[From Bruce Abbott (2018.04.25.0955 EST)]
[Eetu Pikkarainen 2018-04-25_09:07:20 UTC]
This is interesting discussion. First the concept of disturbance has all the time annoyed me because it can mean two different things:
It is (at least from an ordinary or layman point of view) an effect which pushes the control system out of balance changing the perception so that it will go out from reference. So in the beginning there is something which causes a perception and if that perception is near enough to the reference value no output is needed. And then appears a disturbance which changes things and causes the error and requires output. So what is that something which caused the original – in the reference zone staying – perception?
(My idea at the moment is that the disturbance could be divided in two according to the classical actant model of Greimas: helper and opponent.)
Borrowing from sensory physiology,  one wants to distinguish is between the “distalâ€? and “proximalâ€? disturbance. The distal disturbance is the source, e.g., the wind. The distal disturbance acts on qi, its effect on qi (e.g., the push of the wind against your car) being determined by the laws of physics (the function relating cause to effect). This effect (the push on the car that affects qi) is the proximal disturbance.Â
To my knowledge, the terms “distal� and “proximal� have not been used in PCT to make this distinction; usually one understands what the term “disturbance� refers to from the context.  Our system diagrams often leave out the environmental function that mediates between cause and effect, leaving only an arrow labeled “disturbance� that inputs to qi (along with the output of the environmental feedback function).
Secondly about that original quotation. Let’s have again the previous situation where I have a perception which is in reference zone and that requires no output. Say, there is an object in the table in the place where I think it should be. Then appears a disturbance, say a strong wind (or electric magnetism or the table starts to lean) which starts to move the object to a wrong place. That requires my output and I start to push the object back. If I push hard enough I will get the object back to its original place, but because the disturbance continues I cannot stop my pushing. I can keep the error in zero only by continuing the output. So it seems that Bill’s saying cannot hold generally, as Martin already said. And when I read Bruce A’s comment more carefully it fits here too: but if I get the object exactly to its original place will there then remain that “small error�? Perhaps it is just that I am not a “canonical proportional control system�? I think I have asked this before but do there physically exist those?
The �small error� remains only if the control system is a proportional one, so that the output must be proportional to the magnitude of the error. So if there is a disturbance acting on qi, the system can oppose that disturbance only by failing to entirely eliminate the error.
However, an “integral� control system can produce an output in the absence of error. In the integral system, the error at any given moment is the integral (sum) of all previous error levels. If the perception is below the reference, a positive error will appear that drives the perception toward the reference. This error will summate over time, but the rate of increase will be slowing as the perception approaches the reference value. When the two are equal, there will be zero difference but the cumulated error will still be large, so the output will continue and the perception will rise above the reference value. Now the sign of the difference has reversed, so the current difference will subtract from the current integral error. Eventually the integral error will become zero and the system will stabilize at the reference value.
This is true even if there is a constant disturbance acting on qi. The integral error will be zero when the rate of change in qi caused by the disturbance is equaled by the rate of change in qi caused by the output. So with integral error at zero (perception matching reference), the output can be non-zero.
Bruce
Eetu
- Please, regard my statements as questions –
no matter how they are fomulated.
···
From: Bruce Abbott bbabbott@frontier.com
Sent: 24. huhtikuuta 2018 19:47
To: csgnet@lists.illinois.edu
Subject: RE: significance of zero
[From Bruce Abbott (2018.04.24.1245 EDT)]
[Bruce Nevin 2018-04-24_09:22:44]
Martin Taylor 2018.04.23.14.23–
Bruce Abbott (2018.04.24.0840 EDT)–
I agree with both of you, of course, but I understood disturbances to contribute to input.
They do. Disturbances cause the input to change, thus the perception. Some ambiguity may arise in that the term “disturbance� sometimes has referred to the causal agent itself and sometimes to the effect of that agent on the input, but either way, it is the input that the disturbance affects.
The disturbance may push the perception away from its reference value; the error thus generated produces an output of opposite sign that tends to push the perception toward the reference value. But the disturbance also may push the perception toward the reference value, reducing the error, in consequence of which the disturbance-opposing output is reduced.
Bruce
/B
On Tue, Apr 24, 2018 at 8:42 AM, Bruce Abbott bbabbott@frontier.com wrote:
[From Bruce Abbott (2018.04.24.0840 EDT)]
Martin Taylor 2018.04.23.14.23]
[Bruce Nevin 2018-04-23_12:52:05 ET]
A propos of nothing, this might be useful to recall:
the formal definition of a reference level: that level of input at which the output just becomes zero.
(Bill Powers (941024.0945 MDT) = Bill to Phil Runkel, Dialogue p. 495)
Well, Bill may have said it, but according to the rest of his theory, he mis-spoke. He knew that for a perception to equal its reference level, the output quantity must be equal and opposite to the disturbing quantity, and that usually is not zero. Perhaps what he intended was “at which the output does not change unless the disturbance changes”. This doesn’t affect the rest of the material you quoted.
Bill was correct to say that the reference level is� that level of input at which the output just becomes zero,� assuming that he was talking about the canonical proportional control system. When perception equals reference, error is zero and, therefore, output is zero. However, this state of affairs will occur in the steady state only when the disturbance is zero. When the disturbance is not zero, the system will develop a counteracting non-zero output, but to do so it must maintain some small error, the size of that error being inversely related to the system’s loop gain.
Even when a disturbance is present, the error, and thus the output, will become zero whenever the perception equals the reference level, as may happen transiently as the disturbance varies over time.
Bruce
Martin
The reference level, like the output and disturbance, is an empirical observation in the environment that the organism and the investigator have in common.
The corresponding reference signal, like the perceptual signal and the error signal, is imaginary in that peculiar sense that we call theory.
Most physical scientists, of course (with recent exceptions), think they are “discovering reality.” Let them. Whatever they think they’re doing, they’re making models in their imaginations. But they’re doing it in a disciplined way that demands perfection. They would say that nature is governed by exact and immutable laws, so they’re simply trying to improve their analyses to make them into closer and closer approximations to the actual exact laws. It’s nature that is perfect, as it can be only and exactly what it is. The effect is the same: the models are worked over and reworked and tested with ever-increasing finesse, any discrepancy between the model’s behavior and what is observed being reason enough to work on the model some more.
In the behavioral sciences, the long centuries of failure have resulted in a different view of natural laws: organisms are inherently variable and inexact. What’s the point in demanding perfection of models (or any method) when nature itself is largely random? The result of this view has been a drastic lowering of scientific standards.
(Bill to Phil 8/9/89, in Dialogue concerning the two chief approaches to a science of life p. 450)
According to PCT vocabulary it is also disturbance, and it sounds strange even though I have tried to customize to it. J
