Action always equal and opposite disturbance
Unedited posts from archives of CSG-L (see INTROCSG.NET):
"Coach" -Equal and opposite!
Date: Fri Apr 17, 1992 2:05 pm PST
[From Bill Powers (920417.1100)]
On testing models:
Part 1.
Some time ago I remarked that the most common model in psychology is a cause-effectmodel in the form of a regression equation. The hypothesis is that the effectdepends on the cause linearly, as in y = ax + b. To test this model, you'd takethe values of a and b determined from a formal study, and try to predict newvalues of y from new observations of values of x.
David Goldstein commented that this concept of using a model forpredictions is not the way such findings are used in psychology. Once theregression line is drawn through the data points, that's the end of it. Themodel equation describes the data, but isn't then used for predictions.
On thinking this over, I agree that no formal use is generally made of theregression equation, but the findings are certainly used to predict individualbehavior. Suppose the dependent variable y is a clinical measure of depression,and the independent variable x is a depression-factor score on a personality test. In computing the correlation between thetest score and the clinical measure (in a study of many people), a regressionequation of the form y = ax + b is the basic premise behind the correlationcalculation. If the correlation is positive and statistically significant, theconclusion drawn is that depression is predicted by the test score. Then thetest is administered to a new individual (presumably from the same population),and if the depression-factor score is high, the person is diagnosed as depressed.
This isn't a formal application of the regression equation: you don't saythat a test score of exactly 7 predicts a depression of exactly 25 units on theclinical scale, even if that's what the regression equation says. But a personwho measures 15 on the test score would be judged as more depressed than aperson who measures only 3. So while the slope and intercept coefficientsaren't explicitly used, the general trend is implicitly used, and there are semi-quantitativejudgements made.
The scatter in data of this kind is so great, of course, that literalapplication of the regression equation would be silly. The prediction for anyindividual when the correlation is as low as 0.8 would be seriously wrong mostof the time, often even getting the sign of the relationship wrong for oneperson. The only correct way to make a prediction would be to begin withanother equally large sample of the population and do the whole study again.You would predict that the same regression coefficients would be found.
But there is an urge to predict for individuals, and the form of the urgefollows the regression line: a higher clinical score ought to predict a moresevere depression. While it is folly to give in to this urge when the data areso bad, the motive behind doing so is consistent with the principle ofmodeling.
If the principle of modeling were followed through formally, the regressionline would indeed be used to predict behavior. If the line has the equation y =3x + 5, and the depression-factortest score for a new individual is 4, the model predicts that a clinicalevaluation of depression will come up with 17 on the clinical scale for thatperson. To follow the test through, one would then submit the person to thesame clinical evaluation as used in setting up the model, and see what numberactually results.
Suppose the actual depression measure is 12 on the clinical scale. This isa deviation of -5units from the value of 17 predicted from the test score, for an error of -29percent. Is that good, or is that bad? The answer depends on how important itis to get the evaluation exactly right.
Of course in this case we know the clinical measure of depression, and ifwe believe it we can just ignore the test score and the prediction. But what ifwe want to make the diagnosis on the basis of the test score alone? Now thegenerally expected error for an individual prediction becomes relevant. Ifyou're going to prescribe electroshock therapy that will most likely severelydisturb the person's life for many years, maybe even permanently, you mightdecide that a 29 percent error is too large to allow. Perhaps even an error of5 percent would be too large if the person is a borderline case. On the otherhand, if you're going to prescribe a tranquilizer that won't do any permanentharm even if the person isn't really depressed, then perhaps you can allowerrors as large as 29 percent.
I've gone through this to illustrate that prediction errors can't be judgedas good or bad without taking the context into account. But what if the contextis that of testing a general model of behavior? Now the actions taken as theresult of a diagnosis are no longer in the picture. All we want to know iswhich theory is better. Now the errors of prediction under different models arejudged not against practical standards, but against each other. The smaller theexpected error, the better.
I have also tried to show that even in standard approaches, the method ofmodeling is there just beneath the surface. It's probably not mentioned muchbecause the predictions made from literal application of the model --the regression equation --are so poor. But the model is there. It's that model that we have to compareagainst the control-theorymodel, and the way we do the comparison is through making quantitativepredictions using the actual form of the model.
Let's look at the rubber-bandexperiment. Suppose we just measure the position of the experimenter's end ofthe rubber bands and of the subject's end, designating the positions as e ands. Let's confine the experiment to a line, so we consider only one dimension.The zero point on the line can be chosen arbitrarily, with all measurementsmade relative to that zero.
If we now measure the positions e and s over a long series of movements bythe experimenter, we will obtain a data set consisting of pairs of values of eand s. We can do a correlation between e and s. From the normal calculations,we can derive a regression line.
