Perception and PCT

[rsmarken]

[From Rick Marken (2008.04.08.1250)]

I think the reason for the disagreement about uncertainty may be a
difference in conception of what perception is _for_. One conception
is that perception is a process of communicating information to the
perceiver about what is actually out there in the world of the
perceiver. This is the conventional view of perception in psychology;
I'll call it the "communication" view. It is nicely described by
Martin Taylor (2008.04.03.17.03) in terms of Shannon's information
theory model of communication systems:

Shannon started with...the notion that there is a source of data and a
receiver of the data, connected by a transmission line that might alter the
data. There is also the concept of a transmission event that might be
extended in time. At the receiver, the result of this event is an
observation.

In terms of the communication model of perception, the source of data
is the outside world and the receiver of data is the perceiver. In the
context of this view of perception, the concept of uncertainty makes
sense. A perception is data that is evidence regarding what is true in
the outside world. Noise in the perceptual system makes this data
uncertain evidence (for the perceiver) about what is going on in the
outside world. Here is Martin's nice description of the problem:

Before the observation, the receiver knows nothing more about the data
source than a probability distribution of possible transmission events that
could result in observations. After the observation, the reciever's problem
is to determine, given the observation, what the transmission event was. The
best it can do is to assign a new probability distribution. Both probability
distributions determine measures of uncertainty _about_ the source.

The observation is, of course, the perception. The uncertainty of this
observation depends (as Martin says) on the a priori probability of
the different events that might be out there (the probability
distribution of possible transmission events that could result in
observations) as well as the a posteriori probability of the different
observations (perceptions) that occur (this is what Martin calls the
new probability distribution and its variability depends on the level
of noise in the perceptual communication system).

The PCT view of what perception is for seems to me to be quite
different than the conventional (communication) view. In PCT
perception is there to be controlled by the perceiver; it is not there
to provide the perceiver with information about what is going on in
the outside world (unless the perceiver is controlling for doing
things like science, where the goal is to contrive models and
situations that will allow one to infer what might actually be the
real world cause of those perceptions; it is only in this case that I
can see it being meaningful to talk about the uncertainty of
perception from a PCT perspective). Perception, from a PCT
perspective, is a process of computing different functions of external
reality. The outputs of these functions exist in the brain as
variables that are potentially controllable; and many of these
variables are controlled, which, as a side effect, keeps the system
functioning and (hopefully) relatively content. Uncertainty, in the
communication sense, is, it seems to me, irrelevant.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[MartinT]

[Martin Taylor 2008.04.08.16.30]

[From Rick Marken (2008.04.08.1250)]

I think the reason for the disagreement about uncertainty may be a
difference in conception of what perception is _for_. One conception
is that perception is a process of communicating information to the
perceiver about what is actually out there in the world of the
perceiver. This is the conventional view of perception in psychology;
I'll call it the "communication" view. It is nicely described by
Martin Taylor (2008.04.03.17.03) in terms of Shannon's information
theory model of communication systems:

Shannon started with...the notion that there is a source of data and a
receiver of the data, connected by a transmission line that might alter the
data. There is also the concept of a transmission event that might be
extended in time. At the receiver, the result of this event is an
observation.

In terms of the communication model of perception, the source of data
is the outside world and the receiver of data is the perceiver.

That's one part of the control loop. there are others. The next source is the output of the perceptual input function, and the receiver is the comparator. Following that, the source is the comparator output, and the receiver is the output function. The next is the biggie, where the source is the output function's output and the receiver is the environmental correlate of the perceptual signal. That is usually a whole complex of lower-level variables, which does not affect the analysis. Finally, we repeat the first stage mentioned by Rick, the source being this complex of environmental variables that is the correlate of teh perceptual signal, and the receiver being the perceptual input function.

In the
context of this view of perception, the concept of uncertainty makes
sense. A perception is data that is evidence regarding what is true in
the outside world. Noise in the perceptual system makes this data
uncertain evidence (for the perceiver) about what is going on in the
outside world.

I'd prefer to say that a perception is a function of data that is related to states of the world that provide input to the perceptual input function.

Here is Martin's nice description of the problem:

  Before the observation, the receiver knows nothing more about the data
source than a probability distribution of possible transmission events that
could result in observations. After the observation, the reciever's problem
is to determine, given the observation, what the transmission event was. The
best it can do is to assign a new probability distribution. Both probability
distributions determine measures of uncertainty _about_ the source.

The observation is, of course, the perception.

No it isn't always. That's true only if we are talking about that one link, between the environmental correlate of the perceptual signal and the perceptiual signal itself.

The uncertainty of this
observation depends (as Martin says) on the a priori probability of
the different events that might be out there (the probability
distribution of possible transmission events that could result in
observations) as well as the a posteriori probability of the different
observations (perceptions) that occur (this is what Martin calls the
new probability distribution and its variability depends on the level
of noise in the perceptual communication system).

The PCT view of what perception is for seems to me to be quite
different than the conventional (communication) view. In PCT
perception is there to be controlled by the perceiver; it is not there
to provide the perceiver with information about what is going on in
the outside world

Without information about variation in the environmental correlate of the perceptual signal, output is highly unlikely to result in any kind of influence on the perceptual signal, let alone a directed influence that reduces error. In PCT, accurate observation is important for effective control.

The difference isn't what you suggest. The difference is in the end-point. PCT deals in closed loops. Your so-called "conventional" view does not. Within PCT, no single lin is a closed loop, and all of them are appropriately viewed as communication channels.

(unless the perceiver is controlling for doing
things like science, where the goal is to contrive models and
situations that will allow one to infer what might actually be the
real world cause of those perceptions; it is only in this case that I
can see it being meaningful to talk about the uncertainty of
perception from a PCT perspective).

So you really don't go along with Bill in thinking of belief as a perception with uncertainty. Your perceptions can have no uncertainty.

  Perception, from a PCT
perspective, is a process of computing different functions of external
reality. The outputs of these functions exist in the brain as
variables that are potentially controllable; and many of these
variables are controlled, which, as a side effect, keeps the system
functioning and (hopefully) relatively content. Uncertainty, in the
communication sense, is, it seems to me, irrelevant.

I know that you think this. You control strongly against any disturbance to your view that information is irrelevant to control. You thought it in 1993 or thereabouts, and nothing much seems to have changed. In the previous interchange, it was demonstrated mathematically, using straightforward basic control-loop equations, that information from the environmental variable was available in the perceptual signal, and to the extent that control was effective, information about the disturbance was available from the combination of the perceptual signal and the output signal.

It's when control is not very good that the information is unavaialble. That can be turned around, to say that when the information is unavailable, control is not very good.

You didn't believe the math then, for some reason. I don't expect you to believe it now. You prefer to assert that it's irrelevant and leave it at that. Or to misrepresent the argument, as above.

Martin

[rsmarken]

[From Rick Marken (2008.04.08.1810)]

Martin Taylor (2008.04.08.16.30)--

Rick Marken (2008.04.08.1250)

> In terms of the communication model of perception, the source of data
> is the outside world and the receiver of data is the perceiver.
>
That's one part of the control loop. there are others.

I don't think the communication model of perception involves control loops.

