Perceptual distance measures

[Dick_Robertson]

[From Dick Robertson,2007.09.24.1000CDT]

Fantastic! I had completely forgotten this experiment/therapy/theory expansion. Your point that reorganization might be the big bug in such experiments is beautiful. What say you, Martin?

I’m still in touch with Pat. She invited me to a group in which she participates that meets monthly at the Glenview library–interested in flying saucers, science studies, etc. I’ll check out what happened next in her experiences with motion sickness.

Best,

Dick R

···

----- Original Message -----
From: Bill Powers powers_w@FRONTIER.NET
Date: Monday, September 24, 2007 5:43 am
Subject: Re: Perceptual distance measures
To: CSGNET@LISTSERV.UIUC.EDU

[From Bill Powers (2007.09.24.0409 MDT)]

Martin Taylor 2007.09.24.00.47] –

Rick Marken (2007.09.23.2115)] –

I’m copying here a few paragraphs I recently send to Warren Mansell. They
may have a bearing on the Lyell Illusion that’s being discussed.

=======================================================================================

I once worked with a graduate student who was a former student of Dick
Robertson’s, Dick having been an intern in Carl Rogers’ Counselling
Center at the U. of Chicago along with Mary, even before I met her. Just
after Mary and I married, I gave a seminar along with Clark and
MacFarland at the counselling center (1957), and Dick has been aboard
ever since then. He recently retired from Northeastern Illinois
University where he pioneered the teaching of PCT for many
years.

The graduate student suffered from motion sickness to a debilitating
degree, even on subway (Underground) trains and on buses. She wanted to
study it, so I wrote a program to use a (sideways) waterfall illusion to
measure after-“images” of motion (a transition-level
experiment). A computer screen was filled with moving dots, which ceased
to move when a beep sounded. At that point, the participant could affect
the rate of motion of the dots by using a mouse, the instructions being
to use the mouse to keep the dots stationary after the beep. Of course
that means making the dots move oppositely to the direction of the
illusion. The result was a very nice negative exponential decay of the
participant-caused motion, dying out to zero in twenty or thirty seconds.
This made the magnitude and time-course of the illusion directly
measurable. We were probably measuring the motion of fluid in the
semicircular canals!

In refining the experiment and data-taking, this student and I passed
many trial versions of the experiment back and forth, and after a while I
began to have trouble with the program – some bug had crept into it so
the data were not being correctly reported – so I thought. Eventually,
we both had to admit that we had worn out the illusion, so neither of us
had it any more. We had reorganized it away. Not only that, but the
graduate student found that she no longer suffered from motion sickness.
Since that had been her main motivation for doing this thesis, she said
thank you very much and she was changing her thesis to some other
subject, since the old thesis had evaporated. (I’m copying this post to
Dick, and also to Rick Marken who is looking for PCT experiments for his
students at UCLA).

I have felt for a long time that therapy takes precedence over studying
abnormalities. We may as well admit that psychological testing has
effects on the people we’re testing, so we might as well study changes
along with whatever else we think we’re measuring. And as long as we’re
doing that, we might as well select “experiments” that also do
people some good rather than harm.

=======================================================================================

What occurred to me, of course, was that while doing Martin’s
experiments, the participants might have been reorganizing, so that
gradually, over time, the distortions would tend to disappear. Perhaps
the course of the experiments was short enough that this effect would not
appear, but if the comparisons were made in the same order every time,
there could have been some confusing adaptational effects – or even if
they were made in randomized order.

It seems to me that this experiment calls for a pct-style version, in
which the participants simply remove what they see as distortions until
the dots all appear equally spaced. If there really are context effects
of the kind Martin tried to measure, this should show them very clearly,
as my experiment did for the waterfall illusion. And if adaptation really
does take place, the illusion should disappear with extended practice
(though if it doesn’t, that would be informative, too).

I think we’re always reorganizing to maintain the mutual calibration
among sensory modalities, particularly kinesthesia, touch, and vision.
With practice, the cross-calibration seems to get better, and it seems to
deteriorate otherwise. PCT experiments would seem to suit this sort of
experimentation very nicely.

