The top level (11.th)

[From Bjorn Simonsen (2007.10.24, 22:45 EUST)]

I could never explain to myself how the top level functioned in the HPCT.
Where did the reference come from?

Last week I listened to professor in molecular biology (genetics) Thomas
Edlund from the University in Ume� (Sweden). I will give a short account.
What happens just after an egg is fertilized? It develops, but what develops
first? Is it heart, rib, arms or bones? Professor Edlund's specialty is the
embryo evolution. He said that after the first cell lump starts cell
division, the first specialized cells around that is formed is neurons and
skin cells. And the first neurons that is formed are those neurons that we
think upon as the most advanced neurons, the brain neurons. It is not spinal
cells or more primitive neurons. It is the forebrain cells.
I will stop here and continue with my own thoughts relative to HPCT.
The nearest I have been Thomas Edlund on the net is
http://ucmm.cs.it-norr.com/default.asp?id=1470&TID=&efid=1324

My thoughts based on what is written above. I make them point by point and
very simple. My thoughts are a kick-off and I look forward for comments.

1. The first cells formed are the neurons in the 11. level.
2. There will never come cells "above" and no axons and references to the
neurons on the 11. level.
3. (This statement is paraphrased from B:CP/Learning/Intrinsic state and
intrinsic error). To represent that these neurons at the 11. level have
their preferred state, these cells may have a stored reference signal.
4. Maybe the neurons at the top level need a certain frequency to accept the
perceptual signal, or maybe it doesn't accept perceptual signals with
frequency over a certain level.
5. The axon at the 11. level cells brings the reference to levels below.

Could this explain the top level neurons?

bjorn

[From Rick Marken (2007.10.25.1045)]

Bjorn Simonsen (2007.10.24, 22:45 EUST)--

I could never explain to myself how the top level functioned in the HPCT.
Where did the reference come from?

At the highest level the reference doesn't have to "come from"
anywhere at all; it could just exist as the offset in the highest
level comparator; the synaptic connection that computes p10 - r10; the
difference between the next to highest level perception (I call it p10
under the assumption that there are, indeed, 11 levels of control so
the next to highest level of perception is the one at level 10, p10)
and the reference level for that perception, r10. The reference, r10,
would be the one sent from the highest level systems (level 11) but
there are no such systems since r10 is the highest level reference.
This reference, r10, could be built into the cell body of the neuron
doing the highest level comparison; these is no need for an actual
reference neuron to set r10 since r10 is not "used" (ie. varied) by a
higher level system to achieve a higher level goal. Indeed, there is
no higher level goal than r10, which is, therefore,essentially a
constant (except for the effects of reorganization( and represents the
highest level goal (11th level) of the perceptual hierarchy. According
to PCT, the value of r10 is set by reorganization. So if our highest
level controlled perceptions, p10, are system concepts, then the
reference for these concepts (r10) cannot be varied by a higher level
system; they just get set to whatever they are set at by random
reorganization that eventually settles on a value of r10 that works
best for the individual in the context of the environment in which it
lives and the goal hierarchy which it has already developed.

My thoughts based on what is written above. I make them point by point and
very simple. My thoughts are a kick-off and I look forward for comments.

1. The first cells formed are the neurons in the 11. level.
2. There will never come cells "above" and no axons and references to the
neurons on the 11. level.
3. (This statement is paraphrased from B:CP/Learning/Intrinsic state and
intrinsic error). To represent that these neurons at the 11. level have
their preferred state, these cells may have a stored reference signal.
4. Maybe the neurons at the top level need a certain frequency to accept the
perceptual signal, or maybe it doesn't accept perceptual signals with
frequency over a certain level.
5. The axon at the 11. level cells brings the reference to levels below.

Could this explain the top level neurons?

I don't know what's being explained. But if it works for you then
that's fine. At a functional level (which is my main concern) the
order of development of neurons is (currently) of little interest to
me. In fact, I find the current mania for molecular biology that I see
in psychology a rather pathetic sign of how stuck in the dead end of
lineal causal thinking current psychological modeling is.

