World versus disturbance

CSGnet Archive CSG1996
1

[From Bruce Abbott (960713.1155 EST)]

Hans Blom, 960711 --

This is not Hans's most recent post on the subject, but I'd like to back up
and have another go at resolving some confusion. (The confusion may be mine
rather than Hans's, but I'd like to resolve it either way.) Let's go back
to this:

perception action
     > --------- |
     ---<---| world |--<----
            ---------
                >
                ---<--- disturbance

Thus the perception is made up of two (virtual, inseparable) parts:
the result of what the world, with its laws, makes of an action, and
the result of what (part of) the world makes of a "disturbance". This
is, as I understand it, your definition of what a disturbance is.
Right? It is that part of my perception that is not due to my action.
Formula:

   p = f (a) + d, where f can be any function, static or dynamic.

Now, if you mean that a disturbance can be constant, like gravity,
where is the "world"? Doesn't gravity belong to it? Since gravity is
constant, my actions can perfectly well compensate for it, isn't it?
To me, that is a confusion between f and d. Rick's confusion was
between p and d.

The confusion (in my mind, at least) seems to revolve around that rather
vague term "world." I would redraw the above diagram to make the various
parts of "the world" more explicit, as follows:

  perception error
      > > The System
---[f(i)]-----------------------[f(o)]----------------------
      > --------- | The World
input +--<---| X |--<--[f(e)]--+ output

···

---------
                 >
                 +--<---[[f(d)]----- disturbance

"X" is the physical variable whose effect on sensory inputs give rise to the
perception to be controlled. Function f(e) represents how the system's
actions are translated through physical laws into effects on X. Function
f(d) represents how the disturbance affects X, again via physical laws.

Note that "The World" in this diagram is everything below the dotted line.
All the factors that determine the current value of X are out there in the
world.

Now, technically, anything that tends to induce a change in X is a
disturbance to X. If X is the 3-dimensional position of a marble on a flat,
horizontal surface, and gravity is pulling straight down on the marble,
then gravity is clearly affecting the marble, but because of the
counter-force being applied by the rigid horizontal surface, gravity has no
tendency to produce a change in X. Gravity in this example is not a
disturbance to X. But suddenly drop the surface out from under the marble
and watch what happens. The marble begins to accelerate downward. Or tilt
the surface downward toward the west -- the marble begins to roll downward
and to the west. To keep X constant under these conditions, the control
system would have to take some kind of action, action that would oppose the
change in X. Gravity is still constant, but because it now tends to induce
a change in X, this effect of gravity on X constitutes a disturbance to X.

But of course the control system knows nothing of X, or of d, or of the
effect of its own actions on X, for that matter. All the system "sees" is
its perception of X, i.e., p. If you introduce noise into p (variations in
p that are independent of X), the system will respond to these just as it
would to any real change in X that produced change in p. It will vary its
output in an attempt to counter those perceived variations, so long as the
variations are not faster than the system's ability to respond. If the
system's own actions are not properly scaled in speed and magnitude, they
may produce unwanted disturbances to X, which the system will then attempt
to correct through further action. All these effects on p are disturbances
to p, whether or not they affect p by altering X.

Hans, which of these effects would you label as "noise"? The perceptual
changes not linked to the state of X, certainly, but what else (if
anything)? Which of these things would you label as "disturbance"? Would
the constant pull of gravity against the (now unsupported) marble qualify,
even though the marble does not move owing to the counteracting output of
the system? What else would you describe as a disturbance in this system?

Regards,

Bruce

2

[Hans Blom, 960713b]

(Bruce Abbott (960713.1155 EST))

The confusion (in my mind, at least) seems to revolve around that rather
vague term "world." I would redraw the above diagram to make the various
parts of "the world" more explicit, as follows:

  perception error
      > > The System
---[f(i)]-----------------------[f(o)]----------------------
      > --------- | The World
input +--<---| X |--<--[f(e)]--+ output
             ---------
                 >
                 +--<---[[f(d)]----- disturbance

"X" is the physical variable whose effect on sensory inputs give rise to the
perception to be controlled. Function f(e) represents how the system's
actions are translated through physical laws into effects on X. Function
f(d) represents how the disturbance affects X, again via physical laws.

Note that "The World" in this diagram is everything below the dotted line.

Yes, this is exactly how I meant it.

Now, technically, anything that tends to induce a change in X is a
disturbance to X.

Bruce, I like this much better than calling everything we can oppose
a "disturbance" and everything else "noise".

