[From Bill Powers (941021.1635 MDT)]
Tom Bourbon and Rick Marken (various) --
Let's try not to totally confuse those who are trying to understand PCT.
Perceptions DO cause actions. That is not the point on which PCT
disagrees with standard psychological models. Even in an S-R model you
can have a reference signal which sets the effective zero of the input
stimulus; therefore even saying that action is caused by the difference
between the level of input stimulus and the reference signal does not
distinguish PCT from S-R psychology. There is always some level of input
at which the output will be zero; all models contain at least an
implicit reference signal which is not neccesarily zero. I think we have
to go very carefully here to make sure that we don't make statements
that won't hold up even in PCT, and that can confuse the willing
learner.
···
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What really causes actions is the error signal. That's firm, no matter
what the gain of the control system: the error signal is the immediate
determinant of actions.
Where does the error signal come from? From the difference between the
perceptual signal and the reference signal.
If the reference signal is constant, then the only thing that can cause
a change in action is a change in the perceptual signal. So changes in
the perceptual signal cause actions when the reference signal is
constant. No way out of it: they do.
However, as usual, we have a problem with speaking qualitatively about a
quantitative question. _How much_ change in the perceptual signal is
required to cause any substantial change in the output, the action? That
depends entirely on the gain of the output function. With a low-gain
output function, a large change in the error signal is required to
produce a given change in action, in comparison with the amount needed
when the output gain is high. Thus a large change in the perceptual
signal is needed to produce an action (still with constant reference
signal) when the output gain is low.
So far the reasoning is perfectly straightforward, because we're talking
about only part of the control loop. We could be talking about an S-R
system just as well as a control system. The difference begins to show
up only when we close the loop.
When we complete the loop, recognizing that the state of the perceptual
signal depends in part on the output, the reasoning is less simple, and
it leads to the real difference between PCT and S-R theories.
How do we produce changes in the perceptual signal? Not by changing it
directly and arbitrarily; that would break the loop. We do it by
adjusting another variable, a disturbing variable, which contributes to
the state of the perceptual signal. This is the first important
difference between PCT and S-R theory: in PCT we recognize that the
input to a control system can't be treated as an independent variable;
to do so is to make it independent of the output, destroying the closed-
loop organization and changing the character of the behavior entirely.
As soon as the perceptual signal starts to change, the error signal
changes. The output will begin to change, but in doing so it cancels
part of the effect of the disturbing variable, so the perceptual signal
will change less than it would if the disturbance alone were affecting
it. As the effect of the disturbing variable begins to appear, the
output changes in the opposite direction, cancelling part of the effect
of the disturbing variable. We can arbitrarily change the disturbing
variable because it is not part of the loop; we cannot, however,
arbitrarily determine the effect on the perceptual signal that way. The
system's own output simultaneously affects the same perceptual signal.
If the gain of the system is low, then the output changes will be
relatively small, and only a small part of the effect of the disturbance
will be counteracted. The change in the perceptual signal that is left
over passes through the comparator, becomes an opposite change in the
error signal, and drives the action. This process comes quickly to a
balance, with the output just large enough to keep the effect of the
disturbance on the perceptual signal from getting any larger.
Now if the gain of the system is increased, the balance point will be
reached for a smaller change in the perceptual signal. Because of the
increased amplification, a smaller change in the perceptual signal will
now be enough to produce an output sufficient to keep that change from
becoming larger. As the output gain of the system keeps increasing, a
smaller and smaller change in the perceptual signal is sufficient to
bring the output into a balance with the disturbance. In the limit, with
infinite gain, the perceptual signal changes only infinitesimally and
the ouput approaches a perfect balance with the disturbance, cancelling
essentially all of its effect on the perceptual signal.
But that is only in the limit. By speaking as if the control system is
perfect, with infinite gain, one can give the impression that the
perceptual signal has nothing to do with the output, because it "does
not change" when disturbed. However, in any real system with finite
output gain, the perceptual signal _does_ change, even if only by a
small amount, and with a constant reference signal it is that change in
the perceptual signal that accounts _entirely_ for the change in the
output.
It is high gain in the output function that accounts for the fact that
the perceptual signal changes by only a small amount. But that same high
gain assures that even if the amount of change in the perceptual signal
is microscopic, it is sufficient to cause a macroscopic change in the
output. At all levels of gain, the changes in output are caused by
changes in the perceptual signal -- once again, with the reference
signal constant.
We can now see the second main difference between PCT and other models.
The difference is in _which variable is identified as the external
counterpart of the perceptual signal_. Under S-R theory, the "stimulus"
for a system that is really a control system will be identified as the
disturbing variable -- that is, the disturbing variable will be seen as
the cause of the system's output actions, and it will be assumed that
this variable is what the system is sensing. In fact, the operational
definition of stimulus assures that this misidentification will be made.
The stimulus is the physical variable for which changes correlate the
most highly with changes in the output action.
In behaviorism, that is taken as a sufficient demonstration that the
physical variable in question is a stimulus for the observed response.