I'd prefer to say that a perception is a function of data that is related
to states of the world that provide input to the perceptual input function.

The only sense I can make of this is to understand "data related to
states of the world" as sensory data, which I consider to be
perceptions, too.

Without information about variation in the environmental correlate of the
perceptual signal, output is highly unlikely to result in any kind of
influence on the perceptual signal, let alone a directed influence that
reduces error.

Yes, a control system has to be able to perceive the controlled
variable in order to control it.

In PCT, accurate observation is important for effective control.

If "accurate" means "low noise" then this is correct; noise in the
perceptual signal (or anywhere in the control loop) does reduce the
quality (effectiveness) of control. Noise reduces the correlation
between variations in the perceptual signal and environmental
variable.

So you really don't go along with Bill in thinking of belief as a
perception with uncertainty. Your perceptions can have no uncertainty.

I don't believe Bill believes that any perception -- even a belief --
comes along "with uncertainty". I certainly don't.

I know that you think this. You control strongly against any disturbance to
your view that information is irrelevant to control.

My view is that information theory, as applied to psychology, is pure
bathwater. It's fine for data communication systems, though.

You thought it in 1993
or thereabouts, and nothing much seems to have changed. In the previous
interchange, it was demonstrated mathematically, using straightforward basic
control-loop equations, that information from the environmental variable was
available in the perceptual signal, and to the extent that control was
effective, information about the disturbance was available from the
combination of the perceptual signal and the output signal.

Ah, I see. We mean two different things by "information about the
environmental variable". I agree that control depends on having
accurate perceptual information about the controlled environmental
variable if what you mean is that variations in the perceptual signal,
p, must be highly correlated with the controlled environmental
variable, qi. Control is best if the correlation between p and qi is
1.0. When there is noise in the perceptual channel, the correlation
between p and qi will be lower than 1.0. The lower the correlation
between p and qi the worse control will be.

But control does not depend on information about the environmental
variable if that mean is information about the disturbance to that
variable. In a tracking task, qi = o+d. Whether there is a high or low
correlation between p and qi, there is no information in p about d
(the disturbance). In this tracking task there is no information about
the disturbance but the subject is able to control perfectly.

It's when control is not very good that the information is unavailable.

Now you must be talking about information about variations in d, the
disturbance. And, if anything, it's the opposite: the worse the
control, the more information there is about the disturbance. In fact,
if you don't move the mouse at all (so that there is zero control)
then you can see the disturbance perfectly; the information about the
disturbance is complete.

That can be turned around, to say that when the information is unavailable,
control is not very good.

That is true if, by "information is unavailable" you mean that p is
completely uncorrelated with qi; this happens when you can't perceive
qi and, indeed, in this case, control would be very poor; actually it
would be non-existent.

The only information needed to control a perception is the perception
itself. A control system does not need, nor does it usually have,
information about disturbances to the environmental correlate of the
controlled perception, qi, in order to control that perception.

You didn't believe the math then, for some reason. I don't expect you to
believe it now. You prefer to assert that it's irrelevant and leave it at
that. Or to misrepresent the argument, as above.

I don't think I'm misrepresenting any arguments. In order to control
qi a system has to be able to perceive it. Control is best when there
is a high correlation between variations in qi and p. If by
"uncertainty" you mean the size of the correlation between p and qi
then I suppose one could say that a p with a low correlation with qi
is more uncertain than a p that is highly correlated with qi. But this
seems like a peculiar way to describe things since the system itself
knows only p and has no inkling that p is a variable related to qi. So
the system experiences no uncertainty about how well correlated p is
with qi; it doesn;t even know there is a qi. When I control my
perception of the temperature of water in the shower all I am doing is
controlling p -- my perception of temperature -- and I never consider
the fact that what I am actually controlling is a perceptual correlate
of the average rate of molecular motion (which I presume is what qi is
in that case) and a possibly poor correlate at that. I just make my
perception of water temperature what I want it to be (bring it to my
reference) and I'm happy; no uncertainty.

Best regards

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[Bill_Powers1]

[From Bill Powers (2008.04.08.2022 MDT)]

Rick Marken (2008.04.08.1810) --

> Martin Taylor (2008.04.08.16.30)--
> Without information about variation in the environmental correlate of the
> perceptual signal, output is highly unlikely to result in any kind of
> influence on the perceptual signal, let alone a directed influence that
> reduces error.

Rick:
Yes, a control system has to be able to perceive the controlled
variable in order to control it.

> In PCT, accurate observation is important for effective control.

If "accurate" means "low noise" then this is correct; noise in the
perceptual signal (or anywhere in the control loop) does reduce the
quality (effectiveness) of control. Noise reduces the correlation
between variations in the perceptual signal and environmental
variable.

A control system does not need "accurate information about variation in the environmental correlate of the perceptual signal" in order to control the perceptual signal accurately. It needs accurate information about the correlates in order to control the correlates accurately -- which control systems cannot do, do not do, and do not need to do. Control systems control their perceptions quite accurately. In doing so they have effects on external variables which appears to an external observer as control of those external variables, but not as good control as the control of the perceptions. A driver keeps his car exactly centered in its lane, as he perceives it. An external observer would probably see the car's lateral position varying by a good deal more than the driver sees it varying, but as long as no collisions result, that is good enough. Reorganization stops with "good enough," not perfection.

> So you really don't go along with Bill in thinking of belief as a
> perception with uncertainty. Your perceptions can have no uncertainty.

I don't believe Bill believes that any perception -- even a belief --
comes along "with uncertainty". I certainly don't.

Yes I do. A little bit of uncertainty, in the sense that there is always a little noise level. Usually it's not enough to detect: right now I'm just seeing and feeling what I'm seeing and feeling, with no sense of random variations. Of course my fingers miss a key now and then and I have to backspace and retype, but I never get a sense of not knowing what I'm perceiving.

And anyway I said that the need to believe reveals that there is some uncertainty; if you know, you are not uncertain. If you don't know, you believe -- that is, you bring imagination into play.

Actually, even if there were little variations in the perceptions, my actions would automatically change to reduce them close to the limit of detectability. If the cause of the little variations were changes in the perceptual input function itself, my control actions would prevent the perception from varying much, but would cause the external correlate of the perception to vary with each variation in the input function. A good example of this is the autokinetic effect when measured by having a person act to keep a dot of light in a black room from moving. The person actually makes the dot move, while keeping the perception of its position tightly controlled. This proves that it is the perception, not its external correlate, that is controlled.

> I know that you think this. You control strongly against any disturbance to
> your view that information is irrelevant to control.

My view is that information theory, as applied to psychology, is pure
bathwater. It's fine for data communication systems, though.

> You thought it in 1993
> or thereabouts, and nothing much seems to have changed. In the previous
> interchange, it was demonstrated mathematically, using straightforward basic
> control-loop equations, that information from the environmental variable was
> available in the perceptual signal, and to the extent that control was
> effective, information about the disturbance was available from the
> combination of the perceptual signal and the output signal.

Martin, you keep announcing victory for your position when nobody has agreed to it. Your arguments naturally satisfy you, but they haven't convinced either Rick or me. They were based on analyzing the effect of a single known disturbance and calculating the correlation with variations in the perceptual signal, which a control system does not do.