But of course the control system knows nothing of X, or of d, or of the
effect of its own actions on X, for that matter. All the system "sees" is
its perception of X, i.e., p. If you introduce noise into p (variations in
p that are independent of X), the system will respond to these just as it
would to any real change in X that produced change in p.

And this is what I wanted to demonstrate is NOT true. If there is
only ONE observation, you are correct. If you have more -- many --
observations, it is not true anymore: you can tease the two apart,
because they have different effects. And, to our luck, we continu-
ously observe. So we CAN distinguish between both, theoretically.
Practically, too. That the speed of light is constant is generally
accepted. Yet, every measurement shows slightly different values. Now
what is it: are our measurements inaccurate or does the speed of
light fluctuate slightly? To our luck, we can know the difference. If
the speed of light fluctuated, the universe would be very different
from what we observe it to be.

Hans, which of these effects would you label as "noise"? The perceptual
changes not linked to the state of X, certainly, but what else (if
anything)? Which of these things would you label as "disturbance"? Would
the constant pull of gravity against the (now unsupported) marble qualify,
even though the marble does not move owing to the counteracting output of
the system? What else would you describe as a disturbance in this system?

I hope that my other post of a few minutes ago answered these
questions.

Greetings,

Hans

3

[Bill Leach (960713.2241 EDT)]

<[From Bruce Abbott (960713.1155 EST)]

But of course the control system knows nothing of X, or of d, or of the
effect of its own actions on X, for that matter. All the system "sees" is
its perception of X, i.e., p. ...

And a thorough understanding and appreciation of that paragraph of yours
would have saved many a control systems engineer days or week frustration!

Nice post Bruce.
-bill
b.leach@worldnet.att.org
ars: kb7lx

4

[From Rick Marken (960714.0900)]

Bruce Abbott (960713.1155 EST)]

But of course the control system knows nothing of X, or of d, or of the
effect of its own actions on X, for that matter. All the system "sees" is
its perception of X, i.e., p. ...

Bill Leach (960713.2241 EDT)--

And a thorough understanding and appreciation of that paragraph of yours
would have saved many a control systems engineer days or week frustration!

Nice post Bruce

I heartily concur!

Best

Rick

5

<[Bill Leach (960714;1145 EDT)

[Hans Blom, 960713b]

Bruce:

But of course the control system knows nothing of X, or of d, or of the
effect of its own actions on X, for that matter. All the system "sees" is
its perception of X, i.e., p. If you introduce noise into p (variations in
p that are independent of X), the system will respond to these just as it
would to any real change in X that produced change in p.

Hans:

And this is what I wanted to demonstrate is NOT true. If there is
only ONE observation, you are correct. If you have more -- many --
observations, it is not true anymore: you can tease the two apart, ...

Your concern with the "internal model" is much greater than that of (at
least most of) the others present here. We are not "far enough along" in
research and modeling (generative of course) to deal with modeling as a
practical matter.

I am going to say the same thing to you that has been said by Bill, Rich,
Tom and who knows how many others (Martin?):

Give a reproducible experiment that DEMONSTRATES a failure of the standard
control system model to control in the manner of a real living being AND a
suggestion for functional model based system that overcomes this difficiency.

You satellite and speed of light examples are fine examples but fine only
for "proving your point" and are otherwise irrelevant to the current work of PCT
(if you could DEMONSTRATE [NOT JUST DISCUSS OR SUGGEST] how models are
developed for such cognitive feats that could be another matter altogether).

I doubt very much that you are going to pay any more attention to me than
you have to others here with respect to this topic but basically if you
really do want people here to take your control systems engineering
expertise seriously with respect to PCT then you will have to consider the
following:

1. Your examples of standard model failure must be accepted as ligit by
    members of the CSG.

2. You must select an example that is TESTABLE with real living beings!

3. You must produce models that are reproducible, generative, and testable
    with living subjects as well as computer code.
    You don't necessarily have to do the testing yourself but "thought
    experiments" that have no means of verification are not valid material
    for challenging the "standard PCT" positions on behaviour.

I might remind you that Bruce Abbott's challenges of PCT principles received
considerable attention here and no little amount of serious effort and
consideration; but only because he was willing to direct his own efforts
toward the sort of reproducable and testable inquiry that is recognized as
valid scientific effort in this community.

Noise and disturbance

I hope that my other post of a few minutes ago answered these
questions.

I would answer your question with both a yes and a no.

Without an example that can demonstrate in a generative manner that our
research at the practical level is lacking, your position on noise and
disturbance can result only in confusion.

