# S-R & PCT

[From Bill Powers (930112.0900)]

Greg Williams (930112) --

... where does a model for tracking which uses C,H, and T as
its variables fit? And where does a model of gravitational
attraction which uses distance and mass (observationally
proportional to weight) fit?

C, H, and T (and D) are the observable variables whose behavior
we must explain, just as position, velocity, and acceleration are
the observable variables which Newton had to explain. The
explanation goes beyond the observable variables, in proposing
entities like mass, or error sensitivity.

Mass, remember, is not an observable variable (weight is not the
same thing as mass), and neither is the universal constant of
gravitation, nor the inverse-square relationship of force
(acceleration for a free body) and distance. A pound of feathers
and a pound of lead do NOT fall at the same rate. The attraction
between nonspherical objects does NOT go as the inverse square of
the distance between their centers. A cannonball does NOT travel
in an ellipse with one focus at the center of the Earth. The
observations deny Newton's laws. Newton replies, "Yes, but the
underlying relationships are as I suppose. If you calculate
viscious friction, and integrate using my universal law over all
the infinitesimal particles of irregular objects, however
imaginary those particles may be, you will see that the laws
predict exactly what we observe."

Suppose we have a simple control system with a loop gain of
1,000,000 and a slowing factor in the output function that is
sufficient for stable operation. In this case, the true steady-
state relationship between C and H is H = 1,000,000 * (C* - C).
This is not, of course, what we observe. We observe that H = -D
and C = C*, as near as we can measure, give or take random noise
and measurement error. If there are variations in C* we will see
C varying in the same way, but H will not vary a million times as
much. H will vary only as much as needed to cancel the effect of
D on (C* - C). We do NOT, in general, see H varying a million
times as much as C. Yet a generative model in which the error
sensitivity is one million explains the observations.

Still, I think Skinner's "prematurity" warning still counts for
something...

Skinner was denying the usefulness of models of the interior of
the organism at exactly the same time the principles of control
theory were being developed. He defended his views against
cybernetics and cognitive models as against any other proposals.
He took the deviations of others' views from his own as prima
facie evidence that the other views were wrong: no proof needed.
Skinner's main modes of argument were ridicule and assertion. He
did not test hypotheses. He simply offered positive instances
worded so as to support his position.

Suppose that Skinner had really believed, as he seemed to claim,
that models of the inner working of organisms might some day
provide explanatory principles not present in radical
behaviorism. In that case, all his explanations of behavior in
terms of external events and situations should have been appended
with " ... or some cause working from inside the organism."
Obviously there was no such appendage: it would have made his
bold assertions look foolish. What Skinner believed, as far as I
can see, must have been what many cognitive scientists believe
today: that if you followed all more abstract explanations down
to their fundamental bases, the causes would eventually trace
back to the environment. In other words, Skinner considered that
he was only stating in an approximate way what would some day be
shown to be the only accurate way. This was his lifelong faith.

Actually, from what I've read, they actually claim that they
DON'T WANT TO COME UP WITH AN EXPLANATION -- ONLY
PREDICTION/CONTROL. But the upshot is as you say, of course,
and they can't get as close to their professed goal as they
could with PCT models (which, as noted yet again above, might
be very difficult to generate for complex situations).

The trouble with qualitative language is that you don't get any
idea of proportions. To say that they can't get as close to
prediction as PCT can can leave the image of a footrace with PCT
winning in a final burst at the finish line. With respect to
prediction, PCT is crossing the finish line while the operant
approach still has one foot in the starting block.

Do you realize that there is no basis in the operant-conditioning
model for predicting that there will be any behavior at all in a
Skinner box? And that even if you admit as a prediction an
extrapolation from previous experience, this model can't predict
how much behavior there will be, if any? The reinforcement rate
supposedly sustains the behavior rate. But the reinforcement rate
depends on behavior, so unless you know in advance what the
behavior rate is going to be, you can't say what the
reinforcement rate will be. Not being able to predict the
reinforcement rate, you have no basis for predicting any
particular behavior rate. So there is NO PREDICTION AT ALL.

The best that the operant approach can do is to describe what has
already happened, and predict that what has happened will happen
again. All of the mathematical manipulations I have seen in the
operant literature have been manipulations of algebraic
identities; with only one equation to represent a situation
requiring two or more equations for its complete description,
that is all that can be done. It is not that the operant model
predicts less well than PCT. It does not predict AT ALL.

Skinner's extreme historical environmentalism and an extreme
"moment-by-moment" mechanistic organismism need melding into a
broader -- and I think truer -- picture.

As Dennis pointed out, "history" is not a causal mechanism. The
past can't affect the present any more than the future can.
Everything that operates on behavior is present now, or else it
has no effect. The only way for the past to seem to operate in
the present is through memory; and it's only the current contents
of memory, not what actually happened in the past, that has an
effect NOW.

This is a fundamental principle of all the hard sciences. The
history of a variable is irrelevant; the path by which it got to
its present state (including derivatives) is of no consequence.
Generative models work strictly in present time. I don't see any
possibility for a merger here.

···

---------------------------------------------------------------
Avery.Andrews (930111.1905) --

Reading around in the Osherson, ed. `foundations of cognitive
science' (1989) I came across the claim that feedback is too
slow to solve inverse kinematic & dynamic problems for fast
movements.

This is a good one for the collection of myths. In fact this is a
double whammy: a myth based on a myth. In the first place, it's
not necessary to solve for the inverse kinematics because a
control system automatically does that using the environment as
its own model. So it's true that control systems aren't fast
enough to solve the inverse kinematics without feedback: no
neural system is fast enough. But solving the inverse kinematic
problem isn't necessary in any case, and control systems are
certainly fast enough to do what is necessary to control a
dynamical system.

Where can I read about why this claim is false or irrelevant
(e.g., true only for certain kinds of highly skilled movements
that people practice enough to make it plausible that they have
elaborate feedforward schemes for).

Look up analogue computer methods for solving second-order
differential equations. Korn and Korn is the only reference in my