Suppose a controlled variable is subject to the following simultaneous disturbing variables:

1. Da = d0*exp(-kt)

2. Db = 10*sin(12t)

3. if t < 10:00 then Dc= 15 else if t < 15:00 then Dc = 75 else Dc = 0

4. Dd = 100.

These disturbances all affect the controlled quantity at the same time. How could the perception of the controlled quantity contain information about any one of them? There is absolutely no way to represent them individually in a single perceptual signal. Only the state of the controlled quantity itself is represented by the perceptual variable, and that state is a non-separable function of four variables plus the output quantity's effect.

We went through hours and hours of arguments about this point years ago and got nowhere. We are still nowhere.

Rick:
Ah, I see. We mean two different things by "information about the
environmental variable". I agree that control depends on having
accurate perceptual information about the controlled environmental
variable if what you mean is that variations in the perceptual signal,
p, must be highly correlated with the controlled environmental
variable, qi.

But you shouldn't agree with that. That is not necessary for control of perception. As long as there is a reasonable amount of correlation, the perception will be accurately controlled, and the external counterpart will be controlled well enough for the organism's purposes. Come on, guys! Behavior is the control of perception, not external correlates.

Best.

Bill P.

Control is best if the correlation between p and qi is
1.0. When there is noise in the perceptual channel, the correlation
between p and qi will be lower than 1.0. The lower the correlation
between p and qi the worse control will be.

But control does not depend on information about the environmental
variable if that mean is information about the disturbance to that
variable. In a tracking task, qi = o+d. Whether there is a high or low
correlation between p and qi, there is no information in p about d
(the disturbance). In this tracking task there is no information about
the disturbance but the subject is able to control perfectly.

> It's when control is not very good that the information is unavailable.

Now you must be talking about information about variations in d, the
disturbance. And, if anything, it's the opposite: the worse the
control, the more information there is about the disturbance. In fact,
if you don't move the mouse at all (so that there is zero control)
then you can see the disturbance perfectly; the information about the
disturbance is complete.

> That can be turned around, to say that when the information is unavailable,
> control is not very good.

That is true if, by "information is unavailable" you mean that p is
completely uncorrelated with qi; this happens when you can't perceive
qi and, indeed, in this case, control would be very poor; actually it
would be non-existent.

Wrong argument: Martin still thinks that what us important to a control system is controlling the external correlate. Since a control system can't do that, that can't be right.

The only information needed to control a perception is the perception
itself. A control system does not need, nor does it usually have,
information about disturbances to the environmental correlate of the
controlled perception, qi, in order to control that perception.

Now you're talking. In fact the control system's actions will cause qi to vary if there is noise inside the perceptual input function, yet control of the perception will remain good.

> You didn't believe the math then, for some reason. I don't expect you to
> believe it now. You prefer to assert that it's irrelevant and leave it at
> that. Or to misrepresent the argument, as above.

I don't think I'm misrepresenting any arguments. In order to control
qi a system has to be able to perceive it.

But control system's don't control qi. They control p. That's all they CAN control.

Don't think in terms of big fuzzy white-noise disturbances. Think in terms of random wandering that continually distorts the relationship between perceptions and the external world by small unpredictable amounts. That's how most uncertainties enter into control processes. Control sysems automatically counteract those wanderings no matter what is causing them, even changes in the perceptual input function. But that's all right because we end up getting the food into the mouth (off center a little, but in) and so on. Control systems live in an idealized, simplified, stabilized version of the world, and apparently that's good enough for survival.

Best,

Bill P.

[MartinT]

[Martin Taylor 2008.04.09.10.22]

[From Bill Powers (2008.04.08.2022 MDT)]

Rick Marken (2008.04.08.1810) --

My view is that information theory, as applied to psychology, is pure
bathwater. It's fine for data communication systems, though.

You thought it in 1993
or thereabouts, and nothing much seems to have changed. In the previous
interchange, it was demonstrated mathematically, using straightforward basic
control-loop equations, that information from the environmental variable was
available in the perceptual signal, and to the extent that control was
effective, information about the disturbance was available from the
combination of the perceptual signal and the output signal.

Martin, you keep announcing victory for your position when nobody has agreed to it. Your arguments naturally satisfy you, but they haven't convinced either Rick or me.

I know that. It's a fact of life that I have understood for 15 years. I put it down to misunderstanding of the issues. At the time, Rick kept equating "information about the disturbance" with "perception of the nature of the disturbance source(s)", and could not be induced to understand that these were concepts almost from a different universe.

They were based on analyzing the effect of a single known disturbance and calculating the correlation with variations in the perceptual signal, which a control system does not do.

Not correlation, but informational dependance.

Suppose a controlled variable is subject to the following simultaneous disturbing variables:

1. Da = d0*exp(-kt)

2. Db = 10*sin(12t)

3. if t < 10:00 then Dc= 15 else if t < 15:00 then Dc = 75 else Dc = 0

4. Dd = 100.

These disturbances all affect the controlled quantity at the same time. How could the perception of the controlled quantity contain information about any one of them?

Why should it? This is introducing a completely irrelevant new requirement into the mix. The analysis concerned only D = Da + Db + Dc + Dd. If you have a four-dimensional variable you need a four-dimensional set of equations. The analysis in question had a two-dimensional variable to consider: {d, r}, and two known values {p, o}. The loop equations allow each pair to be determined from the other, as functions of time.

There is absolutely no way to represent them individually in a single perceptual signal.

Of course there isn't. Whoever suggested there was? The only point of the argument in the first place was to demonstrate that information about the waveform of the disturbance is available from signals within the control system.

Only the state of the controlled quantity itself is represented by the perceptual variable, and that state is a non-separable function of four variables plus the output quantity's effect.

We went through hours and hours of arguments about this point years ago and got nowhere.

Not about this poitn at all. This point is entirely novel, and non-controversial, to boot.

We are still nowhere.

So I see.

Rick:
Ah, I see. We mean two different things by "information about the
environmental variable". I agree that control depends on having
accurate perceptual information about the controlled environmental
variable if what you mean is that variations in the perceptual signal,
p, must be highly correlated with the controlled environmental
variable, qi.

But you shouldn't agree with that. That is not necessary for control of perception. As long as there is a reasonable amount of correlation, the perception will be accurately controlled, and the external counterpart will be controlled well enough for the organism's purposes. Come on, guys! Behavior is the control of perception, not external correlates.

Yes. Absolutely. I know that, you know that, Rick knows that. What I don't know is why you and Rick keep asserting that I believe the contrary. My hunch (high uncertainty perception, more uncertainty than "belief") is that you do believe that I think it is control of the real environment, and construe my messages so that they conform to that belief, trather than construing them as I intend, in the context that all control is of perception and only perception.

I know it's hard to rid oneself of preconceptions, but surely it can be possible after a decade and a half?

Martin

[Bill_Powers1]

[From Bill Powers (2008.04.09.0852 MDT)]

Martin Taylor 2008.04.09.10.22 --

Suppose a controlled variable is subject to the following simultaneous disturbing variables:

1. Da = d0*exp(-kt)

2. Db = 10*sin(12t)

3. if t < 10:00 then Dc= 15 else if t < 15:00 then Dc = 75 else Dc = 0

4. Dd = 100.

These disturbances all affect the controlled quantity at the same time. How could the perception of the controlled quantity contain information about any one of them?

