Illusion and Loops (was Beyond the Fringe)

CSGnet Archive CSG2010
21

[From Bill Powers (2010.05.25.1150 MDT)]

Martin Taylor 2010.05.25.13.11 –

RM earlier: But then you say
that the stimulus is not itself the disturbance to this relationship
perception? How could that be?

Because the disturbance is the output of a function to which the stimulus
is the input. The question of interest to the psychophysicist is some
property of this function.

Either we decide NOW to resolve the ambiguity of “the
disturbance” or I will go live in Tahiti and try painting naked
ladies. This is getting ridiculous.

As we use the term “disturbance,” and represent it as d, it is
the independent variable, not the effect on the controlled variable. D is
the state of the light bulb. Its effect is a change in the retinal
illumination, and eventually, at some higher level, a change in some
higher perception, the change not being caused by the action of the
system because d is an independent variable.

RM earlier: The stimulus is what
the experimenter manipulates in an experiment, the IV. PCT suggests that
this stimulus must be a disturbance (d) to a controlled variable,

MMT: Nothing in PCT says that the stimulus as perceived by the
experimenter (e.g. the brightness of a light or the intensity of a tone)
must be the actual disturbance.

BP: Of course we can be mistaken if we’re hasty, careless, or ignorant,
but as we are none of those we can take it that if there is a clearly
traceable physical connection from the light bulb to the eyes of the
subject, and if the subject acts the way we expect if and only if the
light from the light bulb gets to the pupil (check it with a blindfold if
you really have any doubt), the state of the the light-bulb can be
treated as d in our diagrams. It is exactly what an experimenter would
call a stimulus because it affects the perceptions of the system but is
not affected by the action of the system.

All PCT says is that if
some action is correlated to the presentation of the stimulus, it is
probable that the stimulus contributes to a disturbance to some
controlled variable and that the action is likely to be an input to the
environmental feedback path, the output of which contributes to the
controlled variable.

BP: In most cases like the Schouten experiment, the probability is around
0.9999, so you’re just quibbling. If you have to calculate probabilities
of this kind, you should redesign the experiment.

RM earlier: I think that
subjects in psychophysical experiments are controlling a perception of
the relationship between stimulus and response.

MMT: Between some property of the stimulus, generated by a perceptual
function inside the subject, and some property of the response (e.g. it
doesn’t matter how hard the response button is predded, in most
psychophysical experiments).

BP:Yes, of course. Isn’t that what he said, with fewer words?

RM earlier: But you could easily
test this using Bill’s suggestion of disturbing qo. If the response to
the stimulus is open loop then there will be no resistance to the
disturbance.

MMT: There will, of course, be no effect of varying qo on the properties
of the preceding stimulus – unless you really do think that time-travel
to the past should be incorporated into PCT.

There will be no effect on the stimulus, period. The stimulus, or
disturbance, is an independent variable. There will be no effect on the
sensory inputs of the organism, either. That’s what we mean by open-loop,
isn’t it? A really long delay of the effect, like a minute or an hour, of
course, brings in the possibility of extraneous causes, but we don’t
generally worry about that time-scale. If there is a control system,
applying a steady disturbance to the output will result in a steady
change in the action of the system just upstream from qo (after an
initial transient); if there is no control system, no such change will be
seen.

If you think only in terms of instantaneous changes in the values of
time-quantized variables you will never understand how a control system
works. The time-travel objection applies to any differential equation
describing a closed loop. How can there be a reaction force from an
accelerated mass, when it always arrives too late to oppose the previous
applied force? A reasonable question, but one which I would have thought
you would have answered long ago.

MMT: Varying qo will affect the
compensation against the disturbance to whatever variables are being
controlled. But the immediately preceding stimulus (and it predecessors)
are not among these variables.

BP: In an open-loop system there are no variables being controlled, with
or without delays. That’s all we need to distinguish between open-loop
and closed-loop systems.

Best,

Bill P.

22

[Martin Taylor 2010.05.25.14.18]

[From Bill Powers (2010.05.25.1035 MDT)]

…

We still agree about that. I will even let you have a
“formulation” phase while the task is being learned. But once
it’s learned, I still think that the real button-press and the
presentation are the elements of the controlled relationship.

So where does that leave us?

It leaves me about to turn off my computer and finish packing.
As to the substance, I think there will be merit in further discussion,
based around your: “As in all diagrams of hierarchical control, a
copy of the
perception at the lower order is sent to the higher order of control.”
I don’t think this is necessary, and am prepared to discuss why I
don’t, but only after I either get a reasonable connection in Europe or
after I come back.
Oh, and one other quick one:“BP: Your way of modeling this would
give the wrong result if the
reference signal supposedly calling for a perception of the button
being
depressed failed to have that effect – if, for example, the person
didn’t push quite hard enough to make the button hit bottom. The
imagined
button would still be perceived as pressed.” I would argue that it
is up to the button-pressing control system to ensure that the
button-press occurs, not up to the control system that selects the
desired answer. As an experimenter, I would expect the subject to
believe herself to be pushing the buttons appropriately, whether by
feedback of the kinaesthetics of the button push all the way back to
the relation control level or at a lower control level.

If the button fails to have the effect of reporting the response to the
experimenter, it is likely that the experimenter has arranged some way
of perceiving the failure and of reporting it to the subject (at least
that’s what I would have done as an experimenter). I would say “Are you
awake? I’m not getting any responses from you.” And the subject might
say “But I’m pushing the buttons”, at which point I might try a few
more trials having asked the subject to push harder, before going in
myself to see whether the fault was in the button technology or in
something unexpected that the subject was doing, such as pushing
buttons 3 and 4 instead of 1 and 2.

Martin

23

[Martin Taylor 2010.05.27.18:20 CET]

My internet connection is sporadic and very slow, or I would add a picture to this message.

[From Bill Powers (2010.05.25.1150 MDT)]

Martin Taylor 2010.05.25.13.11 --

RM earlier: But then you say that the stimulus is not itself the
disturbance to this relationship perception? How could that be?

Because the disturbance is the output of a function to which the
stimulus is the input. The question of interest to the
psychophysicist is some property of this function.

