[From Bill Powers (950213.0600 MST)]
James Wilk (950209.1737 GMT)--
Nice to have you aboard, James, after meeting you in Wales last Spring
and long ago in Northbrook, Illinois.
I still can't figure out how to reply to posts so that they end up
on CSG-net itself.
You just send your message as usual, but to the address
csg-l@vmd.cso.uiuc.edu
···
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If two people look at a situation and one says, "There, _that's_ an
example of positive feedback!" and the other says, "But that's an
example of _negative_ feedback!" are they necessarily contradicting
one another?
Not if they're looking at different relationships among different
variables, so "that" refers to something different for each of them. The
_same_ relationship can't be both positive and negative feedback.
Your explorations of the logic of positive and negative feedback are
leading you in the right direction. There is, however, a limit to how
far you can go using only verbal logic and without some sort of
systematic analysis. Let's look at some of your examples.
The "practical joke," which is risky because it involves deception,
would probably not work as smoothly as it does in your imagination
unless you happened to pick people who are not inclined to reality-
testing. And even then, the existence of positive feedback is not
guaranteed -- both people could simply speak louder than usual. However,
at a party there might well be unexplained (to the victims) laughter
which is raising the noise level; presumably others are in on the joke,
since the whole point of a practical joke is to make the victims look
silly to others, thus showing the instigator's ability to control them.
It's hard to imagine a practical joker who never reveals the practical
joke to anyone but the victims (who, by definition of a practical joke,
must realize that they've been had, or there's no humiliation to enjoy).
But this leads nicely into your example of "social oscillations," the
explanation for the loudness of a party. Your analysis is mostly
correct, but needs to be more systematic.
Remember that feedback always involves a complete closed loop, which you
have to identify. People do not speak more loudly at a party just
because the noise level increases -- that's the S-R concept. They speak
more loudly in order to get an indication from someone else that they
are being heard, and to hear themselves clearly. So the variable they
must be controlling is the level of their own voice _in relation to the
background noise_. A person trying to speak to another person near a
waterfall or in a loud factory will increase the loudness of the voice
until it becomes distinguishable over the background noise, even if the
waterfall or factory doesn't become louder as a result. This is simply
negative feeback counteracting a disturbance: the efforts of speaking
are increased until the contrast of voice with background is acceptable.
We can work our way to the party example by starting with the waterfall.
Let's diagram the waterfall case:
> reference
> contrast
v
-------> Comparator ----->
> >
> perceived |
> contrast |
input func output func
^ |
> v
noise-voice <------------ own voice
intensity
^
>
waterfall
The perceived contrast is own-voice loudness minus waterfall-noise
loudness. An increase in noise loudness decreases contrast, and an
increase in own-voice loudness increases it. So the controlled variable
corresponding to the perceptual signal is noise minus own-voice
loudness, in decibels. If the perceived contrast is less than the
reference contrast, the own-voice loudness is increased to correct the
error.
Assuming this is a good control system, we predict that the controlled
variable will remain essentially constant. If the person talks while the
conversation is carried closer to the waterfall, the waterfall noise
intensity will increase, which alone would decrease the perceived
contrast. But we assume the perception (and hence the controlled
variable) to remain constant; therefore the sound intensity from the
voice must also increase, just enough to prevent the contrast from
decreasing. As the waterfall noise intensity increases, for whatever
reason, we will hear the voice intensity also increasing, just enough to
keep the perceived contrast the same. This is simply negative feedback
in the presence of a disturbance.
So we have established the PCT explanation for why and how much voice
sound intensity will increase as noise sound intensity increases. Let us
now do the same analysis for the party situation, where we assume each
person is trying to maintain a certain contrast of voice over noise, as
perceived.
I'll represent two individuals simply as boxes without internal
structure, the above diagram being understood for each one.
------- -------
> > > >
> A | | B |
> > > >
------- -------
/ \ x / \
ca + la ---------->---- cb + lb
- ^\ <---- / - \ <---- /|
> 1 1 |
\ y /
--------<------------------------
Contrast perceived by A is ca, voice loudness of A is la, and ditto for
cb and lb for person B.
We assume these people are talking not to each other but to different
people not shown, so they are talking simultaneously. If you look just
at person A, you will see the same thing as in the first diagram: the
perceived contrast is increased by the loudness of A's own voice and
decreased by "noise" (the loudness of B's voice). So if B talks more
loudly, A will necessarily talk more loudly in order to maintain a
constant perceived contrast, ca. The plus and minus signs indicate the
effects on perceived contrast.
