Positive Feedback

From Bruce Buchanan (950208.1300 EST)

I have been much puzzled by recent discusions of specific examples of
positive feedback, intended, I would suppose, to illuminate its
characteristics. Without commenting on that discussion I would like to
provide a description of the roles of negative and positive feedback from
the book Thinking by Machine: A Study of Cybernetics, by Pierre de Latil,
foreward by Isaac Asimov (1957), which has influenced my thinking greatly
for nearly 40 years. The following is all direct quotation.

re "Constancy Effectors and Tendency Effectors: (p. 89:) ...

"Here we have a fundamental division of effectors ... according to whether
... able or unable to attain the goal.

"In the first case the goal is a level first of all to be attained and then
maintained. The effector tends to stabilize its useful effect at this
level; deviations can then occur in two directions. We will call this a
constancy effector. Examples: ...respiratory mechanims regulating the CO2
content of arterial blood, [etc]

"In the second case, the goal is the maximum effect (in absolute value).
The effector tends toward this objective without being able to reach it;
there is always a deviation between the real effect and the goal, and this
deviation is always in the same direction. The goal can even be considered
as being infinite. We call this a tendency effector. Examples: machines
that produce power, light or heat; all organisms [incl. some businesses?]
engaged in vital or sporting competetion. ... A lamp is not required to
produce a certain quantity of light, but as much light as possible; if our
lamp gives too much light we do not regulate it so as to give less but we
use a less powerful one which also tends towards its maximum."

Just a reference of possible interest, FYI. Maybe old hat to the old hands.

Cheers!

Bruce B.

[Martin Taylor 950208 16:30]

Bruce Buchanan (950208.1300 EST)

I have been much puzzled by recent discusions of specific examples of
positive feedback, intended, I would suppose, to illuminate its
characteristics.

I didn't think that was the reason for the examples. I thought they were
to show that positive feedback does occur in important ways when control
systems interact.

Anyway, as for what feedback is, positive or negative, let's try some
simple descriptions (not definitions).

Feedback: If a fluctuation in the state of something influences the later
state of that thing, then the state is part of a feedback loop.

Gain: The degree to which a fluctuation in the state of something causes
later fluctuation in that state. This is a very vague statement, because
Gain is not really a numeric quantity, though it is often talked about as
if it were. It is a time function, and the form of that function is
what defines the behaviour of the feedback loop. Gain may be positive
or negative for any part of its time function.

Negative feedback: The fluctuations in the state of something tend to
result in its being influenced back toward its prior state. The loop
gain is said to be negative in magnitude.

Positive feedback: The fluctuations in the state of something tend to
result in its being influenced further away from its prior state. Positive
feedback results in a tendency "toward" some state only by accident, as
a consequence of the state being approached being far from the original
state. Pierre de Latil's example of a "goal" being to have "maximum effect"
is not an example of positive feedback, in that the fluctuations or deviations
from that goal are reduced, not enhanced by the feedback. But the same
effect might be achieved by a positive feedback system that amplified
fluctuations away from zero. One could see the difference if there were
equal possibilities of going toward positive of negative infinity. In the
case of negative feedback, the movement would always be toward positive
infinity, whereas in the case of positive feedback it would be away from
zero in whichever direction the first fluctuation happened to be.

A lamp is not required to
produce a certain quantity of light, but as much light as possible; if our
lamp gives too much light we do not regulate it so as to give less but we
use a less powerful one which also tends towards its maximum.

This is given as an example of positive feedback, but it is wrong. A lamp
has negative feedback embodied in the increase of resistance with temperature
of its filament. When the lamp is first turned on, cold, the resistance is
low, meaning that the current is high --V*I is large. As the lamp heats
up, the resistance increases, reducing the current and the power input V*I.
As the temperature goes up, so does the radiated power we see as light.
At some point, the increasing radiated power equals the reducing V*I input
power. Any further increase in temperature increases the radiated power
and reduces the input power, cooling the filament, and vice-versa. There's
no "control" here, just a balance. But it is negative feedback, in that
fluctuations in the temperature induce effects that oppose those fluctuations.
If there were positive feedback, the resistance decreasing with temperature,
the filament would simply vaporize in a flash.