Either we decide NOW to resolve the ambiguity of "the disturbance" or
I will go live in Tahiti and try painting naked ladies. This is
getting ridiculous.

What is ambiguous about what I wrote? The bit you quote by itself is of course ambiguous, but in context should not have been.

As we use the term "disturbance," and represent it as d, it is the
independent variable, not the effect on the controlled variable.

As we all know, and as we all use the term and the "d" symbol in equations.

RM earlier: The stimulus is what the experimenter manipulates in an
experiment, the IV. PCT suggests that this stimulus must be a
disturbance (d) to a controlled variable,

MMT: Nothing in PCT says that the stimulus as perceived by the
experimenter (e.g. the brightness of a light or the intensity of a
tone) must be the actual disturbance.

BP: Of course we can be mistaken if we're hasty, careless, or
ignorant, but as we are none of those we can take it that if there is
a clearly traceable physical connection from the light bulb to the
eyes of the subject, and if the subject acts the way we expect if and
only if the light from the light bulb gets to the pupil (check it with
a blindfold if you really have any doubt), the state of the the
light-bulb can be treated as d in our diagrams. It is exactly what an
experimenter would call a stimulus because it affects the perceptions
of the system but is not affected by the action of the system.

You are going off in another direction, irrelevant to the discussion. I explain algebraically below, but in words, a change in the voltage of the supply to an incandescent light bulb is a disturbance to the brightness of the bulb, but that change in voltage is not a disturbance to the legibility of the book I am reading. The change in the brightness of the light bulb disturbs the legibility of my book. The change in brightness may be countered by bringing in another bulb, removing the lampshade, or by controlling the brightness of the original bulb, resetting the voltage to the appropriate value. The disturbances at the two levels are different in value and different in kind.

RM earlier: I think that subjects in psychophysical experiments are
controlling a perception of the relationship between stimulus and
response.

MMT: Between some property of the stimulus, generated by a perceptual
function inside the subject, and some property of the response (e.g.
it doesn't matter how hard the response button is predded, in most
psychophysical experiments).

BP:Yes, of course. Isn't that what he said, with fewer words?

ABSOLUTELY NOT!!!!!!!! I've explained why not in several messages. It's the whole point of the experiment!!@!! (I'm tempted to swear more copiously, but this is a family mailing list!

Oh, well. Let's try again.

In the simplest possible case of a two-level system:

p1 = P1(qi1) where qi1 = o + d

p2 = P2(qi2) where qi2 = p1

P1( ) is part of the environmental feedback path for the p2 control system. As Rick has been at pains to point out, the "behavioural illusion" implies that for a controlled variable, the output depends on the environmental feedback path, not on the internal functions. P1( ) is internal to the experimental subject, but not to the p2 control unit.

If the disturbance to p1 is d, the disturbance to p2 is P1(d)+P1(o) if P1 is linear, or some function of o and d if P1( ) is nonlinear. It is NOT "d", unless P1( ) is the identity function and o is null. We can call the disturbance at the second level d2. If p2 is controlled, then o2 will counter d2, NOT d.

o2 = -d2 if p2 control is perfect.

Take this into the experimental situation, where p2 is a relationship control system, with a second input p12 that is a simple function of its output -- I mean that the p2 control system varies p12 so that the relationship between p12 and p1 is equal to the p2 reference value r2, which we will usually take to be zero (p1 and p12 match). Let's suppose further that p12, or a value simply derived from it, is observable (as are d and o). In fact, we might take o2 as a measure of p12, as we have implicitly done throughout this discussion by assuming that the subject truly reports to the experimenter what he perceives as the match.

Now we have p2 = P2(p1, p12) = P2(P1(o+d), p12).

If p2 is controlled perfectly, P1(o+d) = p12 (not -p12 for the relationship control system, since the minus sign occurs in the perceptual function P2 == (p1 - p12) if these are continuous variables or P2 == (p1 diff p12) if they are categorical).

The experimenter wants to know the function P1( ), or some property thereof. Since o, d, o2 (and from o2, p12) are observable, all the experimenter need do is vary o+d and monitor o2. However, if p1 is controlled, o+d will not vary much from r1, the reference value for p1. So, to get a range of variation for o+d, the experimenter clamps o at zero, by not allowing the presentation qi to be influenced by the subject's output. Then P1(d) becomes the disturbance to the relationship control system.

p2 = P2(P1(d), p12) and

P1(d) = p12 if the p2 control system is perfect and the reference value is zero (a match between presentation and perceived response).

Since the experimenter can now freely vary the argument to P1( ) over any range of interest, and observe the output of the relationship control system (or rather, its proxy, the response to the experimenter), the experimenter can measure the interesting properties of the internal function P1( ).

And whether "the experimenter can measure the interesting properties of the internal function P1( )" was the point of the discussion, not that "Martin seems to think psychophysical experiments are open loop" or, more subtly, "the disturbance at any level is the physical variation imposed by some independent influence".

I hope my flaky connection allows this to go out. It would have been easier with a diagram, but I with luck and goodwill in interpretation the text suffices to make the point clear. (As of 2010.05.28.08.05, I haven't been able to get a connection to send this).

Martin

24

[From Bill Powers (2010.05.28.100 MDT)]

What is ambiguous about what I wrote? The bit you quote by itself is of course ambiguous, but in context should not have been.

I wonder how many disagreements on CSGnet come from factual or theoretical disagreements, and how many come from simple bad communication. Of course we all know that d stands for disturbance, in the sense of the variable which, by changing, tends to alter the controlled variable, via its proximal effects on the input quantities just outside the sensors of the system. We also all know that this word disturbance is ambiguous, in that it can refer either to a perturbation of proximal variables or sensory inputs, or to some object or arrangement in the environment that, by changing its state, gives rise to such perturbations. Thus we can talk about light emitted by a light-bulb as a disturbance, or we can talk about the resulting change in retinal illumination (or the neural signal representing it) as a disturbance. If we're allowed to change definitions in midstream, we can say that disturbances cause disturbances. That kind of unfortunate usage, I think, is best to avoid.

