[Martin Taylor 930320 11:00]
(Rick Marken 930319.1300, 930319.0830, 930319.1500)
With the first of these postings (by receipt, as listed above) I thought
that Rick and I were well on the way to convergence and agreement. With the
second, I was in pretty complete agreement, but with the third, quoted here,
I find we seem to be back to square one:
Martin Taylor (930319 14:30)--
With infinite precision perceptual signals and zero transport lag around
the loop, the perceptual signal is always completely under control and
the disturbance is never represented there. If either of these conditions
fails, the passage of the information "about" the disturbance through
the perceptual signal to the output signal can be detected, and was
beautifully illustrated in Bill's diagrams that I quoted.
This paragraph is controversial because it is FALSE. If it is not false,
Martin should at least be able to show us how to detect the information
about the disturbance that passes through the perceptual signal.
Exactly what I did in my posting using Bill's diagrams. I can do it no
more directly and simplistically than that. At present. I may some day
be able to find a demonstration in words of half a syllable, but so far
I haven't managed to learn to talk that way.
It is alarming because it suggests that the output is driven by the
the information in the perceptual signal -- a lineal cause effect notion
inconsistent with the behavior of a control system.
I have a feeling that Rick sees S-R psychologists under the bed at night.
I find no suggestion of a lineal cause-effect relation here, or that the
output is driven by the perceptual signal. It isn't. It's driven by the
ERROR signal. The ONLY reason that the information from the disturbance
is undetectable in the perceptual signal is that it has been used by the
control LOOP and is therefore gone. The output is only the mechanism whereby
the CEV is deprived of whatever influence the disturbing variable might
have had. Once the information has been used, it's gone (though it can
be partially recovered from the output signal if the ECS's imagination
loop contains a good system model.) Whatever hasn't been used in control
(because of low gain or transport lag) is still there.
In 930319.1300 Rick acknowledges that the information about the disturbance
can be found in the perceptual signal if the output signal is zero. I'm
not sure why this is relevant, but at least it's a move in the right
direction. What I have been trying to show is that CHANGES in the disturbance
are detected as CHANGES in the perceptual signal until CHANGES in the
output serve to cancel them. And yes, there's no problem in my mind with
the changes in the CEV having been due to changes in the reference signal
that caused changes in the output signal. A disturbance, to me anyway,
is how the CEV differs from what the ECS would like it to be.
If you think this concept of a disturbance is odd, consider again Bill's
spring diagram:
A--//////////--B--\\\\\\\\\\--C
where A is the disturbing variable, the position of B is the CEV, and
C is the output of an ECS.
Now think of the condition before C was connected, i.e. before this ECS
began to assume control. A was pulling on B, and provided there is some
friction, there is tension on the spring. What is the disturbance? I
claim it is undefined, inasmuch as B is "somewhere," a somewhere that
is related to an environemental context not needed in the discussion.
That somewhere is the same place it would be if A were not pulling.
Maybe friction is insufficient to hold B in place, and B is moving.
It is still "somewhere," at any moment. What is the disturbance in
this situation? The tension in the A-B spring? No-one is sensing that,
either before or after the ECS begins to control the position of B. It
seems to me that the concept of disturbance cannot be meaningful until
there is control going on (successful or not), which is to say, that
there is a perception of the position of B relative to some reference
point, which could hardly be anything other than the point corresponding
to the reference signal in the ECS whose output is C.
The output signal itself does not mirror the disturbance. Suppose A is
pulling, but B is stationary because of static friction. Now the ECS
begins to attempt to control, by making C pull if B is to the left of its
reference position. It takes a finite pull by C to balance the pull by A,
and at this balance point B still does not move. More pull by C does
not move B until C pulls hard enough to overcome the static friction.
The output of the ECS is a force, but the disturbance is an error of
position. And the same applies throughout the period of control. The
output is a force, which CANNOT be added to the disturbance (whether it
be considered as a force or a position) to produce a perception of position.
There isn't even a one-to-one functional relation between the output signal
and the perceptual variable in this case, so p(t) = d(t) + o(t) cannot
be a meaningful statement. p(t) is a combination of the EFFECTS of the
disturbing variable and the output signal on the perceptual signal.
Now let's answer the "focus" questions:
1) Do you believe that the disturbance to a CEV (and the perecption
thereof) typically causes the error (discrepency between reference and
perception) that leads to the output that opposes that disturbance?
I think one has to define the disturbance in respect to the error exactly
as one defines the CEV in respect to the percept. The perceptual input
function defines the CEV (provided you include the operations of all
the PIFs in lower ECSs that provide the sensory signals to this ECS).
The perceptual signal is the current representation of the state of the
CEV. From an outsider's viewpoint, in which the perceptual signal and
the CEV can be independently measured, they may differ. The same applies
to the error and the disturbance. From inside the ECS, the perceptual
signal is all there is.
2) Do you believe that it is necessary that the disturbance at least
occasionally be represented in the CEV?
The disturbance is not "represented" in the CEV. The disturbing variable
may affect the CEV, but representation occurs within the ECS.
I suppose one could say that the reference signal can be represented (by
an outsider, not the ECS) in the CEV space, but this is dubious, since
the PIF may well not be invertible.
(Interesting, come to think of it; this is exactly the inverse problem
of the classical roboticists. They worry about the non-uniqueness of
the inverse kinematic problem, and here I am saying that "many means can
achieve the same goals" can be seen as the same inverse perceptual problem).
If in some way the reference signal could be represented in the CEV, then
I guess one could say the disturbance could be represented in the CEV, but
at the moment this seems to me to be making a VERY big stretch.
3) If you answered "yes" to (2), why do you believe this?
I didn't say "yes."
···
-------------
...it seems to me that you are trying to
squeeze the beautiful concept of control of perception into the
Procrustean bed of conventional linear cause effect thinking.
I find this ironic. Long before I heard of PCT, I was a missionary for
eliminating ALL cause-effect claims, on the ground that in the whole
universe everything is interrelated; the effects of actions react on
the actor, environmental conditions must be right for "causes" to have
"effects," everything is under a multitude of influences. Cause-effect
thinking ruins our justice system and our economy just as surely as it
is a baneful influence in psychology. (Cause-effect thinking leads to
the notion that government deficits can be cut by reducing spending, for
example). So, for my attempts to analyze the control LOOP to be
characterized (repeatedly) as a support for S-R approaches or as an
attempt to maintain an S-R view strikes me as a bit ludicrous. But I
can accept that you might see my comments as lending aid and comfort
to the enemy. There may be something in the wording that triggers your
"Reds under the bed" detector. I don't see it, so I have a hard time
controlling it.
-----------------
I am beginning, at last, to have the feeling that we really do see in
the same way what happens in a control loop. I don't know whether I am
changing my opinions (it doesn't feel as if I am), whether you are (it
doesn't seem so from here) or whether I am simply coming to a better
understanding of what has been underlying your objections to my postings
(I hope that's it). Whenever you say positively what occurs, I have no
problems. It is always as I have understood the situation. I have
problems only with the negative things. The differences are in what
to take from that common understanding.
But I also see that most times somebody else (I mean other than us) says
that they "agree" with another disputant, I get the feeling that they don't.
General note. This is likely to be my last posting before at least
Thursday, (Tuesday is possible but unlikely) and maybe until the following
week. So barbed arrows may have a long travel time, and earthquakes will
remain undetected for a while.
Martin