Positive feedback is probably quite rarely observed, since by its nature
it results in a runaway from some unstable or metastable state, and
the runaway is stopped only by some limiting factor or non-linearity
in the environment. One sees positive feedback only while the runaway is
occurring, whereas one sees negative feedback for as long as the feedback
loop exists and the stabilized state can be observed.

None of the above refers to "control," though negative feedback with
high Gain is required for control.

Martin

<[Bill Leach 950210.02:11 EST(EDT)]

Bruce Buchanan (950208.1300 EST)

I have been much puzzled by recent discusions of specific examples of
positive feedback, intended, I would suppose, to illuminate its
characteristics. Without commenting on that discussion I would like to
provide a description of the roles of negative and positive feedback ...

Therein exists the source of puzzlement. Feedback is an exacting
technical term when used in closed loop control systems.

ALL control systems MUST have a net negative feedback if control is to be
achieved. If feedback is positive then control is NOT occurring.In any
real functional control system feedback IS negative regardless of whether
the control system is controlling successfully or not. For example if
environmental disturbances exceed the output capability of the control
system then control will not be achieved but feedback is still negative.

-bill

<[Bill Leach 950210.03:13 EST(EDT)]

[Martin Taylor 950208 16:30]

Good posting overall.

A couple of comments though:

Gain

In control system engineering, gain usually is numeric and is essentially
the measure of the system sensitivity.

The "time related" functions are typically lumped into "reset", and
"derivative gain".

None of the above refers to "control," though negative feedback with
high Gain is required for control.

Negative feedback is require for control. High gain is required for
"good" control.

-bill

[Hans Blom, 960311b]

I am having trouble seeing how this [donkey between the two stacks
of hay] exemplifies an increase in deviation from the intial status
quo.

I am seeing the example as two negative feedback loops. In one the
donkey wants food; in the other he wants to exert as little energy
as possible. So the donkey controls for the first and second
variable (food and distance) and goes the shorter distance toward
the food.

Scott, I posed my example as one which resolves a _choice_ problem.
Others may see this as a conflict situation, but for me that is the
exact same thing: when in a conflict, choose the better alternative
(rather than procrastinate endlessly). Initially, the donkey has no
guidance in which of the two stacks of hay is more attractive, but as
soon as it moves its head just a little, one of the two becomes more
attractive. And progressively so, the closer its head gets to one of
the stacks. To me, this is the kind of positive feedback that is
required to resolve mutually excluding choices. Other models can be
imagined as well. A model is, after all, a simplification of the
original situation where you loose everything except for the one or
two details that are subjectively important. If other details are
important to you, you'll have a different model.

A very similar example: a meteorite high up in the sky at that point
where the attraction of earth and moon cancel out. Now even the
tiniest influence from outside will make the meteorite plunge
inexorably toward either the earth or the moon. What makes the donkey
different -- and the situation into positive feedback -- is that it
has, presumably, its own internal energy sources for movement, so
that it doesn't depend on "passive" attraction only.

Sorry to be of so little help.

Greetings,

Hans

···

================================================================
Eindhoven University of Technology Eindhoven, the Netherlands
Dept. of Electrical Engineering Medical Engineering Group
email: j.a.blom@ele.tue.nl

Great man achieves harmony by maintaining differences; small man
achieves harmony by maintaining the commonality. Confucius

I appreciate mentioning positive feedback can aggravate, but
I have a specific question relating to this.
Why is the process whereby a high order control system selects a
reference level for a lower order control system not a positive feedback
loop?
My understanding of this proposed process is the reference level is
selected through the error signal from the higher order control system
being used as an “address signal” to retrieve stored reference levels or
signals from memory (Abbott, 2003 referring to Powers, 1973, p217). I
would see the process as a search in the attractor space of memory for an
attractor which positively corresponds with the address signal. This
seems to me from a very basic understanding of PCT and Complexity Theory
a positive feedback loop.
If this is not the case a basic explanation of why would be
appreciated.
Regards Rohan
Rohan Lulham
Ph.D. Student
Environment, Behaviour and Society Research Group
Faculty of Architecture, University of Sydney
Australia
At 02:36 AM 8/04/2005, you wrote:

[From Rick Marken
(2005.04.07.0935)]

Bill Powers (2005.04.07.0936 MDT)

Rick Marken (2005.04.06.2220) –

is it capable of serving as an input to a control
system?