In psychology,"stimulus" has much the same problems. It can mean an object or event, or the proximal effect of same on a sensory receptor. The ambiguities are parallel to those of "disturbance."

If you rely on context to disambiguate your sentences, you run the risk of being misunderstood. Not everyone perceives the context as you perceive it. I know it takes more time to scan for possible communication errors, and to insert the little qualifications that remove the worst of them, but if communication is really the object, the result will be achieved sooner and more accurately.

I'm not aiming this at anyone in particular; we could all do with better communication. Including the author of Layered Protocols.

Best,

Bill P.

25

[From Rick Marken (2010.05.30.1230)]

Martin Taylor (2010.05.27.18:20 CET) --

My internet connection is sporadic and very slow, or I would add a picture
to this message.

Just thought I would acknowledge that this post made it to CSGNet a
couple days ago despite your slow, flaky connection. I haven't
responded yet because I've been waiting for Bill to answer it. This
is obviously a very important topic for you, as evidenced by this
little interchange:

RM earlier: I think that subjects in psychophysical experiments are
controlling a perception of the relationship between stimulus and
response.

MMT: Between some property of the stimulus, generated by a perceptual
function inside the subject, and some property of the response (e.g.
it doesn't matter how hard the response button is predded, in most
psychophysical experiments).

BP:Yes, of course. Isn't that what he said, with fewer words?

ABSOLUTELY NOT!!!!!!!! I've explained why not in several messages. It's the
whole point of the experiment!!@!! (I'm tempted to swear more copiously, but
this is a family mailing list!

So I'm not anxious to reply because I would rather you get mad at Bill
than me;-) But I guess if Bill doesn't reply by the end of May
(tomorrow) I'll chime in.

Best

Rick

···

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

26

[Martin Taylor 2010.05.30.22.05 CET]

[From Rick Marken (2010.05.30.1230)]

RM earlier: I think that subjects in psychophysical experiments are
controlling a perception of the relationship between stimulus and
response.
           

MMT: Between some property of the stimulus, generated by a perceptual
function inside the subject, and some property of the response (e.g.
it doesn't matter how hard the response button is predded, in most
psychophysical experiments).
         

BP:Yes, of course. Isn't that what he said, with fewer words?
       

ABSOLUTELY NOT!!!!!!!! I've explained why not in several messages. It's the
whole point of the experiment!!@!! (I'm tempted to swear more copiously, but
this is a family mailing list!
     

So I'm not anxious to reply because I would rather you get mad at Bill
than me;-) But I guess if Bill doesn't reply by the end of May
(tomorrow) I'll chime in.

I'm not mad at anyone, simply VERY disappointed that neither you nor Bill could see the difference between x and f(x),

The disturbance to the relationship perception is f(x), not x, where x is the "stimulus". f( ) is the internal property that interests the experimenter, and assuming the relationship perception is well controlled, it is possible to assert that the output of its control unit is a fair match to its disturbance (f(x)). Since the experimenter knows x and f(x) for whatever values of x he wishes to use, he can determine f( ) over that range of arguments.

I simply don't understand why that is so difficult for you to comprehend. Unless, of course, it is an ideological issue that disturbs some strongly controlled perception.

Martin

···

On 2010/05/30 3:31 PM, Richard Marken wrote:

27

[From Rick Marken (2010.05.30.1445)]

Martin Taylor (2010.05.30.22.05 CET)--

Rick Marken (2010.05.30.1230)--

So I'm not anxious to reply because I would rather you get mad at Bill
than me;-) But I guess if Bill doesn't reply by the end of May
(tomorrow) I'll chime in.

I'm not mad at anyone, simply VERY disappointed that neither you nor Bill
could see the difference between x and f(x),

I didn't mean to suggest that you were mad. I just said that this is
apparently a very important topic to you (it's certainly very
important to me; it's what I am presenting on at the CSG conference
and if you are right I'll have to completely revise my talk; or just
sing a Dylan song instead;-) so you might get mad at the reply. But
even if you don't get mad at the reply I don't want you to be
disappointed either so I'll still wait to see if Bill will get back to
you on this first, so you can be disappointed in him. But maybe Bill
will finally see the light you want us to see and then I suppose
you'll just be disappointed in me, unless I can see it too. In the
meantime I'll try to see the difference between x and f(x):wink:

Best

Rick

···

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

28

[From Bill Powers (2010.05.30.2305 MDT)]
Just back from seeing my grandson Ethan graduate from high-school in Durango (after three years instead of four). Proud Grampa.

Martin Taylor 2010.05.27.18:20 CET --

RM earlier: I think that subjects in psychophysical experiments are
controlling a perception of the relationship between stimulus and
response.

MMT: Between some property of the stimulus, generated by a perceptual
function inside the subject, and some property of the response (e.g.
it doesn't matter how hard the response button is predded, in most
psychophysical experiments).

BP:Yes, of course. Isn't that what he said, with fewer words?

ABSOLUTELY NOT!!!!!!!! I've explained why not in several messages. It's the whole point of the experiment!!@!! (I'm tempted to swear more copiously, but this is a family mailing list!

Oh, well. Let's try again.

BP: I would recommend that. Your communications are often too elliptical to be understood as you want them understood. Don't blame your poor confused reader.

MMT: In the simplest possible case of a two-level system:

p1 = P1(qi1) where qi1 = o + d

p2 = P2(qi2) where qi2 = p1

BP: This is what I mean. Do the subscripts indicate level, or just different variables at the same level?

What you've written above says that p2 = P2(P1(qi1)). That says that p2 is a second-order perception while p1 is a first-order perception. However, in my conventions, "quantities" are environmental variables. If you're going to change that convention, you have to say so and lead the reader by the hand through the details.

MMT: P1( ) is part of the environmental feedback path for the p2 control system.

BP: This makes me think that your subscripts refer to levels, but if they do, you're making the second level perception depend on only one first-level perception, while in the PCT model perceptual input functions are many-to-one relationships, not one-to-one. That may or may not matter in a specific case.

MMT: As Rick has been at pains to point out, the "behavioural illusion" implies that for a controlled variable, the output depends on the environmental feedback path, not on the internal functions. P1( ) is internal to the experimental subject, but not to the p2 control unit.

