Clarifying Cause and Effect in a Closed Loop

CSGnet Archive CSG2016
1

[From Fred Nickols (2016.06.26.0825 ET)]

I’d like to use the diagram shown below to clarify my understanding of cause-and-effect in a closed loop.

image00348.jpg

Let’s start with the comparison function. If there is a mismatch between the reference signal and the perceptual signal, an error exists. This error “causes” output.

The output, by way of the feedback function, affects some kind of change in the input quantity. Output “causes” change in the input quantity.

Changes in the input quantity are reflected in changes in the perceptual signal; in other words, they “cause” changes in the perceptual signal.

Changes in the perceptual signal “cause” changes in the difference or discrepancy between the perceptual signal and the reference signal.

Changes in the reference signal “cause” changes in the result of comparing it with the perceptual signal, reducing or increasing error, causing output, etc., etc., etc.

And disturbances also “cause” changes in the input quantity, thus further “causing” changes in the perceptual signal, the comparison result, the error signal, etc., etc., etc.

All this is happening lightning fast in most cases. Nevertheless, there is some kind of lag time involved and thus, at any given point in time, one thing can be looked at as the cause of the next one in the loop.

So, depending on how you look at it, any item in the loop can be looked at as cause or as effect.

Do I have it right?

Regards,

Fred Nickols, CPT

Writer & Consultant

DISTANCE CONSULTING LLC

“Assistance at a Distance”SM

www.nickols.us/SeaStories.html

PCT Formal Model - Simplified.SDR (57.6 KB)

2

[From Fred Nickols (2016.06.26.0825 ET)]

      I’d like to use the diagram shown below to

clarify my understanding of cause-and-effect in a closed loop.

image00348.jpg

      Let’s start with the comparison function.

If there is a mismatch between the reference signal and the
perceptual signal, an error exists. This error “causes”
output.

      The output, by way of the feedback

function, affects some kind of change in the input quantity.
Output “causes” change in the input quantity.

      Changes in the input quantity are reflected

in changes in the perceptual signal; in other words, they
“cause” changes in the perceptual signal.

      Changes in the perceptual signal “cause”

changes in the difference or discrepancy between the
perceptual signal and the reference signal.

      Changes in the reference signal “cause”

changes in the result of comparing it with the perceptual
signal, reducing or increasing error, causing output, etc.,
etc., etc.

      And disturbances also “cause” changes in

the input quantity, thus further “causing” changes in the
perceptual signal, the comparison result, the error signal,
etc., etc., etc.

      All this is happening lightning fast in

most cases. Nevertheless, there is some kind of lag time
involved and thus, at any given point in time, one thing can
be looked at as the cause of the next one in the loop.

      So, depending on how you look at it, any

item in the loop can be looked at as cause or as effect.

Do I have it right?

3

[From Richard Kennaway (2016.06.26.1455 BST]

(Simulposted with Martin Taylor, but this is saying basically the same.)

Fred Nickols (2016.06.26.0825 ET) writes:

All this is happening lightning fast in most cases. Nevertheless, there is some kind of lag time involved and thus, at any given point in time, one thing can be looked at as the cause of the next one in the loop.

So, depending on how you look at it, any item in the loop can be looked at as cause or as effect.

The causal links are as you describe then, and there is a lag time around the loop, but the loop cannot be understood in terms of “first this causal thing happens, then this happens, then this happens”, all the way round. Everything is happening simultaneously
and continuously all the time. A new value of the error signal, for example, is not held until its effects have propagated all the way round, whereupon a new value is computed. To take an example from your own field, a manager does not get to see the ultimate
results of his decisions before he must make more decisions.

When you look at the causal loop on a time scale substantially smaller than the time around the loop (itself a rather fuzzy concept: an integral lag is not the same thing as a transport lag), then if you observe a sudden disturbance, or intervene to create
one, you can see its effects propagate around the loop. But on the timescale on which the loop succeeds in controlling, everything is causing and being caused by everything all the time.

Some of the actual causal links will be invisible to observation and experiment that does not look inside the control system. An experimenter intervenes to vary the disturbance, and sees the perception remain constant while the output action varies. This
may give them the false idea that there is a direct path from disturbance to output, and that the perception is not causally linked to either. In fact, the only path from disturbance to output proceeds via the perception, which superficially appears to have
nothing to do with it.

If one knows nothing of the mechanism, measurements will only reveal causal connections to the extent that the controller is failing to control.

– Richard

···

–

Richard Kennaway, R.Kennaway@uea.ac.uk, Richard Kennaway

School of Computing Sciences,

University of East Anglia, Norwich NR4 7TJ, U.K.

4

[From Fred Nickols (2016.06.26.1052 ET)]

Thanks, Martin. I think I get “simultaneous.” The loop is closed, therefore, all aspects/parts/components (whatever) are always active, always “on” so to speak. Thus, as you say, everything is simultaneously cause and effect. My point was that whether something is a cause or an effect can only be determined in relation to something else. I don’t think what we’re saying conflicts.