If we do not speculate about sensory processes, as a pure Skinnerian
psychologist would not do, then this definition of stimulus is perfectly
consistent with observations. We would simply translate directly from
the behaviorist's "stimulus" into the PCT "disturbing variable."
Which brings us to the third major difference. A disturbance does not
directly affect the input to the control system; it influences, but does
not determine, the state of an input quantity, the quantity actually
sensed by the control system. The loop is closed by output effects on
this quantity. Depending on the gain, this input quantity is stabilized
more or less close to a value set by the internal reference signal. As
the disturbing variable changes in magnitude, the output of the control
system changes in approximately an equal and opposite way, _preventing_
the disturbing variable, or the stimulus, from having any large effect
on the input quantity, the actual physical variable that affects the
sensory apparatus.
This input quantity is undetectable by the experimental methods normally
used in psychology. Even if the input quantity is directly observed, as
it often can be, its variations will be very small because of the
control process, while the variations in both the disturbing variable
and the system's output action will be far larger. The higher the gain
of the control system, the smaller will be the variations in the input
quantity in comparison with the disturbance and the output action.
Here is where another factor comes into play: system noise. Inside the
control system in various places are noise sources which create
spontaneous fluctuations in signals in the loop. These fluctuations are
small, and act as small disturbances of the loop which create small
fluctations in the action even when the disturbing variable is constant.
In a reasonably high-gain control system, the changes in the input
quantity that are allowed when the disturbing variable changes are
comparable in size to the spontaneous fluctuations due to system noise.
In fact, the control system can often maintain changes in the _short-
term average_ value of the input quantity at a level smaller than the
changes due to system noise. As a result, even if the real input
quantity is identified, when it is tested as a possible stimulus by
correlating it with the changes in action, the correlation will prove to
be very low -- in tracking experiments it is typically less than 0.1. In
the same situation, changes in the disturbing variable will correlate
with changes in the action at a level typically of 0.9 and upward
(negative). The result will be that the actual input quantity, even if
it is noticed, will be rejected as a candidate stimulus and the
disturbing quantity will be chosen instead.
In this situation, it appears that changes in the input quantity (and
thus the perceptual signal or perception) have no relationship to the
actions worth speaking about. However, if we could measure the system
noise and add that noise to the systematic changes in the input
quantity, we would find that changes in the perceptual signal still
account exactly for the output actions. Perceptions _do_ cause actions
-- but the wrong external variable is very easily identified as the
correlate of the (assumed) perception.
Then there is the final and most obvious difference between PCT and
other models: the reference signal which we had been assuming constant
throughout this development. The reference signal is the output of a
higher level of control system, and in general can change in ways not
related to the input quantity and the disturbance associated with the
lower level system. When we look only at the input of one control
system, we tend to give undue significance to the variations in the
input quantity because we have nothing against which to compare them.
But when the reference signal changes to a new value somewhere else
within its range, we suddenly see the mean value of the input quantity
changing by 10, 20 or 50 times the size of the fluctuations we had been
looking at. What had seemed significant fluctuations are now shrunk to
their proper scale; they are only a few percent of the range of values
at which the input quantity might be maintained with different settings
of the reference signal.
The values over which the input quantity might change with changes in
reference signal are comparable to the total range of values that the
system can sense. Output changes required to bring the input quantity to
various levels set by the reference signal may be anything up to the
maximum output of which the system is capable. In short, we can see
output changes occurring spontaneously which are comparable in size to
those that are needed to oppose the largest disturbances that the system
can handle. They are equivalent to the largest "responses" to the
largest "stimuli." These spontaneous changes reflect the changing
higher-order purposes of the system as a whole. This is a very great
difference from traditional models of behavior, in which the only
actions that were recognized were those due to external causes.
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Lastly, a word on statistics, about which we have given conventional
psychologists a hard time. I think we can maintain a firm stand against
trying to explain individual behavior in terms of statistical
relationships, however good, obtainable only from measures of
populations. But we should not give the impression that there are no
useful and legitimate applications of statistical methods, in or out of
PCT. All scientific investigations begin with trying to find a regular
relationship among variables. Such relationships are not always obvious
from the start; we may get very low correlations even in applying the
test for the controlled variable (and correlations are a useful tool for
applying the Test). The main difference between the way we would use
such correlations and the way they are traditionally used is that we
would not settle for a low correlation, however significant. The point
of PCT is to get into that realm of correlations where we can expect one
wrong prediction in 2,000,000 instead of one in 20. As I have been
pointing out lately, achieving this improvement of 100,000:1 is simply a
matter of refining hypotheses and methods enough to reduce standard
errors of prediction to 40% or less of the values normally considered
acceptable (nobody has yet told me I am wrong about this).
Our arguments with conventional uses of statistics are very simple.
First, we say that mass measures cannot be used to determine individual
characteristics. Second, we say that experiments should end only when
the predictivity of a correlation (or its associated regression
equation) is high enough to achieve 2,000,000 to 1 chances against a
wrong prediction -- or, preferably, better.
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Best to all,
Bill P.