Best regards

Rick

···

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

[From Bjorn Simonsen (2007.10.26,09:35 EUST)]
from Rick Marken (2007.10.25.1045)

At the highest level the reference doesn't have to "come from"
anywhere at all; it could just exist as the offset in the highest
level comparator; the synaptic connection that computes p10 - r10; the
difference between the next to highest level perception (I call it p10
under the assumption that there are, indeed, 11 levels of control so
the next to highest level of perception is the one at level 10, p10)
and the reference level for that perception, r10.

Thank you for spending time to give me better understanding. This is OK for
me. I had a problem understanding what you meant by " the reference at the
real top level exist as the _offset_ in the highest level comparator". But I
think I understand your style.

The reference, r10,
would be the one sent from the highest level systems (level 11) but
there are no such systems since r10 is the highest level reference.

Well, r10 must com from one or more places. This places must be neurons.
I agree that "above" the p10, r10 level, there are no equivalent level.
That is what I think I expressed very well in my last mail. But back to
your comment above. r10 must come from neurons "above" the p10, r10 level.

This reference, r10, could be built into the cell body of the neuron
doing the highest level comparison; these is no need for an actual
reference neuron to set r10 since r10 is not "used" (i.e.. varied) by a
higher level system to achieve a higher level goal.

I read your sentence in a holistic way. There are of course many cell bodies
at the real 11. level, ( a level which is _not_ equivalent the other
levels).
I don't fall for your explanation that r10 could be built into the cell body
of the neuron at the real 11 th level. That is because I think comparators
at the 10 th level can accept different r10 (plural) at different time. I
can't understand your certainty that r10 is _not_ varied by the neurons at
the real 11 th. level

I don't think there is a comparison on the 11th level. I think in the way
Bill writes in B:CP (his words)

3. To represent that these neurons at the 11. level have their preferred

state,

these cells may have a stored reference signal.

In fact, I find the current mania for molecular biology that I see
in psychology a rather pathetic sign of how stuck in the dead end of
lineal causal thinking current psychological modeling is.

OK. Also I find it difficult to read and compare molecular biologists causal
thinking with PCT. But they are able to do experiments I am not able to do
such experiments. Therefore I read some of them. Maybe I can use some of
their descriptive data.
May I ask in another way. How do you model what you say about "it could
just exist as the offset in the highest level comparator"?

Indeed, there is
no higher level goal than r10, which is, therefore, essentially a
constant (except for the effects of reorganization( and represents the
highest level goal (11th level) of the perceptual hierarchy.

I thought the perceptions at the (real) 11 th. level are based on
_combinations_ of principle level perceptions. If that is correct it can't
be constant. Where am I wrong?

According
to PCT, the value of r10 is set by reorganization. So if our highest
level controlled perceptions, p10, are system concepts, then the
reference for these concepts (r10) cannot be varied by a higher level
system; they just get set to whatever they are set at by random
reorganization that eventually settles on a value of r10 that works
best for the individual in the context of the environment in which it
lives and the goal hierarchy which it has already developed.

Yes, I guess all r (plural) are set by reorganization.
I read your text as if r10 is a reference for a certain principle (10 th
level). But I can't understand why it can't be varied. A US Army soldier
wish to do different things if he fights in Iraq or he marching on Broadway
in the Eastern Parade. In both situations he wishes to behave as a US Army
Soldier. A scientist wishes one day to do a chemical experiment and the next
day do a physical experiment.
It is quite OK that r10 can't be varied by higher (than 11th) level system,
but I guess sums of p10 (plural) going to the 11. level can vary r10.

Again. You are the PCT guide. I can't follow you. I still think it is
interesting to read that a molecular biologist can perform an experiment
"day after day" and find that the first neurons that are first formed after
the first cell lump starts cell division, is the forebrain cells (of course
I can't argue that they "are going to be 11 th. level neurons). I also think
it is interesting to ask if such experiments could be explained in a PCT
frame.

bjorn

[From Rick Marken (2007.10.26.1700)]

Bjorn Simonsen (2007.10.26,09:35 EUST)--

Rick Marken (2007.10.25.1045)

>The reference, r10,
>would be the one sent from the highest level systems (level 11) but
>there are no such systems since r10 is the highest level reference.

