information in perception

[Human_Factors_Lab]

[From Rick Marken (930315.2130)]

Avery Andrews (930316.1200)

I don't think that people are all
necessarily as block-headed as Rick Marken thinks they are, but they
will act that way if the presentation isn't tailored to their current
state of mind.

If "block-headed" means stupid then I don't think that people who
reject PCT are block-headed. In fact, I think most of them are very
smart -- a lot smarter than me. If, however, "block-headed" means
resistent to ideas that are disturbances to controlled perceptions
then, yes, I think that people are "block-headed" simply because they
are control systems. The peculiar disturbance resistant properties
of a control system makes it impossible to get people to
accept an idea that is a disturbance to a currently controlled
variable. The reason that PCT has an acceptance problem is because
most behavioral scientists (smart or not) are controlling for a variable
that is disturbed by the concepts of PCT. I think the variable typically being
controlled is something like "the input output model of behavior".
But it might be something else.

Discovering this controlled variable is really why I am pushing
this "information about disturbances" discussion with Martin
and Allan. I believe that the idea that there is no information
about disturbances in the perceptual input to a control system is
very, very easy to understand -- even trivial. It requires no complex
reasoning or the rejection of well understood physical principles. All
it requires is a little, simple algebra (see below). But Martin and Allen
are rejecting the idea that there is no information about disturbances
in the perceptual input to a control system (by simply asserting that this
just can't be so -- there must be such information) and I think they
are doing this because this idea is a disturbance to their way of
thinking about how living systems work. They believe that there
must be something in the perceptual signal that can tell (inform,
cause, guide, whatever) the output what to do. I think they consider
this the only rational possibility because it is the only rational possibility
if you are dealing with an input-output device (like a computer). In other
words, I think they are not getting this very simple idea (no information
about disturbances in the percetual input) -- not because they are
stupid or bull headed -- but because this idea is a disturbance to their
input-output view of behavior.

The fact that there is no information about the disturbance in the
perceptual input to a control system can be easily seen from examining
the formula for this input:

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

What the control system perceives (and controls) is a time varying signal,
p(t) that is at any instant the result of the combined effects of an
indepedent disturbance variable, d(t) and an output being generated
by the system itself, o(t). All the system perceives is p(t); it has no
way of knowing "how much" of p(t) is at any instant the result of d(t)
or o(t). In other words, it has no information about d(t) -- all it has
is p(t). Nevertheless, it generates outputs, o(t) that are a precise mirror
or d(t) -- something that can only be determined by an observer of the
system:

(2) o(t) = -k d(t)

The system does this, not by "seeing" information about d(t) in p(t) and
generating the appropriate output o(t) in response to this information;
that is, o(t) is not generated the way it is described algebraically in
equation (2). Rather, o(t) is generated as the result of a comparison
between p(t) and a (possibly zero) reference value;

(3) o(t) = g(r - p(t))

This output is generated in a loop and each change in o(t) -- in a
dynamically stable loop -- 'nudges' p(t) closer to r. So the loop is
continuously generating o(t) values proportional to the existing error
which tends to move the existing error to zero. A "side effect" of this
process is that o(t) happens to be a mirror of d(t) (eq. 2). But the loop
doesn't "know" anything about the form of the function d(t) -- this is
the sense in which there is no information about d(t) in the input.
There is no information about d(t) because the closed loop doesn't "care"
what causes p(t) to vary ; all that the loop does is generate o(t) (which it
also has no information about) which tends to cancel out whatever is
causing p(t) to move away from r.

The appropriate way to describe this process is "control of perception".
Perception, p(t), has no control over anything; it just IS. Perception
does not "inform" the system about what to do; nor do variations
in perception (when the perception is affected by the outputs of the
system) contain any information about the causes of that variation --
that is, to what extent the variations are a result of disturbance or output.