And my answer to Martin’s comment is that no, I don’t trust anyone’s
experiments that were done without using PCT techniques. There are too
many assumptions about things that PCT makes measurable. Some older
experiments were done by adjustment of objects and relationships and
might be PCT-certifiable, more or less, but most weren’t. I don’t know
how the line-length comparisons to dot intervals were made, so I can’t
judge Martin’s experiment on that basis. It seems that so many details
have been lost that the results can no longer be interpreted. If
reorganization were involved, it would not be surprising to find
temporary inconsistencies in the judgements, but I would expect them to
disappear with practice.

Best.

Bill P.

[rsmarken]

[From Rick Marken (2007.09.24.0930)]

Martin Taylor (2007.09.24.00.47) –

Let’s see. If I undersand you correctly, you assert that in all cases
p = k*log(s) approximately, where p is the perceptual value and s is

the stimulus magnitude, in this case physical distance. I take it
that this is what you mean by a log function, and that changing k is
the way to get a function of the same form that is different between

the A (Arrow) and F (Feathers) context configurations.

No. Changing k is not what I had in mind. What I had in mind is shown in the attached figure. The function labeled f() is the perceptual function mapping physical magnitude (s) into psychological magnitude (Psi). In this case the s values can be thought of inter dot distances within the Muller Lyer figures, either Arrowheads or Feathers. In this figure f() is a log function.

What the context forms (Arrowheads or Feathers) seem to do (according to your data) is change the apparent length of the lines between what you call “points” (the end points of the distance between the Arrowheads or Feathers). For example, the Arrowheads make the same inter point distance look shorter than it does with Feathers; that’s the Mueller Lyer illusion.

What I’m assuming is that estimates of the length of inter-dot intervals – sub-distances of the distance between points – are made relative to the apparent distance between points. Since this between point reference distance is shorter with Arrowheads than with Feathers, I assume that the same inter-point distance will look longer in comparison to this apparently shorter inter point reference distance than it does when the reference distance is elongated by Feathers. This is why you see, in your data, the puzzling result that some inter-dot distances are rated as shorter in the context of the Feathers (which make the overall distance between points look longer) than in the context of Arrowheads. Apparently the effect of the point to point distance context diminishes as the inter dot distance gets closer to the point to point distance. So this discrepancy (of apparently longer inter dot distances in the context of Muller Lyer figures with Arrowheads that make the overall length between points shorter) goes away as the inter dot distance approaches about half (or less) of the inter point distance.

The attached figure shows this “contextual” transformation applied to the Phi values that are the outputs of the f() function for the various stimulus magnitudes (distances). The psychological magnitude of the stimuli (the intensity level perception) is the same for both Arrowhead and Feather contexts. All that changes is how context operates on these Psi values. The Arrowhead context shortens the point to point context and, thus, increases the apparent size of smaller inter dot intervals in this context. The Feather context lengthens the point to point distance and, thus, decreases the apparent size of the smaller inter dot intervals in this context. The crossover of the two curves is consistent with your finding that there is a crossover in judgments of the size of inter dot intervals once these intervals start approaching the size of the inter point interval. This little mode assumes that the Psi values are the perceptual intensity level values and that the context effect occurs at the configuration level. So if the subject can learn to attend to only the intensity level these apparently puzzling context effects that you observed should go away. And I believe you said that some of your subjects were not subject to the puzzling “intransitivity” you observed in the data. So I would say they either learned to focus on the intensity level or were at that level coming in.

I’m not saying that this is the right explanation. Nor am I particularly interested in developing a PCT experiment to properly test this. I just wanted to present this little model to show that your data do not rule out a single functional relationship between perceived and physical distance. There may not be a single functional relationship but your data don’t rule out the possibility that there is one.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com

[Bill_Powers1]

I’m still in touch with Pat. She
invited me to a group in which she participates that meets monthly at the
Glenview library–interested in flying saucers, science studies, etc.
I’ll check out what happened next in her experiences with motion
sickness.
[From Bill Powers (2007.09.24.1055 MDT)}

Dick Robertson,2007.09.24.1000CDT –

Good, I’d like to know if my memory that she got over her motion sickness
is correct. I’d also like to know, but not as much, if it’s
incorrect.

Best,

Bill P.