Why should it? This is introducing a completely irrelevant new requirement into the mix. The analysis concerned only D = Da + Db + Dc + Dd.

So you say that the perception contains no information about any of the actual disturbances, but it does contain information about all of them.

I thought that would be your position -- it was, before. My position is that there is no D out there; only Da, Db, Dc, and Dd. There is no D out there to get information about.

I proposed no natural law saying that the four disturbances actually combine to produce a net disturbing variable, which then affects qi. Each affects qi independently of the others. The state of the input quantity is all that matters or exists, and it is an _effect_ of the disturbances plus the output, not a cause of them. The perception represents the input quantity, not the disturbances -- and certainly not an imaginary disturbance. If you say that the perception contains information about D, you're saying it contains information about something that has no physical existence. The information is thus an illusion.

What you are doing is reifying a calculation, as if it is just as real as the trasmitter that does, in fact, send messages that we can receive with the right equipment. I can't keep you from doing that, but I consider it a serious error -- well, not serious in the sense that you should get 20 lashes, but you know what I mean. I don't believe in D, but I guess you do, so that puts an end to the discussion unless you can think of a way of making D look real to me, or I to convince you it's an illusion.

You are very impatient with Rick and me for what you see as our unjust accusation of naive realism. But that is exactly how we see your belief in D, so I see nothing unjust about it. There is no D except in your imagination, even if we have gobs of evidence to justify believing in Da, Db. Dc, and Dd. That's how it looks to me.

Best,

Bill P.

[rsmarken]

[From Rick Marken (2008.04.09.0910)]

Bill Powers (2008.04.08.2022 MDT)--

Rick Marken (2008.04.08.1810) --

A control system does not need "accurate information about variation in the
environmental correlate of the perceptual signal" in order to control the
perceptual signal accurately.

I'm afraid I said that based only on intuition and my desire to be
nice to Martin;-) I just ran a little simulation to test it out and
found that, as usual, you are absolutely right: good control does not
depend on accurate information about the environmental correlate of
the perceptual signal. In my simulation, control (measured by the
stability factor, S) was nearly perfect even when the correlation
between p and qi was nearly zero.

An external observer would probably see the car's lateral
position varying by a good deal more than the driver sees it varying, but as
long as no collisions result, that is good enough.

Actually, in my simulation (which involved adding random noise to p
and involved a pure integrating output) control of qi (the analog of
the car's lateral position) was somewhat better than control of p (the
analog of the driver's view of the car's lateral position).

> I don't believe Bill believes that any perception -- even a belief --
> comes along "with uncertainty". I certainly don't.

Yes I do. A little bit of uncertainty, in the sense that there is always a
little noise level.

I don't see that as "uncertainty" since the driver is not uncertain
about perceiving the perception, noisy (randomly variable) though it
be. I'm certain I perceive something that is varying randomly.

> Ah, I see. We mean two different things by "information about the
> environmental variable". I agree that control depends on having
> accurate perceptual information about the controlled environmental
> variable...

But you shouldn't agree with that.

You're right. Agreement retracted;-)

Best regards

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[MartinT]

[Martin Taylor 2008.04.09.12.06]

[From Bill Powers (2008.04.09.0852 MDT)]

Martin Taylor 2008.04.09.10.22 --

Suppose a controlled variable is subject to the following simultaneous disturbing variables:

1. Da = d0*exp(-kt)

2. Db = 10*sin(12t)

3. if t < 10:00 then Dc= 15 else if t < 15:00 then Dc = 75 else Dc = 0

4. Dd = 100.

These disturbances all affect the controlled quantity at the same time. How could the perception of the controlled quantity contain information about any one of them?

Why should it? This is introducing a completely irrelevant new requirement into the mix. The analysis concerned only D = Da + Db + Dc + Dd.

So you say that the perception contains no information about any of the actual disturbances, but it does contain information about all of them.

I thought that would be your position -- it was, before. My position is that there is no D out there; only Da, Db, Dc, and Dd. There is no D out there to get information about.

This is not a proposition you had previously mentioned in the earlier discussions, but I'll deal with it, anyway.

Everything you say about D applies equally well to the environmental variable associated with any perceptual signal. If thee is no "real world" out there, well and good. But if the control of perception actually serves to allow the organism to function in the real world, then the action outputs of a control system must act through that real world in order to influence the perception. The effects of output on perception are real, at least as real as anything can be said to be. Of course, the reality of the output is equally in question.

It's easy to say "there is no chair out there corresponding to the chair you perceive, and it is not in a place corresponding to the location you perceive, and there is no disturbance to the chair's location corresponding to the movement you perceive." OK. Maybe there isn't. But if there isn't, then the whole apparatus of perceptual control theory goes out the window, at least insofar as it presupposes that something exists outside the organism, and that the organism's actions influence the something and thereby influence the controlled perceptions.

I proposed no natural law saying that the four disturbances actually combine to produce a net disturbing variable, which then affects qi. Each affects qi independently of the others.

Yes, and the effect, if there exists a real world, is a single-valued D that would, in the absence of control actions, alter qi by some amount. If D does not exist, neither does qi. They have precisely the same claim to existence.

The state of the input quantity is all that matters or exists, and it is an _effect_ of the disturbances plus the output, not a cause of them.

Why _emphasize_ the self-evident?

The perception represents the input quantity, not the disturbances -- and certainly not an imaginary disturbance. If you say that the perception contains information about D, you're saying it contains information about something that has no physical existence. The information is thus an illusion.

Yes it is, to exactly the same extent as is the "information about" qi.

I don't believe in D, but I guess you do, so that puts an end to the discussion unless you can think of a way of making D look real to me, or I to convince you it's an illusion.

You are very impatient with Rick and me

Our perceptions differ. I think of myself as being rather unnaturally patient with your reluctance to consider that the obvious is not always wrong. I expect you have the same perception of your own patience with my inability to recognize what you see as obvious.

for what you see as our unjust accusation of naive realism. But that is exactly how we see your belief in D, so I see nothing unjust about it. There is no D except in your imagination, even if we have gobs of evidence to justify believing in Da, Db. Dc, and Dd. That's how it looks to me.

And I guess you also would say there's no chair in a certain place except in your imagination. There is a seat, four legs, a back, some screws or glue -- oh, wait, there's no legs, no back... and it didn't move when someone seemed to push it away from where I wanted it.

Naive realism? The realism in question is a supposition that the conditions for perceptual control through an environment do actually include an environment, even though what we see of it may have only an informational connection with the way we perceive it at any moment. There's no supposition that our perception (p = p(qi)) consists of a little model chair built in the brain!

The canonical control loop is diagrammed with a connection qi = o+d. That presupposes the equivalent realism of qi, o and d. Deny one, and you deny tham all. You may, of course, argue that disturbances aren't always additive, and you would be right. Perhaps the disturbance is a change of a volume control, making qi = o*d. More generally, qi = f(o, d). The same applies. In no case does the likelihood that d = f (d1, d2, d3,...,dn) diminish or enhance the reality of d, relative to that of qi and o. They stand and fall together.

