<Martin Taylor 940405 15:30>
Rick Marken (940403.1000) Tom Bourbon [940404.0913] Bill Powers (940405.0750)
[Rick--Thank you for reposting Tom's comments. How does it happen that
Tom can post to you but not to CSG-L?]
To my mind, we have made a giant step toward reconciliation of views!
All three finally agree that the derivative of the disturbance and of the
perceptual signal are not independent, and I agree with all three that
the correlation is small, as well as with the following comments:
even though
the statistical analysis proves beyond reasonable doubt that there
is a relationship, there appears to be no useful way to say what
that relationship is for any given pair of measurements. (Powers).
All of that said, you are certainly right, Martin, when you say that the
derivatives are not independent; it's just that they aren't very dependent
-- the relationship is so weak that using it as a basis for predictions
would leave you with predictions that are 96.3 percent as likely to be in
error as they would have been if you didn't even know the correlation.
(Bourbon)
But the correlation between disturbance
and output (and between their derivatives) is typically on the order
of .99. So how does the significant correlation between derivatives of
disturbance and perception account for that fact? Another problem is that
the significant derivative of disturbance - derivative of perception corr-
elation will DECREASE as control improves. And when control improves
the correlation between disturbance and output GOES UP. (Marken)
I put Marken's last although it is chronologically first, because the
other two are simple statements of fact, whereas this has some interpretation
that is worth following up.
It is necessarily true that the correlation between disturbance and
perception will decrease and that the correlation between disturbance and
output goes up as control improves. That's the nature of control. The
better the control, the more the influence of the output dominates that
of the disturbance. As it stands, a correlation of 0.268 means that the
derivative of the disturbance accounts for as much as 7% of the variance
of the derivative of the perceptual signal (delayed--the value tends
to be a little higher without the delay, but not much). If there were
no loop delay and infinite gain, that value would go to zero. But there
always is loop delay.
The existence of that 7% represents the uncontrolled part of the disturbance
effect on the CEV, the part that has yet to be opposed by the output.
One can't attribute it all to an inadequate system gain, though some of
it almost certainly is due to the gain being less than infinite. Some
of it is irreducible, given that there is a loop delay and the disturbance
value may change during the delay time. For the rest, I leave you with the
question "Why is the gain low enough to allow the inadequacy of control
to show through, in a task in which precise control is both demanded and
attempted?"
This makes no
sense if the derivative of the perception is used by the control system
to generate outputs.
"This makes no sense" is where we part company. The difference between
the VALUE of the perceptual signal and the value of the reference is used
to generate outputs. Changes in that difference are not in themselves used
to generate outputs, so we agree on that. But these changes reflect changes
both in the perceptual signal and the reference signal, and since we
usually discuss conditions with a steady reference signal, they reflect
changes in the perceptual signal. As you so often point out, with never
a contradiction from me, those changes are due both to changes in the
output and to changes in the disturbance. In the case brought to trial,
the changes in the disturbance account for about 7%, changes in the
output for about 93%. With less transport lag around the loop, the
proportion due to the output would be higher, and control better.
But you have your next sentence backwards:
It means that the less the derivative of the distrubance
is reflected in perception, the better the system generates outputs that
mirror the distrubance. That is,the less the information about the disturbance
in the perception, the BETTER the system controls.
I would invert both those sentences: the better the system generates
outputs that mirror the disturbance, the less is the derivative of the
disturbance reflected in perception; the better the system controls,
the less information about the disturbance is in the perceptual signal.
If you remember the initial interchange back in Feb 93 or thereabouts, this
is pretty much the position I was trying to argue for.
If there is information
about the disturbance in perception, it looks like it just gets in the
way of control.
I think one of the BIG sticking points in this whole discussion, as I have
often said, is that word "in." Try "the perceptual signal serves as a
channel for information about the disturbance." I don't much like that
wording, but it might reduce the confusion. Information isn't "in"
the perceptual signal, at least not for long, and the better the control,
the less there ever will be "in" the perceptual signal. It's simply not a
repository. The information transmitted through this channel doesn't "get
in the way of control." The faster and better it gets out of the channel
and is used for control, the better control should be, and the less
information about the disturbance will be manifest in the changing values
of the perceptual signal.
But this is encroaching on the discussion I am having with Bill P., and
I really don't want to pursue it further here until we come to some
agreement either on the technical aspects or an agreement to disagree.
Neither has yet happened.
Martin