From Greg Williams (920330-2)
Bill Powers (920329.1400)
We may as well go public with the arm-model discussions.
Regrettably, I won't be able to contribute much to the discussions for some
time. Over the next month, I need to finish up (the final, thankfully!)
CONTINUING THE CONVERSATION, get the galleys of Rick's book to him, do the
April HORTIDEAS, write half of the next Brooklyn Botanic Garden PLANTS &
GARDENS NEWS, and do the next CLOSED LOOP. Then there's a half-finished house
that needs my attention.... So, if you want to try to publish soon, I
recommend that you go ahead. I don't need to be co-author.
I see what you mean by the outward curvature on upstrokes and downstrokes,
although there is a lot more variation between subjects than was my
impression from what you said. I wish we had the original data -- it's hard
to get any quantitative measurements of what the two joints were doing from
the figures. There's also a critical piece of missing data: in these plots
of visual-motor behavior, the position of the eye isn't shown, and it's not
mentioned whether the head bent forward as the arm descended!
Why not contact the experimenters for additional info?
The most interesting problem is the speed of movement and the shape of the
tangential velocity curve. When the traces of tangential velocity are
normalized for duration and amplitude, they all have very nearly the same
shape. This looks like gain control. In my model, there's no provision for
controlling speed of movements. Perhaps, by putting gain control into the
visual system, this effect can be reproduced. This would only be germane
for the upper range of speeds, however.
What do plots of tangengential velocity vs. time look like for the little man
now?
If you introduce variations in the reference signals to the visual systems in
my model, you can create any path you like.
But then how do you justify the particular path you choose? One way to avoid
such criticism would be to show that if you picked a particular rule for
setting the path of the moment-to-moment reference signals, then
experimentally-seen paths would actually be predicted, regardless of where
they started and stopped.
The curvature problem is not so interesting. If the traces of fingertip
movement were drawn with a line one centimeter wide, the difference from my
model's behavior would look a lot smaller, particularly if you merged the
data for all the subjects.
The different DIRECTIONS of curvature for the little man when moving "in" and
"out" still bothers me. No great shakes, except that I suspect it would bother
the reviewers, also.
For my part, if the position of the fingertip stays within a centimeter of
the average real fingertip throughout a movement I'd be satisfied. This model
has only two levels in it, and no correction for distortions at all.
The reviewers probably would be a lot happier if you did whatever is needed to
make the curvature predictions better. But of course you could go with what
you've got and note the limitations. I just think the chances of getting it
published would be improved if the little man (somehow) showed trajectory
curves qualitatively similar to those in the data, in terms of curvature.
Again, I'm sorry I'm too busy right now to work with your model in detail.
Greg