Anyway, none of the above has the slightest relevance to the issues of 1993, which surfaced again in this thread.

Martin

PS. As I have mentioned, I'm trying to prepare for a meeting near Oslo next week, and have been spending more time than I wanted on CSGnet. I do this because I believe it is important to develop PCT, not because it amuses me. However, I have to cut back severely, as I had intended to do several days ago. I return May 5, but I expect to be away again quite shortly after that.

[MartinT]

[Martin Taylor 2008.04.09.16.37]

[From Rick Marken (2008.04.09.0910)]

Bill Powers (2008.04.08.2022 MDT)--

Rick Marken (2008.04.08.1810) --

  A control system does not need "accurate information about variation in the
environmental correlate of the perceptual signal" in order to control the
perceptual signal accurately.

I'm afraid I said that based only on intuition and my desire to be
nice to Martin;-) I just ran a little simulation to test it out and
found that, as usual, you are absolutely right: good control does not
depend on accurate information about the environmental correlate of
the perceptual signal. In my simulation, control (measured by the
stability factor, S) was nearly perfect even when the correlation
between p and qi was nearly zero.

Are you surprised? If I understand your setup, you added a wide-band noise to the input to the PIF but not to qi (which is just fine -- it's what you should have done). The disturbance was fairly slow and the output function was an integrator. You could hardly expect the perceptual signal to be much correlated with qi unless your low-frequency disturbance was very large compared to the noise range.

It shouldn't really be necessary, but given past history I suppose I should point out that your experiment does not validate the comment that you cited from Bill. And perhaps I should also mention, though again it shouldn't be necessary, that correlation is not the same thing as information dependence. You can't have information independence with high correlation, but you can have zero correlation with high information dependence. That, however, is not the issue in this experiment, except insofar as it addresses your correlational approach to the analysis.

> An external observer would probably see the car's lateral

position varying by a good deal more than the driver sees it varying, but as
long as no collisions result, that is good enough.

Actually, in my simulation (which involved adding random noise to p
and involved a pure integrating output) control of qi (the analog of
the car's lateral position) was somewhat better than control of p (the
analog of the driver's view of the car's lateral position).

Wouldn't you expect that, given that the high-frequency variability enters into your calculation of S, but not in the stability of qi?

You have to consider the informational relationships, not the correlation. Informationally, successive values of qi are almost perfectly mutually dependent at the relatively high sampling rate and low-frequency disturbance that I presume you used. If the bandwidth of the disturbance was W, you don't get a new truly independent value of qi until 1/2W seconds later.

At the perceptual signal, it's different. if there was a new random number for each sample, successive samples are almost independent (almost, because of the slight dependence caused by the disturbance, which is reduced by the fact of control), and that sample-to-sample independence carries through to the error signal. Since the integrating output function gives the loop a gain that (apart from the leak) is inversely proportional to frequency, the high-frequency fluctuations you introduced are effectively reduced, in comparison to the control against the slow disturbance.

If you got the same result with a disturbance that varied as rapidly as the introduced noise, or with an introduced noise with the same low bandwidth variation as the disturbance, I might be a bit surprised. Neither would, however, really address the issue. Your experiment does, if interpreted informationally.

I guess what you have done is partially illustrate my comment in [Martin Taylor 2008.04.08.11.00] about possible ways that information about uncertainty could be developed at any level of perception: "I will ... ignore a completely different range that might be more significant at higher levels -- control."

Anyway, it's good to see an illustrative experiment being done so quickly. Thank you for that.

Martin

[Bill_Powers1]

[From Bill Powers (2008.04.09.1646 MDT)]

Rick Marken (2008.04.09.0910) –

An external observer would
probably see the car’s lateral

position varying by a good deal more than the driver sees it
varying, but > as long as no collisions result, that is good
enough.

Actually, in my simulation (which involved adding random noise to p

and involved a pure integrating output) control of qi (the analog of

the car’s lateral position) was somewhat better than control of p
(the

analog of the driver’s view of the car’s lateral
position).

That is because the bandwidth of the disturbance was greater than the
bandwidth of control. If you had used a low-frequency disturbance (say, a
simple sine-wave or a smoothed random disturbance like those I use) added
to the perceptual signal, and a high control gain, you would have found
that the variations in the input quantity were greater than the
variations in the perceptual signal. When the internal disturbance went
one way, the input quantity would have gone the other way to keep the
perceptual signal matching the reference signal.

I don’t believe Bill
believes that any perception – even a belief –

comes along “with uncertainty”. I certainly
don’t.

Yes I do. A little bit of uncertainty, in the sense that there
is always a

little noise level.

I don’t see that as “uncertainty” since the driver is not
uncertain

about perceiving the perception, noisy (randomly variable) though it

be. I’m certain I perceive something that is varying
randomly.

I’m thinking of the case (which I’m sure you’ve encountered in your
studies of perception) where you’re asking yourself if you actually
perceived the stimulus, or imagined it. I agree that there’s no doubt
about the experience itself. The doubt arises about statements you make
about the experience. “That was a real beep” versus “I
imagined that beep.”
The point Martin is raising in his last post to me is not trivial, and it
is the epistomological question. I raise it in the “threesys”
demo and elsewhere.
Given a control system that senses a set of environmental variables
v1…vn, so
p = f(v1…vn).
Clearly, we assume that the environmental variables are really there: our
models require that there be actual physical processes rather than
completely imagined ones. But does p represent something “real”
in this environment? If you control p, are you also controlling some real
environmental correlate? The problem is that we can pick any function f
that we please, so in the same set of v’s, there is the potential for
percieving at least one order of infinity of derived variables. There are
only n independent perceptions perceivable at one moment in the set of
v’s, but there is an infinity of different sets of independent
perceptions.
I think that in order to say that p represents something other than just
the value of a computation, we would have to show that its environmental
correlate is lawfully related to other environmental correlates of
perceptions independently of the perceiving system. An example is
density, which is computed by dividing mass of an object by the volume of
that object. Density determines whether an object will float in water,
for example. It doesn’t matter whether someone is calculating the density
of a piece of wood; it will still (most likely) be floating when we come
back to observe it again. But what if the mass being measured that of one
object, and the volume is that of a different object? We can still
compute density – we can divide the mass by the volume – but now we
don’t expect it to have anything to do with physical properties of the
mass. In fact there’s obviously something wrong with calling the quotient
density even though it’s being calculated in exactly the same way
mathematically, mass/volume.
I’ve tried before to show the difference between a “real”
environmental correlate and one that is not real. Nobody, including me,
has been much impressed. Now, under Martin’s prodding, I think we’re
getting a little closer. I think the key is to ask if there are any
physical relationships that involve the environmental correlate
whether or not something is perceiving it. “Floating”
occurs (we can perceive it) whether or not we compute density, but when
it does occur we always find that the density we compute is less than
that of the fluid in which the thing floats. We can say that the
environmental correlate of density is a real physical property of the
world and not just a creation of perception. On the other hand, dividing
the mass by the mean wavelength reflected by the paint it is covered with
gives us a perception without a real environmental correlate. We can
perceive it and disturb it and control it, but it’s not real. Not unless
you can show that this perception is related to some other perceptions
through external laws (not just other calculations).