Well, r10 must com from one or more places. This places must be neurons.
I agree that "above" the p10, r10 level, there are no equivalent level.
That is what I think I expressed very well in my last mail. But back to
your comment above. r10 must come from neurons "above" the p10, r10 level.

It could, I suppose. But I was thinking that it was more likely to be
a property of the cell body itself. The cell body could act like a
semi-conductor, only producing output (e) if the input (p) is greater
than some amount (functionally equivalent to r). So e = p - r for r
and p> 0. The value of r is a property of the cell; and it defines the
upper limit of p that produces no error. In real nervous systems all
signals are positive (assuming they are firing rates) so there would
have to be another cell that takes an inverted p as input with the
same r and then the outputs of both would have to be combined
appropriately to get the net error, I think. Bill Powers knows how to
build such circuits. But my point is that, since r for the highest
level systems isn't varied by a still higher level system to achieve
that system's goals, it can be a relatively constant property of the
cells involved in the comparator process, being changed only over the
long run by random reorganization.

>This reference, r10, could be built into the cell body of the neuron
>doing the highest level comparison; these is no need for an actual
>reference neuron to set r10 since r10 is not "used" (i.e.. varied) by a
>higher level system to achieve a higher level goal.

I don't fall for your explanation that r10 could be built into the cell body
of the neuron at the real 11 th level. That is because I think comparators
at the 10 th level can accept different r10 (plural) at different time. I
can't understand your certainty that r10 is _not_ varied by the neurons at
the real 11 th. level

I think it's more a matter of modeling rather than of certainty. If
the 11 level is the highest then all it is is references. There is no
higher level reason for those references to be varied to I would model
them (neurologically) as being part of the neural comparator that
transforms level 10 perceptions into level 10 errors. The level 11
references are the constant "offset" of this transfer function and can
be implemented as a fixed property of the neural comparator; there is
no need to have a neural signal carrying r; you could have such a
signal, but why? The data suggest that people rarely vary their
references for their highest level perceptions over the course of an
entire lifetime. How frequently do you change your religious goals
over the course of a year? I know that mine haven't changed much since
I was about 5. As they say, once a secular humanist, always a secular
humanist;-)

>In fact, I find the current mania for molecular biology that I see
>in psychology a rather pathetic sign of how stuck in the dead end of
>lineal causal thinking current psychological modeling is.

May I ask in another way. How do you model what you say about "it could
just exist as the offset in the highest level comparator"?

I hope I gave a better approximation to how I would do it in my first
paragraph above.

I thought the perceptions at the (real) 11 th. level are based on
_combinations_ of principle level perceptions. If that is correct it can't
be constant. Where am I wrong?

If there a perceptions controlled at the 11th level then it is the
12th level references for those perceptions that I am talking about.
If the system level perceptions are 11th level then the references for
those perceptions are what I would call the fixed 12th level
references. It's the top level references -- regardless of the number
of levels in the hierarchy -- that I would say are likely to be fixed
properties of cortical neurons.

Yes, I guess all r (plural) are set by reorganization.

No, I think only the top level references are set (and changed) by
reorganization. All other references are varied as the by higher level
systems as the means of controlling their perceptions.

I read your text as if r10 is a reference for a certain principle (10 th
level). But I can't understand why it can't be varied. A US Army soldier
wish to do different things if he fights in Iraq or he marching on Broadway
in the Eastern Parade. In both situations he wishes to behave as a US Army
Soldier.

Don't get so exact about level numbering. Yes, people vary their
references for principles to control higher level goals. If those
higher levels goals are at the top of the hierarchy (say they are
system concepts) then I am saying that the references for those
perceptions, which would come from a next level up, don't actually
come from a next level up; they are just an offset in the comparator
at that higher level.

Best regards

Rick

···

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

Bjorn Simonsen
(2007.10.26,09:35 EUST)–
But back to

your comment above. r10 must come from neurons “above”
the p10, r10 level.
It could, I suppose. But I was
thinking that it was more likely to be

a property of the cell body itself. The cell body could act like a

semi-conductor, only producing output (e) if the input § is
greater

than some amount (functionally equivalent to r). So e = p - r for r

and p> 0. The value of r is a property of the cell; and it defines
the

upper limit of p that produces no error. In real nervous systems all

signals are positive (assuming they are firing rates) so there would

have to be another cell that takes an inverted p as input with the

same r and then the outputs of both would have to be combined

appropriately to get the net error, I think. Bill Powers knows how
to

build such circuits. But my point is that, since r for the highest

level systems isn’t varied by a still higher level system to achieve

that system’s goals, it can be a relatively constant property of the

cells involved in the comparator process, being changed only over
the

long run by random reorganization.

