p(t) = d(t) + o(t)

[Marken_Richard_S1]

[From Rick Marken (930323.1000)]

Martin Taylor (930323 11:30) --

I would assume (and have assumed) that the disturbed perception is your
perception of other people's beliefs, and that your own postings are actions
in a control loop whose reference level is something like "X should have
a correct understanding of PCT."

I agree. This is what I was assuming when I started to reply to Chuck.
But then I realized that your postings (qua postings) can be considered
disturbances in Chuck's sense (not effects on a controlled variable but
deviations from a reference level). Your postings can be considered
perceptions that I cannot control -- and, in this sense, to the extent
that I have references for these uncontrolled perceptions -- they are
disturbances.

Whatever perception I am controlling in this "information about the
disturbance in percpetion" discussion, it must be a function of both
your posts (d(t)) and my posts (o(t)) because, if a perception
is controlled, it MUST be a function of BOTH disturbances and outputs
SIMULTANEOUSLY (simultaneous within the integration window of the
controlled perception) so that p(t) = d(t) + o(t). This means that
the perception I am controlling contains no information about
your posts, d(t) -- so, with respect to the perception I am
controlling, your posts are NOT a disturbance in the way Chuck
was referring to a disturbance.

Let's say I am controlling for a variable that might be described as
"correct description of the PCT model". This is p(t) and, I presume,
it can have various levels, from "not very correct" to "very correct"
(as I perceive it, of course). I have a reference level, r, for this
perception, p(t), and I am trying to keep p(t) = r.

The important point is that p(t) depends on BOTH d(t) -- your posts;
and o(t), my posts. But at the level at which I am controlling
for p(t) I have NO information about your posts themselves; all I know
is the current value of p(t) -- "degree of correctness of the
description of the PCT model". At this level I have no information
about why I am experiencing this particular level of p(t); that is, I
have no idea how much the level of "degree of correctness of the
description of the PCT model" is determined by the contents of your
posts or mine. All I know is my perception of "degree of correctness
of the description of the PCT model" and I generate outputs (posts)
to keep this perception at my reference level.

Now this may seem screwy, I know. What I am saying is that, at the
level of the perception I have described as the controlled variable
I have no idea what was "said" in your posts OR mine. But I would
argue that this seems screwy only because we can both move our
consciousness to the level of our own perceptual systems that perceive
what was "said" in the individual posts; at that level I can
see that it was obviously your post that made my perception of
the "degree of correctness of the description of the PCT model"
become lower (let's say) -- or that my post obviously made that
perception become higher. That is, at that level I can perceive
the information in d(t) AND o(t). But to do that, I had to "get out"
of the perspective of the control system that is controlling the
the variable that is based on d(t) and o(t) -- the variable called
"degree of correctness of the description of the PCT model" -- and
look at the perceptual outputs of these other perceptual systems;
systems which are not perceiving the controlled variable -- "degree
of correctness of the description of the PCT model".

This is what happens in a pursuit tracking task, for example. At the
level of the system (in the subject) that is perceiving and
controlling the difference between the cursor and the (moving) target,
all that is known is p(t) -- the perception of the difference between
target, d(t), and cursor, o(t). So in putsuit tracking

p(t) = d(t) - o(t).

But when you are the subject in this experiment you CAN perceive
the movements of d(t); they are clear as day (not "hidden" as they
are in compensatory tracking); The subject can see d(t) moving back
and forth, clearly disrupting ("distrubing") his/her ability to
keep the cursor (o(t)) on the target. But this observation is
made from the perspective of a different system in the subject's
control hierarchy -- one that is NOT controlling p(t) = d(t) - o(t).
The system that is controlling p(t) has NO information about
d(t) -- though other systems can detect d(t) and help the
system controlling p(t) take advantage of any regularities in
d(t).

I think the problem with believing the "no information about the
disturbance in perception" argument comes from the fact that we
typically DO have information about disturbances in our
perceptions because we (people) consist of multitude of layers of
perceptions -- some of of these perceptions are controlled
variables and some are not. The d(t) that is a non- informative
aspect of a controlled perception (p(t)) is likely to also be an
informative aspect of an UNcontrolled perception at another level of
the hierarchy; this is what happens in pursuit tracking; I am sure it
is what is happening in this discussion of information about the
disturbance in perception.

Remember, the fact that there is NO information about disturbances
in perception applies ONLY to CONTROLLED perceptions -- that is, to
perceptions that are the JOINT result of disturbance and output --
perceptions which can be described as p(t) = d(t) + o(t). The
components of p(t) -- o(t) and d(t) -- may be (and very often are)
UNCONTROLLED perceptions at lower levels of the control hierarchy.
So information about o(t) and d(t) may be available as UNCONTROLLED
perceptions in the person controlling p(t) -- but p(t) itself
contains NO information about d(t) or o(t).