That still isn’t a succinct statement of the solution to this problem,
but maybe it’s a wordy statement of it. We can obviously perceive and
control variables that have no observable effect on anything, and also
variables that do affect other things in a lawful way even when we’re not
observing them. Jupiter disappears behind the sun, then dutifully
reappears right where it should. It’s real, as best we can determine, and
so is the sun which comes up every morning just when we expect it. And
the orbit of Jupiter is real.

Reality is in the relationships (among perceptions) that we discover to
be independent of our observations. Some perceptions have real
correlates; most, I suspect, do not. I can hold up my thumb and blot out
your head, but I suspect that that is only an appearance.

Best,

Bill P.

[rsmarken]

[From Rick Marken (2008.04.09.1910)]

Martin Taylor (2008.04.09.16.37)--

> Rick Marken (2008.04.09.0910)--

> I'm afraid I said that based only on intuition and my desire to be
> nice to Martin;-) I just ran a little simulation to test it out and
> found that, as usual, you are absolutely right: good control does not
> depend on accurate information about the environmental correlate of
> the perceptual signal. In my simulation, control (measured by the
> stability factor, S) was nearly perfect even when the correlation
> between p and qi was nearly zero.
>

Are you surprised?

You bet.

If I understand your setup, you added a wide-band noise
to the input to the PIF but not to qi (which is just fine -- it's what you
should have done). The disturbance was fairly slow and the output function
was an integrator.

That's it.

You could hardly expect the perceptual signal to be much
correlated with qi unless your low-frequency disturbance was very large
compared to the noise range.

The perceptual signal is perfectly correlated with qi when the noise
amplitude is zero. The quality of control, measured by S, is nearly
perfect (S = ~1.0). When noise is added the correlation between p and
qi goes down in proportion to the amplitude of the noise. However,
adding noise that brings the correlation between p and qi down to
nearly zero hardly affects the quality of control at all (S ~ .98).
This was kind of a surprise to me (although it's actually something I
should have known from my "S-R vs Control" demo) because it means that
control is just as good when you are controlling a very noisy
perception of qi (one that has very little information about qi in the
information theory sense) as when you are controlling a perception
that is a perfect analog of qi.

> Actually, in my simulation (which involved adding random noise to p
> and involved a pure integrating output) control of qi (the analog of
> the car's lateral position) was somewhat better than control of p (the
> analog of the driver's view of the car's lateral position).
>
Wouldn't you expect that, given that the high-frequency variability enters
into your calculation of S, but not in the stability of qi?

I don't think that's the reason. I see that Bill explained the reason
in a recent post [(Bill Powers (2008.04.09.1646 MDT)]

You have to consider the informational relationships, not the correlation.
Informationally, successive values of qi are almost perfectly mutually
dependent at the relatively high sampling rate and low-frequency disturbance
that I presume you used. If the bandwidth of the disturbance was W, you
don't get a new truly independent value of qi until 1/2W seconds later.

In my simulations the correlation between p and qi depends only on
noise amplitude; the frequency of the disturbance seems to have very
little to do with it.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[rsmarken]

[From Rick Marken (2008.04.09.1930)]

Bill Powers (2008.04.09.1646 MDT)

Rick Marken (2008.04.09.0910) --

> I don't see that as "uncertainty" since the driver is not uncertain
> about perceiving the perception, noisy (randomly variable) though it
be.

I'm thinking of the case (which I'm sure you've encountered in your studies
of perception) where you're asking yourself if you actually perceived the
stimulus, or imagined it. I agree that there's no doubt about the experience
itself. The doubt arises about statements you make about the experience.
"That was a real beep" versus "I imagined that beep."

Yes, I've already agreed that there can be uncertainty in that
situation. The uncertainty exists because the the perception is taken
as _evidence_ of another possible state of affairs.

The point Martin is raising in his last post to me is not trivial, and it
is the epistemological question.

I don't think it has to get that deep when we are talking about
uncertainty. In the tone detection task I am told that a tone is
really added on some trials and so I am supposed to take the sounds I
hear as evidence that the tone was or was not added. I would
experience the same uncertainty if the tone wasn't really added; if
the experimenter had lied to me and I was just listening to noise
bursts. It's my attitude toward the bursts -- treating them as
evidence rather than as just sounds -- that creates the uncertainty.
The uncertainty is not in the sounds themselves; the same noise burst
can evoke no uncertainty when I am just asked to judge its timbre,
say, and great uncertainty when I am asked to say whether or not it
had a tone. The epistemological issues you raise are certainly not
trivial but they are not really relevant to my understanding of
uncertainty.

Best regards

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[MartinT]

[Martin Taylor 2008.04.10.21.23]

[From Rick Marken (2008.04.09.1910)]

Martin Taylor (2008.04.09.16.37)--

> Rick Marken (2008.04.09.0910)--

> I'm afraid I said that based only on intuition and my desire to be
> nice to Martin;-) I just ran a little simulation to test it out and
> found that, as usual, you are absolutely right: good control does not
> depend on accurate information about the environmental correlate of
> the perceptual signal. In my simulation, control (measured by the
> stability factor, S) was nearly perfect even when the correlation
> between p and qi was nearly zero.
>

  Are you surprised?

You bet.

If I understand your setup, you added a wide-band noise
to the input to the PIF but not to qi (which is just fine -- it's what you
should have done). The disturbance was fairly slow and the output function
was an integrator.

That's it.

You could hardly expect the perceptual signal to be much
correlated with qi unless your low-frequency disturbance was very large
compared to the noise range.

The perceptual signal is perfectly correlated with qi when the noise
amplitude is zero. The quality of control, measured by S, is nearly
perfect (S = ~1.0). When noise is added the correlation between p and
qi goes down in proportion to the amplitude of the noise. However,
adding noise that brings the correlation between p and qi down to
nearly zero hardly affects the quality of control at all (S ~ .98).

Yes. That's what one would expect, isn't it? It's pretty well what I said, anyway.

This was kind of a surprise to me (although it's actually something I
should have known from my "S-R vs Control" demo) because it means that
control is just as good when you are controlling a very noisy
perception of qi (one that has very little information about qi in the
information theory sense) as when you are controlling a perception
that is a perfect analog of qi.

Apart from the bit in parentheses, yes. But the point is that qi does not provide much information because it changes only slowly. the perceptual signal still contains most of that information, the fast-moving noise being largely averaged out over the time between sucessive independent samples of qi.

> Actually, in my simulation (which involved adding random noise to p
> and involved a pure integrating output) control of qi (the analog of
> the car's lateral position) was somewhat better than control of p (the
> analog of the driver's view of the car's lateral position).
>
  Wouldn't you expect that, given that the high-frequency variability enters
into your calculation of S, but not in the stability of qi?

I don't think that's the reason. I see that Bill explained the reason
in a recent post [(Bill Powers (2008.04.09.1646 MDT)]

I'm surprised you would say this, since Bill's reason doesn't correspond to the experimental conditions you indicated, whereas mine does. Bill assumed you were using a fast disturbance, but you weren't, according to your agreement with my description of what I assumed you did.

> You have to consider the informational relationships, not the correlation.