Sure. At many different levels.

Oh, you clever person. Very nice.

Thank you, dear. Now get back to the far more important work of writing
the

modeling book.

Love

Rick

Richard S. Marken

MindReadings.com

Home: 310 474 0313

Cell: 310 729 1400


This email message is for the sole use of the intended recipient(s)
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Rohan Lulham
Ph.D. Student
Environment, Behaviour and Society Research Group
Faculty of Architecture, University of Sydney
Australia

[From Rick Marken (2005.04.08.0915]

Rohan Lulham (2005.04.07)

Why is the process whereby a high order control system selects a reference
level for a lower order control system not a positive feedback loop?

There would be positive feedback if the sign of the reference connection
were incorrect. The correct sign for the reference connection (so that
positive feedback is avoided), if I remember correctly, is that the sign of
the higher level system's contribution to a lower level reference signal be
the same as the sign of the contribution of the lower level system's
perceptual signal to the perceptual signal controlled by the higher level
system that is setting the reference. I think this rule is very clearly
described (with mathematical precision) by Powers in the last of the 1979
BYTE articles. I think I also describe it in my "Spreadsheet model.." paper
in _Mind Readings_.

My understanding of this proposed process is the reference level is selected
through the error signal from the higher order control system being used as an
�address signal� to retrieve stored reference levels or signals from memory
(Abbott, 2003 referring to Powers, 1973, p217). I would see the process as a
search in the attractor space of memory for an attractor which positively
corresponds with the address signal. This seems to me from a very basic
understanding of PCT and Complexity Theory a positive feedback loop.

If this is not the case a basic explanation of why would be appreciated.

I think the best thing to do is to see how a hierarchy of control systems is
actually implemented. If you can read spreadsheets I recommend downloading
my spreadsheet hierarchy model from

http://www.mindreadings.com/demolist.html

and looking carefully at how I implemented a three level hierarchy with no
positive feedback loops. That is, the control systems at levels 2 and 3
control by varying the references sent to lower level systems so that the
level 2 and 3 systems maintain negative feedback control of their
perceptions. It's a very cool system and it was done by simply reading Bill
Powers' nice, clear mathematical explanation of hierarchical control in the
last of the 1979 BYTE series, which, I believe, is reprinted in LCS I or II
(I think every PCT enthusiast should have both).

Best

Rick

···

--
Richard S. Marken
MindReadings.com
Home: 310 474 0313
Cell: 310 729 1400

--------------------

This email message is for the sole use of the intended recipient(s) and
may contain privileged information. Any unauthorized review, use,
disclosure or distribution is prohibited. If you are not the intended
recipient, please contact the sender by reply email and destroy all copies
of the original message.

[From Bill Powers (2005.04.08.1045 MDT)]

Rick Marken (2005.04.08.0915]

> Rohan Lulham (2005.04.07)

> Why is the process whereby a high order control system selects a reference
> level for a lower order control system not a positive feedback loop?

A positive feedback loop is one in which the output action affects the input in such a direction as to increase the difference between the perceptual signal and the reference signal. That, of course, makes the output larger and causes a still larger difference or error. If the total steady-state amplification factor around the loop is less than 1, the overall effect is to amplify errors and make the loop less stable. If the steady-state loop amplification factor (or loop gain in logarithmic terms) is greater than 1, the error will increase until some physical limit is reached somewhere in the loop. Positive feedback always makes errors larger, and when it is strong enough it creates self-destructive runaway effects.

In any case where there is a reference state, target state, or goal state (or fictitious "attractor") and the action of the system makes the outcome approach that state, the sign of the feedback is necessarily negative. That is the only case that produces convergence, which we call control when it is pronounced enough.

Common misunderstandings of positive and negative feedback arise from using the common-language meanings of good, complementary, favorable, or supportive for "positive" and the opposite for "negative." Those usages have nothing to do with control theory.

