# Low correlations

[From Bill Powers (920310.1700)]

Look at my address: I now have my own logon at Fort Lewis College, and my
new name is powers_w. Legal at last!

Mark Olsen and others interested: back issues of Closed Loop are available
for \$5 each from

CSG Press
10209 N. 56th St.
Scottsdale, AZ 85253

That's Ed Ford.

···

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To inquiries about my giving seminars at various places: not this year. I
have too many committments. I suggest contacting Tom Bourbon, Rick Marken,
Kent McClelland, etc.
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Martin Taylor (920309), Bruce Nevin (920310) --

You guys are going all around the point here. I have a distinct feeling
that you're avoiding it. On the other hand, there may be some critical fact
that I don't seem to be communicating, so let's try again:

Here's my diagram of the operational definition of a controlled variable,
with those "low correlations" shown:

------- low correlation ------
> >
------------ | ------------- --------
> > > > > > >
> BEHAVING |----->ACTION-->|ENVIRONMENTAL|----->|OBSERVED|
> SYSTEM | | TRANSFORMA- | |OUTCOME |
> > > TIONS | | |
------------ -------------- --------
> ^
--low correlation-- |
> >
> >
VARYING INDEPENDENT DISTURBANCE -->--

We have here a situation in which the action of a behaving system affects
an observed outcome, and an independent disturbance also affects the same
outcome. Ordinarily, we would expect action and disturbance to correlate
with the outcome. If action and disturbance were unrelated, we would expect
the variance of the outcome to be the sum of the variances of action and
disturbance -- that is, in fact, a definition of the statistical test for
NO control.

When there is control, the variance of the observed outcome is
significantly less than the sum of the variances of the action and the
disturbance. When the reference level is reasonably constant, the variance
of the observed outcome approaches zero, when the variances of both action
and disturbance are large. The only way for this to be possible is for the
effect of the action, transformed, to be systematically opposed to the
effect of the varying disturbance.

So what is meant by a "low" correlation is one that is less than the
expected correlation, in the above situation.

While I suppose it's abstractly conceivable to test all triples of
variables in the universe to see if they fit the above conditions, there is
a way that won't take so long.

What we need to do is start with behavior as it has been observed under the
old interpretation, which is diagrammed this way:

FIG 1.
------------ ------------- --------
> > > > > >
> BEHAVING |--->RESPONSE-->|ENVIRONMENTAL|----->|CONSE- |
> SYSTEM | | | TRANSFORMA- | |QUENCES |
> > > > TIONS | | |
------------ | -------------- --------
^ medium-low
> correlation
> >
> >
STIMULUS --------

In fact the arrow between stimulus and behaving system is seldom verified
as existing. The stimulus is defined on the basis that there is a response
correlated with it. So basically we have some variable, situation, or other
entity in the environment defined as a stimulus on the basis that when it
occurs, the behaving system exhibits a response.

If in fact the "consequence" above is under control, then what is usually
interpreted as the stimulus variable is really a disturbance, and the
actual stimulus is the "consequence," as shown below:

FIG. 2
(actual sensory path)
----------------------<-----------------------
> >
------------ ------------- --------
> > > > > >
> BEHAVING |--->RESPONSE-->|ENVIRONMENTAL|----->| CONSE- |
> SYSTEM | | | TRANSFORMA- | | | QUENCE |
> > > > TIONS | | | |
------------ | -------------- | --------
medium-low high |
correlation negative |
> correlation |
> > >
STIMULUS --->--------------------------------------

Note that for some environmental transformations, especially variable ones,
the "medium-low" correlation will be very low indeed, while the "high
negative" correlation will remain high. Note also that the high correlation
is between EFFECTS (lines) and not variables (boxes). The stimulus (a
variable) may exert a force (line) on the consequence (another variable,
such as a position), while the response (really a box) acts through some
environmental transformation (a nonlinear rubber lever) to produce a second
force (line) acting on the consequence (position). The force exerted by the
lever will be nearly equal and opposite to the force exerted by the
stimulus variable: the two forces will show a very high negative
correlation. The response variable will show a medium-low correlation with
either the stimulus variable or its effect. By medium-low, I mean in the
range normally accepted as significant, but far below 0.95.