If the disturbance to p1 is d, the disturbance to p2 is P1(d)+P1(o) if P1 is linear, or some function of o and d if P1( ) is nonlinear. It is NOT "d", unless P1( ) is the identity function and o is null. We can call the disturbance at the second level d2. If p2 is controlled, then o2 will counter d2, NOT d.

This is totally confused. I don't mean you are necessarily confused, but your exposition is. You need to lay out the model you're using in detail, show what each relationship in the model is, and then derive the relationships you want to talk about from the model. I don't think you're using the same PCT model I'm using. If you are, you're leaving so much out of the description that I don't recognize the result.

Perhaps you're too used to moving in circles where everyone is so talented and advanced that you can get the most complex ideas across with a wink and a nod and nobody ever embarrasses himself by having to ask "what do you mean?" I, at least, don't claim to belong to such circles, nor do I have any problems with asking that question. It's up to you to make your meaning clear if you care whether I understand.

Anyway, if I interpret your statements above as you intended, I think I may see why you don't want lower-order perceptions to be under control at the lower level (as you hinted in a message a few days ago). A disturbance applied to a lower-level variable is not simply reflected in the perceptual signal at that level -- unless it is uncontrolled at the lower level. In order for a disturbance to have its effect uncontaminated by actions at the lower level, it must pass upward through appropriate layers of perceptual input functions without any control actions entering to change the effect of the disturbance before the perceptual result is passed to the next level up. That seems to be what you're assuming, as near as I can see, though you haven't actually said so.

Actually I can agree with this, in that I see disturbances of higher-level variables arising primarily from uncontrolled perceptions from lower levels. One of the effects of control is to protect higher levels against the effects of disturbances at a lower level. But there are uncontrolled lower-level variables, too, which can be perceived but not affected by behavior.

However, you seem to be saying that d2 can be representings at level 2 as a function of both d and o at level 1. That contradicts your idea that p1 is not controlled, as must be the case if d is to be reflected directly at the next level up. There would be no o in the equations if the perceptions were uncontrolled.

A dog chasing a cat can control its own spatial position, but not that of the rabbit it is chasing. It can perceive the rabbit's position, velocity, and so on, but it has no way to control it directly. "Chasing", I would propose, is how we characterize control of a relationship variable, maybe the distance between the dog and the rabbit. The dog can control this relationship by changing its own position and derivatives, and the rabbit can disturb that relationship by running and dodging independently, in a way the dog can't control. So here the disturbance itself shows up as a higher-order variable, an element of a relationship.

Normally, however -- as I envision the hierarchy -- the lower-level systems do control the more critical lower-order variables, thereby preventing all but a small residual effect (on higher levels) of disturbances operating at the lower levels. In those cases the effects of the external disturbing variable are far smaller and contain large contributions from the outputs of the controlling system, and can't usefully be distinguished by examination of the net state of the higher-order variable.

It could be that this is the basis of our disagreements about the Schouten experiment. You don't want the state of the button to be perceived directly, because you need that state to be an uncontrolled response.

Best,

Bill P.

29

[From Rick Marken (2010.05.31.0920)]

Bill Powers (2010.05.30.2305 MDT)--

Just back from seeing my grandson Ethan graduate from high-school in
Durango (after three years instead of four). Proud Grampa.

Congratulations. Apple doesn't fall far from the tree, I see.

Martin Taylor 2010.05.27.18:20 CET --

MMT: As Rick has been at pains to point out, the "behavioural illusion"
implies that for a controlled variable, the output depends on the
environmental feedback path, not on the internal functions. P1( ) is
internal to the experimental subject, but not to the p2 control unit.

If the disturbance to p1 is d, the disturbance to p2 is P1(d)+P1(o) if P1
is linear, or some function of o and d if P1( ) is nonlinear. It is NOT "d",
unless P1( ) is the identity function and o is null. We can call the
disturbance at the second level d2. If p2 is controlled, then o2 will
counter d2, NOT d.

BP: This is totally confused. I don't mean you are necessarily confused,
but your exposition is. You need to lay out the model you're using in
detail, show what each relationship in the model is, and then derive the
relationships you want to talk about from the model. I don't think you're
using the same PCT model I'm using. If you are, you're leaving so much out
of the description that I don't recognize the result.

I think it's important that this laying out of the model include a
clear description of how the model maps to behavior in an actual
experimental situation. I suggest the we assume a simple
psychophysical experiment, such as the magnitude estimation experiment
(as described here:
http://www.mindreadings.com/BehavioralIllusion.pdf). Assume that tones
of different amplitudes are the stimuli and numerical magnitude
estimates are the responses. Another possibility is a tone detection
experiment, where one of two different tone amplitudes is presented on
each trial and the subject is asked to rate (say on a 1-5 scale) their
confidence that a tone occurred on each trial.

Without this mapping of model to actual behavior I think we will get
nowhere in understanding Martin's model of the behavior in
psychophysical experimental and why it leads him to consider the
results of such experiments immune to the behavioral illusion.

Best

Rick

···

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

30

[Martin Taylor 2010.056.01.00.35]

[From Bill Powers (2010.05.28.100 MDT)]

What is ambiguous about what I wrote? The bit

you quote by itself is of course ambiguous, but in context should not
have been.

If you rely on context to disambiguate your sentences, you run the risk
of being misunderstood. Not everyone perceives the context as you
perceive it.

I think that when the context is the IMMEDIATELY preceding material, it
is reasonable to suppose that it might be incorporate into most
readers’ understanding of what follows. If we can’t assume that,
communication becomes rather difficult!

Here’s the “ambiguous” quote in context. The bit deemed “ambiguous” in
respect of what is the disturbance to the relationship perception is
the last two-sentence paragraph:

-------quote--------

[From Rick Marken (2010.05.25.0950)]

Martin Taylor
(2010.05.25.11.34)–

I’m saying that X, where X is
the magnitude of the perception of the stimulus, is the disturbance to
the controlled perception of the relation between the magnitude
perception and the subject’s choice of response. X = P(qi) at a lower
perceptual level. The experimenter’s stimulus is not itself the
disturbance to the relationship control unit.