I suspect that Martin and Allen will still want to defend the idea that
there is information in p(t) which guides o(t). I, of course, will resist
this defense because I am controlling for my understanding of the
operation of a control system. All I can say is that their defense will
be most effective if they can tell me how I can find the information
in p(t) that will allow me to reconstruct the d(t) that was (partially) the
cause of p(t) (see eq. 1). As I have said before, I have already tried one
approach to finding the information in p(t); and I found no
such information. What I found was that

o1(t) = o2(2) when d1(t) = d2(t) even though p1(t) <> p2(t)

where the 1's and 2's index the tracking trial during which these functions
were obtained. In fact, the equality o1(t) = o2(2) was not perfect;
the correlation between o1(t) and o2(2) was typically .997865 or so.
Similarly, the inequality, p1(t) <> p2(t) is not perfect -- the correlation
between p1(t) <>and p2(t) was not zero -- it was .0032 (or more, but never
much greater than .2).

I think that Martin and Allan would have to claim that, in the tiny
little correlation between p1(t) and p2(t) is the common "information"
that is used to guide o1(t) and o2(t) -- making them approximately equal;
I say that Martin's and Allen's position (that there is this information
about d(t) in p(t)) invokes "magic" and, thus, I propose A NEW CHALLENGE:

I challenge Martin and Allan (and anyone else) to show me how to get
the information about d(t) out of p(t) and reconstruct d(t) from it. I
would bet a LOT of money that such a reconstruction algorithm will NOT be
forthcoming --- but I think betting on the net is probably frowned upon
-- so how about a big, embarassed concession from me when I get the
algorithm and construct my first d(t) from the p(t) of your choice. The
only caveat is that the reconstructed d(t) [call it d'(t)] represent the
actual d(t) just as well as o(t) did in the actual run of the experiment.
That is, the correlation between d'(t) and d(t) should be about the same as
the correlation between d(t) and o(t).

Best

Rick

[_Martin_Taylor]

[Martin Taylor 930316 10:20]
(Rick Marken 930315.2130)

The peculiar disturbance resistant properties
of a control system makes it impossible to get people to
accept an idea that is a disturbance to a currently controlled
variable.

We (Martin and Allan) are not in that group, but we recognize, all too well,
that people do exhibit resistance to disturbances of cherished perceptions,
and that we, like you, are people.

But Martin and Allen
are rejecting the idea that there is no information about disturbances
in the perceptual input to a control system (by simply asserting that this
just can't be so -- there must be such information) and I think they
are doing this because this idea is a disturbance to their way of
thinking about how living systems work.

I could very easily paraphrase this with only changes from "Martin and Allan"
into "Rick" and deleting the word "no" in the second line. What good
would it be to do so, except to point out the symmetry of the situation?

However, there are substantive comments that can be made.

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

What the control system perceives (and controls) is a time varying signal,
p(t) that is at any instant the result of the combined effects of an
indepedent disturbance variable, d(t) and an output being generated
by the system itself, o(t). All the system perceives is p(t); it has no
way of knowing "how much" of p(t) is at any instant the result of d(t)
or o(t). In other words, it has no information about d(t) -- all it has
is p(t)

Fine, except that the last sentence is a non-sequitur. It indicates that
the core of the argument is a misunderstanding about the nature of
information. p(t) = d(t) + o(t), and therefore p(t) contains information
derived from d(t). This in no way implies that d(t) can be recovered
from p(t) without knowledge of (as distinct from information from) o(t).

Nevertheless, it generates outputs, o(t) that are a precise mirror
or d(t)

That word "precise" is an argument killer. o(t) is NOT a precise mirror
of d(t). It differs by an proportion that is roughly 1/Gain. In an
integrating control, 1/Gain approaches infinity at infinite time, and
then you can talk about o(t) being a precise mirror of d(t), but only
if no disturbing "events" have happened in the interim. You can't use
infinite gain without going to zero bandwidth, because otherwise you would
be infinitely amplifying the least little noise in the comparator or
perceptual input function. That again is a question of information.

But the loop
doesn't "know" anything about the form of the function d(t) -- this is
the sense in which there is no information about d(t) in the input.

I'll certainly go along with this sense. But it is irrelevant to the
points Allan and I have been trying to get across.

All I can say is that their defense will
be most effective if they can tell me how I can find the information
in p(t) that will allow me to reconstruct the d(t) that was (partially) the
cause of p(t) (see eq. 1)

I have no intention of defending the straw man Rick posts for me to defend,
but as I mentioned to him privately, this question is quite interesting
in its own right, and some day I'd like to look into it, if no-one else
has done so and if it doesn't fall out of the information-theory analysis
of the control loop.

