Disturbances, Chasing Ricky

CSGnet Archive CSG1997
1

[From Rick Marken (970422.1330 PDT)]

Something Hans Blom (970422) said made me think it might be worth it to
talk a little about the PCT notion of a "disturbance". Hans said:

when a perception is contaminated by a disturbance

which suggests that disturbances are an intermittant nuisance, like
radio frequency interference. This is _not_ what a disturbance is in PCT.

In PCT, a disturbance is simply an environmental variable that has
an independent influence on a controlled variable (or variables). A
disturbance variable doesn't "contaminate" or "interfere with" perception.
A disturbance _contributes_ to the variation in the controlled perception
_along the dimension(s) of variation of that perception_. A disturbance
doesn't _contaminate_ a perception; it influences where the perception sits
on its perceptual dimension. A disturbance doesn't come and go; it's always
there. It just _varies_ (or, like gravity, it has a constant value over
long periods of time).

Consider one of my favorite examples (wolf that I am;-)): controlling the
retinal location of the image of an attractive passer-by. The controlled
variable is the location of the image of the passer-by on the retina. One
disturbance to this variable is movement of the passer-by relative to the
retina. This disturbance influences the value of the controlled variable in
terms of the position of the image on the eye; but it doesn't obscure this
variable, or contaminate it. It just influences it.

If movements of the passer-by (the disturbance) move the image away from the
observer's reference for that position (on the fovea, say) then, I suppose,
the influence of the disturbance is "disturbing". But the term "disturbance"
just refers to a variable, independent of the control system, that has an
influence on a controlled variable. Movements of the passer- by are
independent of the observer and they influence a variable controlled by the
observer so these movements are a disturbance.

Variable aspects of the control system's behavior also have an influence on
a controlled variable. These variables are called output variables. The
output variables that influence the position of the image of the passer-by
on the eye are head and eye movements.

Note that the output variable and the disturbance variable influence the
state of the controlled variable _at the same time_! The position of the
passer-by on the retina depends on movement of the passer-by (even when that
movement is 0) and on movement of the eye and head (even when that movement
is 0). So the position of the image of the passer-by on the eye (qi) depends
at _all times_ on the value of the output variable, o, and the value of the
disturbance variable, d. The complete equation is qi = f(o) + g(d) where
f is the trigonometric function that relates the angles of eye and head to
position on the retina and g is the trigonometric function that relates
the position of the passer-by to position on the retina.

Disturbances are simply variable aspects of the environment that are
_independent_ of the control system. The mass of a book is a disturbance to
the perception of the rate of fall of the book; if you want that perception
to be 0 you have to add exactly the right force to compensate for the force
(mass*gravity) acting on the book; the thickness of the handle of a hammer is
a disturbance to the perception of how tightly you are gripping it; if you
want to grip the hammer tightly you have to shape your hand properly around
the handle.

I think it's important to understand that disturbances are not occasional
nuisances; they are the environmental context in which we control.

Martin Taylor (970422 13:30) --

His [Rick's] (wrong) point is that when there is a summation,
information about the sum conveys no information about the
components of the sum. What's that got to do with the irrelevant
qd? Why is it relevant that qd = Fd(qd) if Fd() is the unity
transform? You have a numerical equality, not a conceptual
equivalence.

He's insisted upon his point three times at least in the last
couple of days. It's a good friend who tries so hard to get him
off the hook, but it would be a better friend who tried equally
hard to get him to see the problem.

I think it's time for your pill now, Martin :slight_smile:

Best

Rick

2

[Hans Blom, 970424e]

(Rick Marken (970422.1330 PDT))

Something Hans Blom (970422) said made me think it might be worth it
to talk a little about the PCT notion of a "disturbance". Hans said:

when a perception is contaminated by a disturbance

which suggests that disturbances are an intermittant nuisance, like
radio frequency interference. This is _not_ what a disturbance is in
PCT.

And then Rick goes on to chase an imaginary rabbit...

Rick, did you understand my formulas? They are far more exact than my
words. Don't take my word for it, investigate my algebra ;-). Already
I have the tendency to put many of my words in scare quotes. I should
have done that in this case as well, maybe. In the future, consider
_all_ my words to have square quotes! That might prevent you from
taking me too literally. Whether the disturbance is intermittent or
not is spurious. In the theodolite controller, for instance, there is
_always_ a d although d's _value_ may be zero for extended periods.
That -- and my algebra -- is fully in line with your

In PCT, a disturbance is simply an environmental variable that has
an independent influence on a controlled variable (or variables).

