S-R "Part" of PCT models; stiffness tensor

From Greg Williams (930108)

Rick Marken (930108.2030)

So an SR model is PART and PARCEL of the control model.

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. The feedback part of the PCT model for tracking
(the second equation, relating C to H and D) contains only observables
(observable to the experimenter, that is) which are at the level of the
phenomena to be explained. Where are the underlying variables INTERNAL to the
organism?

As I've said before, IF PCTers made a generative model of the "noise"
exhibited by the tracker, using hypothetical internal variables, THEN the "S-R
PART" of the PCT model WOULD be different than the behaviorist's input-output
equation, because the behaviorist would add a statistical noise term to
DESCRIBE the noise, instead of a term to GENERATE the noise.

So I think that, with regard to PCT models of tracking TO DATE, the
behaviorists would have no difficulty in adopting the same models. They would
interpret BOTH equations as purely descriptive and as containing only
observable variables. And they would see nothing revolutionary in PCT. If
there is feedback from "responses" to "stimuli," they would include that in
their "descriptive" models without wincing. But if PCTers went on to include
in new models some underlying hypothesized variables to generate "noise," so
as to be able to predict cursor position adequately for True Science, then
there would be two upshots: (1) the behaviorists' models would be genuinely
different from the new PCT models; (2) if the new PCT models could predict
cursor position very accurately, and the behaviorists' descriptive models
could not, then the behaviorists would need to take the PCT models (and,
indeed, the whole notion of needing EXPLANATORY generative models using
underlying internal variables) seriously -- PCTers would have solved a problem
that the behaviorists couldn't solve, and would have beat them at their own
game. The sort of PCT-boosting result which I was talking about the other day.
Of course, whether it is POSSIBLE in the near term to develop such Truly
Scientific generative models for tracker "noisiness" is another question,
about which I have previously raised concerns. But it would be interesting for
those who aspire to be True Scientists to try. The potential rewards might
well repay the efforts.

ยทยทยท

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Avery Andrews 930110.1700

Can anyone tell me a quick story about what a stiffness tensor is (or at
least the kind of book title to find it described in).

Look in a text on mechanical behavior of materials (solid mechanics). A
dimensional spring can be modeled as having a (generally different for each
point on its extension curve, unless it is linear) scalar stiffness, k, such
that the force to stretch or compress the spring, F, depends on the current
amount of stretch (from rest), x, via the function F = k x. In a three-
dimensional solid, there are SEVERAL stiffnesses (which, together, make up the
stiffness tensor) because there are SEVERAL ways to stretch and compress the
solid.

As ever,

Greg