The regression line will have the form s = ae + b. The position of thesubject's end will depend on the position of the experimenter's end. If therubber-bandsare identical, the coefficient a will be very close to -1.Half of the intercept b will correspond to a position on the line. Thatposition will be the average position of the ends of the rubber bands: with a = -1,we will have (s + e) = b, or (s+e)/2 = b/2.
In fact, half of the intercept b will turn out to be a position nearlyunderneath the knot where the rubber bands are connected. The knot, as it willturn out, remains very nearly at the position b/2 all during theexperiment.
There's a moral to this story, but it's not quite obvious yet. The firstpart of it is that when you do an SR experiment in the usual way, to get aregression coefficient, you can SOMETIMES translate it directly into a control-systemexperiment. If you find that the intercept b corresponds to something in theexperimental situation that's remaining nearly constant at that value, you'vefound a controlled variable --actually, by finding its reference level first.
The second part of the story concerns the accuracy of the prediction. TheSR prediction will be accurate only if the two rubber bands have identicalcharacteristics, or strictly proportional characteristics. If theircharacteristics are different, the correlation coefficient you derive from thedata corrected for the different rubber-bandproperties will be very much higher than the one derived from the model s = ae+ b, which assumes identical rubber bands.
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Part 2.
In testing the control-systemmodel, the basic procedure is to assume that all behavior without exception iscontrol behavior, predict behavior on that basis, compare the prediction withthe appropriate data, and let the match or mismatch decide the issue. You cannever prove that a particular control-systemmodel is the only correct one, but you can show that it is incorrect.
Considering the low correlations that are found in S-Rexperiments, it might seem hopeless to substitute a PCT model for the linearregression model. When the data are that noisy, how can any clear decision bemade? This objection, however, assumes that the SR experiment has correctlyrepresented the data. While we can't prove that ALL SR experiments could betranslated into relatively noise-freePCT experiments, there are excellent reasons to think that this can be done ina significant number of instances, maybe even most instances. To do this,however, can require some changes in viewpoint that may be hard toachieve.
An SR "fact" is expressed as an effect of a cause. Doing something to aperson results in that person's doing something else. If the relationshipexpressed in this "fact" isn't clearcut and quantitative, then the controltheorist has to start asking questions about the data.
The basic question is, what is it that was affected by the "stimulus" thatwas also affected by the "response?" If you utter encouraging words to someone,and that someone then shows added efforts to achieve something, you have an SRrelationship. Now you have to try to guess: what did the encouraging wordsaffect that was affected EQUALLY AND OPPOSITELY by the increasedefforts?
Equally AND OPPOSITELY? There's the rub. You would like to think that thereis something you said that helped this person do better. But control theorysays that if your words of encouragement had some regular effect on theperson's behavior (apparently), that behavior was aimed at COUNTERACTING yourinfluence. If this is true, then you don't have the control over the person'sbehavior that you thought you had, even for the good. You are seeing yourselfas helping the other person to do better. The other person, however, is seeingthe situation differently: you're disturbing something, and the other person isacting to cancel the effect of the disturbance.
This may not be true, but if you're going to test the PCT model honestly,you have to pretend it's true and try to make sense of it. You can't test amodel if you don't follow its logic faithfully and literally as far as you can.You can't look ahead and think "If PCT is right, then I haven't been helpingpeople the way I thought I was --so PCT must be wrong." You have to be prepared to change your ideas aboutanything at all. Otherwise your reasoning is just a sham.
Let me give you a real example from my high-schooldays. We had a coach, named Coach, who was tremendously popular, a great guy.We all loved him and wanted his approval above anything else. Coach would say"You can do better than that, I know it --just give it one more try and you'll make it." And by golly, we'd give it onemore try and we'd make it, sometimes.
Now it would seem that his encouragement and belief in us caused us to trya little harder than we thought we could, so we achieved something we couldn'tdo before (sometimes). I suppose that Coach looked at it that way, as anyreasonable person would. But I can tell you that from inside at least oneperson (and at the time I guessed this was true of a lot of the others), itwasn't all that nice.
The basic problem was that Coach went around all the time saying to people,"What you're doing isn't good enough to please me." That's what "You can dobetter" says. I was already doing better than I thought I could, in number ofpushups, speed of climbing a rope, time in the 40-yarddash, or whatever. And I was damned tired and hurting, and not necessarilyinterested in doing any better. I liked physics a lot better than physicaleducation. But here's Coach telling me that he doesn't like what I'm doing.That mattered to me. So I got myself together and made it REALLY hurt, and Ifelt great --because now Coach wasn't displeased with me. Not because I'd achieved somethingI wanted, but because I'd done something to counteract his disapproval.