Informationally, successive values of qi are almost perfectly mutually
dependent at the relatively high sampling rate and low-frequency disturbance
that I presume you used. If the bandwidth of the disturbance was W, you
don't get a new truly independent value of qi until 1/2W seconds later.

In my simulations the correlation between p and qi depends only on
noise amplitude; the frequency of the disturbance seems to have very
little to do with it.

That's one way of making my point, yes.

Martin

PS. I keep saying so, but I really will have to leave this discussion apart from possible small interjsctions. I leave Saturday afternoon, and am far from prepared.

[Bill_Powers1]

[From Bill Powers (2008.04.10.2003 MDT)]

Martin Taylor 2008.04.10.21.23--

I think someone has to do the right experiment and post the results. I'll do it in a few days if nobody else does.

    Low frequency noise ---> r
                            > >
     D ----> qi -->[PIF]--->p --->[Comp]-->e -->[Output Funct] --->o --
              > >
               -------------<-----------[Feedback Funct] <-------------

The noise that adds to the perceptual input function has the same bandwidth as the bandwidth of the control system. The PIF is a unity transform. The gain of the output function (a pure integrator) is raised until the variations in p are very small. The disturbance can be zero or non-zero -- it's easier to figure out what happens if the disturbance is zero. In that case, to a first approximation, the variations in qi will be equal and opposite to the variations in the low frequency noise, and the perceptual signal will be constant and will match the reference signal. The input quantity qi will vary a great deal more than the perceptual signal will, if you have set up the control system properly.

Best,

Bill P.

[rsmarken]

[From Rick Marken (2008.04.10.2310)]

Bill Powers (2008.04.10.2003 MDT)--

Martin Taylor 2008.04.10.21.23--

I think someone has to do the right experiment and post the results. I'll
do it in a few days if nobody else does.

Done. Though I don't see why this is the right experiment. It seems
like whatever I find it makes Martin's point. I thought that nearly
perfect control of p when there is no correlation between p and qi
would prove the point. But I just did the experiment where I added low
frequency (narrow band) noise to p and the result is exactly as you
say: with no disturbance to qi and a fixed reference for p the
variance in p is 2.3 and the variance in qi is 51.2 and the
correlation between qi and p is -.003. The noise added to p was a low
frequency sine wave with a little bit of high frequency broad band
noise added for spice (and to keep the correlation between qi and p
close to zero). The results are almost exactly the same when a low
frequency disturbance is added to qi (variance of p = 2.1, variance of
qi = 51.1 and correlatoin between qi and p = .030).

These results seem completely inconsistent with the idea that control
depends on having perceptions that are contain accurate information
about qi. But I'll bet that Martin finds that these results, just like
the results of my earlier experiments, are completely consistent with
an informational analysis of control.

Best regards

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[Bill_Powers1]

[From Bill Powers (2008.04.11.0759 MDT)]

Rick Marken (2008.04.10.2310) --

Done. Though I don't see why this is the right experiment. It seems
like whatever I find it makes Martin's point. I thought that nearly
perfect control of p when there is no correlation between p and qi
would prove the point.

I wish you would stop making snide remarks about Martin. He is being just as honest about his thoughts as you are. Or perhaps I should say no less honest than you are.

In your [previous post, you said

"The perceptual signal is perfectly correlated with qi when the noise
amplitude is zero. The quality of control, measured by S, is nearly
perfect (S = ~1.0). When noise is added the correlation between p and
qi goes down in proportion to the amplitude of the noise. However,
adding noise that brings the correlation between p and qi down to
nearly zero hardly affects the quality of control at all (S ~ .98).

I find that very hard to understand. Without the noise, p = r and is constant. So control looks perfect. But when you add internal high-frequency noise to p without directly affecting qi, p begins to vary right along with the (internal) disturbance, because the integrating output function can't keep up with the random variations in error signal. The input quantity therefore can't change as much as it needs to to keep p from changing. So p ought to be varying a LOT more, and control of p should be very poor -- in fact, almost nonexistent. Control of qi relative to the same internal disturbance would be far better, because the high-frequency variations don't get through the output function to make qi vary as much as p is varying. I guess I don't understand how you set up the situation -- what was the internal disturbance of p that you used? Were you also using an external disturbance of qi? Could there also have been some low-frequency noise ijn the internal disturbance, which would tip the balance the other way?

But I just did the experiment where I added low
frequency (narrow band) noise to p and the result is exactly as you
say: with no disturbance to qi and a fixed reference for p the
variance in p is 2.3 and the variance in qi is 51.2 and the
correlation between qi and p is -.003. The noise added to p was a low
frequency sine wave with a little bit of high frequency broad band
noise added for spice (and to keep the correlation between qi and p
close to zero). The results are almost exactly the same when a low
frequency disturbance is added to qi (variance of p = 2.1, variance of
qi = 51.1 and correlatoin between qi and p = .030).

These results seem completely inconsistent with the idea that control
depends on having perceptions that are contain accurate information
about qi.

"Information" is a technical term in Martin's argument, and the only way to draw conclusions is to calculate the information content according to the definitions. We should wait for Martin to do that. Give the man a chance to prove that he's right -- arguing qualitatively certainly won't prove he's wrong. Saying that results "seem" inconsistent doesn't say anything about whether they ARE inconsistent with something else in any publicly-tested way. Having a bias like yours (and mine) against information theory requires being extra careful not to let it substitute for publicly laid-out reasoning.

But I'll bet that Martin finds that these results, just like
the results of my earlier experiments, are completely consistent with
an informational analysis of control.

Martin has already said that he thinks that no matter how rigorous his proof that he is right, you will find some excuse to dispute it. So you are both accusing each other of being blinded by bias, and you are both right. You are both blinded by a belief that the other guy has nothing but bias behind his argument. This is the exact opposite of the layered protocol strategy for communication. As a result, neither of you is addressing the other person's actual argument. So do we now have a definitive resolution of the disagreement? Not bloody likely.

Best,

Bill P.

[rsmarken]

[From Rick Marken (2008.04.11.0940)]

Bill Powers (2008.04.11.0759 MDT)

>Rick Marken (2008.04.10.2310) --

> It seems like whatever I find it makes Martin's point.

I wish you would stop making snide remarks about Martin.

I don't see what's snide about that remark. But I'll wish for me to
stop making then, too. Though I think it's part of my charm.

> "The perceptual signal is perfectly correlated with qi when the noise
> amplitude is zero. The quality of control, measured by S, is nearly
> perfect (S = ~1.0). When noise is added the correlation between p and
> qi goes down in proportion to the amplitude of the noise. However,
> adding noise that brings the correlation between p and qi down to
> nearly zero hardly affects the quality of control at all (S ~ .98).

I find that very hard to understand. Without the noise, p = r and is
constant. So control looks perfect. But when you add internal high-frequency
noise to p without directly affecting qi, p begins to vary right along with
the (internal) disturbance... Control of qi relative to the same internal
disturbance would be far better... I guess I don't understand how you set
up the situation

I think you understand the set up. What was unclear, I think, was what
I meant by control of p and qi. When the high frequency (broad band)
noise was added to p, the variance of p was, indeed, greater than the
variance of qi (which is 0.0). However, control of p, was measured as

S = 1 - sqrt(var(p)/[var(d)+var(o)])

where d is the narrow band disturbance to qi and o is the output
effect on qi. The value of S is nearly perfect (1.0 is perfect and I
get S values of .98 or more) when low amplitude broad band noise is
added to p, even though the correlation between qi and p goes down to
near 0.0.

