Models, Schmodels

[From Rick Marken (960823.0900)]

Martin Taylor (960822 18:40) --

Whatever it is in the network that allows for good control, it would
not allow good control if the environmental feedback functions were
randomly altered (in phase, delay, attenuation, or what have you). The
actual environmental functions may not be accessible (as you suggest they
are not) from a knowledge of the control hierarchy's parameters, but the
knowledge of them is indeed distributed through the hierarchy.

Well, I hate to cast the harsh light of empiricism on all this deep
speculation about the number of "world models" that can dance on the
head of a PCT hierarchy but I set up a simple little experiment last
night to help my scholastically challenged brain understand where "world
models" fit into the PCT hierarchy.

The experiment is a compensatory tracking task (what else?). The feedback
function (the connection between mouse output, m, and cursor position, c)

c = a* m + b * m^3

where a and by are variables that change continuously over time; a varies
between -1 and 1 and b varies between -.001 and .001. So the feedback
(environmental) function that connects the subject's outputs (c) to
the subject's inputs (c) is continuously changing -- from linear
(when b = 0) to cubic (when a = 0) to something "in-between" (when
b <> 0 and a <> 0).

I, as a subject and expert compensatory tracker (what are compensatory
tracking jobs paying these days?), had no problem performing the tracking
task "pretty darn well" right off the bat. I then had a simple integral
control system perform the task; the control system's gain and slowing
parameters were _constant_. The model controlled the cursor even better
than I did. This was true even though the parameters of the control model
were constant. Because the parameters were constant, there was no way to
see these parameters as implicit or explicit "models" of the changing
environmental feedback function.

This experiment suggests to me that, even if you want to call the gain
and slowing factors in a control loop "models of the environmental feedback
function", such "models" don't really need to do much "modeling"
(approximating the feedback function); the control system controls
satisfactorily even though the same "model" (same gain and slowing factor)
is used to approximate a feedback function that changes from linear to
cubic to polynomial several times in the course of a single session.

I think this little experiment provides a nice testbed for comparing
PCT and MCT models of human performance. I have not measured the fit of
the PCT model to the human performance, but that would be easy to do. And
it would be easy to compare the fit of any version of the PCT model (I'm
sure a two level model with the higher level adjusting the gain and slowing
of the lower level to maintain good control) to any version of the MCT
model. If the human controller (unlike the PCT model) is trying to "model"
the feedback function, then a version of MCT model should fit the human
data better than any version of the PCT model. To do this comparison, all
I need is the code for the appropriate MCT model. I think I have Hans'
Pascal code for an MCT controller. I'll try to translate that into
HyperTalk unless Hans has version that is more appropriate for this