We are concerned here with the practical (practical in the sense that we
always want to create generative models) aspects of behaviour. There are
thousands of folks that "pontificate" upon the subject of behaviour with
varying degrees of credibility (mostly low).

Much of what you have suggested in the past concerning model based control
systems has been accepted as a plasible explaination for "macro-behaviour"
that is still beyond our ability to examine and test in detail.

You have often appeared to have been quite concerned because our models did
not "control as well" as your hypothetical models (and in some instances
were correct IF WE WERE CONCERNED ABOUT THE BEST POSSIBLE CONTROL as opposed
to what we ARE concerned with--modeling observed behaviour).

In our analysis of our model specifics we find it necessary to consider our
own perceptions of the environmental variable (I still like Martin's CEV
best). From our analysis standpoint, forces acting upon the CEV that produce
changes in the perception of the CEV by control system of interest other
than those forces generated by the control system of interest are
"disturbances to the CEV" or just "disturbances".

Should a force act upon the perceptual input function such that we observers
could see a control system malfunction (such as observing that the CEV is
controlled at a value different than the reference when we have strong
reason to believe that we do correctly know the reference value) then we
would likely look for a "disturbance to the perception". I am not sure that
necessarily any single person here would even accept my "disturbance to the
perception" term much less the community in general but in neither case
would such influences usually be termed noise (although the disturbance to
the perception might be so considered).

When we try to "split hairs" at some point virtually all of our term "fall
apart". Within PCT noise is considered to be a signal property that reduces
control quality. Disturbances are forces acting upon a CEV such as to
produce a chance in the system's perception of CEV DUE to actual changes in
properties of the CEV that the control system is attempting to control.

We have (as you well know) at times gone well beyond our typical control
system analysis to consider noise, response time/bandwidth, phase
relationships between parameters both within the system and the "world".
Such analysis is useful and necessary at times but for general use is like
trying to tell a child why an undicator light on the automobile dash board
came on starting with a discussion of nuclear strong forces.
-bill
b.leach@worldnet.att.org
ars: kb7lx

6

[From Bruce Abbott (960715.0925 EST)]

Hans Blom, 960713b --

Bruce Abbott (960713.1155 EST)

Hans, which of these effects would you label as "noise"? The perceptual
changes not linked to the state of X, certainly, but what else (if
anything)? Which of these things would you label as "disturbance"? Would
the constant pull of gravity against the (now unsupported) marble qualify,
even though the marble does not move owing to the counteracting output of
the system? What else would you describe as a disturbance in this system?

I hope that my other post of a few minutes ago answered these
questions.

I think so, but let me check to make sure. In your view, gravity would not
constitute a disturbance to the marble lying on the flat surface, but would
constitute a disturbance to the unsupported marble and to the marble lying
on the tilted surface. If so, then a "constant disturbance" (gravity) WOULD
qualify as a disturbance. Yet this seems to contradict your earlier
assertion in which you held that a variable could NOT act as a disturbance
if it were constant:

Hans Blom, 960711, to Bill P.

The disturbance in the above diagram makes sense to me only if it is
variable. I truly do not understand a lapse like this from both Rick
and you! And if I don't understand you now, I have never understood
you. Imagine that: talking past each other for, what is it, four, five
years?

Please explain.

Regards,

Bruce

7

[Hans Blom, 960715]

Bruce, I got your rat data and program. Thanks, I'll be back. I need
some time to ponder things.

Bill, I received your Artificial Cerebellum program. I'd like to have
the equations that it implements. I hate reverse engineering!

Have a great conference, all of you!

(Bill Leach (960714;1145 EDT))

Your concern with the "internal model" is much greater than that of (at
least most of) the others present here. We are not "far enough along" in
research and modeling (generative of course) to deal with modeling as a
practical matter.

Seems that way, but only superficially. That HPCT is hierarchical
means that each level "tunes" the level below it. But that tuning is
only partial: redefinition of reference levels. Redefinition of
parameter values would allow input and output functions to be retuned
as well. I am certain that (some) others will consider this useful --
and realistic.

Give a reproducible experiment that DEMONSTRATES a failure of the standard
control system model to control in the manner of a real living being AND a
suggestion for functional model based system that overcomes this difficiency.

You satellite and speed of light examples are fine examples but fine only
for "proving your point" and are otherwise irrelevant to the current work of PCT
(if you could DEMONSTRATE [NOT JUST DISCUSS OR SUGGEST] how models are
developed for such cognitive feats that could be another matter altogether).

Bill, what would satisfy you as a demonstration? Would the following
do?