[Martin_Taylor2]

[Martin Taylor 2007.09.24.17.06]

[From Bill Powers (2007.09.24.0409 MDT)]

Martin Taylor 2007.09.24.00.47] --

Rick Marken (2007.09.23.2115)] --

I'm copying here a few paragraphs I recently send to Warren Mansell. They may have a bearing on the Lyell Illusion that's being discussed.

Your geological interest is showing!

=======================================================================================
I once worked with a graduate student who was a former student of Dick Robertson's,...
The graduate student suffered from motion sickness to a debilitating degree, even on subway (Underground) trains and on buses. She wanted to study it, so I wrote a program to use a (sideways) waterfall illusion to measure after-"images" of motion (a transition-level experiment). A computer screen was filled with moving dots, which ceased to move when a beep sounded. At that point, the participant could affect the rate of motion of the dots by using a mouse, the instructions being to use the mouse to keep the dots stationary after the beep. Of course that means making the dots move oppositely to the direction of the illusion. The result was a very nice negative exponential decay of the participant-caused motion, dying out to zero in twenty or thirty seconds. This made the magnitude and time-course of the illusion directly measurable. We were probably measuring the motion of fluid in the semicircular canals!

When was this? in 1957? I wish I had known you then. We would have made quite a team. Here's the abstract of M. M. Taylor, "Tracking the neutralization of seen rotary movement", Perceptual and Motor Skills, 1964, 16, 513-519.

"Ss controlled a rotating disc for 10 min,. with instructions to keep the speed of the disk constant. Ss actually increased the physical speed of the disc as the trial continued. The logarithmic increase in speed was proportional to the square root of the inspection time, and was less for high initial speeds than for low. It was proportional to the Weber ratio. Most Ss showed less neutralization on the later trials"

"Logarithmic increase in speed" means that the speed increase in log units was linear with the square root of time. (There's something rather special about the square root of time. I did a literature survey ("The effect of the square root of time on continuing perceptual tasks" Perception and Psychophysics, 1966, 1, 113-119) and found that a wide range of changes over time are linear if plotted against the square root of time.

Before this, I had done what you did, except it wasn't computerized (M.M.Taylor, "Tracking the decay of the after-effect of seen rotary movement", Perceptual and Motor Skills, 1963, 16, 119-129). In that study, I exposed subjects to a rotating disk for varying periods of time, and then gave them the speed control and asked them to keep the disk stationary.

The tracks of actual disk speed as a function of time were quite interesting. You say that the decay in your study was exponential. So it was in mine, very nicely, if the initial viewing period was short enough, but for longer viewing the decay followed two exponentials, an early one with a short time constant that gave way after a couple of minutes to one with a much longer time constant (roughly an order of magnitude longer). A bit like this, on log paper:

        >*
        > *
  log | *
speed | *
        > *
        > *
        > *
        >_____________________________________
                      time

There's a perceptual effect in this compensatory tracking study that really worried some subjects, and its weird enough even when you know what to expect. You have been keeping the rotating disk absolutely still, and you are sure you have been doing it quite accurately, but nevertheless the disk keeps changing position (without moving). You perceive the change of position simultaneously with the stillness and it's quite disconcerting.

You also note:

In refining the experiment and data-taking, this student and I passed many trial versions of the experiment back and forth, and after a while I began to have trouble with the program -- some bug had crept into it so the data were not being correctly reported -- so I thought. Eventually, we both had to admit that we had worn out the illusion, so neither of us had it any more.

In those years when I was worrying about figural after-effects, including motion, one of the puzzles was why people seldom if ever experience a motion after-effect from riding in a car looking forward, but most have a strong after effect if they look out of the back window long enough. I attributed it to the development of an anchor for the familiar motion, but that's really not very satisfactory, because the speed doesn't seem to make much difference. You and your student experienced this diminishment of the illusion while you were studying it, but most of us experience it without ever noticing that it happens.

We had reorganized it away.

Isn't this applying a "dormitive principle"? What actually would you see as happening, and why, in reorganization as we usually consider it? There's no loss of control in the experiment, just a lot of experiences with the stimulus. Usually we think of reorganization as happening when there's a control problem.