Fred Nickols

image00348.jpg

···

From: Martin Taylor [mailto:mmt-csg@mmtaylor.net]
Sent: Sunday, June 26, 2016 9:54 AM
To: csgnet@lists.illinois.edu
Subject: Re: Clarifying Cause and Effect in a Closed Loop

[Martin Taylor 2016.06.26.09.29]

[From Fred Nickols (2016.06.26.0825 ET)]

I’d like to use the diagram shown below to clarify my understanding of cause-and-effect in a closed loop.

cid:image001.jpg@01D1CF84.2B5839D0

Let’s start with the comparison function. If there is a mismatch between the reference signal and the perceptual signal, an error exists. This error “causes” output.

The output, by way of the feedback function, affects some kind of change in the input quantity. Output “causes” change in the input quantity.

Changes in the input quantity are reflected in changes in the perceptual signal; in other words, they “cause” changes in the perceptual signal.

Changes in the perceptual signal “cause” changes in the difference or discrepancy between the perceptual signal and the reference signal.

Changes in the reference signal “cause” changes in the result of comparing it with the perceptual signal, reducing or increasing error, causing output, etc., etc., etc.

And disturbances also “cause” changes in the input quantity, thus further “causing” changes in the perceptual signal, the comparison result, the error signal, etc., etc., etc.

All this is happening lightning fast in most cases. Nevertheless, there is some kind of lag time involved and thus, at any given point in time, one thing can be looked at as the cause of the next one in the loop.

So, depending on how you look at it, any item in the loop can be looked at as cause or as effect.

Do I have it right?

Nobody can say absolutely that you have it right, but what you say mostly agrees with what I think is right, apart from “All this is happening lightning fast in most cases.” That’s true only at the lowest levels, if there. In most cases it takes time for the effects through the environmental feedback path to start affecting the perception, and more time until those effects cease affecting the perception. Think of a pendulum, which, when pushed away from hanging straight down, continues to swing for a long time. Think of your own field, and a manager deciding to hire a secretary. The first effects return when someone else reports back that the hiring process has been initiated, the perception that a secretary is working in the post doesn’t change for days or weeks, and the effects may last a lifetime if the manager falls in love with the new secretary, and they live together ever after. Granted, most of these effects are side-effects, but perhaps they make the point. In political news, the term “ripple effect” often appears, for the same reason.

A more important comment is that even though everything may be correct, it would also be correct of the TOTE (Test Operate Test Exit) system, in which things happen sequentially around the loop. The difficult point to get across is the important one Rick frequently and correctly pushes. In your words “any item in the loop can be looked at as cause or as effect”, which I would reword as “every item in the loop is simultaneously cause and effect all the time.”

People new to PCT often fail to see that although everything in the loop is causing and being affected simultaneously all around the loop, every cause is only of future values of the next item around the loop and every effect is only from past values of the previous item around the loop. Strict causality is always maintained in the way your individual line items say.

Martin

5

[From Dag Forssell (2016.06.26.0845 PDT)]

[From Fred Nickols (2016.06.26.0825 ET)]

FN: I'd like to use the diagram shown below to clarify my understanding of cause-and-effect in a closed loop.

DF: One more nitpick. You may want to include a Disturbance Function to signify that the (one or more) Disturbance an observer can discern, D, is similar in kind to the Output function, O.

Compare "Once around the Loop" in the Book of Readings.

Best, Dag

6

[From Fred Nickols (2016.06.26.1258 ET)]

I'm not sure what you're getting at, Dag. I included a comment about the
effects of a disturbance on the input quantity, just as can the Output. Did
you have something else in mind?

Fred Nickols

···

-----Original Message-----
From: Dag Forssell [mailto:csgarchive@pctresources.com]
Sent: Sunday, June 26, 2016 11:48 AM
To: csgnet@lists.illinois.edu
Subject: Re: Clarifying Cause and Effect in a Closed Loop

[From Dag Forssell (2016.06.26.0845 PDT)]

[From Fred Nickols (2016.06.26.0825 ET)]

FN: I'd like to use the diagram shown below to clarify my understanding of
cause-and-effect in a closed loop.

DF: One more nitpick. You may want to include a Disturbance Function to
signify that the (one or more) Disturbance an observer can discern, D, is
similar in kind to the Output function, O.

Compare "Once around the Loop" in the Book of Readings.

Best, Dag

7

[From Fred Nickols
(2016.06.26.1258 ET)]

I’m not sure what you’re getting at, Dag. I included a comment
about the

effects of a disturbance on the input quantity, just as can the
Output. Did

you have something else in mind?

