positive and negative feedback

[From Bill Powers (950209.0920 MST)]
RE: positive and negative feedback

Lars Christian Smith (950209 12:00 CET)--

     If you diagram the interaction between clockmakers and customers,
     you can diagram the interaction as being either negative or
     positive. More demand from customers leads to more production of
     clocks going clockwise. Or you can diagram it as avoidance of
     counter clockwise clocks leading to less production of those
     clocks. Do clockmakers maximize profits, or do they minimize
     losses? One is as true as the other. In either event, the result is
     self-reinforcing growth of clocks with arms going clockwise till a
     stable state at a 100% is reached.

I think we need to spell out some of the details here -- not necessarily
for your sake but just for general interest.

"Negative" and "positive" need to be used very carefully. The basic
relationship that creates positive feedback is this:

···

+
             variable 1 -----> process 1 -------> variable 2
                 ^ |
                 > + |
                  <---------- process 2 <-------------

The + sign above each process indicates either

  positive input change --> positive output change or
  negative input change --> negative output change.

A negative sign associated with a process would indicate that

  positive input change --> negative output change, or
  negative input change --> positive output change.

In the diagram above where both processes carry positive signs, an
increase in variable 1 causes an increase in variable 2, and an increase
in variable 2 causes an increase in variable 1. Also, a decrease in
variable 1 causes a decrease in variable 2, and a decrease in variable 2
causes a decrease in variable 1.

The _direction of change_ of any variable has nothing to do with whether
the feedback is positive or negative. In either case above there is
positive feedback. Imagine a small perturbation of variable 1, and trace
its effects all the way around the loop. If the returned effect via
processes 1 and 2 is IN THE SAME DIRECTION as the initial perturbation,
the feedback is positive. Whether the initial perturbation of variable 1
is positive or negative, the returned effect will be of the same sign,
so the feedback is positive. Positive feedback has nothing to do with
whether a variable gets larger or smaller. It describes relationships
between variables.

To turn this into a negative feedback situation, we would have to change
the sign of either process 1 or process 2 (but NOT both!). If we made
the sign of process 1 negative and left that of process 2 positive, an
increase in variable 1 would result in a decrease of variable two, and a
decrease of variable 2 would result in a decrease of variable 1. So the
returned effect on variable 1 is now of _opposite_ sign from the initial
perturbation, whether that perturbation be in the positive or the
negative direction. That is negative feedback.

I leave it as an exercise for the student to show that if both processes
carry a negative sign, the feedback is positive.

In the clock example, there is positive feedback if there are two
processes that have the same sign:

1. increasing demand for x relative to y causes
    an increase in supply of x relative to y, and

2. Increasing supply of x relative to y causes
    an increase in demand for x relative to y.

If the assumed relationships are correct, this is an example of positive
feedback.

Similarly, for the side of the road on which cars are driven, there is
positive feedback if

1. An increase of accidents on the drivers' left results in
    more drivers choosing to drive on the right, and

2. An increase in drivers choosing to drive on the right causes
    more accidents to occur on the drivers' left.

As we can see, the second statement is incorrect: it should be

2a. An increase in drivers choosing to drive on the right causes
   fewer accidents to occur on the left.

That would be negative feedback.

This shows us that we have misstated the underlying proposition, because
it implies that there will be no tendency to drive on either side,
whereas intuition (as well as observation) says that drivers will all
end up driving one way or the other.

We can get the right answer by changing the variables:

1. When more drivers drive in the same lane as most other cars going
    in the same direction,
    the number of head-on collisions in the other lane decreases, and

2. When the number of head-on collisions in the other lane decreases,
   more drivers drive in the same lane as most other cars going
   in the same direction.

Somehow that second statement doesn't sound too convincing -- perhaps
someone else can come up with still other variables that will uphold
Lars' conclusion. Or maybe we will conclude that this is why we have
traffic laws.