Best,

Bill P.

[From Erling Jorgensen (2005.04.08 1510 EST)]

Rohan Lulham (2005.04.08 1222 Australia time?)]

Why is the process whereby a high order control system selects a
reference level for a lower order control system not a positive
feedback loop?

The sign of the feedback, with the control loops we customarily talk
about on CSGNet, refers to the entire loop, from a given reference
signal all the way around until the corresponding perceptual signal
is compared with it. If the net sign of all the amplication factors
on that transit is negative, then the loop will operate with negative
(i.e., error-reducing) feedback. If the net sign is positive, then
the loop will operate with positive (i.e., error-amplifying or
runaway) feedback. In the later instance, the loop would not be
controling, in the sense of bringing a perceptual signal to the value
of its respective reference signal. It would in fact be making
matters worse.

In practical terms, as far as designing any simulations, it usually
amounts to making sure the respective signs for the reference &
perceptual signals are opposite, although it doesn’t matter which is
which.

My understanding of this proposed process is the reference level is
selected through the error signal from the higher order control system
being used as an “address signal” to retrieve stored reference levels or
signals from memory (Abbott, 2003 referring to Powers, 1973, p217). I
would see the process as a search in the attractor space of memory for an
attractor which positively corresponds with the address signal. This seems
to me from a very basic understanding of PCT and Complexity Theory a
positive feedback loop.

The process you describe here would constitute only a portion of a complete
control loop. It is a form of retrieval process for generating the output
to the next lower control system. But the loop would not be closed until
the lowest loop’s output exits through the environment & works its way
back up the hierarchy in terms of successively higher perceptual input
functions. At least that is the basic hierarchical model as it currently
stands.

I do not believe the proposed “addressing” process itself has actually
been modeled in any simulations. In other words, the field is open for
whatever might do the trick. It might be some kind of attractor space,
as you speculate, and if so, Complexity Theory might have something to
add to the dynamics of specific components of the loop. But in any case,
the retrieving of a suitable reference signal, & sending it on its way to
the next lower level, is a feature of only a segment of the loop we usually
look at.

I would certainly be interested in proposals for how this addressing
function of selecting references actually operates. A working model of
this specific feature has puzzled me for quite some time.

All the best,
Erling

[From Erling Jorgensen (2005.04.08
1510 EST)]

Rohan Lulham (2005.04.08 1222 Australia time?)]

Why is the process whereby a high order control system selects a

reference level for a lower order control system not a positive

feedback loop?

The sign of the feedback, with the control loops we customarily talk

about on CSGNet, refers to the entire loop, from a given reference

signal all the way around until the corresponding perceptual signal

is compared with it. If the net sign of all the amplication factors

on that transit is negative, then the loop will operate with negative

(i.e., error-reducing) feedback. If the net sign is positive, then

the loop will operate with positive (i.e., error-amplifying or

runaway) feedback. In the later instance, the loop would not be

controling, in the sense of bringing a perceptual signal to the value

of its respective reference signal. It would in fact be making

matters worse.

In practical terms, as far as designing any simulations, it usually

amounts to making sure the respective signs for the reference &

perceptual signals are opposite, although it doesn’t matter which is

which.

My understanding of this proposed process is the reference level is

selected through the error signal from the higher order control
system

being used as an “address signal” to retrieve stored
reference levels or

signals from memory (Abbott, 2003 referring to Powers, 1973, p217). I

would see the process as a search in the attractor space of memory
for an

attractor which positively corresponds with the address signal. This
seems

to me from a very basic understanding of PCT and Complexity Theory a

positive feedback loop.

The process you describe here would constitute only a portion of a
complete

control loop. It is a form of retrieval process for generating the
output

to the next lower control system. But the loop would not be closed
until

the lowest loop’s output exits through the environment & works its
way

back up the hierarchy in terms of successively higher perceptual input

functions. At least that is the basic hierarchical model as it
currently

stands.