Fred Nickols

From: Dag Forssell
[
mailto:csgarchive@pctresources.com]

Sent: Sunday, June 26, 2016 11:48 AM

To: csgnet@lists.illinois.edu

Subject: Re: Clarifying Cause and Effect in a Closed Loop

[From Dag Forssell (2016.06.26.0845 PDT)]

[From Fred Nickols (2016.06.26.0825 ET)]

FN: I’d like to use the diagram shown below to clarify my
understanding of

cause-and-effect in a closed loop.

DF: One more nitpick. You may want to include a Disturbance Function
to

signify that the (one or more) Disturbance an observer can discern,
D, is

similar in kind to the Output function, O.

Compare “Once around the Loop” in the Book of
Readings.

Best, Dag
[From Dag Forssell (2016.06.26.1045 PDT)]

Fred, Your descriptions run in parallell, but the graphic does not.

You include a grey box labeled FEEDBACK FUNCTION between OUTPUT QUANTITY
and INPUT QUANTITY. I am suggesting you consider showing an
equivalent DISTURBANCE FUNCTION between DISTURBANCE and INPUT QUANTITY.
You may also want to show Unintended effects.

You say this is for you to understand, but I figure you are about to post
it, so I compare to

http://www.livingcontrolsystems.com/download/pct_readings_ebook_2016.pdf
page 115.

Best, Dag

···

-----Original Message-----

At 10:00 AM 6/26/2016, you wrote:

8

[From Fred Nickols (2016.06.26.1358 ET)]

Nope. Not about to post it; just trying to make sure I am following a conversation and that I am following it with understanding.

I looked at page 115. It has the disturbance function you mention. I’ve not seen that before.

I’ll have to ponder all this.

Fred

···

From: Dag Forssell [mailto:csgarchive@pctresources.com]
Sent: Sunday, June 26, 2016 1:45 PM
To: csgnet@lists.illinois.edu
Subject: RE: Clarifying Cause and Effect in a Closed Loop

[From Dag Forssell (2016.06.26.1045 PDT)]

Fred, Your descriptions run in parallell, but the graphic does not.
You include a grey box labeled FEEDBACK FUNCTION between OUTPUT QUANTITY and INPUT QUANTITY. I am suggesting you consider showing an equivalent DISTURBANCE FUNCTION between DISTURBANCE and INPUT QUANTITY. You may also want to show Unintended effects.

You say this is for you to understand, but I figure you are about to post it, so I compare to http://www.livingcontrolsystems.com/download/pct_readings_ebook_2016.pdf page 115.

Best, Dag

At 10:00 AM 6/26/2016, you wrote:

[From Fred Nickols (2016.06.26.1258 ET)]

I’m not sure what you’re getting at, Dag. I included a comment about the
effects of a disturbance on the input quantity, just as can the Output. Did
you have something else in mind?

Fred Nickols

-----Original Message-----
From: Dag Forssell [ mailto:csgarchive@pctresources.com]
Sent: Sunday, June 26, 2016 11:48 AM
To: csgnet@lists.illinois.edu
Subject: Re: Clarifying Cause and Effect in a Closed Loop

[From Dag Forssell (2016.06.26.0845 PDT)]

[From Fred Nickols (2016.06.26.0825 ET)]

FN: I’d like to use the diagram shown below to clarify my understanding of
cause-and-effect in a closed loop.

DF: One more nitpick. You may want to include a Disturbance Function to
signify that the (one or more) Disturbance an observer can discern, D, is
similar in kind to the Output function, O.

Compare “Once around the Loop” in the Book of Readings.

Best, Dag

9

[From Rick Marken (2016.06.27.1715)]

···

Richard Kennaway (2016.06.26.1455 BST]

RK: (Simulposted with Martin Taylor, but this is saying basically the same.)

RM: Excellent posts from both of you!

RK: The causal links are as you describe then, and there is a lag time around the loop, but the loop cannot be understood in terms of “first this causal thing happens, then this happens, then this happens”, all the way round. Everything is happening simultaneously
and continuously all the time…

RK… on the timescale on which the loop succeeds in controlling, everything is causing and being caused by everything all the time.

RM: Excellent point. And that is basically the time scale on which we look at a control system when we do an algebraic analysis of the loop. The simplest algebraic analysis treats a control loop as consisting of two causal links that are occurring simultaneously. One causal link is the “system equation”, which defines the causal path from system input to output:

o = k.s(r-p)

and the other is the “environment equation”, which defines the causal path from system output to input:

p = k.f*o +d

RM: We solve these equations simultaneously to see what the control system does. This is equivalent to assuming all variables are causing and being caused by each other at the same time. The result we get --the solution to the simultaneous equations – is what we would observe if we watched the behavior of the control loop on the proper time scale. What we would see is

p ~ r (1)

and

o ~ r - 1/k.f*d (2)

