[From Bill Powers (2012.07.24.1127 MDT)]
Martin Taylor 2012.07.24.00.44
From [Richard Pfau (2012.07.23
1500 EDT)]
The statement that “in PCT, a disturbance is an independent
variable that has some effect on a controlled variable” [Bill
Powers (2012.07.07.0901 M<DTY)] seems to imply that independent
variables that result in perceptual signals not related to perceptions of
controlled variables are not disturbances. That is,
not all environmental events are disturbances.
True.
A productive discussion here. The basic problem here is ambiguity that
doesn’t bother people in ordinary informal discourse, but which
causes all sorts of problems in scientific descriptions.
I’ve discussed this before in terms of disturbance applying both to
causes and to the effects of those causes. A crosswind, it is said, is a
disturbance affecting a car’s path on the road, calling for opposing
actions to keep the car in its lane. But we also speak of a deviation of
a car from its path as a disturbance that needs to be countered. Clearly,
the physical wind itself is not being sensed or controlled directly; it
is the path of the car that the driver is controlling. More
precisely, the driver is controlling the visual appearance of the car in
relation to the road as seen through the windshield, and it is an
unwanted change in that appearance that is considered a disturbance, an
unexpected, undesired deviation of the controlled variable from its
reference level.
These are clearly two different meanings of the term disturbance. The
crosswind is a measurable variable, and by measuring its velocity and
direction we can use physical formulas to calculate the amount of effect
it will have on the path of a car moving at a particular speed. But the
same word also applies to a perception of the path of the car: an
unexpected and unwanted change in the perceived path is a disturbance,
too.
When we use models we are not constrained to speak only of variables that
a person can perceive. We can speak of the crosswind as if we can see or
otherwise sense it out there, in the world. But that is when we are using
a model based on physics, in which we are allowed to imagine what we have
no way to experience. When driving, we don’t really experience the
crosswind itself, the moving air outside the car. We imagine it.
In fact, when you pause to reflect on this for a while, you have to
realized that while we have many kinds of perceptions, some controlled
and some not at any given time, we never experience what is causing those
perceptions. We experience only the effects of external variables on
internal perceptual signals. While we can imagine variables in the outer
world which are causing the perceptual signals (whether changing or
not), we do not perceive the causal variables as they are outside
us.
In the canonical PCT diagram, there is a disturbing variable depicted
just outside the input-output boundary of the control system. An arrow
shows the path from that disturbing variable to another variable called
the input quantity, from which the control system extracts a perception
of a controlled variable. Clearly, the disturbing variable is not
perceived by the control system in question.
There is another variable affecting the same input quantity, which is
also unperceived by this control system: the output quantity which is a
measure of the action of the control system. The net effect on the
controlled quantity, the state of this quantity, is the sum of the
effects of these two variables, Qo and D.
Since the perception under control is a representation of the controlled
quantity, it can behave quite differently from the way the action of
either the control system or the disturbing variable changes. In fact, if
control is reasonably good, the effect of the disturbing variable on the
controlled variable is nearly cancelled by concurrent changes in the
action of the system, the output quantity. So the disturbance does not
necessarily cause any significant disturbance.
There we have the two meanings of disturbance in the same sentence. One
refers to a cause, the other to an (absent) effect. The only
“disturbance” that can actually be sensed by this control
system is the change in the controlled quantity that results from the
difference between effects of Qo and D. That is obviously not at all the
same as the magnitude of the disturbing variable. So when we say we
“perceive a disturbance,” do we mean we are perceiving the net
change in the controlled variable, or a change in the disturbing
variable? A need to ask that question is best avoided.
I think, therefore, that we can say that disturbing variables are never
perceived by the system controlling the input variable being affected by
the disturbances. In PCT-speak, this means NEVER.
We are left, then, with other physical variables that do not affect
controlled quantities, but do affect inputs to the organism that are not
themselves controlled. The perceptual effects of those other variables do
not result in any correlated behaviors, because all behaviors, according
to PCT, exists only as part of a feedback loops involving controlled
variables.
If we want complete clarity and uniqueness, we should not call those
other variables disturbances, although informally we can say that they,
too, disturb input variables. In the context of discussing control,
disturbances are only the variables outside the input-output boundary
that affect controlled variables and result in opposing actions. Other
variables are just physical variables, and their effects on perceptions
on other physical quantities are just effects.
I don’t know if that clarifies or confuses, but it’s the best I can come
up with now.
Best,
Bill P.