I do not believe the proposed “addressing” process itself has
actually

been modeled in any simulations. In other words, the field is open
for

whatever might do the trick. It might be some kind of attractor
space,

as you speculate, and if so, Complexity Theory might have something to

add to the dynamics of specific components of the loop. But in any
case,

the retrieving of a suitable reference signal, & sending it on its
way to

the next lower level, is a feature of only a segment of the loop we
usually

look at.

I would certainly be interested in proposals for how this addressing

function of selecting references actually operates. A working model
of

this specific feature has puzzled me for quite some time.

All the best,

Erling

Thanks Erling, Bill and Richard,
I had a look at Richards exel model, and will read the paper relevant to
it. I am not on top of the modelling and programming techniques but aim
to make this a priority in the next year. I probably am a bit limited in
my ability to comment on the models directly until this time, and may be
missing some key concepts in this discussion as a result.
However I think there may have been a bit of confusion in the question I
was asking (or alternatively there is the chance my understanding may be
at fault). I was talking specifically about the process at the output
function where a reference level for the next lower level is selected. I
have included a diagram of the region. I don’t get the sense that this
process can be modelled as a negative feedback loop. The process of
identifying a reference signal from memory seems to be an expansive
process (where a value is created) rather than a controlled process
(where a value is reduced) (although at all times there is the regulating
negative control system the level above monitoring error and bringing the
system back in line (another iteration) if it gets out of
control).
My sense is this retrevial process which has been suggested to have some
random features (Powers, 1973) works to seek out possible best selections
from memory. While as indicated it may result in more error on occassions
for the higher control system, it also alternatively may result in less
error where the expansive process identifies a reference signal that
reduces error in the higher order system.
The problem I have to a degree is that without such a process it seems as
though a series of reference level in a hiearchy must need to be
scripted in the brain. I am not sure how the exel model does this as yet,
but my sense is that the quality (rather than quantity) of the reference
level for the lower system are pre-set.
Thankyou for your responses and discussion, it is likely something I will
need to think more about.
Rohan

area of interest.doc (31.5 KB)

···

At 05:41 AM 9/04/2005, you wrote:
Rohan Lulham
Ph.D. Student
Environment, Behaviour and Society Research Group
Faculty of Architecture, University of Sydney
Australia

[Martin Taylor 2005.04.09.09.41]

Rohan Lulham -- apparently Sat, 9 Apr 2005 17:53:31 +1000

However I think there may have been a bit of confusion in the question I was asking (or alternatively there is the chance my understanding may be at fault). I was talking specifically about the process at the output function where a reference level for the next lower level is selected. I have included a diagram of the region.

I'm sure you will get several replies about this diagram, because it isn't at all the normal multi-level PCT diagram, in two important respects.

The less important of the two is in the representation of the Environment and the disturbance within each individual loop. The "Environment" is usually considered to be the transformation that turns the output into its effect on the perceptual signal, so you have correctly put it between the output function and the perceptual input function. But you have located the disturbance in such a way that its effects go through the same transformation. The addition of the disturbance should come _after_ the environmental transform, because whatever its (unknown) source, it won't necessarily be affected by the same things that affect the way the output influences the perceptual input.

The more important problem is that the Environment for the upper level loop is actually the lower level loop, not something separate. The upper loop can't see or act upon the external environment directly. It has to do it _by way of the lower-level's actions and perceptions_. In your diagram, take away the bottom half of the upper loop, and connect the lower perceptual signal (the output of the perceptual input function) to what you have called "Stimuli (S)" of the upper loop (as well as to its own comparator).

When you've made those two reconnections, you will have a conventional two-level hierarchy, but with only one loop at each level. You will see that the negative feedback loop of the upper system is completed ONLY through the action of the lower-level loop.

Normally, in a hierarchy, we consider that each higher-level loop feeds reference signals to, and receives perceptual input from, several lower-level loops in parallel. That's the way coordinated action happens. In your diagram, you could make multiple copies of the lower-level loop, and connect each one's perceptual signal into the same upper-level perceptual input function, and each one's reference input from the same upper-level output. That creates a one-many hierarchy.

Likewise, each lower-level loop serves several upper-level loops, so you could equally replicate the upper-level loop, and show the perceptual signal from your lower one fanning out to feed al, the upper level perceptual input functions, and getting its reference signal from all the upper-level output functions. If you did that, you would have a many-one hierarchy.