RM: These are the solutions to the simultaneous equations that define the control loop. The algebra (using different symbols, unfortunately) is shown in the Appendix (p. 36-37) to the “Blind Men and the Elephant” paper in “More Mind Readings”, available at:

https://www.amazon.com/s/ref=dp_byline_sr_book_1?ie=UTF8&text=Richard+S.+Marken&search-alias=books&field-author=Richard+S.+Marken&sort=relevancerank

RM: These “steady state” solutions to the causal equations are much more informative about what a control system does than a “step by step” analysis of the causal links in a control loop. Equation (1) says that a control loop keeps a perceptual variable, p, approximately matching the reference specification for that perception, r: the behavior of a control loop is the control of perception. Equation (2) says that variations in the output of a control system, o, depend on variations in r and the disturbance, d, to the controlled variable – the basis for the “behavioral illusion”.

RM: Equations (1) and (2) are what are important to understand about the controlling done by living systems and I think it would be difficult to understand these facts about the behavior of a control loop by just tracing the causal links around the loop. When teaching PCT I think that, after describing the causal links, you should say that all these causal links can be viewed as occurring at the same time – simultaneously – and the result is that the system controls a perceptual variable (equation 1) and, in doing so, can appear to be reacting to stimuli (disturbances, as per equation 2).

Best regards

Rick

Some of the actual causal links will be invisible to observation and experiment that does not look inside the control system. An experimenter intervenes to vary the disturbance, and sees the perception remain constant while the output action varies. This
may give them the false idea that there is a direct path from disturbance to output, and that the perception is not causally linked to either. In fact, the only path from disturbance to output proceeds via the perception, which superficially appears to have
nothing to do with it.

If one knows nothing of the mechanism, measurements will only reveal causal connections to the extent that the controller is failing to control.

– Richard

–

Richard Kennaway, R.Kennaway@uea.ac.uk, http://www.cmp.uea.ac.uk/~jrk/

School of Computing Sciences,

University of East Anglia, Norwich NR4 7TJ, U.K.

–
Richard S. Marken

Author, with Timothy A. Carey, of Controlling People: The Paradoxical Nature of Being Human.

10

BL: Fred, the disturbance function (and that includes changes to
the feedback function being considered to also be disturbances) and
the very reason why living things have to be closed loop negative
feedback control systems. Were it not for the disturbances and
possible cases where the effect(s) of the feedback from the output
to the controlled variable changes then S-R could probably actually
work… or at least the cognitive calculate the necessary action and
execute said action.

···

On 06/26/2016 12:02 PM, Fred Nickols
wrote:

        [From

Fred Nickols (2016.06.26.1358 ET)]

        Nope.

Not about to post it; just trying to make sure I am
following a conversation and that I am following it with
understanding.

        I

looked at page 115. It has the disturbance function you
mention. I’ve not seen that before.

        I’ll

have to ponder all this.

Fred

From:
Dag Forssell Sunday, June 26, 2016 1:45 PM
RE: Clarifying Cause and Effect in a
Closed Loop

[From Dag Forssell (2016.06.26.1045 PDT)]

        Fred,  Your descriptions run in parallell, but the graphic

does not.
You include a grey box labeled FEEDBACK FUNCTION between
OUTPUT QUANTITY and INPUT QUANTITY. I am suggesting you
consider showing an equivalent DISTURBANCE FUNCTION between
DISTURBANCE and INPUT QUANTITY. You may also want to show
Unintended effects.

        You say this is for you to understand, but I figure you are

about to post it, so I compare to http://www.livingcontrolsystems.com/download/pct_readings_ebook_2016.pdf
page 115.

        Best, Dag



        At 10:00 AM 6/26/2016, you wrote:

[From Fred Nickols (2016.06.26.1258 ET)]

        I'm not sure what you're getting at, Dag.  I included a

comment about the
effects of a disturbance on the input quantity, just as can
the Output. Did
you have something else in mind?

        Fred Nickols

        > -----Original Message-----
        > From: Dag Forssell [
          mailto:csgarchive@pctresources.com]
        > Sent: Sunday, June 26, 2016 11:48 AM
        > To: csgnet@lists.illinois.edu
        > Subject: Re: Clarifying Cause and Effect in a Closed

Loop
>
> [From Dag Forssell (2016.06.26.0845 PDT)]
>
> [From Fred Nickols (2016.06.26.0825 ET)]
>
> FN: I’d like to use the diagram shown below to clarify
my understanding of
> cause-and-effect in a closed loop.
>
> DF: One more nitpick. You may want to include a
Disturbance Function to
> signify that the (one or more) Disturbance an observer
can discern, D, is
> similar in kind to the Output function, O.
>
> Compare “Once around the Loop” in the Book of Readings.
>
> Best, Dag

mailto:csgarchive@pctresources.com
Sent:
**To:**csgnet@lists.illinois.edu
Subject: