# least action-efficiency

From [Marc Abrams (2006.07.04.1334)]

> [From Rick Marken (2006.07.03.2040)]

> I don't think so. But I do think we have to be controlling for it. But it would be nice to know exactly what you mean by "efficiency". A >quantitative definition in terms of the variables involved in control would be best.

Mathematical manipulation does not reify data, though it often provides a handy way of testing the adequacy of our conceptualizations.

All mathematical reasoning is completely dependent upon the premathematical construing process which gives it something to enumerate.

> I'll believe this if you can show me why this is true. Not with more words but with a mathematical analysis of computer model. .

It might be worthwhile to keep something Albert Einstein once said;

"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."

Regards,

Marc

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[From Bryan Thalhammer (2006.07.05.1321 CDT)]

I don't know why the focus is so heavy on efficiency. The definition of control suffices alone. But after reading the post and getting to this sentence, I think I see the flaw.

> [Rick Marken (2006.07.05.1100)]
> ...
> I guess our difference is over this: I think efficiency and control are two essentially independent
> measures of performance and you don't. So I guess we'll have to leave it at that.

Efficiency: An observer-based measure of a person's performance. It has nothing at all to do with the person's subjective measure of control (the error signal) at the control system level. When a person, after the fact, acts to reduce a timing/duration of an operation, expenditure of energy or some other valued input, or some other saveable, that person can be said to be controlling for a certain efficiency. However, that is still control of a perception.

Control: The description of maintaining perceptions of the world/self (on a range of complexities) in accordance with a desired state for that perception (reducing the error between reference signal and perceptual signal). There is a certain thing that I have always had a hard time with, called "gain" which I believe describes the rapidness of the reduction of the error signal. Efficiency is not a part of this, since high gain implies that additional effort/behavior can be directed to reducing that error, but it may take away attention (I am almost afraid to use that term, but anyway). However, the bottom line is to continue to control the system image, allowing the living control system to continue to live and reproduce. Efficiency is not necessarily part of this mandate.

Math. I have always been math-challenged. I do well, but I am in awe of those who can see through the formulas and calculations to the function, being described. Really. But perhaps what Rick means, by doing the math, is not restricting the presentation to math, but to ensure that what is described is measurable in the data that are allegedly described. Words are not really measureable.

I just don't see why efficiency is so important in understanding PCT. Unless efficiency is a principle or program that is being maintained at high gain. Or?

Best,

--Bryan

From [Marc Abrams (2006.07.05.1426)]

> [From Bryan Thalhammer (2006.07.05.1321 CDT)]

>I don't know why the focus is so heavy on efficiency.

Because that is where Jim wants it to be.

> Math. I have always been math-challenged. I do well, but I am in awe of those who can see through the formulas and calculations to the >function, being described. Really. But perhaps what Rick means, by doing the math, is not restricting the presentation to math, but to >ensure that what is described is measurable in the data that are allegedly described. Words are not really measureable.

An interesting and important point. In my post yesterday I tried to point out that mathematics is but another metaphor that we use in trying to understand the world we live in. When you start viewing mathematical models _as_ the reality I believe you have crossed the line and are headed for big trouble. The map is _never_ the territory.

Mathematical manipulations do not make something real or concrete. What makes something "real" and "concrete" are our perceptions, and when you replace words with numbers, what exactly do those numbers actually represent? That is, what characteristics of the object do they purport to represent? If you are using symbols in your manipulations, than what the specific meaning those symbols have must also be "interpreted" as well. What does not have to be "interpreted" are the relationships between functions

Mathematics is extremely important and useful but in and of itself is not sufficient for good science; and the reason model building is so difficult is because it is half art and half science. The difficulty in "translating" what we perceive into useful mathematical functions, constructs and relationships is really an art form and like most everything else, some are better at it than others.

But I believe anyone who actually wants to, can learn the necessary math and can learn to model, if not well, than adequately.

>I just don't see why efficiency is so important in understanding PCT.

It's not, its useful for understanding some of Jim's ideas and point of view.

>Unless efficiency is a principle or program that is being maintained at high gain. Or?

I think Rick is right by calling "efficiency" a measure of human performance. I'm not so sure I would say the same of perceptual control. Perceptual control _is_ human performance (behavior) not simply a measure of it.