Not only that, but the graduate student found that she no longer suffered from motion sickness.

That's a wonderful finding. Or perhaps I should say "occurrence" since it's not been replicated (or has it?).

=======================================================================================

What occurred to me, of course, was that while doing Martin's experiments, the participants might have been reorganizing, so that gradually, over time, the distortions would tend to disappear. Perhaps the course of the experiments was short enough that this effect would not appear, but if the comparisons were made in the same order every time, there could have been some confusing adaptational effects -- or even if they were made in randomized order.

It's not impossible, but if it happened, it wouldn't account for the results, would it? But I don't think it's likely to have happened, because usually these "avoidance of illusion" effects take rather a long time to occur, unless one is actually controlling something in which the feedback path is influenced by the illusion. If you are controlling through an illusion-affected feedback path, then reorganization, in the form of changes in conscious perception, can happen quite fast. That, I suppose, was at the heart of Jim Taylor's book "The Behavioural Basis of Perception). You can get these internally inconsistent conscious perceptions in those cases, too (e.g., after coming to see the world the right way up while wearing inverting spectacles, cigarette smoke may still seem to be weirdly floating downward to the ceiling).

It seems to me that this experiment calls for a pct-style version, in which the participants simply remove what they see as distortions

There's a problem with this, in that nobody would ever have the occasion to see anything as a distortion. All they do is look at a figure, and by one means or another report what they see. They have no opportunity to compare the "Arrowhead" with the "Feathers". But I have suggested to Rick that he set up a PCT-style version. He's a good programmer, and it shouldn't be hard to set up in Java for us all to see and act as subjects.

until the dots all appear equally spaced. If there really are context effects of the kind Martin tried to measure, this should show them very clearly, as my experiment did for the waterfall illusion. And if adaptation really does take place, the illusion should disappear with extended practice (though if it doesn't, that would be informative, too).

I think we're always reorganizing to maintain the mutual calibration among sensory modalities, particularly kinesthesia, touch, and vision.

Again, in this kind of experiment, there's no opportunity for cross-modal recalibration.

With practice, the cross-calibration seems to get better, and it seems to deteriorate otherwise. PCT experiments would seem to suit this sort of experimentation very nicely.

And my answer to Martin's comment is that no, I don't trust anyone's experiments that were done without using PCT techniques. There are too many assumptions about things that PCT makes measurable. Some older experiments were done by adjustment of objects and relationships and might be PCT-certifiable, more or less, but most weren't. I don't know how the line-length comparisons to dot intervals were made, so I can't judge Martin's experiment on that basis.

That's why I'm suggesting to Rick that he try replicating the essence of the experiment with full understanding of PCT.

Martin

[Martin_Taylor2]

[Martin Taylor 2007.09.24.17.56]

[From Rick Marken (2007.09.24.0930)]

Martin Taylor (2007.09.24.00.47) --

Let's see. If I undersand you correctly, you assert that in all cases
p = k*log(s) approximately, where p is the perceptual value and s is
the stimulus magnitude, in this case physical distance. I take it
that this is what you mean by a log function, and that changing k is
the way to get a function of the same form that is different between
the A (Arrow) and F (Feathers) context configurations.

No. Changing k is not what I had in mind. What I had in mind is shown in the attached figure. The function labeled f() is the perceptual function mapping physical magnitude (s) into psychological magnitude (Psi).

OK

In this case the s values can be thought of inter dot distances within the Muller Lyer figures, either Arrowheads or Feathers. In this figure f() is a log function.

What the context forms (Arrowheads or Feathers) seem to do (according to your data) is change the apparent length of the lines between what you call "points" (the end points of the distance between the Arrowheads or Feathers). For example, the Arrowheads make the same inter point distance look shorter than it does with Feathers; that's the Mueller Lyer illusion.

What I'm assuming is that estimates of the length of inter-dot intervals -- sub-distances of the distance between points -- are made relative to the apparent distance between points.

As do I, which means that f is NOT "the perceptual function mapping physical magnitude (s) into psychological magnitude (Psi)", but a function mapping some configurational variable (which necessarily includes s) into psychological magnitude.

I've always agreed with your interpretation of what is happening, for maybe 30 years before I ever heard your name.

