H=k*int(T-C) is a generative model

[From Bill Powers (930109.1530)]

Greg Williams (930108) replying to Rick Marken (930108.2030)

Rick said "So an SR model is PART and PARCEL of the control

But I thought that the typical S-R model was construed by
PCTers as containing reference ONLY to observable variables and
as purely descriptive at the level of the phenomena being
DESCRIBED, and that the typical PCT model was construed by
PCTers as containing observable variables AND hypothetical
underlying (or, eventually observable, but at any rate INTERNAL
to the organism) variables and as a generative model
postulating mechanisms at a level below the level of the
phenomena being EXPLAINED.

Greg, I've just realized something that may clear up this whole
argument. You've been proposing that in the pursuit tracking
experiment, the observed relationship between handle, cursor, and
target is H = k*int(T-C). I've been accepting that as true, but
it isn't true. That is not an observed relationship; it's a
HYPOTHETICAL relationship. It is, in fact, a generative model of
the control system that would explain the observable behavior.

This would actually be easier to see with a slightly more
complicated model, one with a leaky integrator in the output
function. Suppose we say that H = k*[lint(T-C,tau)] where "lint"
means a leaky integrator with a time constant of tau. To match
the model behavior to the real behavior, we must adjust both k
and tau. However, the apparent time constant in the observable
behavior is not tau, but some shorter time constant (it could be
a factor of 10 or 20 shorter). We must give the model a LONG time
constant in order to match it to behavior that exhibits a SHORT
time constant. The time constant measured by perturbing the
controlled variable is not the correct one to use in the model.

In fact, what is observed in the relationship among disturbance,
cursor, and handle with the organism present is the outcome of
connecting two functional relationships together in a negative
feedback loop. One of these relationships can be observed in the
environment. If the organism is removed, we can arbitrarily
manipulate H to determine how H and D work together to set the
position of the cursor, C. We observe that C = H+D. And that is
ALL that we can observe. If we remove the environment, the
organism no longer behaves.

When the organism is reconnected, we find a new relationship: it
is, approximately, C = 0 and H = -D (in the case where the
reference signal can be assumed 0). These relationships represent
the solution of a pair of simultaneous equations: the one we can
determine by examining the environment, and an UNKNOWN one that
represents the internal organization of the organism. We do not
OBSERVE that H = int(T-C) (in the original case). We HYPOTHESIZE
that equation as a generative model of the way the invisible
insides of the organism work. We TEST this model by seeing
whether that equation, combined with the known relationship C =
H+D, gives behavior that matches the real behavior.

In some cases it may be possible to deduce the organism equation,
if suitable inverses exist. Whether or not deduction can be used,
the fact is that the result describes the behavior of the insides
of the organism, which are not directly observable in normal
behavioral experiments. In general that transfer function is not
visible in the external variables or their relationships. By one
means or another, we must venture to propose a function inside
the organism.

And that, I think, separates PCT from S-R psychology once and for
all -- at least in closed-loop situations.



Bill P.