I also think Rick is right in replacing the word efficiency with control in the same way I would replace the word "rational" with control. That is, people are not efficient, they are controllers and they are not rational, they are controllers. This of course does not preclude an observer from saying that he/she is observing rational/efficient behavior.

Regards,

Marc

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[From Bryan Thalhammer (2006.07.05.1436 CDT)]

Marc,

Fer sure, I agree with this part of your post. Control means neither to be rational nor efficient. It is, I think, just what is necessary to get to the next step (next action, next day, next whatever). And that does not surprise me a bit, since control is an evolved capability. Dawkins probably describes what I want to say here better than I can.

>> [Marc Abrams (2006.07.05.1426)]
"I also think Rick is right in replacing the word efficiency with control in the same way I would replace the word "rational" with control. That is, people are not efficient, they are controllers and they are not rational, they are controllers. This of course does not preclude an observer from saying that he/she is observing rational/efficient behavior."

On the Math thing, you are right as well, but I would reply that math and verbal descriptions can be equally subjective. (Mark Twain: "there are lies, damned lies, and stats...").

"Mathematics is extremely important and useful but in and of itself is not sufficient for good science; and the reason model building is so difficult is because it is half art and half science. The difficulty in "translating" what we perceive into useful mathematical functions, constructs and relationships is really an art form and like most everything else, some are better at it than others."

However, if the data description is sufficiently discrete or lean, the math (and its graphic results) would be hard to deny, when presented properly. Edward Tufte presents several data maps that are remarkably clear (and get to the point much better than a narrative): 1) The cholera map of London, showing the wells that were in use and plotting the cholera incidents. 2) The map of Napoleon's army on its march to and from Moscow, showing the entrance of various troops and their demise during the march. (Yet I could argue with myself that rich narratives can better describe an interaction than math and charts.)

Regarding learning math (and language): Anyone can learn, given the means.

Yessir,

--Bry

From [Marc Abrams (2006.07.05.1540)]

> [From Bryan Thalhammer (2006.07.05.1436 CDT)]

> On the Math thing, you are right as well, but I would reply that math and verbal descriptions can be equally subjective. (Mark Twain:

"there are lies, damned lies, and stats...").

Yes, and that was my point, the use of mathematics _is_ "subjective", and the use of it does not make something objective as you astutely point out.

"Mathematics is extremely important and useful but in and of itself is not sufficient for good science; and the reason model building is so difficult is because it is half art and half science. The difficulty in "translating" what we perceive into useful mathematical functions, constructs and relationships is really an art form and like most everything else, some are better at it than others."

> However, if the data description is sufficiently discrete or lean, the math (and its graphic results) would be hard to deny, when

presented properly.

OK, I'm not sure what you mean by "sufficiently discrete or lean" can you expand on that a bit? Also, what would it mean to "present it properly"?

>Edward Tufte presents several data maps that are remarkably clear (and get to the point much better than a narrative): 1) The cholera >map of London, showing the wells that were in use and plotting the cholera incidents. 2) The map of Napoleon's army on its march to >and from Moscow, showing the entrance of various troops and their demise during the march. (Yet I could argue with myself that rich >narratives can better describe an interaction than math and charts.)

OK, I think we are making different points here. If I understand you correctly here you are saying that "maps" are often useful tools for understanding the "geography" or "data" and I certainly don't disagree with that notion. Indeed that is one of the reasons for utilizing mathematics, but my point was that a map is _never_ a _literal_ representation. It is an abstraction. If it were not, a "map" would have to be the same size as the "territory" it depicts.

There is a funny story Karl Weick tells of a European army who got lost in the mountains in a snow storm. When they finally got home the commander was asked how he got himself out of that mess. He than took out this map of the Alps. Unfortunately he was lost in the Pyrannies (Sic?). ;-).

Regards,

Marc

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[From Bryan Thalhammer (2006.07.05.1540 CDT)]

>> From [Marc Abrams (2006.07.05.1540)]
OK, I'm not sure what you mean by "sufficiently discrete or lean" can you expand on that a bit? Also, what would it mean to "present it properly"? ... [The] point was that a map is _never_ a _literal_ representation. It is an abstraction. If it were not, a "map" would have to be the same size as the "territory" it depicts.

Sure. Sufficiently discrete or lean: By this I mean objective values, such as intensity, color, weight, altitude, and so on. By presented properly, I mean consistently using computer-manipulated images. So, astronomical data, brain/body scans, terrestrial scans, scans of natural or artificial structures can produce mathematical data that can be consistently manipulated to show certain aspects of the object of the scan. Some other lean data could be eye-movement data, impulses recorded on a steering wheel, accelerator and break system. Also touches on a touchscreen, key scans, and mouse movements. These are all data that can be treated in a discrete or lean manner. Narratives, napkin drawings, and logical arguments don't qualify as data in that way.

So long as they are described as what they are rather than what they mean, they are discrete or lean. That is why I like the cholera map and the Napoleonic troop movement map examples, among others. The cholera example descriptions say: Wells are here, here, and here. Cholera cases are recorded as being there, there, there, there, and there... And from the map, one can make the conclusion: "it looks like the dirty well is this one." Let's close that one and see if the cholera stops. And, as I recall, it _did stop the cholera outbreaks_. So, no, the map was not confused with the real events, but the representation was lean, and the experiment (the real event of closing that well) was the test of the real events through the data.

Getting back to PCT, and what Rick said, models are a way of abstracting real events, and mathematical ones work pretty well. What you are saying (?) is that a map is not the real event. I agree. A map is a tool for making predictions regarding real events. You can interact with a model to test it, to see if it works consistently. But the real test [of the controlled perception] happens as an event in the real world. Yes?

Yessir,

--Bry

From [Marc Abrams (2006.07.05.1756)]

> [From Bryan Thalhammer (2006.07.05.1540 CDT)]

Thanks for the clarification.

> Getting back to PCT, and what Rick said, models are a way of abstracting real events, and mathematical ones work pretty well.

Yes, but even mathematical abstractions need to be provided with meaning, as Martin pointed out with his metaphor

>What you >are saying (?) is that a map is not the real event. I agree. A map is a tool for making predictions regarding real events.

Agreed

>You can interact >with a model to test it, to see if it works consistently. But the real test [of the controlled perception] happens as an >event in the real >world. Yes?

That's how I would view it, yes.

Regards,

Marc

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[From Rick Marken (2006.07.05.1530)]

Bryan Thalhammer (2006.07.05.1321 CDT)

Efficiency: An observer-based measure of a person's performance...

Control: The description of maintaining perceptions of the world/self (on a range of complexities) in accordance with a desired state for that perception (reducing the error between reference signal and perceptual signal). ...

Control is also a variable that can be measured by an observer. The stability measure, for example, (which is the measure of control used in the "Mind Reading" demo;http://www.mindreadings.com/ControlDemo/ThreeTrack.html) is a measure of a person's control performance. The stability measure of control is defined as:

S = 1- sqrt(Ve/Vo)

where Ve and Vo are the expected and observed variance of the controlled variable, respectively. So S (stability) is 0 when Ve = Vo, which is the case when there is no control. The better a person's control, the smaller Vo will be relative to Ve, and the more _negative_ S will be. So the larger and more negative the value of S, the better the control. A large, positive value of S means that actions are destabilizing the controlled variable: there is positive feedback, which is basically the opposite of control.

I think of efficiency as a measure of output per unit input. Indeed, energy efficiency is defined as power output/power input. In the case of control, what I think efficiency might mean is actual output relative to the minimal output required to achieve a certain level of control: minimal output/actual output. Given this definition, maximal efficiency is 1.0 and a control system with an efficiency less than 1 is not doing as well as it could. It is this definition of efficiency that I'm thinking of when I say that efficiency is not necessarily related to control, as in the baseball demo, where control is excellent (reliable catching meanings large negative S) but efficiency is low (the actual output that produces the catches is not the minimal amount that can be used to achieve a certain level of control. At least, I don't think so; I'd have to compute it.