Of course, the value of S for qi -- S = 1 -
sqrt(var(qi)/[var(d)+var(o)]) -- is higher than for p (1.0 compared to
~.98) but the point of the demo (from my perspective) was to show that
control (measured in terms of stability of qi or p) can be quite good
even when there is no correlation between qi and p. It seems to me
that this demo proves that accurate information about qi (which would
be a high correlation between qi and p) is not needed for control.

"Information" is a technical term in Martin's argument, and the only way to
draw conclusions is to calculate the information content according to the
definitions. We should wait for Martin to do that.

I was going to suggest, in my original description of the simulation,
that Martin calculate the information transmitted about qi when the
correlation between qi and p is 0. I can't remember the exact formula
for transmitted information (which Shannon called H) but I think it
was something like:

H = Sum [log2 (Pr(p|qi))]

That is, information is, technically, a log (base 2) function of the
conditional probability of getting particular values of p given
particular values of qi summed over the range of possible qi (the
messages). I can't see how H can come out to be anything other than 0
when the correlation between qi and p is 0. But I agree that we should
wait for Martin to do that. In the meantime I'll try to find the
information transmission measure myself and see how much information
is actually transmitted in this simulation. If anyone out there
happens to know off hand Shannon's formula for H please let me know
and I'll compute it in my simulation.

Best regards

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[MartinT]

[Martin Taylor 2008.04.11.13.47]

I told myself I wouldn't even look at CSGnet until I return, but this deserves at least one comment.

[From Rick Marken (2008.04.11.0940)]
... When the high frequency (broad band)
noise was added to p, the variance of p was, indeed, greater than the
variance of qi (which is 0.0). ...
I was going to suggest, in my original description of the simulation,
that Martin calculate the information transmitted about qi when the
correlation between qi and p is 0.

There's no necessary relationship. You can have high information transmission with zero correlation, but not high correlation with low information transmission. In fact, if indeed qi does not vary, no information could be transmitted between q and p, other than its initial constant value. The prior uncertainty of that value is given by the possible range of output values of p. Every measure (sample) contributes to a reduction in that uncertainty. Whether the uncertainty eventually approaches zero depends on the algorithm by which the sample values influence the end result. If the system is designed to alow for real variation in qi, then the uncertainty won't asymptote at zero.

This is an analysts view, since there's no way the single perceptual signal can discriminate between variation in qi and variation in the channel from qi. However, the control system itself is designed on the prior assumption that it will not control against high frequency variation (the integrator). In other words, it acts as though it is getting information about slow variation in qi, forgetting older samples as time goes by. If p varies too fast, those fast variations will be damped or ignored. That's why I said you should try with low-frequency noise in the transmission path, because under those conditions the system would indeed try to control against those fluctuations, which are (unknown to the system) actually noise.

Remember that even though control of perception is what is happening, the reason why organisms control perception is that by doing so they survive in the real world. If they act to control too rapidly against variations that turn out not to correspond to anything happening in the real world, that might be detrimental to survival. So our systems are likely to have evolved with time constants for the perception-error-output path that match the rates at which variables important for survival are likely to change in the real world. Those are the rates that have to be considered when thinking in informational terms, which is why nothing in your experimental results seems the least bit surprising.

I can't remember the exact formula
for transmitted information (which Shannon called H) but I think it
was something like:

H = Sum [log2 (Pr(p|qi))]

At first sight that looks right for the uncertainty of p given qi. If qi is always zero, it is the noise uncertainty.

Now I really must stop reading CSGnet until some time around May 6 or 7 (if not too much else has piled up in the meantime.

Martin

[rsmarken]

[From Rick Marken (2008.04.11.1150)]

Martin Taylor (2008.04.11.13.47) --

> Rick Marken (2008.04.11.0940)--

> I was going to suggest, in my original description of the simulation,
> that Martin calculate the information transmitted about qi when the
> correlation between qi and p is 0.
>

There's no necessary relationship. You can have high information
transmission with zero correlation

Could you please show me how that works mathematically. Then I can
make the measure of transmitted information part of the model. Forgive
me for not taking your word for it, by the way.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[Bill_Powers1]

[From Bill Powers (2008.04.11.1329 MDT)]

Martin Taylor 2008.04.11.13.47

You won't see this for some weeks, but I thought I'd unload my comments before I forget them.

There's no necessary relationship. You can have high information transmission with zero correlation, but not high correlation with low information transmission.

So if the variations in p are not related to the variations in qi, there can still be a large amount of information in p about qi? That sounds paradoxal and I don't understand it. Suppose the variations in qi are those of the Morse code. If p is a string of alphanumeric characters that is unrelated to their Morse code meanings, how can there be any information transmitted from qi to p?

This is an analysts view, since there's no way the single perceptual signal can discriminate between variation in qi and variation in the channel from qi.

The analyst could not discriminate between them, either.

However, the control system itself is designed on the prior assumption that it will not control against high frequency variation (the integrator). In other words, it acts as though it is getting information about slow variation in qi, forgetting older samples as time goes by.

The forgetting would indicate a leaky integrator. It's not necessary for our example.

If p varies too fast, those fast variations will be damped or ignored. That's why I said you should try with low-frequency noise in the transmission path, because under those conditions the system would indeed try to control against those fluctuations, which are (unknown to the system) actually noise.

Yes, this is what my proposal assumed.

Remember that even though control of perception is what is happening, the reason why organisms control perception is that by doing so they survive in the real world.

The control system does not control its effects in the real world. It controls its perceptions -- the perceptual signal p. If there is another control system that alters the parameters of control in order to control some objective side-effect of controlling qi, that is a different system and is not involved in the system we are discussing here. And it, too, controls its own perception, not the thing that the perception partially represents.

If they act to control too rapidly against variations that turn out not to correspond to anything happening in the real world, that might be detrimental to survival.

That is irrelevant to the present analysis. We have a control system with given properties, however they got to be that way, and whether this is a good design for survival or a bad one.

So our systems are likely to have evolved with time constants for the perception-error-output path that match the rates at which variables important for survival are likely to change in the real world. Those are the rates that have to be considered when thinking in informational terms, which is why nothing in your experimental results seems the least bit surprising.

Informational terms have nothing to do with it.You have to know the time constants and rates of change before you can even start to apply information theory. All we need are the control-system equations for an integrating control system, and we can figure out from first principles what the relationships will be among the different variables in different frequency bands. Adding an informational analysis will not alter these results. After that analysis is done, you can go back and calculate how much information is present in each channel. However, that is not what makes the control system work. In fact, you have to know how the control system works before you can apply the calculations of information theory. Information theory is derivative from more fundamental representations of the system (in the same way thermodynamics is). That is my sole objection to the way many people use information theory and other such higher-order abstractions. Information theory is to systems analysis as the smile is to the Cheshire cat, as used in higher academia.

Best,

Bill P.