What I don't agree with is your approach to the word "function". If "s" is a physical magnitudes, and x = f(s), then x has the same value for a given value of s no matter what else is in the world. In the situation we are discussing, Psi = f(s, context).

I'm not saying that this is the right explanation. Nor am I particularly interested in developing a PCT experiment to properly test this.

Pity. You are the best in this group to do it.

I just wanted to present this little model to show that your data do not rule out a single functional relationship between perceived and physical distance.

Ah, but they do, if you aren't talking about parameterization of the function according to the configuration.

Martin

[Bill_Powers1]

[From Bill Powers (2007.09.24.1735 MDT)]

[Martin Taylor 2007.09.24.17.06 –

Your spinning disc experiment preceded my waterfall illusion by about 30
years.

You’re right in objecting to the term “reorganization.” The
fading of the illusion is much too systematic for the e.coli effect. But
reorganization could have been working

behind the scenes to alter the initial magnitude of the illusion. I
didn’t record enough data to detect a random walk of the initial
magnitude toward zero…

Were the data really good enough to distinguish two exponentials? I was
happy just to get a reasonable fit to a single exponential.

Re the PCT version of your experiment. I would simplify it, looking for a
global context effect. By making the dot spacing symmetrical about the
center of the line, and using a single control to adjust the
nonlinearity, we could at least see if there is any kind of effect from
the direction of the arrows at the ends.

The distance between dots from center could be increased or decreased
according to distance from center, a fairly simple function. With a
simple mouse motion the distribution could go from bunched up in the
center to bunched up at the ends. I’ll try to work out a program for
that. If people produce even spacing I think we could doubt the context
effects.

Best,

Bill P.

···

[Martin_Taylor2]

Re: Perceptual distance
measures
[Martin Taylor 2007.09.24.23.09]

[From Bill Powers (2007.09.24.1735
MDT)]

[Martin Taylor 2007.09.24.17.06 –
Your spinning disc experiment preceded my
waterfall illusion by about 30 years.

Were the data really good enough to distinguish two exponentials? I
was happy just to get a reasonable fit to a single
exponential.

Here’s a scan from the publication of parts of two traces from
the same subject. Note that the “speed” scale is
logarithmic.

This is one experiment from which I just possibly might have the
original traces. TThe records are actually quite long in some cases. I
remember seeing them not too many years ago, but I’ve made two office
moves since then, and if they have survived they are probably in one
of 21 carboard boxes. But if I can find them I’ll see what I can do
about copying them. They are on long rolls of instrument recording
paper of the 1960s, so they might fall apart when unrolled, even if I
do find them.

Re the PCT version of your experiment. I
would simplify it, looking for a global context effect. By making the
dot spacing symmetrical about the center of the line, and using a
single control to adjust the nonlinearity, we could at least see if
there is any kind of effect from the direction of the arrows at the
ends.

That’s an interesting variant of the experiment. It doesn’t
address the same issue, but it’s interesting in its own right. My
results don’t suggest that there would be any distortion at a given
inter-dot spacing, but it doesn’t suggest there is no distortion,
either. It’s agnostic on the issue.

My intuition is that you would find distorions in the perceptual
space around the arrow or feather points. But centre-symmetric placing
doesn’t seem to me to buy you much. It would be a surprise if there
were much of a consistent difference between left and right (there
probably would be some, but that wouldn’t be from the Mueller-Lyer
effect).

Here’s a variant that should be workable with one degree of
freedom: have the usual empty Mueller-Lyer figure (empty meaning with
no line connecting the points). Somewhere between the points place
four dots, and give the subject control of one of them, say the left
one. Ask that the subject keep the left-to-second-left distance the
same as the right-to-second-right distance while you, as a
disturbance, vary the right-to-second-right distance and at the same
time move the dot pairs to different places in the area of the points.
(As I was writing this paragraph, I realized that there’s no need for
the dots and points to be colinear. One could map out the distortions,
if there are any, all around the figure this way, and there needn’t
even be two opposed arrowheads or feathers, one right angle should
show some effect.)

The distance between dots from center
could be increased or decreased according to distance from center, a
fairly simple function. With a simple mouse motion the distribution
could go from bunched up in the center to bunched up at the ends. I’ll
try to work out a program for that. If people produce even spacing I
think we could doubt the context effects.