This reference, r10, could be built into the cell body of the
neuron

doing the highest level comparison; these is no need for an
actual

reference neuron to set r10 since r10 is not “used”
(i.e… varied) by a

higher level system to achieve a higher level goal.

I don’t fall for your explanation that r10 could be built into the
cell body

of the neuron at the real 11 th level. That is because I think
comparators

at the 10 th level can accept different r10 (plural) at different
time. I

can’t understand your certainty that r10 is not varied by the
neurons at

the real 11 th. level

I think it’s more a matter of modeling rather than of certainty. If

the 11 level is the highest then all it is is references. There is
no

higher level reason for those references to be varied to I would
model

them (neurologically) as being part of the neural comparator that

transforms level 10 perceptions into level 10 errors. The level 11

references are the constant “offset” of this transfer function
and can

be implemented as a fixed property of the neural comparator; there
is

no need to have a neural signal carrying r; you could have such a

signal, but why? The data suggest that people rarely vary their

references for their highest level perceptions over the course of an

entire lifetime. How frequently do you change your religious goals

over the course of a year? I know that mine haven’t changed much
since

I was about 5. As they say, once a secular humanist, always a
secular

humanist;-)

In fact, I find the current mania for molecular biology that I
see

in psychology a rather pathetic sign of how stuck in the dead
end of

lineal causal thinking current psychological modeling
is.

May I ask in another way. How do you model what you say about
"it could

just exist as the offset in the highest level
comparator"?

I hope I gave a better approximation to how I would do it in my
first

paragraph above.

I thought the perceptions at the (real) 11 th. level are based
on

combinations of principle level perceptions. If that is correct it
can’t

be constant. Where am I wrong?

If there a perceptions controlled at the 11th level then it is the

12th level references for those perceptions that I am talking about.

If the system level perceptions are 11th level then the references
for

those perceptions are what I would call the fixed 12th level

references. It’s the top level references – regardless of the
number

of levels in the hierarchy – that I would say are likely to be
fixed

properties of cortical neurons.

Yes, I guess all r (plural) are set by reorganization.

No, I think only the top level references are set (and changed) by

reorganization. All other references are varied as the by higher
level

systems as the means of controlling their perceptions.

I read your text as if r10 is a reference for a certain principle
(10 th

level). But I can’t understand why it can’t be varied. A US Army
soldier

wish to do different things if he fights in Iraq or he marching on
Broadway

in the Eastern Parade. In both situations he wishes to behave as a
US Army

Soldier.

Don’t get so exact about level numbering. Yes, people vary their

references for principles to control higher level goals. If those

higher levels goals are at the top of the hierarchy (say they are

system concepts) then I am saying that the references for those

perceptions, which would come from a next level up, don’t actually

come from a next level up; they are just an offset in the comparator

at that higher level.

Best regards

Rick

Richard S. Marken PhD

rsmarken@gmail.com

No virus found in this incoming message.

Checked by AVG Free Edition.

Version: 7.5.503 / Virus Database: 269.15.11/1094 - Release Date:
10/26/2007 8:50 AM

No virus found in this incoming message.

Checked by AVG Free Edition.

Version: 7.5.503 / Virus Database: 269.15.11/1094 - Release Date:
10/26/2007 8:50 AM
]From Bill Powers (2007.10.0430 MDT)]

Rick Marken (2007.10.26.1700) –

I’m confused by this contraction of the hierarchy. What level are you
both leaving out? I have always considered that there are 11 levels, the
11th level being complete with an input function that perceives a
collection of principles to produce a perception of the state of a system
concept, and an output function that converts an error in system concept
into a set of reference signals specifying various principles. I would
have thought that the problem is the source of the 11th level reference
signals, which can’t come from any higher systems (unless, as is
perfectly possible, there is at least a 12th level of control that is so
much taken for granted that it’s so far invisible).