An organism is twice presented with exactly the same perceptual field
from exactly the same position. Between the two presentations, there
is something like a "tracking experiment", just like in my satellite
example. On the second presentation, the organism "sees" more because
uncertainty has been removed, although it _sees_ exactly the same.
Would that do?

1. Your examples of standard model failure must be accepted as ligit by
    members of the CSG.

I don't say that the standard (whose standard?) model fails. It's a
good paradigm. I just want to improve on it.

2. You must select an example that is TESTABLE with real living beings!

We'll probably always have interpretation problems. When do you
accept the comparison between what happens in a model and what
happens in an organism as legitimate? See my question above. If I
would present such an example, would that demonstrate the correctness
of my model? If not, what would?

3. You must produce models that are reproducible, generative, and testable
    with living subjects as well as computer code.

Ever seen anything that is reproducible in a living being? Even in E.
coli or rats things don't reproduce. Generative is fine, but as soon
as "noise" or "disturbances" or uncertainties are introduced, we have
a problem. Then things can be at most comparable, never identical. It
is my impression that this is a basic problem that cannot be
resolved.

I get the impression that you largely accept my approach as useful
for engineered systems, but that you don't believe it helps to
explain the behavior of organisms. Is that correct?

Greetings,

Hans

8

[Hans Blom, 960715c]

(Bruce Abbott (960715.0925 EST))

I think so, but let me check to make sure. In your view, gravity would not
constitute a disturbance to the marble lying on the flat surface, but would
constitute a disturbance to the unsupported marble and to the marble lying
on the tilted surface. If so, then a "constant disturbance" (gravity) WOULD
qualify as a disturbance. Yet this seems to contradict your earlier
assertion in which you held that a variable could NOT act as a disturbance
if it were constant

What makes a marble move? Forces. So forces can start, stop or change
movement of a marble. Gravity cannot. Gravitational forces can. But
since gravity itself is constant, it cannot manipulate gravitational
forces; something or somebody else does.

Physics has this "action = - reaction" thing. If the action is
constant, the reaction is also constant, from minus eternity to plus
eternity. So I just cannot see something constant as the "cause" of
something that evolves over time.

>The disturbance in the above diagram makes sense to me only if it is
>variable. I truly do not understand a lapse like this from both Rick
>and you! And if I don't understand you now, I have never understood
>you. Imagine that: talking past each other for, what is it, four, five
>years?

See above. In particular, I've never seen anyone design a control
system to combat something constant. Something constant must be
opposed, if that is what is wanted, by something constant, something
hard, rigid. Not that it cannot be done: it is trivial to design a
control system that opposes something constant. But the control
system's action -- or rather reaction -- will also be constant. So
why a control system? Makes no sense to me.

Greetings,

Hans

9

[From Bruce Abbott (960716.0840 EST)]

Hans Blom, 960715c --

See above. In particular, I've never seen anyone design a control
system to combat something constant. Something constant must be
opposed, if that is what is wanted, by something constant, something
hard, rigid. Not that it cannot be done: it is trivial to design a
control system that opposes something constant. But the control
system's action -- or rather reaction -- will also be constant. So
why a control system? Makes no sense to me.

Sort of like designing an "antigravity machine" to hold your table top up --
it works but draws power. Then somebody says, hey, why don't you just put
legs on it and pull the plug?

But seriously, the question was not whether one would want to design a
control system to oppose something constant, but whether that constant
something should be considered a disturbance. If it requires a counterforce
to prevent this constant something from changing X (or more accurately, the
perception of X), I say it should. We may not wish to design systems to
actively oppose constant forces that far more easily could be opposed
passively, but (relatively) constant disturbances do arise all the time in
living systems and ARE actively opposed. Consider the simple problem of
maintaining an adequate fuel supply. The organism is essentially a leaky
bucket, in constant need of refilling if the organism is to survive. It
must take constant action to keep fuel coming in at the same rate it is
being burned and excreted. There is simply no way to generate something
"hard" or "rigid" that will passively oppose metabolic losses (although
some organisms can reduce the rate of leakage to a minimum when necessary).

Oh, by the way, the "antigravity" device I described exists. It consists of
a ferromagnetic disk suspended in mid-air by the attraction of an
electromagnet. A sensor detects the position of the disk and varies the
current to the electromagnet so as to keep the disk neither rising nor
falling. The system is of course an ordinary servomechanism.

