[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
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
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
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
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.
"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.