[spam] Re: Elements in the PCT model

CSGnet Archive CSG2006
21

[Martin Taylor 2006.11.26.11.31]

[From Fred Nickols (2006.11.26.0722 EST)] -

> [Martin Taylor 2006.11.25.22.55]

... what I was trying to get at with my original example - that a disturbance is only a disturbance in relation to something you're controlling for. Despite having gone round and round, I think that's borne out by the conversation so far.

Yes, it's why I said your original example was a good one.

Let's proceed on the assumption that the person is indeed controlling for variable X or whatever it is and the aim is to determine if some other factor (Y) is indeed a disturbance. If you remove what is believed to be the disturbance and behavior (output) changes too, is that evidence that Y was a disturbance but now no longer needs to be compensated for?

Removing the factor V could mean at least two things:

Original situation: V -------> qo <-------control output (V non-zero)

Interpretation 1: V -------> qo <-------control output (V = 0)

Interpretation 2: V qo <-------control output (V any value at all)
                      \
                       \
               (does not influence qo)

Under interpretation 1, V remains a disturbance, and the output continues to compensate, though the compensating output quantity is zero at the moment (assuming that zero produces the reference value of the perception).

Under interpretation 2, V is no longer a disturbance, and the output does not compensate for changes in V. Qo reamins zero (assuming that zero produces the reference value of the perception).

I'm thinking of the sun dipping below the horizon and now I no longer need my sunglasses or sun visor. The sun's rays have ceased to be a disturbance.

That's case 2. The sun could brighten or dim, and it wouldn't affect your use of sunglasses and visor.

Martin

22

[From Bill Powers (2006.11.26.1005 MST)]

Martin Taylor 2006.11.26.10.36 --

Rick Marken (2006.11.25.2240) --

I don't know what's going on here, except perhaps this:

                                            I am right
                                                >
                                   ---------> Comp -------------->
                                  > >
Your statement ------> My state of rightness < --------------My statement

There is no "official" definition of a disturbance in PCT. One variable d, obviously, disturbs the state of another variable qi if the value of qi depends partly on the value of d, and d is nonzero. That's just common sense, not PCT. It is true not only of d and qi, but of x and y, h and z, and any other pair of interacting variables. That is all there is to it, whether there is a control system or not.

The independent variable d is termed the disturbing variable, and the dependent variable qi is the disturbed variable. Again, there is no special difference when this happens outside a control situation. A raindrop falling into a bucket disturbs a water level upward a little bit. A lot of raindrops disturb it a lot. A loss of drops through a leak in the bucket disturbs the water level the other way.

If the variable qi that is disturbed by the disturbing variable d is also a function of a second variable, qo, then the state of qi depends on two variables at the same time: qi = f(qo,d). This is true of any similarly-related variables, not just variables that happen to be involved with or in a control system. If the effect of qo varies equally and oppositely to variations in the effect of d, then qi will remain constant,no matter what makes qo behave that way. If qo varies almost equally and oppositely to d, qi will remain almost constant. Forget about control systems -- that's just a fact about physical variables. It doesn't matter how you say it, as long as you are saying qi = qo + d or qi ~ qo + d (or if you want to be fancy, qi = f(qo) + g(d) and so on). If it is raining, the level of water in the bucket will come to a value such that the leak rate almost equals the rate at which water falls into the bucket ("almost" because some water splashes out and some evaporates)..

A control system makes qo vary in such a way that its effects on qi are almost equal and opposite to the way the sum of any number of disturbances affects qi. The control system organization explains how it is that qo can vary to compensate for, or to cancel, or to oppose, or to nullify, or however you want to say it, the effects of d. There is nothing abstract or magical about that explanation.

There are almost no terms in PCT that would have to be used differently outside of PCT. Consider "reference signal". A stimulus-response system can have a reference signal (it might be called a "threshold"), because a reference signal is simply a bias added to or subtracted from the effects of the stimulus before the result causes a reponse. There can be input quantities, perceptual signals, and output quantities in an S-R system. There can be input functions and output functions. It might be a little strange to speak of a comparator in an S-R system, or an "error" signal, but there must a place where the reference signal's bias is applied, whatever we call that place, and surely it is not critical whether we call the result an "error" or a "difference" signal. And of course there can be disturbing variables, called "remote stimuli," acting on the input quantity (qi is a "proximal stimulus").

What makes the difference is the feedback connection and the gain in the control system's input-to-output function. In an S-R system, the gain has to be just right so a given distal stimulus will cause the appropriate amount of output quantity (response, behavior). In a control system, the gain can be 10, 100, or 1000 times that large, but the output quantity is then no larger than it was before, because of the negative feedback. And of course in the control system, the input quantity is controlled, whereas in the S-R system is it not controlled by the behaving system (it would be controlled by the experimenter).

Arguments about what is and isn't a disturbance make all this seem very complex, and I don't think that furthers the cause.

Best,

Bill P.

23

[Martin Taylor 2006.11.26.14.09]

[From Bill Powers (2006.11.26.1005 MST)]

There is no "official" definition of a disturbance in PCT. One variable d, obviously, disturbs the state of another variable qi if the value of qi depends partly on the value of d, and d is nonzero. That's just common sense, not PCT. It is true not only of d and qi, but of x and y, h and z, and any other pair of interacting variables. That is all there is to it, whether there is a control system or not.

All of what you say is very sensible (as usual). But it leads to the kind of difficulties Bjorn was getting wound up in at the beginning of this thread, using "disturbance" to mean both anything perceptible and things that influence a controlled variable away from its reference state.

We do need some verbal way to make that distinction, since we perceive a lot that we don't control at the moment, and a lot more that we never will control or try to control. It's useful to distinguish between events that affect controlled variables and events that don't, and useful to do that verbally as well as mathematically.

When we build simulations, or analyze models, we must make the distinction, and we have no problem doing so. It's when we observe or experiment with the behaviour of other people that the problem arises. It's even a problem when we observe our own behaviour, as the Method of Levels attests. Fred Nickols has just observed in himself a possible control system whose perceptual signal may be disturbed by the facing sun, which he hadn't observed in himself earlier.

If you prefer not to restrict "disturbance" to the case in which what is disturbed is a controlled perception, then we need a different word to cover that case in contradistinction to the case in which no control is involved.

Arguments about what is and isn't a disturbance make all this seem very complex, and I don't think that furthers the cause.

I think that "the cause" is improved understanding (of behaviour, of the way the world works ...). It's not a political question, in which immediate and decisive answers are rewarded with more votes. The hope is that by morking through the thicket of partial understandings, we arrive at greater clarity in the end. Each of us has to do that individually, but those who have arrived in the clearing can (and do) aid those of us still looking for the pathways.

I think we do have to be concerned about what is happening when we talk about a disturbance to a controlled variable. And I think that words matter.

Martin