From Coach's point of view, he had helped me put out that extra bit ofeffort to surpass my previous achievements. No doubt if I had continued to goalong with this, worked out, built up a lot of strength, learned the footballplaybook by heart, and all of that, satisfying the coach more and more all thetime, I might have achieved even more. I might have been a college footballstar; I might even have become a professional football player and ended up as acoach myself, by now. I might be bold, aggressive, commanding, and rich. But Icertainly wouldn't be writing this. I also wouldn't be the Bill Powers youknow.
What actually happened was that many of us simply gave up on pleasing Coachbecause we didn't buy the goal. It wasn't pleasant to do that --to decide we were trying as hard as we cared to try toward that particular end,and that we would simply endure the disapproval. We still loved Coach, and wetried to fend off his disapproval by seeming to try harder. But the price wastoo high to really do it. When Coach was called into the Navy and left in 1944,there was a huge tearful farewell ceremony for him, and I'm sure that amid thesorrowful participants there were many hearts filled with relief.
To apply the PCT model, this is the sort of thing you have to think about.It's especially difficult when the hoped-foreffect on a person is beneficial. There's an almost-inescapabletendency to suppose that what you think of as beneficial is also consideredbeneficial by the other person; that what you consider harmful is also thoughtharmful by the other. Coach would have been completely baffled by the presentdiscussion. He would have said "Well, you did try harder, didn't you? And youdid do something you thought you couldn't do, didn't you? What's so bad aboutthat?"
The SR viewpoint encourages this sort of naive projection of one's owngoals onto the behavior of others. I shouldn't even call it the "SR" viewpoint.It's really this viewpoint, adopted innocently by well-meaningpeople who have never heard of stimuli and responses, that led naturally intoSR theory.
To test the PCT model in real life, you have to be prepared to follow itslogic all the way. Forget about whether the "response" is good or bad. Thequestion is how to find the controlled variable, the thing that is disturbed bywhat is done to the person, and is protected against more disturbance by theaction that the person takes. If you find such a controlled variable, you willunderstand that person far better than you did before. If you want to help thatperson, you might even find out what he or she really wants and figure out waysthat person could get there.
It's possible that you won't find any such controlled variable in a givencircumstance. But if you don't look for one, you will certainly not find oneeven if it's there staring you in the face.
The basic message here is that to test PCT, you have to make predictionsfrom it and from nothing else. You have to follow out the logic even when itseems to say things you don't believe. Then you have to look carefully to seewhether, in fact, the prediction holds true. This requires being consciouslyopen-mindedand willing to take a chance. You simply have to trust that if the theory doespredict correctly, you'll be better off knowing what it predicts than notknowing, letting the chips fall where they may.
Best to all Bill P.
Date: Sat Apr 18, 1992 2:34 pm PST
Subject: Coach; conflict
[From Bill Powers (920418.1500)]
Martin Taylor (920418.1340) --
You've sort of taken off at right angles to the line of thought I wasdeveloping. The "Coach" example was meant to illustrate how an apparent SRrelationship (encouragement -->doing better) can lead to quite a different interpretation when explored fromthe viewpoint of control theory. I wasn't trying to generalize from theparticular way I and probably others dealt with Coach's urging us tooverachieve. With another person or in another circumstance, a similarencouraging remark leading to improved performance could work in a differentway. But it will never be a cause-effectway. My point was that to test control theory you have to think ofpossibilities other than the surface appearances.
Since I'm into high school stories, I remember another instance with amathematics teacher. I didn't much like or dislike this teacher --he knew his stuff but wasn't strong on making things clear. The class was doingan exercise, each person trying to prove a trigonometric identity. I was stuck --something was wrong and I didn't know if I was even getting close. The teacherwas going around the room seeing how everyone was doing. When he got to me, hesaid "That's fine, you're almost there."
This told me that I hadn't made any mistakes so far and was headed in theright direction. So I stopped worrying and went ahead and finished the proof,my first one. That felt nice. The 60th proof didn't feel so nice.
Apparent SR relationship: he said what he said, I then went ahead to reachthe goal. Cause and effect? No. Information. I wanted to know if I'd made somestupid mistake, and he told me (in effect) that I hadn't. With thatinformation, I could stop looking for a mistake and devote my efforts tosomething more productive. I didn't finish because I liked the teacher or inorder to please him. I finished because I wanted to be able to prove theidentity. His remark wasn't a disturbance of something I was trying to control;it provided a missing perception so I could get unstuck from looking for anonexistent error.