Best

Rick

[_Martin_Taylor]

[Martin Taylor 930325 11:30]
(Rick Marken 930323.1000)

I apologize in advance for an inadequate response. While I was oaway
yesterday I did a count, and realized that I have 19 workdays here between
now and June 15. PCT is not what I am paid to do, although I am incorporating
it in the "real" work so far as possible. So I can spend little time on
PCT discussion, unless the particular item seems likely to further the
integration of PCT with my work.

Having said that, and given the CSG-L community the good news that the
volume of my posting will be drastically reduced over the next 3 months,
I can comment on Rick's posting.

There are several reasons why the discussion of information in PCT has
explored so many blind alleys, but apart from the differences among
participants in the definitions of words, the most significant one is
in a general non-realization that we have been taking multiple views
simultaneously.

The "inside view": The result of applying the perceptual input function
    to the set of sensory inputs--i.e. the perceptual signal. Other, but
    different inside views could be at the ouput of the reference signal
    collector function, the comparator, or even the output function. Any
    one of these inside views is (not "represents") a scalar signal that
    has a single momentary value that is a number. It exists, in and of
    itself, representing, from the inside view, nothing at all. An inside
    viewer recording the signal can see only a waveform, which according
    to Fourier and subsequent mathematicians, can be represented exactly
    by a discrete set of numbers. These numbers represent the waveform,
    and are the most extreme "representative" view that can be taken from
    inside the ECS.

The "outside view": from outside, any aspect of the universe can be seen
    and incorporated into some analysis. This includes the signals within
    the ECS, the state of the CEV that is defined by the Perceptual Input
    Function (PIF) of the ECS, and the actions of any disturbing variables.
    An outside view can incorporate all the structure of the hierarchy. It
    is undetermined what is and what is not in a generic "outside view,"
    though restricted outside views can be postulated for the purposes of
    specific discussions.

Now, using those quasi-definitions, we can perhaps see why there has been
an argument. It is transparently obvious that from an inside view the
perceptual signal, being scalar, cannot distinguish between two independent
effects upon it. There is nothing there but a unidimensional waveform
(ignoring for the moment the fact that the successive independent samples
do define a multidimensional space). Nothing in any sample can indicate
more than that it has "that" value. From this viewpoint, it is
straightforwardly correct that "there is no information about the
disturbance (or disturbing variable) in the perceptual signal."

Inside the protagonist (subject), at one level considered alone, no
ECS has any information other than "about" its CEV, and even that
"aboutness" is not visible from the inside viewpoint.

In the hierarchy, the various PIFs define a mirror hierarchy of CEV's in
the world, as we have drawn in the mirror diagram many months ago. A
higher PIF represents a CEV that includes among its effects (as seen from
outside) a "disturbance" to a lower CEV. Bill Powers reinforced this
view a week or two ago when he pointed out that a higher PIF could be
formed to represent a CEV that was "the" disturbing variable for a given
one and that in this way a disturbance could be extracted out of the
perceptual signal of the lower ECS. Apart from some scepticism that one
could in this way detect all the external influences on a CEV, this
simply is a description of the phase of reorganization that builds new
levels in the hierarchy.

The situation is different if we take a full-blooded outside view of the
action of a CEV. It is from this kind of view that we argue that the
disturbance provides information that passes through the perceptual
signal to the output signal. From the outside we can see the disturbing
variable do whatever it does to affect the CEV, and we can see the ECS
modifying its output to bring the perceptual signal back to its controlled
value. From outside we can see the reference signal of the ECS changing,
and the ouput changing to move the CEV so that the perceptual signal comes
to its new controlled value. From outside, the arguments about there
being no information from the disturbance in the perceptual signal lose
their force. The use I made of Bill's example was from this point of
view, and still seems to me to be correct.

I have no idea how much the level of "degree of correctness of the
description of the PCT model" is determined by the contents of your
posts or mine. All I know is my perception of "degree of correctness
of the description of the PCT model" and I generate outputs (posts)
to keep this perception at my reference level.

Now this may seem screwy, I know. What I am saying is that, at the
level of the perception I have described as the controlled variable
I have no idea what was "said" in your posts OR mine.

No, it doesn't sound screwy. You are expressing a one-level inside
view.

But I would
argue that this seems screwy only because we can both move our
consciousness to the level of our own perceptual systems that perceive
what was "said" in the individual posts; at that level I can
see that it was obviously your post that made my perception of
the "degree of correctness of the description of the PCT model"
become lower (let's say) -- or that my post obviously made that
perception become higher.

I'd modify that (and the rest of your posting) to identify where the
"degree of correctness of the description of the PCT model" exists.
Is it in your perception of my belief, your perception of your own
belief, your perception of the change your posting is likely to make
in my belief, or what? Otherwise, I agree. The change in level changes
the representativeness (as seen from outside) of the perceptual signal.

Enough. 46 messages await my attention. I either don't read them
and continue this response, or quit and hope for the best.

Martin