“The comparator” at any level is a reification of the function
of comparison, and comparison is just one way of viewing the fact that it
takes a nonzero amount of perceptual input to produce zero output action
(or put differently, that zero input produces non-zero output). What I
refer to as comparison might take place in a specialized comparator cell
or network, but it could also take place in an input function or an
output function if the reference signal went there instead, with suitable
excitatory or inhibitory connections.

As Rick suggests, and as I said or implied in B:CP (I believe), any
property of neural connections that produces (and possibly varies) the
offset mentioned above qualifies as a reference signal, even though there
may be no explicit neural signal carrying the reference information. If
the threshold of response of a neuron to another neural signal is 10
impulses per second (that is, the output frequency does not begin to rise
above zero until the input frequency is at or above 10 impulses per
second), there is an effective reference signal of -10 impulses per
second. If this threshold is affected by the concentration of circulating
chemicals, then that contribution to the net reference signal is
chemical, not neural.

We should also not forget that a magnitude of zero is a perfectly good
magnitude for a reference signal. If the reference signal is zero, then
any amount of perceptual signal will produce an error signal (but, of
course, only if the reference signal is inhibitory and the perceptual
signal is excitatory). The error will be zero if and only if the ensuing
actions at lower levels succeed in bringing the perceptual signal close
to zero. This is what we call “avoidance” behavior. To avoid a
perception is to try to bring its magnitude to zero. When any new level
of control is just starting to be organized, and for the time being is
the highest level, we might expect the resulting control behavior to be,
at first, avoidance of the newly-formed perception. This might also be
the case for perceptions that appear unexpectedly, even if one normally
sets high reference levels for them.

Let’s think about inhibitory and excitatory signals for a
moment.

Suppose the INHIBITORY reference signal has a magnitude of 100. Then
excitatory perceptual signals must have a magnitude of at least 100 units
to start producing an error signal. There will be no behavior until the
perceptual signal has reached 100 units of magnitude. A perceptual signal
of 110 units will produce 10 units of error signal, and that will result
in behavior tending strongly to bring the perception down toward a
magnitude of 100.

To an observer, it will appear that this system simply doesn’t detect
anything less than some minimum amount of the stimulus, and that it
responds to any larger amount by producing some action. If the proximal
effect of the stimulus isn’t known or observed, it will not be apparent
that the effect of the action is to keep the effect of the stimulus on a
perception from getting any larger than the threshold amount.

So we can discover one-way control systems with excitatory perceptual
signals and inhibitory reference signals by looking for “thresholds
of detection.” The fact that there is a threshold shown by the
response to the stimulus does not mean that there is no perceptual signal
below that amount of stimulus. It just means that there is some nonzero
amount of inhibitory reference signal that has to be exceeded by the
excitatory perceptual signal to result in error, and thus action. This
may have a considerable significance for phenomena such as
“blindsight.”

The other side of the coin is one-way control systems with inhibitory
perceptual signals and excitatory reference signals, more like the kind
we normally talk about. If the perceptual signal exceeds the reference
signal in magnitude by any amount, the action will just be zero. There
will be action if and only if the perceptual signal is less in magnitude
than the reference signal. If the reference signal is positive and the
perceptual signal is zero, the action will quickly raise the perceptual
signal to match the reference signal. So one-way control systems of this
kind are typified by what seem to be voluntary actions which cause
perceptions to arise that would not otherwise have appeared. If large
magnitudes of the same perception are caused externally, there will be no
action: the same system with a low reference signal will ignore
them.

I now leave it as an exercise for the student to deduce what will be
observed when there are two systems controlling perceptions that depend
on the same environmental variable,with one system being of the first
type and the other system being of the second type. What will happen when
the two reference signals specify the same level of the controlled
variable, and what will happen if the two reference signals differ by a
substantial amount in either of the two possible directions (A larger
than B, or B larger than A). Qualitative answers will receive a D, and
quantitative answers will be graded on correctness (by someone
else).

Best,

Bill P.