Greetings,

Hans

3

[Martin Taylor 970424 09:40]

Rick Marken (970422.1330 PDT)]

Something Hans Blom (970422) said made me think it might be worth it to
talk a little about the PCT notion of a "disturbance". Hans said:

>when a perception is contaminated by a disturbance

which suggests that disturbances are an intermittant nuisance, like
radio frequency interference. This is _not_ what a disturbance is in PCT.

In PCT, a disturbance is simply an environmental variable that has
an independent influence on a controlled variable (or variables). A
disturbance variable doesn't "contaminate" or "interfere with" perception.
A disturbance _contributes_ to the variation in the controlled perception
_along the dimension(s) of variation of that perception_. A disturbance
doesn't _contaminate_ a perception; it influences where the perception sits
on its perceptual dimension. A disturbance doesn't come and go; it's always
there. It just _varies_ (or, like gravity, it has a constant value over
long periods of time).

An excellent description of what a disturbance does and is. At least _I_
think so. I can't guess what Bill P. thinks about it at the moment.

Rick is talking about the influence that one or more sources of disturbance
has on a complex controlled environmental variable (CCEV) defined by the
Perceptual Input Function (PIF) of an Elementary Control Unit (ECU). I,
too, have used the term "disturbance" for this influence, but I've been
told in no uncertain terms that the word is reserved to refer to the
source of the influence, not to the influence itself.

The influence, like the CCEV, is not accessible to an external experimenter,
because it depends on the CCEV, and that in turn depends on the PIF, which
is unknown to the experimenter. The experimenter can influence sources of
disturbing influence, such as lights, noises, and so forth, and it is
those _sources_ to which Bill P. gives the name "disturbance." It causes
him great distress to see the word used as I have sometimes used it, and
as Rick uses it here.

When we are talking about a CCEV, the disturbing influence is a numerical
value at any moment. It may vary over time, or it may stay constant. Either
way, there always exists a value. As Rick so clearly says:

A disturbance
doesn't _contaminate_ a perception; it influences where the perception sits
on its perceptual dimension. A disturbance doesn't come and go; it's always
there. It just _varies_ (or, like gravity, it has a constant value over
long periods of time).

However, the sources of disturbing influence may come and go. Lights may
be physically removed, loudspeakers taken away. The coming and going of
these sources in no way changes the fact that so long as the perception
is being controlled, the CCEV is affected both by the control system output
and by influences from outside the control system, even when those external
influences (disturbing influences) have a net effect of zero over some period.

In analyzing the control loop, it matters not a whit where the disturbing
influences come from. What matters is their net influence on the CCEV. And
that ties in with "the Test for the controlled variable." Before attempting
"the Test" an observer cannot do more than guess what variables another
person is controlling, and at what values the controlled variables are
being referenced. "The Test" uses _sources_ of disturbance perceptible
by the experimenter/observer, anticipating that variations in those sources
will induce variations in the true CEV. (The experimenter naturally has an
idea of what the CEV might be, but that idea is a function of the
experimenter's own perceptual functions, and not of the PIF of the subject).
The experimenter has to deduce the effect of the source variations on the
supposed controlled environmental variable. Bill P. says that it is because
the external observer/experimenter can see only the sources that the word
"disturbance" must be restricted to them, rather than to their influence
on the controlled environmental variable.

From the point of view of the control loop, the controlled perception is

a function of the values of sensory variables. These sensory variables
depend on the actual value of the complex environmental variable, and
not on how these values were caused. Simplified, they depend on the
external influence (the value of the disturbance signal) and on the
influence of the control loop output, and on how these two influences
actually jointly affect the complex environmental variable (for example,
the CCEV may be the position of a mass, and the influences may be forces
that accelerate the mass in a way determined by the physics of the situation).
There are only two influences, regardless of how many _sources_ of influence
there may be. In Bill P's usage, there may be may "disturbances". But there
can be only one value of the "disturbance signal." And even if the number
of sources goes to zero, yet the disturbance signal still has a value--zero.

Perhaps this elaboration of Rick's comment may not be necessary, but on the
other hand, it may help to reinforce his comment that it is improper to say:

when a perception is contaminated by a disturbance

as if the perception could fail to incorporate a disturbing influence.

Martin