I still don’t get it. You seem to agree that subjects in a
psychophysical experiment are controlling a relationship between their
perception of the stimulus and a perception of their own response.

No, I tried to make crystal clear that they are NOT " controlling a
relationship between their perception of the stimulus and a perception
of their own response" but they ARE controlling a relationship between
their perception of the magnitude (identity, some property) of the
stimulus and a perception of their own response

But then you say that the stimulus is not itself the disturbance
to this relationship perception? How could that be?

Because the disturbance is the output of a function to which the
stimulus is the input. The question of interest to the psychophysicist
is some property of this function.

---------end quote-----------

I don’t see how I can be clearer than that, especially since it is the
Nth attempt to get across the same idea using different words.

Of course, if you deliberately choose to ignore the preceding material,
I don’t think I can be held responsible for that. I suppose that if I
had imagined the possibility that you would do this, I could have made
the preceding text red and bold-faced, but since I have no idea which
bits of my writing you will subject to this “telescope to the blind
eye” treatment, I would probably be marking the wrong material.

On the other hand, I suppose I could have been a bit more redundant,
and written the offending paragraph thus, despite that I had already
made the algebraic point a few lines earlier:

--------paraphrase-------------

But then you say that the stimulus is not itself the disturbance
to this relationship perception? How could that be?

Because the disturbance “d” is the output of a function P( ) to which
the
stimulus “s” is the input, meaning that d = P(s), not “s”. The question
of interest to the psychophysicist
is some property of this function P( ).

Martin

.

···

On 2010/05/28 4:37 PM, Bill Powers wrote:

31

[From Bill Powers (2010.06.01.0350 MDT)]

Martin Taylor 2010.056.01.00.35 –

MMT: Here’s the
“ambiguous” quote in context. The bit deemed
“ambiguous” in respect of what is the disturbance to the
relationship perception is the last two-sentence
paragraph:

RM (Marken earlier): I still
don’t get it. You seem to agree that subjects in a psychophysical
experiment are controlling a relationship between their perception of the
stimulus and a perception of their own response.

MMT:No, I tried to make crystal clear that they are NOT "
controlling a relationship between their perception of the stimulus and a
perception of their own response" but they ARE controlling a
relationship between their perception of the magnitude (identity, some
property) of the stimulus and a perception of their own
response.

BP: So the total difference between the version you reject and the one
you offer in its place is the phrase " the magnitude (identity, some
property)" inserted between “perception of” and “the
stimulus.” Apparently this makes a qualitative difference to you; it
doesn’t to me.

RM earlier: But then you say
that the stimulus is not itself the disturbance to this relationship
perception? How could that be?

MMT: Because the disturbance is the output of a function to which the
stimulus is the input. The question of interest to the psychophysicist is
some property of this function.

BP: WHAT function outputs the disturbance? In my conception of a
disturbance, there is no organismic function either preceding or
following it. d is an environmental variable, not a perceptual signal.
Between d and qi there is only a physical function outside the organism,
not a perceptual input function. The actual input to the organism is not
d, but qi.

Perhaps you’re trying to describe a higher-level control system which has
an environment made of lower-level control systems as well as
uncontrolled perceptual signals. In that case, “d” could be a
perceptual signal coming out of a lower-level input function that is not
part of a control system. Is that the function you’re talking
about?

MMT: I don’t see how I can be
clearer than that, especially since it is the Nth attempt to get across
the same idea using different words.

Of course, if you deliberately choose to ignore the preceding material, I
don’t think I can be held responsible for that.

BP: The “preceding material” is not being ignored, it simply
doesn’t accomplish any explanatory function. To you, " the magnitude
(identity, some property)" seems fraught with meaning, but whatever
meanings you assign to it are unknown to me. My own meanings for that
phrase are no different from what I ordinarily mean by perceiving
something. All perceptions have magnitudes that stand for the magnitude
of a function of lower-order variables. Whether the magnitude refers to
the amount of a property, or degree of identity, or category, or
sequence, or configuration depends on the level in the hierarchy that
you’re talking about.

MMT: I suppose that if I had
imagined the possibility that you would do this, I could have made the
preceding text red and bold-faced, but since I have no idea which bits of
my writing you will subject to this “telescope to the blind
eye” treatment, I would probably be marking the wrong
material.

Shouting words that have different meanings to others does not make them
have your meanings.

On the other hand, I suppose I
could have been a bit more redundant, and written the offending paragraph
thus, despite that I had already made the algebraic point a few lines
earlier:

--------paraphrase-------------

RM: But then you say that the
stimulus is not itself the disturbance to this relationship perception?
How could that be?

MMT: Because the disturbance “d” is the output of a function P(
) to which the stimulus “s” is the input, meaning that d =
P(s), not “s”. The question of interest to the psychophysicist
is some property of this function P( ).

You seem to be saying that d is a perceptual signal inside the organism,
and that s is what we refer to as qi, the variables that immediately
affect sensory endings, so d = P(s). What we have been assuming is that
qi = D(d), where D is the function in the environment giving an
independent variable d an effect on qi. Perceptions are then P(qi). Since
stimuli also act by affecting proximal environmental variables, we equate
d to s: qi = S(s) where S() is an instance of D(). Thus it makes no sense
to Rick or me to make s depend on d. If you have some way of looking at
it that does make sense of this, you haven’t communicated it. We are
using d as the generic name for an independent variable that affects qi,
with s being merely an instance, one kind of disturbance. We see s and d
as being at the same level: they are independent variables, with d being
the generic term and s a subset of d.

When you say that d = P(s), you’re contradicting the model that we have
been using for two or three decades. That’s OK, but not without
explanation, since the effect on the rest of the PCT model would be
pretty drastic. You have to offer some justification for this departure,
or you aren’t likely to get agreement to it. Simply making the same
assertion over and over, in the same words or different words, is not
enough to get understanding, much less agreement.

Best,

Bill P.

