[From Rick Marken (930402.1800)]
Allan Randall (930402.1130 EST) --
Are you then saying that this almost perfect information about the
first derivative is not "significant" information?
It is not really information at all. This perfect correlation is
a result of having a perfect integrator in the output and a
linear contribution of o to p (with a coefficient of 1). Anything
else would have produced a much lower correlation between the
first derivative of the disturbance and perception. So if you
are thinking that the perception carries information about the
disturbance (tells you what the disturbance is) then you would
sometimes be guessing WRONG about the form of the disturbance based
integrating the perecptual signal.
Let's say that you now claim that the integral of the perceptual
signal, int(p) , equals the disturbance (as shown in Bill's demo).
Now I give you 100 segments of p obtained in different tracking
tasks. Fifty of these segments have been obtained in tasks where the
cursor (p) was determined by the following equation -- p = o + d.
Fifty were obtained in tasks where p = ko + d, where k was differnt
in each case. Now you run all 100 segments through your disturbance
detector , int(p). You would consider all 100 resulting estimates of
d to correctly represent the d actually presented on each trial. In
fact, you are only right about half of them (and you don't know
which half). It is in this sense that the int(p) detector -- which
correlates perfectly with the disturbance in Bill's example --
actually provides NO information about the disturbance. It's because
you have no way of knowing (except by looking at the disturbance itself)
when int(p) is and when it is not an accurate representation of d.
You and Rick continually insist on measuring information with things
like correlation and variance statistics. This is not accurate.
I think this is a misunderstanding; but I am willing to admit that I
have not been clear about this -- until now, I hope (see my comments
above).
Martin Taylor (930402 11:10) --
Up until today (or rather two days from now), you have said that the
disturbance and the output correlate 0.99xxx in many many postings. Now,
to retain your position that there is no information about the disturbance
in the perceptual signal, you have suddenly shifted to the position that
the correlation between disturbance and output is 0.00.
The first part of this seems a bit strong (there is no information
about the disturbance in perception regarless WHAT position I might have
changed) and the second part is just wrong -- I never said that the
correlation between disturbance and output is 0.00. In fact, the
correlation can range from close to 1 to close to 0. What I realized was
that the relationship between distrubance and output in IRRELVANT to the
question of whether or not there is information about the disturbance
in perception. What is relevant is how well a receiver can determine
D given P. Hopefully, you are working on the perceptual signals I sent
to determine how well this can be done. Think of it as a signal detection
experiment. I'll give you signals (p strings) and you tell me which
D you think they represent.
You can't have it both ways. Either the disturbance and the output are
correlated, as experiment and model both show, or they are not,
Not so simple, I'm afraid. This correlation depends on many things;
the gain of the output and the feedback function from output to input
being two of them. By varying these parameters the correlation between
o and d can be made to range from near 1.0 to near 0.0; through it all,
there is no information about the distrubance in the perceptual signal.
P = O + D was a given because that is what has always been
claimed as a basic property of the loop.
Well, it's now time to go beyond p = o + d. In order to really
bring the point home we're just going to have to admit that
p = g(o) + f(d). And that's functional notation; I'll tell you
right now that it's the g function that is the killer for the
idea that there is ANY information in p about d. I've tried to
be linear about this -- but now it's no more mister straight guy.
It [information about the disturbace] IS used, most explicitly and
adequately.
We shall see.
If it's any comfort to you, I will succumb to data. I was perfectly
willing to accept Bill Powers' first derivative data; and I was all
set to admit that there IS information about the first derivative of
the disturbance in p. But then I realized that this was information
in the same way that Martin's old perceptual transient provided
information about the disturbance; it only provides information on the
information that you know a lot about what the information is being
sent about.
I won't consider the information you claim exists in p to be worthy
of the name "information" if you can't use the p strings (messages)
to reliably tell me which d strings "sent" them.
Best
Rick