Newsgroups: bit.listserv.csg-l
Date:         Sat, 3 Oct 1992 12:35:18 EDT
From:         mmt@BEN.DCIEM.DND.CA
Subject: Re: Sundry subjects

[Martin Taylor 921003 12:15]
(Greg Williams 921003)

>>=Tom Bourbon
>>Now we see some model-person correlations below .99, but they still
>>exceed by orders of magnitude the modal and median correlations in
>>the behavioral literature.
>
>I encourge you not to give up the PCT goal of 0.99+ correlations. Otherwise, I
>believe, you will not be able to decide WHICH PCT model is the correct one.
>Fairly low (but higher than typically found in the behavioral sciences)
>correlations are convincing (at least to me) that PCT models are correct,
>generically, for tracking. But I next want to know WHICH PCT models are better
>than others, and this requires comparing various PCT models' correlations with
>what people do UNDER CONDITIONS AFFORDING ENOUGH SENSITIVITY TO SHOW
>SIGNIFICANT DIFFERENCES IN CORRELATIONS. Such conditions, I claim, are "poor"
>control conditions.

Please don't fall into the trap of thinking that "significant differences"
have any meaning other than that an experiment is sensitive enough to show
them.  They have no relevance to the real world, ever.

Good control, almost by definition, obscures the structure of the controller.
Finding high correlations means two things: (1) Once again, here is a situation
in which PCT works [would that be news, except to someone with a belief that
it wouldn't?], and (2) the experimenter intuited a CEV pretty close to the
one being controlled, and that control was being performed with high gain.

If one is interested in finding out HOW the control is being done, that
information is mostly to be found in the 1% error that remains.  It is easier,
but less interesting, to find structure in the error when control is poor.
It is less interesting because there are several possible reasons why the
control may seem to be poor, one of them being that the experimenter has not
intuited a CEV close to the one really being controlled.

I think it is the very high correlations achieved by PCT models in various
situations that provide the opportunity really to tease out what is happening
in the brain.  S-R approaches do it the opposite way, by (partially) breaking
the feedback loop.  That prevents the subjects from behaving in a way that
they can control, but provides a wide latitude for variations that indicate
structures or functions internal to the mind/brain system.  There are too many
sources of variability to make it easy to find which components are important,
and there are therefore many competing schools of thought on what is going on.
Within PCT, there is a much better opportunity to concentrate on the effects
that are really due to structural/functional factors.

Let's consider an example brought up by Rick Marken (920929.1000):
> For example, in my "area" vs
>"perimeter" control study, I did the test for the controlled variable to
>determine whether the subject is controlling x+y vs x*y (where x and y
>are height and width of a quadrilateral figure). Using x+y as the
>hypothesized controlled variable the error in predicting responses was,
>I think, about 2%. With x*y as the hypothesized CEV, the error was halved,
>to 1%. You could probably do slightly better with some other hypothesized
>CEV -- maybe sqrt(x*x+y*y) -- but clearly you are on the right track
>with x*y.

The interesting evidence is not that people control with high accuracy, but
that the residual error is different if one presumes different perceptual
functions (and therefore CEVs).  If it turns out that x*y is the best that
can be achieved, the residual error probably includes the failure of lower-level
control systems to achieve their reference levels.  But it also signals the
_effective_ gain of the x*y control loop, and much more important it shows
that something in the system is capable either of computing a product or of
adding logarithms.  Which is it?  The statistics can give a clue.  If the
residual variance is proportional to x and to y, logarithms are the likely
answer.  If it is more or less independent of x+y, then mutiplication is
probable.  What then?  If a logarithm can be developed in one part of the
hierarchy, is it not likely that it can be done in another part?  Then perhaps
we should look for logarithmic relations elsewhere in the hierarchy.  But
if it looks more as if the answer is multiplication, then a host of different
relations seem reasonable candidates as the CEVs in other situations.

It seems to me that the high correlations support the idea that "PCT triumphs
again," whereas the small errors, properly analyzed statistically, show how
the brain works.

Martin
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