1 Like

[From Bjorn Simonsen (2007.10.27,18:15 EUST)]
from Bill Powers (2007.10.0430 MDT)]

I'm confused by this contraction of the hierarchy. What level are
you both leaving out? Well, I must have expressed myself vague.
I took as a startingpoint 11. level, but the 11 th level was different
from the lower levels.

I expressed:

3. (This statement is paraphrased from B:CP/Learning/Intrinsic state and
intrinsic error). To represent that these neurons at the 11. level have
their preferred state, these cells may have a stored reference signal.

Since I thought there were no reference signal coming from oven, I
disregarded the comparator. I asked (meant to ask) if the input function had
a stored reference signal with axons pointing to lower levels.
Now you taught me something new; the invisible 12 th. level.
I now assume an ordinary 11 th level in one of the ways you indicated.

As Rick suggests, and as I said or implied in B:CP (I believe), any
property of neural connections that produces (and possibly varies)
the offset mentioned above qualifies as a reference signal, even though
there may be no explicit neural signal carrying the reference information.

I think you said it at page 186 B:CP 2. ed. when you talked about intrinsic
reference signals.

If this threshold is affected by the concentration of circulating
chemicals, then that contribution to the net reference signal is
chemical, not neural.

This was interesting. I think we have many chemical intrinsic reference
signals. I am just reading Tinoco, Sauer, Wang, Puglisi: Physical Chemistry.
Principles and Applications in Biological Science.
I tried to discuss this on the net a year ago. Next year I will try again.

Let's think about inhibitory and excitatory signals for a moment.

What you wrote about them, I hope I understand. Therefore I jump to your
exercise.

What will happen when the two reference signals specify the
same level of the controlled variable, and what will happen if
he two reference signals differ by a substantial amount in either
of the two possible directions (A larger than B, or B larger than A).
Qualitative answers will receive a D, and quantitative answers
will be graded on correctness (by someone else).

Let me make a story.
1. I wish to _not_ be near any police. Reference A is inhibitory, A=100
2. I wish to be near a police. Reference B ( Excitatory), B=100
3. The police is far away biking toward me with full speed. at the moment
p=20.

At the moment the first loop with reference A=100 has no error, the sum is
negative.
The other loop, B=100 has a great error. e =100-20 =80. I action to come
nearer the police.

At a later moment the police is nearer and p=100
At this moment the first loop with reference A=100 (inhibitory), has an
error like zero.
At the same time the other loop, B=100 (excitatory) also has an error like
zero
I have a conflict without any actions.

At still a later moment the police is still nearer and p = 120.
At this moment the first loop with reference A=100 (inhibitory), has an
error 20. I change my actions and action to escape the police.
The other loop, B=100 (excitatory) has no error. No actions to come nearer
the police.

Well now it depends, who is running fastest. I who try to escape the police
or the police biking toward me.
Correct??

bjorn

[From Rick Marken (2007.10.27.1030)]

Bill Powers (2007.10.0430 MDT)--

I now leave it as an exercise for the student to deduce what will be
observed when there are two systems controlling perceptions that depend on
the same environmental variable,with one system being of the first type and
the other system being of the second type. What will happen when the two
reference signals specify the same level of the controlled variable, and
what will happen if the two reference signals differ by a substantial amount
in either of the two possible directions (A larger than B, or B larger than
A).

System 1: e1 = p1 - r1 if p1 - r1 > 0

System 2: e2= r2 - p2 if r2 - p2 > 0

Where p1 and p2 are perceptions that depend on the same environmental variable,
so p1 = p2 = p.

1. Assume r1 = r2 = r

then e1>0 when p >r and e2>0 when p < r

So these two systems act (e>0) when p <> r.

2. Assume r1 > r2

then e1>0 when p >r1 and e2>0 when p < r2

So there two systems act (e>0) when p > r1 or p < r2 and there is no action when
r2<p<r1.

Qualitative answers will receive a D, and quantitative answers will be
graded on correctness (by someone else).

Oh, go ahead and grade me, baby;-)

Best

Rick

···

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

[From Bjorn Simonsen (2007.10.27,20:00 EUST)]
from Rick Marken (2007.10.26.1700)

I feel as boy in a sandbox. And then the teacher comes and give me a lesson.