Maybe I’m not visualising the same pattern as you are. If the
points are symmetric about the centre, I’m not at all sure what you
would expect to see.

My study suggests that short distances along the line connecting
the points are seen differently relative to longer distances in the
two figures. To put it crudely, if with no arrowheads or feathers, 1 +
1 + 1 = 3, then in one case 0.9 + 0.9 + 0.9 = 3.1 while in the other
1.1 + 1.1 + 1.1 = 2.9. If I imagine your layout properly, what you
would find would be that 0.9 = 0.9, 1.1 = 1.1, and 3.1 = 3.1 and 2.9 =
2.9. But I’m probably not seeing in my mind what you are seeing in
yours.

Martin

[Bill_Powers1]

[Martin Taylor 2007.09.24.17.06

Your spinning disc experiment preceded my waterfall illusion by about 30
years.

Were the data really good enough to distinguish two exponentials? I was
happy just to get a reasonable fit to a single
exponential.

Here’s a scan from the publication of parts of two traces from the same
subject. Note that the “speed” scale is
logarithmic.
[From Bill Powers (2007.09.24.2306 MDT)]

Martin Taylor 2007.09.24.23.09 –

The illusory speed seems to have decreased to about 2.5 degrees per
second after about a minute and a half and then stopped decreasing . I
wouldn’t believe any fluctuations beyond that point. Of course there’s
nothing to prevent fitting another exponential to the remainder of the
data, but why not 1/t or even just a straight line? Just about any line
would produce an equally good fit. after the 1.5 minute mark. What was
the accuracy with which your apparatus could maintain a specific speed
below 2.5 degrees per second?

After a minute and a half there isn’t much waterfall illusion left,
either, and imagination is all too easy to inject into the experience. I
don’t recall the illusion lasting that long, but maybe it did. It’s a
fairly easy illusion to create on a computer screen, as would be your
rotating disk. What sort of background surround was there, against which
to judge the rotation? The eye can rotate about +/- 5 degrees around a
vertical axis, so there are possible ‘rotary nystagmus’ effects from
that. It’s so easy to do the experiment again, there’s no reason to
dredge up the old data. The experimental details would be
useful.

Yes, the two subjects I talked to (myself and the student) found the
experience of continued motion without any actual change of position
rather strange. Wilbur Penfield found a place the brain stimulation of
which made the patient see the doctor as rushing toward her, while at the
same time not getting any closer. Quite upsetting. This gave me a lot of
confidence in the transition level of the HPCT model.

As to the other subject,

That’s an
interesting variant of the experiment. It doesn’t address the same issue,
but it’s interesting in its own right. My results don’t suggest that
there would be any distortion at a given inter-dot spacing, but it
doesn’t suggest there is no distortion, either. It’s agnostic on the
issue.

The question is whether you were seeing a local dot-to-dot interaction of
perceptions, or an interaction of the dot spacings with the images of the
arrows at the left and right of the space where the dots were. It’s hard
to judge from the data, which are very noisy even when presented as
averages across subjects. The data you showed isn’t even symmetrical
around the midpoint of the bounding arrowheads, is it? It’s hard to speak
of an illusion when not everyone has it, or has it in the same direction.
I definitely think the experiment needs to be done again.

Here’s a variant
that should be workable with one degree of freedom: have the usual empty
Mueller-Lyer figure (empty meaning with no line connecting the points).
Somewhere between the points place four dots, and give the subject
control of one of them, say the left one. Ask that the subject keep the
left-to-second-left distance the same as the right-to-second-right
distance while you, as a disturbance, vary the
right-to-second-right distance and at the same time move the dot pairs to
different places in the area of the points. (As I was writing this
paragraph, I realized that there’s no need for the dots and points to be
colinear. One could map out the distortions, if there are any, all around
the figure this way, and there needn’t even be two opposed arrowheads or
feathers, one right angle should show some
effect.)

Wouldn’t you expect left-right symmetry in the effect? Oh, I see, you
would move the dots in each pair by the same amounts along the horizontal
axis, symmetrically around the center between the two arrowheads, or even
to different points. Yes, that might be a good way to do it.