Regards,

Bruce

10

[Hans Blom, 960717]

(Bruce Abbott (960716.0840 EST))

                               We may not wish to design systems to
actively oppose constant forces that far more easily could be opposed
passively, but (relatively) constant disturbances do arise all the time in
living systems and ARE actively opposed. Consider the simple problem of
maintaining an adequate fuel supply. The organism is essentially a leaky
bucket, in constant need of refilling if the organism is to survive. It
must take constant action to keep fuel coming in at the same rate it is
being burned and excreted. There is simply no way to generate something
"hard" or "rigid" that will passively oppose metabolic losses (although
some organisms can reduce the rate of leakage to a minimum when necessary).

Then the organism of which you speak is a unicellular one, I presume.
In these, there is a leakage in, but also a leakage out. Much of that
is passive, without control, through diffusion, just like in the
cells of our body. Higher organisms are NOT in _constant_ need of
refilling -- although their cells are -- because they have "designed"
buffering mechanisms, not only for food (intestines), but also for
oxygen (hemoglobin), carbon dioxide, energy (ATP), etc. These are all
"hard, rigid" non-control mechanisms, although they are USED IN
higher level control loops. Higher organisms have freed themselves
from the need to "take constant action to keep fuel coming in at the
same rate it is being burned and excreted". I do not eat and drink all
of the time, and I'm sure you don't either...

Oh, by the way, the "antigravity" device I described exists. It consists of
a ferromagnetic disk suspended in mid-air by the attraction of an
electromagnet. A sensor detects the position of the disk and varies the
current to the electromagnet so as to keep the disk neither rising nor
falling. The system is of course an ordinary servomechanism.

I have no time and desire to analyze this example. But you are fully
aware that it is NOT an "antigravity" device, I hope. Its workings
depend on the ferromagnetism of the disk. The device opposes a
gravitational force (not gravity) with an electromagnetic force. That
can be done, because both are forces. Instead of an electromagnetic
field, one could also float it on a jet of gas or liquid. If you were
to design a device that opposed the gravitational force with another
gravitational force, you would need to manipulate the position of
another eartlike planet just above the disk. Kind of hard to do.

In physics, there is this principle that the units must be right. You
cannot oppose gravity with length or velocity. Although our nervous
system regularly compares apples and oranges, physics does not. A
force can only be resisted by a force. Gravity can only be changed by
gravity. In a control system, something constant would need to be
opposed by something constant. Confusing gravity with forces due to
gravity is, well, confusing...

Yet, popular literature does it all the time. Standing upright, I
read a while back, is a "continuous battle with gravity". Sounds
nice, and we immediately know what is meant. But as an explanation, in
the sense of what physics requires for an explanation, it's of course
incorrect. Physics would talk about a dynamic equilibrium between
muscular forces and gravitational forces.

By the way, note the contrast between "battle" and "equilibrium".

Greetings,

Hans

11

Hans Blom wrote:

[Hans Blom, 960717]

(Bruce Abbott (960716.0840 EST))

> [SNIP]
Yet, popular literature does it all the time. Standing upright, I
read a while back, is a "continuous battle with gravity". Sounds
nice, and we immediately know what is meant. But as an explanation, in
the sense of what physics requires for an explanation, it's of course
incorrect. Physics would talk about a dynamic equilibrium between
muscular forces and gravitational forces.
[SNIP]

A teacher of the Alexander Technique would have a lot to contribute to
this discussion. The AT is entirely concerned with gaining conscious
control over the proprioceptive(sp?) reflexes so as to perfect the
individual's use of the minimum necessary muscle tone in standing,
sitting, walking, and all other activities that we undertake in our
'continuous battle with gravity'. The theory is that we use all sorts
of inappropriate/ineffective muscle tension in our daily lives because
we are constantly reacting to the epiphenomena of our stream of
consciousness. (This is my own re-formulation of F. M. Alexander's
ideas.)

AT teachers don't use control theory terminology but they could swap it
into their own idiosyncratic terminology without missing a beat.

···

--
--------------------------------------
Kevin C. Cole
6222 Kincaid Road
Cincinnati, OH 45213
(513) 731-0868
kccole@one.net

Managing Editor, NASTAT News
President, Cole Consulting
R&D Manager, Comware Incorporated
--------------------------------------

12

<{Bill Leach (960718.1331)]

[Hans Blom, 960717]

Then the organism of which you speak is a unicellular one, I presume. ...
... Higher organisms have freed themselves from the need to "take constant
action to keep fuel coming in at the same rate it is being burned and
excreted". I do not eat and drink all of the time, and I'm sure you ...

I would suggest that you are "playing with words here". Bruce's point was
that there are constant forces that must be resisted by living control systems.

bill leach
b.leach@worldnet.att.net
ars KB7LX