Now it could be that Jim Dundon has a different measure of efficiency in mind. Perhaps he is thinking of efficiency as the degree to which the output of a control system (o) is equal to the output required to perfectly cancel the disturbance to a controlled variable (o'): Vo/Vo', say. This measure of efficiency is perfectly correlated with a measure of control, such as S. When control is perfect, Vo = Vd (output variance precisely equals disturbance variance). So Vo' = Vd. T the extent that control is not perfect, Vo< >Vo' and the ratio Vo/Vo' <> 1. When control is perfect, Vo/Vo' = 1.0. So a perfectly efficient control system can be considered one where Vo/Vo' is 1.0. [This is really not the best measure since it also must be true that o = -d and it's possible (though unlikely) that Vo=Vo' when o<>-d]. Anyway, using this measure of efficiency, we cans that any deviation of Vo/Vo' from 1 is inefficiency: the system is either producing more output than it needs to (Vo>Vo') or less than it should (Vo<Vo').

So, without a quantitative definitions of efficiency I don't really know what Jim is talking about.

Best

Rick

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[From Bryan Thalhammer (2006.07.05.1830 CDT)]

> [Rick Marken (2006.07.05.1530)]

Whew. Yes! But I think that the problem with the descriptor of efficiency by Jim is that it is _not_ a PCT descriptive. I often hear about it in business management and ergonomics/human factors, where analysts would design a work station for an assembler so that all actions would be as "efficient" as possible, this having nothing to do with PCT and everything to do with external observers measuring apparent lost motion vs. good motion. There may be other settings in which "efficiency" is pertinent, but I don't think that the venn diagrams of motion efficiency and control necessarily overlap. BTW, I agree with the Cheaper by the Dozen guy, Frank B. Gilbreth, but he may have taken it to extremes.

Control IS in indeed a variable that can be measured by an observer. We sure have done that in tracking, self as the living control system, etc.

Efficiency as a measure of output per unit of input, you said. Well, yes, one's input can be exactly what is needed to maintain relative zero error. Is that what you are saying? I am just wondering what happens when conflict happens. Efficiency by that description must plummet as inputs are varied across the demanding (high error) control systems, no? There has got to be lost effort/input as you are multi-tasking?

As above, I think that there are different definitions of efficiency, and that while both you and Jim reference external measures of apparent efficiency by an individual, your model is PCT and Jim's is one of waste vs. good movements. I could be wrong... but I think that is the thing. The PCT measure only trys to analzye what input is necessary to reduce error to zero, where as Jim's is a measure of motion or something else.

--Bry

[From Rick Marken (2006.07.05.1845)]

Bryan Thalhammer (2006.07.05.1830 CDT)

> [Rick Marken (2006.07.05.1530)]

Whew. Yes! But I think that the problem with the descriptor of efficiency by Jim is that it is _not_ a PCT descriptive.

I don't think there is a measure of efficiency that comes out of PCT in particular. And we don't know what Jim's definition of efficiency is anyway. Based on reading Jim's comments I think that Jim may be using the word "efficiency" to describe what we would call "control" (as measured by a quantity like S, the stability factor). I think.

I often hear about it in business management and ergonomics/human factors, where analysts would design a work station for an assembler so that all actions would be as "efficient" as possible, this having nothing to do with PCT and everything to do with external observers measuring apparent lost motion vs. good motion.

I think this approach to efficiency is perfectly consistent with PCT. A human factors engineer can design a machine that requires large or small movements to achieve the same level of control. The machine that requires smaller movements will allow the person to control more efficiently. What the human engineer is doing is increasing loop gain by changing the feedback function that connects assembler to the result to be produced. I think this would mean that a more efficient system -- one with higher loop gain, allowing smaller movements to have large effects -- would also control better. So I think this kind of efficiency may be tied to how well one controls. But there is the well known trade off between gain and speed in control; the higher the gain of a control system the more slowly it must act or the system will be unstable. So it may be that any increase in efficiency that comes from increasing loop gain is cancelled out by the decrease in efficiency (in terms of speed of action) that is required to maintain the stability of control.

I think a quantitative analysis of all this could be done using the equations for a quasi-static analysis of control described in Powers' 1978 _Psychological Review_ paper. But they could be used only if we have a quantitative definition of efficiency. Maybe I'll give it a shot (using my own definition of efficiency) sometime before I leave for China. It is kind of an interesting question: does the efficiency of control (I would say in terms of how much energy it uses to produce a particular level of control) vary depending on the parameters of control? I would guess that it does. But I'll see if I can come up with a nice, clear analysis (if Martin doesn't come up with one first: hint hint Martin)

Best

Rick

···

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