In the above form, the relationships are clear: the stimulus is really a
disturbance of a controlled variable, a consequence of the response. A more
illuminating arrangement of the diagram may show what the problem is more
directly;

FIG 3.
------------
> >
<----| BEHAVING |---<-----

> SYSTEM | |
> > >
------------ | |
^ sensing of | This part unknown to
> controlled variable | conventional
> > > behavioral-psychological
------------ | | research
> > > >
> CONTROLLED |---->---- |
---->| VARIABLE | |
> > >

v ------------ |
"RESPONSE" ^
>
>
DISTURBANCE-
OR
"STIMULUS"

Now, unbeknownst to the experimenter, there is some aspect of the
environment between the apparent stimulus and the behaving system. This
could be something observable, or it could be inside the behaving organism.
It is affected by the "response" of the system, and also by the supposed
"stimulus." The real stimulus is what is sensed of the controlled variable,
but the apparent stimulus is the one shown at the bottom. Not being aware
of the possibility of controlled variables, the experimenter (a) assumes
that the STIMULUS is directly affecting the senses of the organism, and (b)
that the response is simply the result.

So the search for controlled variables can begin with existing observations
of behavior and its apparent dependence on environmental variables. A more
detailed examination of the experimental situation, plus suitable
manipulations that interrupt the effects of the system's action on the
controlled variable and/or the ability of the system to sense the state of
the controlled variable, will show whether the actual situation is that of
Fig. 1 or Fig. 2. If it's found that Fig. 1 applies, we have control, not
reaction.

For higher-level variables, a slower time-scale has to be adopted so that
action and disturbance can be seen as concurrent.

This approach does not force all behavior to be interpreted as control. It
simply opens the possibililty of control and shows how to differentiate
control (Fig. 1) from reaction (Fig. 2).
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As to William James, CSGers (including myself) have been citing him for
some years as showing clear recognition of the phenomenon of control. This
only serves to show the difference between control as a phenomenon, and
control theory.
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Language later.

Best to all

Bill P.

[Martin Taylor 920311 11:15]
(Bill Powers 920310 17:00)

Martin Taylor (920309), Bruce Nevin (920310) --

You guys are going all around the point here. I have a distinct feeling
that you're avoiding it. On the other hand, there may be some critical fact
that I don't seem to be communicating, so let's try again:

I'm not sure which way the lack of communication goes, but it sure seems to be
there. I see nothing in your posting, whether by diagram or in the explanations
that is not crystal clear, and has been so for ages, at least in my mind, if
not in my writings. It's the starting point for most of what I have been
trying to write over the last couple of months. What might be the point
that Bruce and I are missing? Could you put it another way?

I think that if you take your posting together with the following paragraph
from mine of 920309 11:00, you may see why I think we have a communication
problem, and perhaps will be able to resolve it:

If, as an experimenter, one can presume some pattern in the mutually observable
environment represents a perceptual variable being controlled by the subject,
then one can attempt to disturb that pattern and see whether the subject
acts so that the pattern is restored or maintained. The pattern will show
little correlation with the experimenter's disturbances or with what the
experimenter observes of the subject's actions. If the experimenter happened
to be correct that what she did would have disturbed the pattern if the
subject had not been there, then there is evidence that the subject is
controlling. The presumption that the experimenter would have disturbed the
pattern is just that, a presumption. It is not an observation, because it
didn't happen. Explaining why things do not happen is trickier than providing
rationales for why they do happen. The failure of a presumed "cause" is
easier to justify as that it was not a cause than as that an exactly
countervailing cause was applied at the same time. I think this is at the root
of the communication difficulty with cause-effect psychologists. Causes have
effects, and PCT is supported when what should be causes are observed to
have little or no effects.

Note the words in the 6th and 7th lines: "If the experimenter happened

to be correct".

At the same time, I would love to pursue my degrees-of-freedom discussion, but
I can't until the question of zeros is resolved. Could you explain the
matter of the error signal for sequence, which is one part of the remaining
problem? Rick has partly resolved the other part--that the spreadsheet
provides a counter-example--by pointing out the considerable non-orthogonality
among the ECSs in the spreadsheed. The necessary non-zeroing related to
non-orthogonality was to be part of the later discussion, but I had forgotten
that it could come up even when the degrees of freedom for input and output
of the hierarchic CS are in balance.

Martin