We also find that if A talks more loudly, B will also maintain a
constant perceived contrast by talking more loudly.
You have correctly deduced that A and B are in a positive-feedback
relationship, unwittingly. But we do not yet have a runaway situation.
In the diagram, a "1" is shown on the path from each person's output to
that person's input contrast (assumed to be perceived contrast). This
means that a 1-unit change in the voice output will always produce a 1-
unit cbange in perceived contrast for that person.
A corresponding factor is indicated on the line from A's output to B's
input (x) and from B's output to A's input (y). Suppose that both x and
y are 1. Because control is assumed perfect and the perceived contrast
in both cases is assumed to remain constant, this means that a 1-unit
increase in B's output loudness lb will result in a 1-unit increase in
A's output loudness la. But a 1-unit increase in la will result, for the
same reason, in a 1-unit increase in lb.
We can now trace the effect of A's output loudness on A's perceived
contrast via two pathways, one local and direct, the other remote, via
B's response to A. The local effect has a magnitude of 1 unit of effect
per unit of cause. If you trace the remote effect from A's output,
through B, back to A, and remember that B's output _decreases_ contrast,
you find that A's effect on A's perceived contrast by that path has an
effectiveness of -xy or -1 unit of contrast ca per unit of increase in
output loudness la.
So the NET effect of A's output loudness la on A's own perceived
contrast ca is ZERO! The local negative feedback is just cancelled by
the remote positive feedback, and the net feedback strength is zero.
We can now imagine A having a strolling conversation with A's partner
(not shown), and B doing likewise with B's partner (also not shown).
Recalling the physical principle that sound intensity falls off as the
square of distance d, we can see that x and y both vary as 1/(d^2).
Also, if you hadn't noticed, the total positive feedback effect is x
times y, because both multipliers appear in the remote feedback path. So
the total positive feedback goes as the inverse _fourth_ power of
distance.
When the strolling couples are far apart, x and y are much less than 1,
so local feedback predominates. There is a slight positive feedback
effect which results in slightly elevated voice levels, but only
slightly.
As the couples approach to pass very near each other, x and y will begin
to increase rapidly. As they do, the voice levels on both sides will
increase. As x and y approach 1, the voice levels will get louder and
louder. At x = y = 1, the speakers will be speaking quite loudly, and
even though they don't realize it, they have both lost control of
perceived contrast. As the approach becomes even closer, x and y
approach 1.414, so the total positive feedback is 1.414 x 1.414 or 2,
and the net magnitude of positive feedback approaches (2 - 1) or unity.
At this point the process is on the verge of running away. Any further
approach will result in a net positive feedback factor greater than 1,
and both speakers will quickly escalate to screaming as loudly as they
can, at the limit of output.
Of course this is an unlikely scenario, because we're forgetting about
higher-level systems. Suppose that David, "A", is saying to Felicia, "I
think Nigel is trying to get into Andrea's pants," while Andrea ("B") is
saying to Nigel "I think David is two-timing Felicia." Both of them, of
course, are shouting. If the speakers themselves don't realize that the
objects of their discussion are one foot away, their silent partners
very well might; anyway, it is unlikely that such subject-matter would
actually be discussed at the top of one's voice. The couples would
simply avoid a close approach: they would stay far enough apart so they
could maintain net negative feedback while speaking near a whisper.
So that is the basic analysis. Now let's extend it to N persons at a
party.
Let's consider A the person in question. B is now a large collection of
other people all talking at once (if there are N people at the party,
presumably the number of other people talking is about (N-1)/2). These
people are relatively far from A, so the value of x is smaller than 1
between any one other person and A. But the total positive feedback for
A is x (the outgoing path to the average other person) times y(N-1)/2
(the average return path from _all_ the others who are talking), or
xy(N-1)/2. The dimensions of the room, its acoustics, and the number of
other people will determine the net positive feedback. When N gets too
large for the room, everyone ends up screaming into the nearest person's
ear.
After the first few people have arrived at the party, we will thus see a
few conversations being held here and there in the room. As more people
arrive, the conversations will spread apart to maintain maximum
distance, and when N reaches a large number, people will be huddled
together into little groups shouting to be heard over the din. By "over
the din" we now indicate the phenomenon of "maintaining contrast".
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Don't be fooled by Tom Bourbon's heuristic tricks. He knows what
positive feedback is, and how it shows up in two-person control
experiments when the cross-connection is too strong. He just wanted
someone to come up with a detailed analysis proving that positive
feedback exists. My own style is more to reveal the secret first and
show how an analysis can be done, and THEN see if others can apply it in
other situations.
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Best to all,
Bill P.