# Is that a fly swatter?

From Greg Williams (920108 - 2)

Rick Marken (930108.0900)

My point is that you have not reached
that goal in predicting cursor position.

After reading this I got out my HyperCard conflict stack and
did a tracking run and model run (400 data points each) with a
low conflict and got a correlation between subject and model
mouse movements of .996831 -- the correlation with cursor
movements would be lower but at least we seem to have part of
a true science. I repeated this with a slightly higher level
of conflict and got a sublject/model correlation of .993398. Still
in the "true science" range. Higher conflicts will take us
well below .99 (to .98 maybe?) suggesting that there is something
to be learned there.

If "true science" is your aim, why not compute the subject/model correlation
for the INTEGRAL of the handle movement? That should get you within spittin'
distance of 1.0! But if you want to be sobered a bit, use your model to
compute the correlation between the modeled derivative of handle position and
the derivative of the subject's handle position. That might even be lower than
the cursor-prediction correlation.

How about H = K * integral(C - T)? (K is a constant to be adjusted for best
fit to the data by running the simulation with the model in it). That's
just a first cut, of course, since it doesn't predict the cursor position
well enough for "true science."

I think the idea, now, is to use your S-R model in a real tracking
situation. As I understand the challenge, you are to derive an S-R
relationship between S (cursor) and H (handle movement). Bill
apparently sent you that data. I'd throw in the disturbance too -- I
don't think it's an unfair advantage for you at all -- in many experiments
you CAN see the disturbance (or the cause thereof) even if the subject can't.
So I would suggest that Bill give you D, C and H from a tracking task. Based
on that data, you come up with an S-R model that generates H based on what
the subject can see (C and T).

We're back to what is and is not an "S-R" model. If I can't fit parameters
with the model taking the place of the subject with the loop closed, I won't
be able to get reasonable values for K. If fitting parameters with the loop
closed makes the model above into a PCT model, rather than an S-R model, why
is that? As required, the model has the form H = f(C,T). Input-output. But if
I try to adjust K to make H follow the data, GIVEN THE FIXED C data, my "best"
K will not be best when the loop is closed. By adjusting K with C NOT fixed,
and the (given; it is just the difference between the other two givens)
disturbance operative, the K WILL be best for OTHER disturbances, too.

Your model must then be tested by seeing if it can do what the subject
does -- control the cursor in a new situation. So your model must be
"run" (this could be cone analytically but it's easier with a computer
simulation) with a new disturbance -- to see if it generates the H that
controls the cursor (as the subject would).

I would go beyond that, and try to change the FORM of the model to predict C
better, too. Maybe even get the subject-model cursor correlation up to the
"True Science" range... of course, that might not be possible, given noise in
the subject. My challenge to you and Bill would then be to make an underlying
generative model for the noise which results in a better s-m C correlation
than is possible with behaviorist "models" which contain no underlying
hypotheticals.

As ever,

Greg

[From Rick Marken (930108.2030)]

Greg Williams (920108 - 2)--

We're back to what is and is not an "S-R" model.

Yep. It's kinda interesting how easy it is to go around in circles
when talking about a circular model of behavior.

If fitting parameters with the loop
closed makes the model above into a PCT model, rather than an S-R model, why
is that?

It's the closing of the loop itself; remember there are two SIMULTANEOUS
equations that characterize this situation. One equation is your beloved
S-R model (really, only half of a model);the other equation is the
R-S model -- our beloved "feedback connection" (the other half of the
model of the behaving system). So S is both a cause AND a result of R;
this is just a "closed loop" model of behavior; it is not fair to call
it SR because that is only half of the story; it is also RS. That last
part is an important part of the model because 1) it has a hell of a lot
to do with how the model behaves (when the relationships are set up
for negative feedback the "behavior" is "control") and 2) it MIGHT not
actually exist; putting in the RS connection is not a tautology; it is
a guess (a part of the model) -- the guess is that the S that leads (hypo-
thetically) to R is ALSO influenced by that very same R. IT MIGHT NOT BE!!
So the RS connection IS PART OF THE MODEL. There are systems that are SR
(in that their output is strongly dependent on the input) but whose input
is not strongly or reliably a result of their output (there is no connection
from R to S); the two simultaneous equations of the control model could be
shown to be a demonstrably WRONG model of such a system. A computer is
an example of such a system. Its behavior is completely comprehensible in
SR terms; one can ignore any RS connection (which usually exists in the
form of an operator basing new inputs on previously produced outputs --
this RS link is very weak; the feedback link between output and input
is VERY loosely coupled). The test of all this is that you can describe the
behavior of a computer EXTREMELY accurately in SR (actually S-O-R) terms;
no RS connection need be considered.

So an SR model is PART and PARCEL of the control model. But I would not,
therefore, give behaviorists any credit for noticing it (they usually
noticed the wrong one anyway -- taking the disturbance rather than
the sensory effects of the disturbance as S, which, of course, could be
quite unlike the disturbance due to the feedback effects). You seem to
want to give the behaviorists credit for equation (1) in my "blindmen"
paper, which says, essentially, that R = f(S) where S is the SENSORY
stimulus. But this is giving them credit for what everyone knew since
Descartes -- the world influences our sensors which cause afferent neural
impulses which cause efferent neural impulses which cause responses.
This picture is essentially correct (qualitatively) but the functional
picture changes when you take into account the fact that responses are
CONTINUOUSLY influencing the very sensory events that are causing them.
The functional result of this closed loop relationship (with negative
feedback and high gain) is CONTROL of the sensory input -- relative
to an EXPLICIT OR IMPLICIT reference value; even if there is NO reference
signal, the sensory input will be held at a value that corresponds
(approximately) to a value of sensory signal that corresponds to ZERO
efferent (error) signal (which might be zero sensory signal).

So I'm not impressed by the fact that the behaviorists know that R = F(S)
or that they sometimes even admit the S = G(R). What they don't seem to
know is that these two little facts, taken simultaneously, make it
possible to understand how organisms behave purposefully ( by
controlling their own sensory input). But understanding this phenomenon
doesn't seem to be the purpose of behaviorists -- so they can avoid the
problem by looking at only half of the loop at a time; kind of a half-vast
approach.

Best

Rick