My Coach example was one in which the apparent stimulus actually diddisturb something I was controlling for, and my response opposed the effect ofthe disturbance. The result was to put a very different light on what seemedlike a simple S->Rchain. That's all I was trying to show --not that there's something inherently bad about encouragement or that being aspushy as Coach was necessarily leads to resentment and bad feelings. In fact Inever resented Coach; not many did. He was a nice guy. I just resisted him. Iregretted not wanting to live up to his expectations, but not enough to changemy mind.
Re: your comments on conflict.
Conflict doesn't "lead to" anything in particular. What it leads to dependson how you resolve it, or fail to resolve it. Most conflicts are unimportant;we just shrug and turn to something else, or go into a little fit ofreorganizing and think of a different way out. This happens all the time; wehave natural machinery for resolving inner conflicts and it usually works verywell.
The degrees-of-freedomproblem doesn't normally cause conflict because we've learned to use only thosecontrol systems that are compatible when working at the same time. Thebalancing of reference signals contributed by many higher-levelsystems isn't a conflict unless one of the higher systems is unable to keep itsown error reasonably small because of the interference of other systems at thesame level. The usual case is that all active higher-levelsystems keep their errors small despite the fact that no one lower-ordersystem's reference signal is the exclusive property of one higher order system.The systems just find the analog solution of the simultaneous equations andthey all are successful.
When opposing muscles are used to control limb position, there's noconflict. In fact there are two controlled variables that are independentlyadjustable: for the tendon reflex, one is the difference between the tensionsin the two muscles, the other is the sum. The sum-of-tensionssignal is controlled to produce a specific muscle tone. The difference signalcontrols the net applied force. Because the muscle is highly nonlinear, the sum(muscle tone) signal effectively alters the spring constant of the combinedmuscles near the zero-errorcondition, thus adjusting the static loop gain of the tension control system(and also the stretch control system).
Conflict is a problem only when it concerns some variable important to theorganism, is severe, and goes unresolved for a long time. That's what bringsthe clients to the therapist or counsellor. Serious conflict destroys controlor reduces its effective range to the point where it's not sufficient for thepurposes normally served by the control systems.
A control system that keeps its error very small isn't likely to be "placidand content." It's able to keep the error small because it has a very high loopgain. This means that even the smallest disturbance will evoke an opposingeffort, and that opposition will keep the controlled variable nailed to itsreference condition. When you're driving a car along a mountain road with awashout on the cliff side, you tighten up that control system so the car staysprecisely on the path you've picked to squeeze past the danger point. I don'tthink that "placid and content" describes that control system. But it's not inconflict, either: if it is, you have a problem because you won't be able tomove the wheel as much as if there weren't any conflict.
There's a problem with your suggestion that "a system with tension andconflict will be more robust than one that is placidly content." The problem isthat reorganization will start because of the chronic conflict. As a result,precise control will become impossible: the parameters of the control systemsare going to be changing at random. What you get is a jittery and unpredictablecontrol system that could literally do ANYTHING without warning.
Just because of neural response curves, I can believe that some slightamount of tension would help with rapidity of response to disturbances, becausenear zero signal the slopes of the functions will be very low and the loop gainwill be low. But this is relevant only when the control point is set to zeroand there are no disturbances. Most reference signals specify values ofperceptual signals that are far from zero --somewhere in the normal range between zero and maximum. And there's normallysome amount of disturbance to raise the error signals above zero, if onlygravity. In those cases, there's no advantage to conflict because conflictwon't raise the sensitivity or speed of the system and will only reduce itsrange of control. I think that the best state to be in for possible action isone of alertness and calm. You should feel just a little zingy, but youcertainly shouldn't be in white-knuckleconflict with yourself. You want everything working in the samedirection.
So I guess I agree with your concluding remark: tension, conflict, anduncorrectable disturbance are good, but not in excess. I would figure somethinglike 5 percent of the range of control. The rest of your reserve you would wantto save for affecting the environment.
Uncalled-forremarks on social conflict.
In the background I suspect is an idea that competition is good for us (ifnot in your mind, then in others). Up to a point, while it's fun, I agree. Welike to set problems for ourselves and solve them, and get better at solvingthem. But competition as a way of life doesn't work that way, except for a fewwinners. A social system based on serious competition is just a step fromviolence (in the US, a very short step). The losers vastly outnumber thewinners: we end up with a society of losers, winners being an anomaly. Insituations where the terms of the game determine that only a few can win,chronic losers can get very nasty; in fact, they tend to abandon whateversocial principles there might be that make civilization better than life in thejungle. I don't think that the price is right. Competition --interpersonal conflict --is the lowest level of social intelligence. I don't like to admit that even alittle conflict can be a good thing, because we've accepted a HUGE amount ofconflict as good and natural for far too long. It's time to get smarter.
Best Bill P.