32

[From Rick Marken (2010.06.03.0810)]

Bill Powers (2010.06.01.0350 MDT) --

Martin Taylor 2010.056.01.00.35 --

MMT: Because the disturbance "d" is the output of a function P( ) to which
the stimulus "s" is the input, meaning that d = P(s), not "s". The question
of interest to the psychophysicist is some property of this function P( ).

BP: When you say that d = P(s), you're contradicting the model that we
have been using for two or three decades...

Could this post have stunned Martin into silence? Or is the internet
infrastructure in Europe as lousy as their deep sea drilling
technology? :wink:

Best

Rick

···

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

33

[From Bill Powers (2010.06.03.1007 mdt)]

Rick Marken (2010.06.03.0810) --

> BP: When you say that d = P(s), you're contradicting the model that we
> have been using for two or three decades...

Could this post have stunned Martin into silence? Or is the internet
infrastructure in Europe as lousy as their deep sea drilling
technology? :wink:

You sure like to pile on to people and put in the boot when you think they're down.

Bill P.

34

[From Rick Marken (2010.06.03.0945)]

Bill Powers (2010.06.03.1007 mdt)--

You sure like to pile on to people and put in the boot when you think
they're down.

Yes, I suppose so. But it depends on who the "people" are. If they
are people who are helping me in my work then, no, I don't.

Best

Rick

···

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

35

[Martin Taylor 2010.06.03.23.55]

[From Bill Powers (2010.06.01.0350 MDT)]

Martin Taylor 2010.056.01.00.35 --

MMT: Here's the "ambiguous" quote in context. The bit deemed "ambiguous" in respect of what is the disturbance to the relationship perception is the last two-sentence paragraph:

RM (Marken earlier): I still don't get it. You seem to agree that subjects in a psychophysical experiment are controlling a relationship between their perception of the stimulus and a perception of their own response.

MMT:No, I tried to make crystal clear that they are NOT " controlling a relationship between their perception of the stimulus and a perception of their own response" but they ARE controlling a relationship between their perception of the magnitude (identity, some property) of the stimulus and a perception of their own response.

BP: So the total difference between the version you reject and the one you offer in its place is the phrase " the magnitude (identity, some property)" inserted between "perception of" and "the stimulus." Apparently this makes a qualitative difference to you; it doesn't to me.

RM earlier: But then you say that the stimulus is not itself the disturbance to this relationship perception? How could that be?

MMT: Because the disturbance is the output of a function to which the stimulus is the input. The question of interest to the psychophysicist is some property of this function.

BP: WHAT function outputs the disturbance? In my conception of a disturbance, there is no organismic function either preceding or following it. d is an environmental variable, not a perceptual signal. Between d and qi there is only a physical function outside the organism, not a perceptual input function. The actual input to the organism is not d, but qi.

Perhaps you're trying to describe a higher-level control system which has an environment made of lower-level control systems as well as uncontrolled perceptual signals. In that case, "d" could be a perceptual signal coming out of a lower-level input function that is not part of a control system. Is that the function you're talking about?

MMT: I don't see how I can be clearer than that, especially since it is the Nth attempt to get across the same idea using different words.

Of course, if you deliberately choose to ignore the preceding material, I don't think I can be held responsible for that.

BP: The "preceding material" is not being ignored, it simply doesn't accomplish any explanatory function. To you, " the magnitude (identity, some property)" seems fraught with meaning, but whatever meanings you assign to it are unknown to me. My own meanings for that phrase are no different from what I ordinarily mean by perceiving something. All perceptions have magnitudes that stand for the magnitude of a function of lower-order variables. Whether the magnitude refers to the amount of a property, or degree of identity, or category, or sequence, or configuration depends on the level in the hierarchy that you're talking about.

MMT: I suppose that if I had imagined the possibility that you would do this, I could have made the preceding text red and bold-faced, but since I have no idea which bits of my writing you will subject to this "telescope to the blind eye" treatment, I would probably be marking the wrong material.

Shouting words that have different meanings to others does not make them have your meanings.

On the other hand, I suppose I could have been a bit more redundant, and written the offending paragraph thus, despite that I had already made the algebraic point a few lines earlier:

--------paraphrase-------------

RM: But then you say that the stimulus is not itself the disturbance to this relationship perception? How could that be?

MMT: Because the disturbance "d" is the output of a function P( ) to which the stimulus "s" is the input, meaning that d = P(s), not "s". The question of interest to the psychophysicist is some property of this function P( ).

You seem to be saying that d is a perceptual signal inside the organism, and that s is what we refer to as qi, the variables that immediately affect sensory endings, so d = P(s). What we have been assuming is that qi = D(d), where D is the function in the environment giving an independent variable d an effect on qi. Perceptions are then P(qi). Since stimuli also act by affecting proximal environmental variables, we equate d to s: qi = S(s) where S() is an instance of D(). Thus it makes no sense to Rick or me to make s depend on d. If you have some way of looking at it that does make sense of this, you haven't communicated it.

I find it extremely hard to believe that your inability to conceive that I am using exactly the same multilevel hierarchy as is considered conventional on CSGnet is anything other than wilful. It is getting harder and harder to believe that every different linguistic or algebraic way I try to express the extremely simple idea that a perceptual signal does not necessarily have the same value as the input to its perceptual function, even if it has only a single input!

When you say that d = P(s), you're contradicting the model that we have been using for two or three decades.

I am absolutely NOT contradicting that model, as you should know from many years of recognizing my knowledge of that model. When I want to contradict it, I say so explicitly. I am here using it in pristine form. Nothing in the model even suggests that the output of a perceptual function necessarily has the same value as its input. The disturbance to a level n perception is not the disturbance to any level n-1 perception. If a level n-1 perception is uncontrolled, and is a function P(qi[n-1]) of its input, then qi[n-1] is simply the level n-1 disturbance d, and the output to level n, which in this instance is the disturbance to the relationship perception, is P(d).

Let's take P( ) to be a logarithmic function, which is the function you and Rick have deduced to be a perceptual function that would account for Stevens' power law. How did you make this deduction? Was it not by noting that if the relation between stimulus input an d magnitude perception was logarithmic, then control of the relationship perception would lead to a power law relation between the stimulus and the response? Did you not use exactly the same analysis as you say contradicts the model we have been using for two or three decades?