Aside from the sign of the feedback, there is also the question of the
amount. When the size of the fed-back effect is less than the effect of
the initial perturbation, positive feedback does not cause runaway, and
negative feedback has little effect. Most of what is said about positive
and negative feedback assumes that the returned effect is larger than
the initial effect. Positive feedback then causes a runwaway condition,
and negative feedback produces significant resistance to disturbances of
any variable in the loop.
-----------------------------------------------
The most pernicious misuse of the terms positive and negative feedback
confuses the names of algebraic signs with evaluations of the
desirability of changes in variables. Here is an example of positive
feedback:

1. A person utters remarks which
   a listener perceives as discouragement, and

2. The listener then replies with remarks which
   lead the first person to feel even more discouraged.

And here is an example of negative feedback:

1. An gunner fires a round 100 yards off target, and
   the spotter says "You missed 5 degrees to the left", and

2. Aiming to the right by five degrees results in
   hitting the target, and
   the spotter says "Great, that was right on."

-----------------------------------
Finally, it is not possible for one person to "give another person
feedback." Feedback is the effect of a variable on itself. A person's
actions have feedback effects because they are effects of the action on
the same person. The feedback effect must depend in a reliable way on
the action, so a second person, in order to be part of the feedback
loop, must have no choice as to what response to give as "feedback". If
the other person has a choice of producing any response at all, there is
no feedback loop, but only a disturbance.

Horrible example:
"Mr. Picasso, I'd like to give you some feedback on the way you use
forms in your paintings." This means, of course, that I am going to
express an opinion whether Picasso wants it or not.
-----------------------------------
The technical terms of control theory and systems analysis have been
adopted by many people who have never learned the underlying displine.
As a result, the meanings of these terms have drifted in a random walk,
sometimes into nonsense and sometimes into exactly the opposite of the
original meaning. It sometimes seems that people will go to any lengths
to avoid learning what they are talking about.
-----------------------------------------------------------------------
Best,

Bill P.

[Lars Christian Smith 950210 13:00 CET]

···

To: Bill Powers

Subject: Positive Feedback, Research Priorities

Positive feedback:
------------------
How about,

1. An increase in the number of accidents on the left causes more drivers
   to drive on the right.

2. More cars driving on the right mean more accidents on the left, as
   those driving on the left encounter more cars driving in the opposite
   direction in the same lane.

Research priorities:
--------------------

There have been discussions of what needs to be done to get PCT accepted,
and why it isn't accepted. But what needs to be done to advance the state
of the science of PCT. What are the top 5 or 10 research priorities? What
are the most important unresolved questions, in order of priority?

Best regards,
Lars

[From Bill Powers (960604.1140 MDT)]

Jeff Vancouver 960603.1430 EST --

It occurs to me that I should really find out whether your departures
from PCT in discussing positive and negative feedback are deliberate or
the result of your not knowing what these terms mean in PCT.

One way for me to find out is to offer you a little test, which you can
take if you want to check out your understanding. Consider the following
scenarios, and indicate whether positive or negative feedback is
involved, or neither, or "it depends", and explain why:

A.
When John is hungry, he get crabby.
The crabbier John gets, the harder the baby cries.
As long as the baby cries, Mom tries to comfort her instead of making
lunch.

B.
When John fails at a task he gets discouraged and the coach worries.
When the coach worries about John's failing, he reminds him of other
things once John failed at, but eventually mastered.
When John remembers succeeding, he does better at the new task.
When John does better, the coach worries about him less.

C.
The Crackerjack motto: "The more you eat, the more you want."

D.
The Jay's Potato Chip motto: "Can't stop eatin' 'em."

E.
When the market drops, John sells his stocks.
When the market rises, John buys stocks.

F.
The teacher says "John, you did very well on that test, and I'm sure
you'll do even better on the next one."

G:
The question is, "How many bushels of wheat were produced in Russia last
year?" John is permitted to offer answers as many times as he wants, but
is told only whether he has answered right. If he answers wrong, nothing
is said.