If I could hazard a guess, the imagination loop is going to figure quite
strongly in the solution.

Martin

[Marken_Richard_S1]

[From Rick Marken (930316.1400)]

Martin Taylor (930316 15:30)--

I give up.

Aw. Common. We're workin' on it.

Every attempt at explanation is gobbledygook or
plain wrong.

Well, every time I say something you don't understand it's a
non-sequiter -- but I keep tryin'.

It's obvious that there is NO explanation that will suffice,
other than simple capitulation.

That is not true (for me). I just want an explanation of where
the information is in p(t). If there is no way to get at that
information or if it is unusable then I want to know why you
think it is so important. I just want to know what you (and Allan)
are trying to say. Believe me, your claim that there is information
about the disturbance in p(t) sounds just as crazy to me as my claim
(and Bill's) that there is NO such information in p(t) appears to
sound to you.

So, for the purposes of clearing the
CSG airwaves, I capitulate,

That avoids it; it doesn't clear it.

and will continue this information-theory
discussion with Bill Powers separately. At least Bill and I can see
common ground, even if we don't yet have a common understanding.

I look forward to that discussion; but I warn you; Bill P. may
seem seem a lot nicer than me, but he understands PCT just as well
as I do (he he). So you will still be stuck with the problem of
explaining why you think there is information about anything (let
alone the disturbance) in p(t).

With Rick, as soon as there appears to be the possibility of common
ground, the rug gets whipped away to reveal a chasm. I don't like
that style of argument. T'is so, t'aint so. Stupid.

It's not a style of argument; it's an approach to knowledge. I'm
all for common ground when that ground is, indeed, common. But
I can't agree with something that just flat out contradicts a basic
tenet of the PCT model. If what I hear from you just seems wrong
because of our disparate ways of using language then let's try to
work that out -- and the only way I know of to get past language is
to agree on what experiences we expect our models to produce in
agreed on circumstances. I've described my attempt at a demo of
lack of information in p(t). You have never said what is
wrong with that demo (described in chapter 3 of Mind Readings)
or what the appropriate demo would be to show that there is
information in p(t).

For an example, one final quote from Rick:

What does the lack of precision that comes from having a loop gain
of 1,000,000 instead of infinity have to do with INFORMATION.

Everything.

I'm willing to believe this, really. It's just not obvious at all
to me. I am really trying to understand you. Could you please get
quantitative; what is the information in p(t) that exists when the
loop gain is less than infinity but is gone when it is infinity.
Since most real control systems have loop gains that are considerably
less than infinity it should be easy to explain how I could set
up a control demo that would convince me that there is information
in p(t); show me how to do it.

Best

Rick

[Human_Factors_Lab]

[From Rick Marken (930403.1000)]

Kent McClelland. How nice to hear from you -- and on a nice new
topic too. Stay tuned. I will have a comment on your sociology
post later this (one hour short) weekend; promise.

First, I would like to propose MY solution to the "information
about the disturbance in perception" debate. Perhaps I can
make both sides happy with this proposal:

1) There IS information in the perceptual signal of an ECS! (Happy
IT people?). It is information in the IT sense, in that it reduces
the receiver's uncertainty about the message being sent. All the
theoretical paraphenalia of IT is, thus, relevant to PCT.

2) The information in the perceptual signal is about the REFERENCE
SIGNAL, NOT THE DISTURBANCE. The state of a controlled perception,p,
in a hierarchy of control systems is information that can be used by
other control systems in the hierarchy to determine the value of the ref-
erence signal being sent to the system controlling p. MOST IMPORTANT:
the state of the perceptual signal is information that can be used by
an OBSERVER of the control system (an observer who has access to p or
to an observable correlate thereof) to determine the value of the control
system's reference setting for p.

This solution opens up the possibility of an IT approach to doing
The Test for the controlled variable. In The Test, an observer
(the experimenter) wants information about 1) what p corresponds
to in the observer's own perception and 2) what the reference level
is for p. We can only get information about r (goal 2) if we have
properly defined the perception, p. IT might be able to contribute
to our ability to quantify The Test -- ie. measure how much infor-
mation we are getting about r from our current hypothesis about
the observable corelate of p.

How's this?

Best

Rick