If you do both replications, you have a many-many hierarchy, and that's the standard HPCT structure (if you add several more levels on top, too).

The structure in your picture isn't of a "standard" HPCT hierarchy, but it is a possible structure. I'd call it a "trusted slave" helping system. The "master" instructs the slave what to do and trusts the slave to do it. The only perceptual feedback in such a system is through the Environment, and then only if the slave's actions affect a portion of the environment observed by the "master". (For a more extended discussion of "helping", you can see <http://www.mmtaylor.net/PCT/Helping/helping.html>.

I hope this helps and is not too redundant with what you will undoubtedly get from others.

Martin

[Martin Taylor
2005.04.09.09.41]

I’m sure you will get several replies about this diagram, because it
isn’t at all the normal multi-level PCT diagram, in two important
respects.

Thanks Martin it is always good to be pulled in line
(in the nicest possible way). I accept your comments and agree with them
and hopefully have not lost everyone. I will update my conceptual
diagrams and be more mindful in the future.
I’ve attached Bill’s diagram most commonly used (Powers, 1989) locating
the area to which the question relates.
This diagram may highlight the original point. This looks like a very
scripted process. How does the higher order system set the reference
level (not control it) for the lower level system? How is this best
conceptualized?
The purpose of my question is trying to get a better conceptual
understanding of this process at a basic level. It often appears to me
that the dynamics of this process, coupled with reorganization, gives the
control system the degrees of freedom to be a living control system.
Hopefully my scientific naivity is not confounding my question.
Regardless thanks for the opportunity.
Rohan
Rohan Lulham
Ph.D. Student
Environment, Behaviour and Society Research Group
Faculty of Architecture, University of Sydney
Australia

Doc3.doc (25.5 KB)

···

At 12:08 AM 10/04/2005, you wrote:

[From Rick Marken (2005.04.10.2240)]

Rohan Lulham writes:

I've attached Bill's diagram most commonly used (Powers, 1989) locating the area to which the question relates.

This diagram may highlight the original point. This looks like a very scripted process. How does the higher order system set the reference level (not control it) for the lower level system? How is this best conceptualized?

Just think of the reference for the lower level system as a _variable_. There is no scripting involved. The reference for the lower level system varies continuously as the means of keeping the perception controlled by the higher level system at it's reference.

Consider the reference going into one of the level 1 systems in the diagram you sent, say the third one over from the left. Call this reference r13, where the first subscript number is the level of the system in the hierarchy and the second is the system at that level. This reference represents the summed value of the outputs of several level 2 systems -- o22,o23, o24, to be exact. These outputs are proportional to the errors in the systems that produce them. So, for example, o22 = k (r22-p22). The problem is figuring out how the outputs should combine to contribute to the lower level reference, r13, in his case. That is, should r13 = o22+o23+o24? Or should some outputs contribute negatively to r13, such as r13 = -o22+o23-o24?

It turns out that the sign of the contribution of a higher level output to a lower level reference should be the same as the sign of the contribution of the lower level system's perception to the perception controlled -- by means of varying r13, in this case -- by the higher level system. In this example, the sign of the contributions of o22, o23 and o24 to r13 depend on the sign of the contribution of the lower levels perceptions -- p 12, p13 and p14 -- to the perceptions controlled by systems 22, 23 and 24.

This may seem complicated, but it's really not necessary to think about this when you are thinking about the operations of a properly functioning control hierarchy, one in which al the connections from higher level output to lower level reference have been made properly (as is true in the spreadsheet hierarchy that you downloaded from the web). All you have to know is that all higher level systems are continuously varying their outputs, as necessary, so as to keep their perceptions at the specified reference values. As the higher level systems vary their outputs they are varying the references for the lower level systems, which are acting to keep their perceptions matching there references.

In a functional hierarchy, you can deal with any system in the hierarchy as an independent control system, acting to control it's perception. Higher level systems do this by varying the references of lower level systems; the lowest level systems do this by varying their effects on the environment.

Does this help at all?

Best

Rick

···

---
Richard S. Marken
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400