[From Bill Powers (921220.1330)]
John Gabriel (921220.1001) --
I assume that Gary won't have unsubscribed you so quickly, but
I'll copy this to you direct anyway.
I'm going to avoid the word "Control" because it has so many
different meanings.
Control seems to have more different usages than it actually has.
People use this term in what seem to be quite different ways, but
when you examine the circumstances in which they use the word, I
think you often, maybe always, find that they have an incomplete
understanding of the situation to go with the incomplete
understanding of what control means. They're really assuming a
complete control loop, but paying attention only to part of it
and taking the rest for granted.
To see how common usages are incomplete, just ask a few questions
organized around PCT.
Control is used in the sense of restraining or limiting. Consider
controlling a dog by leashing it. Clearly you need an action,
pulling on the leash. But suppose you weren't allowed to perceive
any consequence of this action: you can't feel any pull on the
leash and you can't see any dog on the end of it. This would
clearly be an unsatisfactory kind of "control." You want to
perceive that the dog is in fact on the end of the leash: see the
dog and feel the pull. If you chain a dog in the yard, you must
be able to see that the chain is attached between a stake and the
dog and that the dog remains on the end of the chain and the
stake remains in the ground. If you can't perceive those things,
you feel uneasy about claiming that the dog is under control.
Control is used in the sense of a "control experiment." You do a
control experiment by duplicating every condition except the one
you manipulate for the real experiment. Suppose you were allowed
to do a control experiment, but were not allowed to see the
results. Would you still think of it as a control experiment?
Control is used to describe the relationship between an authority
and a subordinate. Would the authority feel that commanding a
subordinate's action amounted to control if there were never a
report on or observation of the action or its effects?
Control is used in the sense of "determine." The temperature of
reactants controls the rate of the reaction, because the reaction
rate is a function of temperature. If you were not allowed to
perceive either the temperature or the reaction rate, would you
be able to claim that temperature was in fact controlling the
reaction rate? More subtly, could you say that the reaction rate
was controlled if you weren't both perceiving it and comparing it
with some reference reaction rate?
A control is something like a steering wheel or a brake pedal.
When a control is operated, it has an effect on something, like
speed. But does the control by itself bring the speed to some
specified value? Could you use the brake pedal as a control of
the car's speed if you could not somehow perceive the car's
speed?
I won't drag this out. In all the cases I find as synonyms of
control in a thesaurus, the meaning would become irrelevant if
perception of the consequences weren't allowed and if there
weren't a preferred, expected, or desired state of the
consequences. In all such situations, the speaker is taking for
granted the perception and the reference level. Normal usages of
control amount to synecdoche: referring to a whole by mentioning
some part of it.
Even in the technical world, this sort of synecdoche happens. I
have heard people talk about "open-loop control." But suppose you
design an open-loop controller, and are allowed to see only the
input that you give it, not its output effects. You would be
unable to calibrate it, and while it was operating you would not
know (perceive) whether it was having the effect it was supposed
to have (i.e., the reference condition).
I think that when people use the word control, there is ALWAYS a
closed loop involved or implied even when it's not mentioned. In
the background there is always someone perceiving the result and
comparing it with an intended or desired result.
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The term "Reference Signal" is replaced by "Desired State (of
the observed environment)" for similar reasons. The term
"Reference" has Rock of Gibraltar like connotations, but I
think we can all agree it's possible to change our desires from
time to time, just as the BCP signal topology allows and
encourages - i.e. the "desire" comes from within, not from
without.
Reference signals in the HPCT model are continuously adjustable;
they are the means by which higher systems act to control their
perceptions. A reference signal is not supposed to connote
something fixed. It is simply the momentary target toward which
perceptions are being adjusted. We often say "desired state".
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Thus we begin with two states of the external environment,
Desired (D), and Perceived (P).
This is right in terms of commonsense usage, but in the model we
explicitly recognize that all the system knows about its
environment is represented by its internal perceptual signals. So
we would say that we begin with two states of perception, not of
the environment: the actual perception, and the reference
perception embodied as an adjustable reference signal.
You say that for the unified theory it is sufficient for D and P
to have "representations" in the mathematical sense, as points in a "metric
space". This presumes that we know what D and P
"really are" outside the perceptual system -- that is, it assumes
that we know how to take the inverse of the perceptual functions
that lie between our perceptions and the world from which they
are drawn. My view is that D and P are ALREADY representations in
a metricized perceptual space at the time we become aware of
them. The problem of perception is not to translate from real-
world or objective variables to the perceptions that we assume to
represent them in the brain, but to translate from the
perceptions that we experience BACK to the hypothetical objective
world which we assume to underlie the phenomena -- the world we
imagine in terms of physical models. The real world is the
inverse of an unknown function of the variables we experience.
Skipping ahead:
Now the central thesis of BCP can be stated.
People behave to move P closer to D, where this is
possible at an acceptable cost.
The term "acceptable cost" hides the rest of the story: cost in
terms of what variables, and relative to what reference states,
and in whom?
I would generalize it more or less this way:
People behave to move P[i] closer to D[i], where this is
does not cause the set of all P[k] to move significantly away
from D[k], k <> i.
If you like, you can let k range over people as well as within
people.
"Significance" of a deviation of P[k] from D[k] is evaluated in
terms of error sensitivity: how much corrective action results
from a unit of deviation. Thus we don't count a deviation as a
cost if a person makes no effort to correct it.
In this way we get rid of the quasi-objective connotations of
"cost," and cast the whole process in terms of the system's own
operations and internal goals.
Notice this is a constrained minimisation process. Also unlike
the error P-R of BCP, DP is always positive, and may not always
attain the desired minimum of zero.
"Minimization" of DP is not an effective mode of control, because
a departure from minimum doesn't contain the information needed
to direct action the right way. A system that simply "minimizes
error" without regard to its sign would have to use some sort of
hill-climbing strategy to get the sign of the output right. The
error signal in BCP is signed for a good reason.
Furthermore, to say that DP is minimized doesn't pin down the
state of D or of P at which this happens. In fact, during control it is
normally not minimized. If I desire to be eating 3 units of
ice cream and perceive myself eating 3 units of ice cream, the
error becomes 0 but DP becomes 9. Actually the minimum of DP
would occur in a state of large error: e.g., D = 3 and P = 0, or
P = 3 and D = 0. Somehow I don't think that the system tries to
minimize DP. Why would it try to do that?
But the version of control theory used in BCP does in fact
minimise DP for the cases considered in practice.
No, it minimizes |D - P|, which is not at all the same thing as
minimizing DP. And it doesn't "minimize" anyway; that's a side-
effect. The response of a control system to D - P is SIGNED, so
there is no need for hill-climbing or other such ways of
achieving minima. Naturally, if you make P approach D, then
D-P| is in fact minimized even though the system does not
calculate that absolute value. But I can't think of any case in
which DP would be minimized unless D = 0.
Enough for one post. Take a nap.
Best,
Bill P.