his actual output, o'.

I understand the "else" value for qi. If the coercer is
controlling qi, then qi is the sum of the two disturbances
d and qo' cancelled out by the coercer's output qo. If the
coercer is controlling qo, she's not controlling qi any more,
so it is just the sum of the disturbances, with no resistance.

Yes! Exactly. Does the change from s' to o' help make sense of
the coercer's control of the coercee's output also?

Best

Rick

···

--

Richard S. Marken Phone or Fax: 310 474-0313

[From Bruce Nevin (980625.2023 EDT)]

Rick Marken (980625.1400)--

Aw shucks. I just did a little rearranging.

I've changed the test string to qi in the attached spreadsheet, for a
simpler user interaction, and I also included both qo and qo'. (I assume
you meant qo to be the coerced system's qo' since you colored it the same
as qi, the other value that might be controlled.) With these cosmetic

Coercer : : Coerced
: :
r=50 : : r'=1
if qi p=qi : : p'=qi
else p=qo' : :
s=0.9 : : s'=0.01 System
................: :......................................
o=o+s*(r-p) o'=o'+s'*(r'-p') Environment

if qi qo'=o'
else qo'=s'+o

d=10
if qi qi=qo'+d+qo
else qi=qo'+d

"If qi" means the coercer is controlling qi, and "else" means the coercer
is controlling qo'.

I don't understand the "else" value for qo'. If the coercer is controlling
qi, then you add the strength multiplier for the coerced system to the
output effort of the coercer and that's the observable output of the
coerced system? I don't see why s' (a multiplier for deriving o from the
error signal in the coerced system) is an *additive* factor for deriving
the observable output of the coerced system from the coercer's output effort.

Deriving qo' this way when the coercer is controlling it does get a small
deviation from the coercer's output, but doing it this way breaks if you
increase the strength of the coerced system. (Increase the value of s' from
.01 to .1, 1, and 10, and watch the output of the coercer drop as the
coerced system gets stronger, while the controlled variable qo' stays
constant and equal to the coercer's reference value.)

Perhaps this is what we want:

qo'= (qo'+(s'*o'))-(qo'+(s*o))

Cell D24 of the attached spreadsheet shows this formula, but I have been
unable to substitute it for the expression that means s'+o in cell D21 (for
the value of qo').

There are two versions of the model in the attached file. In the lower one
o=e=(r-p) and o'=e'=(r'-p'). It's informative to see the error signal
(which would differ from the output signal if there were multiple error
signals coming into an output function). This complicates the formula for
qo and qo' because of the embedded conditional, but I don't think that is
the problem.

I understand the "else" value for qi. If the coercer is controlling qi,
then qi is the sum of the two disturbances d and qo' cancelled out by the
coercer's output qo. If the coercer is controlling qo, she's not
controlling qi any more, so it is just the sum of the disturbances, with no
resistance.

Can you help me out here?

Bruce Nevin

Coercion3b.xls (63 Bytes)

[From Bruce Nevin (980627.0810 EDT)]

Rick Marken (980625.2210)--

if qi qo'=o'
else qo'=s'+o

the "else" should be qo'=o'+o

Guess I was too tired to see that. Thanks.

[...] Does the change from s' to o' help make sense of
the coercer's control of the coercee's output also?

Yes, the performance makes much more sense. Here are values of qo' and qi'
in the two spreadsheets with the coercer controlling qo' and the victim's
strength set at .01:

qo' qi'
qo'=s'+o 50.0 60.0
qo'=o'+o 49.4 59.4

With the victim's strength set at .001:

qo' qi'
qo'=s'+o 50.0 60.0
qo'=o'+o 49.9 59.9

I was trying to make s and s' refer to effector strength (e.g. muscle mass,
limb length, and the like) rather than loop gain affecting the neural
signal. (In the above spreadsheet, the victim doesn't care as much as the
coercer does. I want the victim to be weaker than the coercer.) The
attached spreadsheet does this as follows:

Coercer Coerced
r= 50.0 r'= 1.0
p= qi p'= qi
qo' <qo' controlled
e= r-p e'= r'-p'
o= o+e o'= o'+e'
s= 0.9 s'= 0.1
qo= o*s qo'= o'*s'
qo'= (o'*s')+qo <qo' controlled

qi=qo'+d+qo <no qi' label now
d= 10

Recursion is used only to calculate o and o'. When qo' is controlled by the
coercer, the values of o, o', and qo vary each time I recalculate (^S does
it), but qo' stays constant. The value of qi also stays constant. This is
of course because the victim's output qo' still determines qi. As a side
effect of controlling the victim's output, the coercer is controlling the
environment variable that the victim wishes to control. The appearance to
an observer is that the coercer is controlling qi against the wishes of the
victim, using the victim's output qo' as means to do this. I do not see any
way to distinguish the two cases, where the coercer is controlling both qo'
and qi' vs. where the apparent control of qi is a side effect of
controlling qo'. In an actual environment, the victim's output might cease
to affect the qi that the victim had intended to affect. Perhaps this is
what the missing environment feedback function could show?