H:
Same question, but John is told only when he has answered wrong. If he
answers right, nothing is said.

I:
Same question, but John is told whether his answer was high or low.

[With respect to G, H, and I: in each case, how long will it take John
to get the right answer within 1 bushel per million?]

···

-----------------------------------------------------------------------
Best,

Bill P.

[From Jeff Vancouver 960606.12:30 EST]

[Bill Powers (960604.1140 MDT)]

It occurs to me that I should really find out whether your departures
from PCT in discussing positive and negative feedback are deliberate or
the result of your not knowing what these terms mean in PCT.

One way for me to find out is to offer you a little test, which you can
take if you want to check out your understanding. Consider the following
scenarios, and indicate whether positive or negative feedback is
involved, or neither, or "it depends", and explain why:

Given that you are Bill Powers and that it has been some time since I
posted last on here, I will answer one.

A.
When John is hungry, he get crabby.
The crabbier John gets, the harder the baby cries.
As long as the baby cries, Mom tries to comfort her instead of making
lunch.

This is a nice example of a positive feedback loop in a results (system
dynamic's) model. It is also an example of several negative feedback
loops in a control theory sense, although, these can only be speculations.
First, the output function of John's hunger regulating system seems to be
to make him "crabby." As it now stands, it is not a effective control
system. THe output function needs to be reorganized to reduce the
discrepancy between the perception of hunger and the reference signal of
no hunger. Until that happens, John is out of control (hence the positive
results loop), but the control system is negative. The baby has a control
system (negative feedback loop) where crying is the output and John's
crabbiness is an input that throws the perception of, say comfort, out of
alignment. The quality of this system depends on whether Mom's comforting
changes the perception, although, persumable reducing John's crabbiness
would probably be more effective (of course, it is asking a lot of the
baby to reorganize it's output function here, it might reorganize it input
function/reference signal such that it don't care about John's
crabbiness). Mom has a negative feedback loop/control system designed to
maintain no crying in baby. How effective it is depends on the baby's
input functioned as mentioned above - if comforting translates to the
baby's perception, fine.

I could do this with every one of your questions, but I think you get the
point. As I said, I describe the different meanings of the terms in some
detail in the paper. I do not wish to reproduce it here. I ran out of
time the other day. I should not start something I cannot finish (it has
been a long time since I posted on here).

Let me see if I can be more descriptive.

The research question relates to learning (reorganization) and
performance. Assuming that a person wants to achieve/maintain a goal
(usually a performance goal provided by some organization/researcher), the
output function must be organized such that the person can reduce an
error. Over the long run, for any system in the perceptual hierarchy (not
the intrinsic one), information about the state of the environmental
variable will have different influences on the control system. Once a
control system is established and well-functioning (unlike John's above)
information that indicates a disturbance, results in an error which is
corrected by some behavior(s). Information that indicates a disturbance
is often called negative feedback in our literature. I am not condoning
that term, just acknowledging it. In many contexts, the information
about an environmental variable is in the hands of a supervisor or other
external agent. Thus, the PCT model suggests the importance of "negative
feedback" if the external agent wants the environmental variable
controlled too.

On the other hand, when the system in not well-functioning (e.g. novel
task). THat is, outputs do not reduce error, reorganization much take
place. In this case information that some behavior resulted in a
reduction in error would, I hypothesis and model, result in halting or at
least slowing down reorganization such that the output function holds the
values that "work." Information that results in a reduction in error is
what you (and me) would call negative feedback, but if that information
comes from an external agent, it is called positive feedback in our
literature (because the agent is able to say "yes, that's it" or something
like that).

Thus, I am trying to show how, why and when positive and negative feedback
(in psychology's use of the terms) is useful using a negative feedback
model of behavior (perception control).

OKAY!

E.
When the market drops, John sells his stocks.
When the market rises, John buys stocks.

John is stupid. - Sorry, I
had to answer this one.

Later

Jeff