coordinate structures and fig-leaves

[Avery Andrews 931003.1030]

First, a bit on the theme that 2nd order feedback systems are implementations
of coordinative structures. Consider the task of holding a coffee cup
vertically with a three jointed arm (shoulder, elbow, wrist), all movement
in the vertical plane. If you measure the angles appropriately, and
assume the right kind of grip on the cup, keeping the cup vertical will
follow from maintaining the following relationship between the joint

   0 = shoulder+elbow+wrist

But this is just the format of a coordinative structure. Furthermore,
if we want to tilt the cup at an angle T, we can do so by `tuning' the
structure by using some value of T instead of 0:

  T = shoulder+elbow+wrist.

Similarly we can specify a shoulder-cup elevation angle by the relationship:

  E = shoulder+1/2*elbow

and a shoulder to cup distance:

  D = (pi-elbow)

  (nonlinear distance scale, in the range [pi, pi-elbow_flexion_limit])

What a coordinative structure is supposed to be is some kind of dynamic
system that tends to enforce these relationships, but the neo-Gibsonians
seem to be rather vague on the details of what kind of system might
actually do the job. (Though I note in passing the Fowler and Turvey
1980 (Butterworth vol.) state explicitly that any kind of `index
over muscle function', including perceived joint angles, might be
linked by a c.s..

2nd order feedback systems, as illustrated by Rick in the spreadsheet
model, will clearly be able to implement these kinds of relationships,
but I can think of at least two considerations that might serve as
fig-leaves for F&T.

First, the original description of 2nd order feedback systems in BCP
doesn't correspond to the working systems presented later by Rick,
because it doesn't have the integrators that Rick has in the
first-order reference functions. If I'm reading the spreadsheet
correctly, a first order reference signal should be thought of
as produced by a circuit element that tends to output a constant
signal, with higher order output signals tending to raise or
depress the signal (I'd think that a capacitor-type element would
be more realistic here, in fact). These thing aren't in the BCP model,
as far as I can see, so it's not clear to me that the original model
would actually work. This makes it less reprehensible that F&T
didn't like or understand it.

A second consideration is this: contemporary 2nd order control systems
do implement coordinative structures, but can we be sure that there
aren't other kinds of systems that would as well? If we can't be,
then the notion of coordinate structure shouldn't be immediately
discarded, because it is a concise description of a problem for which
we have a proposed solution (or rather, family of solutions, since
there are various different 2nd order control systems that could be used
to implement a single coordinative structure), but perhaps not the
only solution.