With the coercer controlling qo', here are relative strengths of qo' and
qi' for different values of s and s':

s s' qo' qi
0.9 .01 49.4 59.4
0.9 .001 49.9 59.9
0.999 .01 49.4 59.4

Similarly, when the coercer is controlling qi and relative strengths are
0.9 and 0.01 qi stays at 49.5. Dropping the victim's stength an order of
magnitude to 0.001 brings qi up to 49.9. Increasing the strength of the
coercer to 0.99 or even 0.999 makes no difference, but of course these are
much smaller changes. This means that a coercer who wants complete control
must make the victim give up. Even weak resistance from the victim is a
disturbance that cannot be eradicated simply by increasing the output of
the coercer. With every recalculation, the values of o and qo vary, even as
the value of the controlled perception (qo' or qi) remains constant. This
suggests the power of an irritant, and the power of small resistance
activities. This is one of the keys of nonviolent actions that Gandhi and
Martin Luther King understood very well. Another, of course, is that
coercion against non-coersive action is such bad press.

It is interesting that changing the reference does not affect the output
values other than the small effect seen by simple recalculation.

As before, this spreadsheet can demonstrate the continuum between coercion
of A by B, through gradations of conflict, to coercion of B by A (at least
with respect to qi), by varying their relative strengths.

Lurking in the wings is the case where a control system controls some
aspect of its own output qo, and how conflict and coercion play out there.
Yes, I have heard of proprioception. I am interested in its role in
language and culture.

Bruce Nevin

Coercion4.xls (62 Bytes)

[From Rick Marken (980626.0820)]

Bruce Nevin (980627.0810 EDT) --

Version 4.0 is really nice!

When qo' is controlled by the coercer, the values of o, o', and qo
vary each time I recalculate (^S does it), but qo' stays constant.
The value of qi also stays constant.

Yes. As long as the disturbance is constant. If you change the
disturbance number you will see that qi changes with the disturbance
(indicating no control) while the victim's output (qo') remains
constant (assuming qo' is what the coercer is controlling) .

I think I should try to explain what I think is the difference
between o (o') and qo (qo'). o is the integrated effect of error.
I think it would be like "muscle tension"; qo (qo') is actually
the environmental result of variation in o (o') -- like "hand
position". qo (qo') is the aspect of the output variable that
can actually be influenced by another control system (the coerer
in this case).

The equation in cell D8 (=IF(C12="qi", D6,D6+B6)) says that the
environmental consequence (qo') of the victim's output (o') is
proportional only to o' when the coercer is not controlling qo'.
However, qo' is a result of _both_ o' and qo when the coercer is
controlling qo'. This seems right to me. Look at it in terms of hand
position; when a coercer is not trying to control the position of
muscle tensions (o'). Whan a coercer is trying to control the
muscle tensions (o') _and_ forces (qo) that _result_ from muscle
tensions (o) produced by the coercer.

Note that I could not add the coercer's output (o) directly to the
cell that computes o' because then the coercer's output is
integrated into the victim's output. This is not a correct
representation of the physical situation and it produces bizarre
results in the model. This is a nice demonstration of the fact that
a big part of modeling is figuring out how the mathematics of the
model _map_ to the physical situation being modeled. It is at this
aspect of modeling (science) at which I think Bill Powers is
particularly awesome (to borrow an overused word from my children's
generation) -- so I'm sure he will correct any mistakes in
interpretation that I am making here.

As a side effect of controlling the victim's output, the coercer
is controlling the environment variable that the victim wishes to
control.

I think it looks that way only because you are not _varying_ the
disturbance number (in cell C10) to qi; type in different
disturbance numbers and you will see that, when the coercer is
controlling qo, qi varies right along with it.

