[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.