[From Rick Marken (930403.1600)]
Martin Taylor (930403 15:15) --
Remember that the claim was ONLY that the information in the perceptual
signal is enough to permit the OUTPUT signal to be reproduced.
So what you are claiming is that given the equation o = int(p) and
p you can compute o. If that's all you meant by "there is information
about the disturbance in p" then I must admit that you are correct:
if y = 2 * x and I give you the value of x, you probably could
determine the value of y. IT sure gives some incredible insights.
The original claim that the output signal was a mirror of the disturbance
was yours.
Yes. I made that claim when I was assuming that p = o + d. When the system
has reasonably high loop gain, it is indeed approximately true that o = -d
(in tracking tasks where p = o + d, the correlation between o and d is
nearly -1.0).
Our claim is only that to the extent that the perceptual
signal is controlled, it has passed information about the disturbance
that has come to be manifest in the output signal.
What is this "come to be manifest" stuff? How can I tell that it did
that? Is it sort of like what happens to Christ's body in that little
wafer in the communion ceremony (who would imagine a nice Jewish boy
like me would know about that, eh)?
Now that you have renounced the claim that there is information about
the disturbance in the output signal, you have to think hard about what
is meant by "control,"
Once again we're getting a little too ecclesiastical for my taste. If
by information about the disturbance we mean that one signal waveform
reproduces the other then I didn't "renounce" anything. When p = o + d
and there is high gain then o is nearly a perfect mirror of d -- and
thus o contains perfect information (signal reproduction sense) about
d. If, however, p = g(o) + d and g is non-linear or the loop gain
is low then o will not have much information about d (again, in the
signal reproduction sense).
What I think you might be referring to is my realization that, regardless
of how well o reproduces d, o NEVER has any information about d inasmuch as
it does not communicate which d was present when o was generated. This is
because the system cannot know whether the observed o occurred when p = o+d
or when p = g(o) + d.
Since I don't renounce the idea that there is information (in the
signal reproduction sense) about d in o (given the conditions stated
above -- ie. p = o + d and high gain) are you going to get out the stake
and hay?
but your original logical inconsistency has been
removed
Thank you, holy father!
(we had a little pool about how you would get around the problem,
but none of us bet that you would renounce the idea of control to be able
to retain the claim that there's no information about the disturbance
in the perceptual signal.
What are you guys running over there? I didn't "renounce" the idea
of control. I still "believe" in control and will make the pilgrimage
to the CSG meeting still believing in it. I believe in the fact that
negative feedback systems act to keep their perceptual inputs matching
a fixed or variable reference for that input; that's control. What I
don't believe is that this process of control depends on the system
having any information about the variations in the environment that
make it necessary to act (vary output) in order to keep perceptions
at their references. It only seems like it's necessary when you look at
control systems from the SR perspective.
Say, the guy who wins one of these pools should give me a cut, don't
you think?
That was really a breathtaker for us).
Thanks. But the magic is most effective when the audience doesn't
understand what you are doing.
I'll let Allan, probably on Monday,
check out your perception sequences, but a first visual glance suggests
that at least one of them involves fast-changing disturbances. But we
shall see.
Indeed, we shall.
If the perception is well controlled, then the result will
be like the disturbance. Come to think of it, the perceptual signals
you have provided are clearly not well controlled, since you assert
that the reference is zero throughout, and the perceptual signals are
drifitng away from zero in one case.
You can specify the level of control desired in future tests, if you like.
I think that is an excellent idea. But I did tell you the gain (ko) and
sampling interval (dt) of the system that produced the perceptual signals
that I sent you. Still, feel free to specify the desired level of control;
I suggest specifying it in terms of stability, S -- ie. S = sqrt(ve/vo) --
S is the square root of the ratio of expected to observed variance of the
controlled variable (p). S is very easy to measure in these simulations.
The larger the S value, the better the control. How about trying for an S of
100?
I said:
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.
You reply:
If the output function can be generated from the perceptual signal, as
we have shown, this paragraph is equivalent to saying that red can
be green or blue, but throughout it all, 3 is greater than 7. It is
a total renunciation of logic (or of mathematical definition).
There I go again -- renouncing stuff.
Well, fortunately for me, I'm right. I am going to build a "logic
renumciator" stack; it should be ready by monday. That stack will show
how the correlation between d and o can range from nearly 0.0
to nearly 1.0 while the perceptual variable is kept at the reference
level all along -- ie. it will renounce "logic" but it will not
renounce control.
If I build this stack, will you finally give up on this "there is
information about the distrubance in perception" stuff?
Wonderful. Now we can start talking seriously about information.
That function g(o) isn't even a function, is it?
Yes. I'm afraid it is. In PCT we call it the "feedback function".
It is the reason for all the "inverse kinematics" calculations in
output generation models of behavior. It is the reason that output,o,
doesn't bear any reliable relationship to d. It is the reason why
there is unquestionably no information about the distrubance in
perception. g(o) is not just a function; it is an information
theorist's worst nightmare.
Great to get here at last!
My feelings, exactly.
Best
Rick