The question is whether we’re seeing an effect that varies with distance
from the arrow or feather end, or an effect that spreads equally across
the space between the bounding arrows/feathers. In your tests, did you
select points so that you could see if the effect was symmetrical left
and right? If the arrows/feathers have anything to do with it, the
effect should be the same for dot-pairs whose centers are equally far
left and right from the point of symmetry.

My study suggests
that short distances along the line connecting the points are seen
differently relative to longer distances in the two figures. To put it
crudely, if with no arrowheads or feathers, 1 + 1 + 1 = 3, then in one
case 0.9 + 0.9 + 0.9 = 3.1 while in the other 1.1 + 1.1 + 1.1 = 2.9. If I
imagine your layout properly, what you would find would be that 0.9 =
0.9, 1.1 = 1.1, and 3.1 = 3.1 and 2.9 = 2.9. But I’m probably not seeing
in my mind what you are seeing in yours.

I’ve visualizing points arranged like this,ranging smoothly from (1) to
(5):

(1) * *

···

•  * * <--- squeezed at ends
  

(2) * *
*

•   *    
  

(3) * *

• *    
  

• *     * <--- equal
  

spacing

(4) * *

---

•   *
  

(5) *

---

•     * <--- squeezed at
  

center

If there is an effect that varies with distance from the ends, we would
not expect to see the spacing of line (3), but one of the others, and to
see an effect from arrows opposite to the effect from feathers.

What would your proposed distortions predict for the outcome above?

Best,

Bill P.

[Richard_H_Pfau]

What I don’t agree with is your approach to the word “function”. If “s” is a physical magnitudes, and x = f(s), then x has the same value for a given value of s no matter what else is in the world. In the situation we are discussing, Psi = f(s, context).
Doesn’t Psi = f(s,context) get back to the question of priming effects due to the context, an idea that some of us feel may be important?

With Regards,

Richard Pfau

···

-----Original Message-----

From: Martin Taylor mmt-csg@ROGERS.COM

To: CSGNET@LISTSERV.UIUC.EDU

Sent: Mon, 24 Sep 2007 6:05 pm

Subject: Re: Perceptual distance measures

[Martin Taylor 2007.09.24.17.56]

[From Rick Marken (2007.09.24.0930)]

Martin Taylor (2007.09.24.00.47) –

Let’s see. If I undersand you correctly, you assert that in all cases

p = k*log(s) approximately, where p is the perceptual value and s is

the stimulus magnitude, in this case physical distance. I take it

that this is what you mean by a log function, and that changing k is

the way to get a function of the same form that is different between

the A (Arrow) and F (Feathers) context configurations.

No. Changing k is not what I had in mind. What I had in mind is >shown in the attached figure. The function labeled f() is the >perceptual function mapping physical magnitude (s) into >psychological magnitude (Psi).

OK

In this case the s values can be thought of inter dot distances >within the Muller Lyer figures, either Arrowheads or Feathers. In >this figure f() is a log function.

What the context forms (Arrowheads or Feathers) seem to do >(according to your data) is change the apparent length of the lines >between what you call “points” (the end points of the distance >between the Arrowheads or Feathers). For example, the Arrowheads >make the same inter point distance look shorter than it does with >Feathers; that’s the Mueller Lyer illusion.

What I’m assuming is that estimates of the length of inter-dot >intervals – sub-distances of the distance between points – are >made relative to the apparent distance between points.

As do I, which means that f is NOT “the perceptual function mapping physical magnitude (s) into psychological magnitude (Psi)”, but a function mapping some configurational variable (which necessarily includes s) into psychological magnitude.

I’ve always agreed with your interpretation of what is happening, for maybe 30 years before I ever heard your name.

What I don’t agree with is your approach to the word “function”. If “s” is a physical magnitudes, and x = f(s), then x has the same value for a given value of s no matter what else is in the world. In the situation we are discussing, Psi = f(s, context).

I’m not saying that this is the right explanation. Nor am I >particularly interested in developing a PCT experiment to properly >test this.

Pity. You are the best in this group to do it.

I just wanted to present this little model to show that your data >do not rule out a single functional relationship between perceived >and physical distance.