I've been trying to create a trivial diagram, but my program keeps crashing when I try to save, and I have to go to bed so I can catch a morning plane to the UK. Since this my be my only access to a good internet connection for the next week, I'll try to do it in ASCII. It's pretty crude, but since it uses only components you have used, I think it should, with goodwill, be intelligible.

                       > Relationship reference value
             ----------o--------
             > >
       Relationship Output
        perception varies
         > > response selection
         > > or magnitude
       P1(d) selected |
         > answer---<-------|feedback pathway is not explicitly defined. Could be an imagination
         > >loop, could be from button presses, etc.
Perceptual function |
of interest P1( ) |response to experimenter switched in when appropriate
         > >
         >qi = d (stimulus | response seen by experimenter
         > provided by |
         > experimenter)

Is that so complicated and difficult to understand? I've said it many different ways, I've provided the algebra that should have made any linguistic explanation superfluous, and I've worked always within the standard HPCT model. I've even allowed for your direct feedback of the button push as the source of the comparison response in the relationship perception, so as to avoid that red herring.

I do hope that you can recognize that perceptions at different levels are very unlikely to have the same values, even if the perceptual functions involved have only one input.

Martin

36

[From Rick Marken (2010.06.03.1615)

Martin Taylor (2010.06.03.23.55)--

Bill Powers (2010.06.01.0350 MDT)]

BP: Thus it makes no sense to Rick or me to
make s depend on d. If you have some way of looking at it that does make
sense of this, you haven't communicated it.

MT: I find it extremely hard to believe that your inability to conceive that I
am using exactly the same multilevel hierarchy as is considered conventional
on CSGnet is anything other than wilful...

See, I knew Martin wasn't down and that I wasn't "piling on" at all.

Glad to see the internet is working for you Martin!

Best

Rick

···

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

37

[From Bill Powers (2010.06.03.1805 MDT)]

Martin Taylor 2010.06.03.23.55 –

This is a very strange interchange and we need to solve the puzzle.
You’re making assumptions that remain unspoken, which is causing a total
breakdown in communciation.

MMT: Because the disturbance
“d” is the output of a function P( ) to which the stimulus
“s” is the input, meaning that d = P(s), not “s”. The
question of interest to the psychophysicist is some property of this
function P( ).

BP: Your usage of the symbol P leads me to think you’re talking about a
perceptual input function. If that is so, then P() describes a neural
network (possibly just a single receptor) which transforms environmental
variables into neural signals. Is this your understanding, too?

If that is your understanding then you are using the term s to mean an
environmental variable proximal to a receptor, and d to mean a neural
signal inside the organism. I do not use d to indicate a perceptual
signal inside the organism, and I do not use s to designate the proximal
environmental variable that, via a sensor or sensor plus functions, gives
rise to a perceptual signal. You appear to be saying that d is a
perceptual signal, and in PCT it is not a perceptual signal. You appear
to be saying that s is a proximal environmental variable (like a light
flux being absorbed by the retina), while I, and I would say
psychologists, too, would identify a stimulus as the independent physical
object or event that gives rise to the proximal variables – in other
words, the stimulus IS a disturbance.

As I write this I realize that I’m having trouble with the two meanings
of “stimulus,” which is why I’m using the awkward phrase
“proximal environmental variable.” We all quite casually speak
of the state of the light bulb as the stimulus (light on or light off),
and in the same breath can say that the light absorbed by the retina
stimulates the sensory receptor, so the stimulus is the light actually
absorbed. In PCT we separate causes and effects and use different symbols
for them. The symbol d (and I would say s as well) designates a physical
variable in the environment relatively remote from the sensors. For the
proximal environmental variables that directly affect the sensors, we use
the symbol qi or input quantity. So d affects the input quantity, and the
input quantity affects the sensor, and the sensor produces the perceptual
signal p. Psychologists very seldom (if ever) measure qi.

This is why I can’t understand your saying that d is the output of a
perceptual input function – a neural signal inside the organism. Neither
can I understand your use of s where I would use qi; qi is generally NOT
what psychologists mean by “stimulus.” You seem to think I
don’t understand the “extremely simple idea that a perceptual signal
does not necessarily have the same value as the input to its perceptual
function, even if it has only a single input!”. That is not the
issue I have at all. I claim that d is not the output of a perceptual
input function, and that s is not the proximal input to a perceptual
input function. Whether s and d are different is irrelevant: you are
misplacing both variables as I see it. s is not proximal and d is not
inside the organism.

MMT: I find it extremely hard to
believe that your inability to conceive that I am using exactly the same
multilevel hierarchy as is considered conventional on CSGnet is anything
other than wilful. It is getting harder and harder to believe that every
different linguistic or algebraic way I try to express the extremely
simple idea that a perceptual signal does not necessarily have the same
value as the input to its perceptual function, even if it has only a
single input!

BP earlier: When you say that d = P(s), you’re contradicting the model
that we have been using for two or three decades.

MMT: I am absolutely NOT contradicting that model, as you should know
from many years of recognizing my knowledge of that
model.

BP: When you say that d, the disturbing variable, is a perceptual signal,
you are contradicting the model. If it doesn’t seem that way to you,
please explain.

Your statement “Nothing in the model even suggests that the output
of a perceptual function necessarily has the same value as its
input” shows that you completely misunderstand, or I have completely
miscommunicated, my point. If by P() you mean a perceptual input function
as we usually define it, then d is not the output of that function and s
is not the input to it. That is my point.

MMT: The disturbance to a level
n perception is not the disturbance to any level n-1 perception. If a
level n-1 perception is uncontrolled, and is a function P(qi[n-1]) of its
input, then qi[n-1] is simply the level n-1 disturbance d, and the output
to level n, which in this instance is the disturbance to the relationship
perception, is P(d).

BP: The only way a disturbance can directly affect a level n perception
is by affecting a chain of lower-level perceptions starting with the
first level, all uncontrolled. A disturbance is an independent variable
(or a set of them) in the environment, not inside the organism. The
effect of such a disturbance is a change in perceptions at one or
more levels – perceptions that we conventionally designate as p, not d.
If such a perception has the effect of altering a higher-level
perception, then the lower perception can be called a disturbance, but we
have to designate it as different from d, which is not a perception. I
think you’re probably doing this in your head, but the result isn’t
getting written down so anyone else can see it.

