Causal schmausal

[From Rick Marken (930914.2200)]

Avery Andrews (930915.1309) --

This discussion seems to be going the way of many, wherein PCT people
seem to want to perceive themselves as clearly enunciating the
principles of PCT, rather than figuring out what actually is on the
other person's mind, and seeing whether there is a difference between
that and any claim of PCT.

I agree that, in previous discussions, PCT people have wanted to perceive
themselves as clearly enunciating the principles (and actual behavior)
of a PCT model (I don't think that's going to change, either) but I do
think that we have made every effort to try to figure out what was
"actually" on the other person's mind. That's why we got down to math
and models -- to see if we could get to an agreement about what we were
talking about. I don't think there is any magic way to figure out what
another person is really thinking -- and whether it differs from
one's own position -- but the strength of the disturbance resistance
(on both sides of the debate) testifies to the fact that the parties
were controlling a similar variable relative to quite different
references.

Nevertheless, I have asked Michael to explain what he means when he
says that PCT is a causal model. Maybe we have no disagreement;we'll see.

I agree that the nature of the relationship between variables in a control
loop, when behaving outside the context of the loop, is "causal". Using
the notation from BCP (sort of), p (perception) is causally related to q.i
(input), q.i is causally related to o (output) and d (disturbance), o is
causally related to e (error) and e is causally related to r (reference)
and p. By "causal" I mean that the value of one variable (the dependent
variable) is influenced in a lawful manner by the value of another variable.
p = f(q.i) means that the value of p depends on the value of q.i
according to the "law" f(). This dependency is causal if its reverse
does not hold in real life -- if, for example, the value of q.i does
not depend on p. So if p becomes 10 when q.i is 100 it is not
true that one can drive q.i to 100 by driving p to 10. f() determines
how q.i influences p. Other influences on p (besides q.i) can change
the value of p, but this does not change the nature of the dependence
of p on q.i; if q.i is 100, the effect on p is 10.

The "magic" of the control loop is that, while the functional components
of the loop are causal (by my definition above) when they are observed
outside of the loop, this causal dependence disappears -- and a new sort
of behavior emerges -- when the components are hooked together in a
negative feedback loop. For example, in the feedback loop it is no longer
true that p = f(q.i) as it was when the relationship between p and q.i
was observed outside of the context of the loop. In the control loop
things have changed -- now p = r; the perceptual signal is a function
of a different variable; r rather than q.i. So without the loop,
p = f(q.i); with the loop p = r. Most important, by the above
definition of causal, p is NOT causally related to r. This is because,
if an attempt is made to change r by driving p to a new value, it not
only won't work (due to the one-way direction of the influence of
r on p ) but also becuase you will find that your efforts to drive
p to a differnet value are strongly resisted. In fact, you simply
cannot (in a suffiently high gain system) budge p away from r.
This is quite different from the situation where p = f(q.i). There,
we had no problem testing for the backward influence of p on q.i by
changing the value of p. We were able to do this because p and q.i
were causally related; in a control loop, the relationship between p
and r is one of control.

The only relationship that could qualify as causal in a control loop
is the one between o and d. The only problem here is that the apparent
effect of d on o will always be unpredictably changing due to what will
appear to be completely spontaneous (and unpredictable) changes in r --
as well as changes in the functions relating o and d to q.i.

So there are influencial relationships between variables in a control
loop. It's just that these relationships are not causal -- they are
controlling.

By the way, dynamics will not rescue the causal relationships between
the variables in the loop; p = r continuously. But I'll leave the
explanation of this esoteric little detail to those of the differential
equation persuasion.

Best

Rick

[Michael Fehling 930915 4:44 PM PDT]

In re Rick Marken (930914.2200) responding to Avery Andrews 930915.1309 --

Rick,

You tell Avery that you've "... asked Michael to explain what he means when he
says that PCT is a causal model."

  Look carefully over my previous posts. I've already done this. There
you'll find my claim that (a) you've co-opted some terms about causality and
given them very "interesting" interpretations, and (b) that it provides no
advantage to PCT to force people to buy into this co-opted terminology to
come to grips with PCT.

  You seem to have an equally "interesting" interpretation of controller
dynamics. In fact, p _seldom_ equals r, _dynamically_. If it did, one
wouldn't need the control loop in the first place. Static analysis is
important and useful, but it's not the whole story in understanding control.

  Well, as Avery suggested, maybe we've beaten the topic of PCT as a
"non-causal theory" to death. In any case, I'm off to the National Air Races
for a few days.

- michael -