I didn't follow you the whole way, but I throw away the most part of this
mail after I read through Bill's mail.
I think we stop here.

bjorn

System 1: e1 = p1 -
r1 if p1 - r1 > 0

System 2: e2= r2 - p2 if r2 - p2 > 0

Where p1 and p2 are perceptions that depend on the same environmental
variable,

so p1 = p2 = p.
[Ferom Bill Powers (2007.10.27.1345 MDT)]

Rick Marken (2007.10.27.1030) –

Good so far. A quantitative analysis: your grade is better than D. Now
you get three points, one for each possible case. It helps to remember
that under your definitions, System 1 is the reversed case, System 2 is
the “normal” case we’re used to.

  1. Assume r1 = r2 =
    r

then e1>0 when p >r and e2>0 when p < r

So these two systems act (e>0) when p <>
r.
2. Assume r1 > r2

then e1>0 when p >r1 and e2>0 when p < r2

So there two systems act (e>0) when p > r1 or p < r2 and there
is no action when

r2<p<r1.

One system will act when p < r, and the other system will act when p

r. When one system is experiencing error, the other is not. You did
not state that only one system acts at a time. TGhis combination is the
equivalentof a sinbgle bidirectional control system. Half credit. Here is
a diagram:

R

P
P

  e1 =

0
e1 = p - r

  e2 = r -

p
e2 = 0

I will not take off another half credit for not saying that only one
system acts at a time, because you said “or” (barely credible).
Full Credit.

R2
R1

P
P
P

  e1 =

0
e1 = 0
e1 = p - r1

  e2 = r2 -

p e2 =
0 e2 =
0

You missed the third case: R2 > R1:

R1
R2

P
P
P

  e1 =

0
e1 = p -
r1 e1 =
p - r1

  e2 = r2 -

p e2 = r2 -
p e2 =
0

In this case, when p is between r1 and r2, both control systems will be
turned on and acting in opposite directions. This may result in conflict
and loss of control if either system reaches a limit of output.In the
case of opposing muscles, the degree of opposition determines muscle
tone. When p is less than both r1 and r1, only System 2 will be
controlling; when it’s greater than both, only system 1 will be
controlling. No Credit.

So you got 1.5 out of a possible 3, which produces a B.

Bjorn, maybe you can apply these diagrams to your verbal example and
grade yourself. I couldn;'t figure it out in the time I have (I’m going
to bed in two hours, after dinner which will be at 4:00 PM. Trying to get
on Manchester time). See you soon!

Best,

Bill P.

[From Rick Marken (2007.10.27.1420)]

Bill Powers (2007.10.27.1345 MDT)--

So you got 1.5 out of a possible 3, which produces a B.

Very generous. But I think you should also take off at least 1/2 point for this:

Where p1 and p2 are perceptions that depend on the same environmental
variable, so p1 = p2 = p.

It is not correct to say that p1 and p2 are the same (= p) simply
because they depend on the same environmental variable; they might be
different functions of that variable.

So I'm down to 1 out of 3, a C at best. At least that qualifies me to
run for President, in the US anyway.

Have fun in jolly olde.

Best

Rick

···

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

[From Richard Kennaway (2007.10.38.0833 GMT)]

[Ferom Bill Powers (2007.10.27.1345 MDT)]
Bjorn, maybe you can apply these diagrams to your verbal example and grade yourself. I couldn;'t figure it out in the time I have (I'm going to bed in two hours, after dinner which will be at 4:00 PM. Trying to get on Manchester time). See you soon!

Everyone going to Manchester, remember daylight saving time ended (over here, at least) today.

···

--
Richard Kennaway, jrk@cmp.uea.ac.uk, http://www.cmp.uea.ac.uk/~jrk/
School of Computing Sciences,
University of East Anglia, Norwich NR4 7TJ, U.K.

from Richard Kennaway (2007.10.38.0833 GMT)

Everyone going to Manchester, remember daylight saving time ended
(over here, at least) today.

The same happened in Bergen, but can that explain why it is dark and cloudy
the whole day.
If you are going to Manchester I look forward to meet you. Do you bring with
you thel MOL tape?

bjorn