And you are committing the “disturbance offense” that I have
been complaining about, it seems, forever. When you say “The
disturbance to a level n perception is not the disturbance to any level
n-1 perception,” you are confusing the causes of disturbances with
the effects of disturbances, calling them both disturbances. “The
disturbance to a level 1 perception” is a variable in the
environment that causes the (uncontrolled) level 1 perception to change.
What causes the level 2 perception to change is the change in the level 1
perception, which may be some function of d, but is certainly not the
observable d. And the change in the level 2 perception is certainly not
the same as the change in the level 1 perception, and is even less
connected to changes in d.

Let’s take P( ) to be a
logarithmic function, which is the function you and Rick have deduced to
be a perceptual function that would account for Stevens’ power law. How
did you make this deduction? Was it not by noting that if the relation
between stimulus input and magnitude perception was logarithmic, then
control of the relationship perception would lead to a power law relation
between the stimulus and the response? Did you not use exactly the same
analysis as you say contradicts the model we have been using for two or
three decades?

Certainly, proposing logarithmic functions is a definite change from the
basic PCT model. We showed that this will lead to a power law of the kind
Stevens observed, but we have yet to show what happens if we make the
functions in a tracking model logarithmic. I don’t know if that’s going
to work. It will be tried, of course.

I’ve been trying to create a
trivial diagram, but my program keeps crashing when I try to save, and I
have to go to bed so I can catch a morning plane to the UK. Since this my
be my only access to a good internet connection for the next week, I’ll
try to do it in ASCII. It’s pretty crude, but since it uses only
components you have used, I think it should, with goodwill, be
intelligible.

[Note: the diagram comes out right if you widen the window sufficiently.
I shortened some lines to make it work in narrower windows.]

Relationship reference value

----------o--------

Relationship
Output

perception
varies

     response

selection

      or

magnitude

  P1(d)

selected |

    >

answer—<-------|feedback pathway is not explicitly
defined.

Could be an imagination

loop, could be from button presses, etc.

Perceptual
function

of interest P1(
)

response to experimenter switched in

when appropriate

    >qi = d

(stimulus |

    >  provided

by |response seen by
experimenter

    >  experimenter)

Is that so complicated and difficult to understand?

BP: Not a bit. If you choose the “could be from button presses”
option, it’s the same model I proposed. If you choose the imagination
loop, it’s yours. P1(d) is one input to the relationship input function,
the selected answer (the button press) is the other. This system, in my
version, controls the relationship between the state of the light bulb
and the state of the button press. In yours, it does not, because the
button press is only imagined, then later emitted.

MMT: I do hope that you can recognize that perceptions at different
levels are very unlikely to have the same values, even if the perceptual
functions involved have only one input.

I never disputed that. If you can abandon the idea that this had anything
to do with my objections, perhaps we can get this sorted out
yet.

Best,

Bill P.

38

[Fropm Bill Powers (2010.06.03.2150 MDT)]

Martin Taylor 2010.06.03.23.55 --

Attached is a diagram of conflict I sent to Tim Carey so he can
practice combining them and solving for various variables. Others are
invited to practice on this, too. Note how I use different notations
for disturbances depending on the level at which we start paying
attention to them. This sort of notation would save a lot of
pointless disagreements. Clearly these disturbances are not the "d"
that we would observe from outside the organism.

Best,

Bill P.

conflict.JPG

39

[Martin Taylor 2010.06.04.07.30]

[Fropm Bill Powers (2010.06.03.2150 MDT)]

Martin Taylor 2010.06.03.23.55 –

Attached is a diagram of conflict I sent to Tim Carey so he can
practice combining them and solving for various variables. Others are
invited to practice on this, too. Note how I use different notations
for disturbances depending on the level at which we start paying
attention to them. This sort of notation would save a lot of pointless
disagreements. Clearly these disturbances are not the “d” that we would
observe from outside the organism.

Gotta be quick, so I can pack to catch a plane.

I refer you to [Martin Taylor 2010.05.27.18:20 CET]: “If the
disturbance to p1 is d, the disturbance to p2 is P1(d)+P1(o) if P1 is
linear, or some function of o and d if P1( ) is nonlinear. It is NOT
“d”, unless P1( ) is the identity function and o is null. We can call
the disturbance at the second level d2. If p2 is controlled, then o2
will counter d2, NOT d.”

After I got up this morning I was able to generate the diagram that I
tried to reproduce in ASCII yesterday. It is a general diagrom for
psychophysics (including pursuit tracking).

psychophysics.jpg

Martin

40

[From Rick Marken (2010.06.04.0820)]

Martin Taylor (2010.06.04.07.30)–

After I got up this morning I was able to generate the diagram that I
tried to reproduce in ASCII yesterday. It is a general diagrom for
psychophysics (including pursuit tracking).

Just one little problem. The “relationship control” system isn’t really controlling anything other than an imagined relationship. You are basically modeling a psychophysical experiment as an S-R experiment since the subject’s response pops out of the system, apparently just for the sake of the experimenter. The subject’s behavior is modeled just the way conventional psychologists view it; in Powers’ felicitous phrase “as a show put on for the benefit of the observer”. In fact, this diagram could be applied to any psychological experiment, showing that the behavior in the experiment is S-R.

I think it would be pretty easy to test this model. Since the relationship between stimulus and response is controlled only in imagination, a disturbance to that relationship should not be resisted. In a tone detection experiment, for example, a simple disturbance to the relationship between stimulus and response would be for the experimenter to follow the subject’s response with “You said X” where X is the opposite of what the subject said (“Tone” if the subject said “No Tone” and “No Tone” of the subject said “Tone”). If your model is correct, this disturbance should be completely effective – the subject should not protest – since the all that the subject is “controlling”, according to your model, is the relationship between the perception of the stimulus and his or her imagined response. I think something very different would actually happen.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com

www.mindreadings.com