t+tau, model fit, reaching

[From Rick Marken (950112.1020)]

Martin Taylor (950111 15:20) --

It is because I am interested in that aspect of control [bandwidth of
disturbance over which good control can be maintained] that I try to make
sure that the existence of the loop delay is kept in mind.

Well, I'm sure relieved. I seems to me that the last time you talked about
loop delays, it was your way of showing how it was possible for information
about the disturbance to be carried by (in, whatever) the percetual signal.
I'm sure glad that's over.

Perhaps you could describe some of your research on the relationship between
disturbance bandwidth and control. It sounds like it is quite interesting.

Martin Taylor (950111 18:20) --

For the six subjects, under conditions where, so far as I can see, the model
should fit best, the median correlation of model to data is about 0.93, 0.91,
0.90, 0.90, 0.84, 0.83. Only a total of 32 out of the 480 runs produced
correlations of >0.99, 13 of them by one subject. This doesn't seem to me
to be very good, especially in view of comments that one ought perhaps to
think of throwing out models that don't fit better than 0.95 correlation.
I'm wondering what should be done to improve the fit.

Did you go through separate parameter fits for each of the six trials on
which the median fit is based? If so, it might be that during this early part
of the experiment the subjects' control parameters are still unstable
(reorganization is still happening) during a run. I would expect things to
get better (for the subjects with the low median fits) for later runs. Did
the .99 fits for the one subject happen for the very first runs in the
sequence or did the fit improve? I assume, by the way, that you are
describing the fit of the model to data from the standard tracking task. If
the fits don't improve using the simple model -- especially for later runs --
I would suggest that you look at a graph of the time variations in model and
subject handle movements (overlaid on the graph) to see what's going on; it
may be that you just had a sticky handle or somethong like that.

Bruce Abbott (950112.0830 EST) --

it would seem from abrief scan of some of these articles that there is a
general concensus that the simple explanation for such astonishing abilities-
- what we would call PCT--has been considered and rejected

Note that the researchers in this area either have no idea or consider it of
only minor importance that the "astonishing abilities" they are trying to
model (like "reaching") involve control, so Bizzi et al are not trying to
explain reaching from the point of view of the "reacher". Moreover, for
reasons that are beyond my comprehension, they also reject the "control of
perception" approach itself, which can help them model reaching even if they
don't conceive of reaching as a control process. W. T. Powers and G. Williams
(in an article rejected by Science) showed that the PCT approach achieves
what the Bizzi et. al. approach achieves (and then some), only the PCT
approach does it more simply and realistically (no need for computing inverse
dynamics and kinematics).

Best

Rick