The appearance to an observer is that the coercer is controlling
qi against the wishes of the victim, using the victim's output
qo' as means to do this. I do not see any way to distinguish the
two cases, where the coercer is controlling both qo' and qi' vs.
where the apparent control of qi is a side effect of controlling qo'.

Try the test I suggest; vary the disturbance and watch for any
change in qi. A change is _expected_ if qi is _not_ controlled.
If the coercer is controlling qi, there will be little or no
change. You will be doing the test for the controlled variable.
You can also add a disturbance to qo and qo'; this will allow you
to test to determine whether or not these variables are controlled.

As before, this spreadsheet can demonstrate the continuum between
coercion of A by B, through gradations of conflict, to coercion
of B by A (at least with respect to qi), by varying their relative
strengths.

Yes!

Best

Rick

···

---
Richard S. Marken Phone or Fax: 310 474-0313

[From Bruce Nevin (980627.1228 EDT)

Rick Marken (980626.0820)--

Version 4.0 is really nice!

Thanks!

Note that I could not add the coercer's output (o) directly to the
cell that computes o' because then the coercer's output is
integrated into the victim's output. This is not a correct
representation of the physical situation and it produces bizarre
results in the model.

Yes, I ran into that. When I got errors proliferating through cells I had
to substitute constants until numbers displayed again, then piece in the
formulae again. Yuck!

As a side effect of controlling the victim's output, the coercer
is controlling the environment variable that the victim wishes to
control.

I think it looks that way only because you are not _varying_ the
disturbance number (in cell C10) to qi; type in different
disturbance numbers and you will see that, when the coercer is
controlling qo, qi varies right along with it. [...]
You will be doing the test for the controlled variable.

Yes, I see that. It is interesting, though, that changes in the disturbance
also affect the value qo' that the coercer is controlling. This gives the
appearance that d (a disturbance to qi) is a disturbance to qo'. In a sense
it is, but we don't usually model the path from a disturbance source to a
disturbed variable as traversing a control loop. Food for thought there,
evoking Bateson's ideas about the cybernetic properties of the environment.

In a natural setting what usually happens, probably, is that the victim
stops trying to control qi and starts trying vainly to control qo, at which
point changes in d would cease to affect qo'. I think sometimes there can
be a progressive focussing of intentions in a conflict to more and more
narrowly defined environment variables. I'm not prepared to back that up
with anything specific just now, but this reminds me of that observation.

As before, this spreadsheet can demonstrate the continuum between
coercion of A by B, through gradations of conflict, to coercion
of B by A (at least with respect to qi), by varying their relative
strengths.

Yes!

There is no particular point on this gradation at which you can say that
coercion stops and conflict begins. It's a question of what constitutes
"adequate" control for the coercer. Subjectively, it might be that each
party to a conflict feels coerced by the other.

Bruce Nevin

[From Bruce Nevin (980627.1315 EDT)]

Rick Marken (980626.0820) --

Version 4.0 is really nice!

I'm disgusted to report that I left out most of the changes I had put in. I
had two models in the spreadsheet, one for backup in case the recursion
went into error-error land. I evidently deleted the wrong one before
posting the file!

I had values for e and e' separated out. I calculated o and o' as internal
signals (recursively defined). I multiplied o (o') by the strength factor s
(s') to get the observable output qo (qo'). This made the formulae simpler
and cleaner. I wanted to put in k (k') as a multiplier of e (e').

I'll see if I can get to redo that, starting from your 4b.

My notes must not have made much sense.

Bruce Nevin

[From Bruce Nevin (980627.1315 EDT)]

Here's version 4c. If I've got it right, output of the coercer never gets
anywhere near the maximum, and the poor victim's output (unconstrained
flavor) runs away until it reaches the maximum number of iterations
configured for Excel (see below, default 100). Can't just use the
constrained outputs and throw away the line with unconstrained o and o'.
Formula for o' in D8 is

=IF(D11>0,D8+(D6*D7),0)
=IF( s'>0,o'+(e'*k'),0)

Formula for (o') in D9 is

=IF(ABS(D8)>D10,SIGN(D8)*D10,D8)
=IF(ABS(o')>max,SIGN(o')*max,o')

Can't modify the latter by substituting (s'>0,o'+(e'*k'),0) in place of D8
because that would run the recursive loop twice.

Suggest turning off automatic calculation with Tools>Options, Calculation
tab, click Manual. Then press <F9> for each iteration. Can change the limit
on recursion (number of iterations) in the same dialog box.

Bruce Nevin

Coercion4c.xls (63 Bytes)