Ah, but they do, if you aren’t talking about parameterization of the function according to the configuration.

Martin

---

Email and AIM finally together. You’ve gotta check out free AOL Mail!

[rsmarken]

[From Rick Marken (2007.09.25.0915)]

Martin Taylor (
2007.09.24.17.56)–

I’ve always agreed with your interpretation of what is happening, for
maybe 30 years before I ever heard your name.

What I don’t agree with is your approach to the word “function”. If

“s” is a physical magnitudes, and x = f(s), then x has the same value
for a given value of s no matter what else is in the world. In the
situation we are discussing, Psi = f(s, context).

This is not my model of what is going on and it is not how I derived the functions in the graph I showed you. My model of perception is that there are hierarchical layers of perceptual function (gee, what a coincidence; isn’t there is esoteric theory of mind that says the same thing;-).

In my model of perception the lowest level perceptual functions produce a perception that is related to the magnitude of physical stimuli. This is what is called the psychophysical function in psychology and can be represented as Psi = f(s). In the chart I sent I assumed that f() is logarithmic when s is the length of a line so that Psi = k log s.

In my model of perception, the effect of context is included in perceptions at a higher level; perceptions created by perceptual functions that take the outputs of lower level perceptual functions as inputs. So the perception of line length in the context of other lines is created by a perceptual function that takes Psi values (call them Psi1 to indicate that they are level 1 perceptions) as inputs. I assume that the output of these higher level functions, which we can call Psi2, are the basis for judgments of line length when we see context affecting these judgments. So a higher level perception that is used in judging line length in the context of other line lengths (as in your Mueller Lyer study) might be Psi2 = g(Psi11, Psi12,…Psi1n). What I plotted in my graph as the Psi values for the Arrowhead and Feather contexts were actually Psi2 values; I just picked g() functions that would transform the log s (Psi1) values to give the right results.
The log function that produces the Psi1 values is the same for both the Arrowhead and Feather context.

My model of perception assumes that the low and high level perceptions (Psi1s and Psi2s) are present simultaneously. Subjects who show a pronounced context effect are mainly paying attention to the higher level perception, Psi2; those who do not show pronounced context effects (or who learn not to show them) are able to focus on the lower level perception, Psi1. In most psychophysical experiments, context is held constant so it it shouldn’t matter whether judgments are based on Psi1 or Psi2 level perception.

Whether this model is correct or not, I hope it shows what I mean when I say that your results doesn’t rule out the possibility of a single psychophysical function. I see the psychophysical function as the level 1 perceptual functions, which seem to be either logarithmic or, certainly, loggish;-) Context effects, like those seen in your study, don’t necessarily change the nature of the psychophysical (level 1) functions; indeed, they don’t have to change these functions at all. They just change the outputs of higher level – I would say configuration level – perceptual functions.

Best

Rick

···

–
Richard S. Marken PhD

rsmarken@gmail.com

[Bill_Powers1]

[From Bill Powers (2007.09.25.1108 MDT)]

Rick Marken (2007.09.25.0915) –

My model of perception
assumes that the low and high level perceptions (Psi1s and Psi2s) are
present simultaneously. Subjects who show a pronounced context
effect are mainly paying attention to the higher level perception, Psi2;
those who do not show pronounced context effects (or who learn not to
show them) are able to focus on the lower level perception, Psi1. In most
psychophysical experiments, context is held constant so it it shouldn’t
matter whether judgments are based on Psi1 or Psi2 level
perception.

I didn’t see this coming at all, Rick. How elegant. It allows you to
explain not only the findings that fit the hypothesis, but the findings
that don’t fit. More than anything, I appreciate your use of relative
levels, Psi1 and Psi2, rather than trying slavishly to adhere to my
11 defined levels. This is how we will eventually find the right
definitions of levels.

Context effects would quality as relationship effects, wouldn’t
they?

I think there’s still a lot we don’t know about internal adjustments of
perceptual properties. I was talking with David Goldstein just now about
getting used to bifocals, and the learning that takes place so you don’t
get dizzy when you look down (either when putting the bifocals on or when
switching to single-focus computer glasses).

Best,

Bill P.

[rsmarken]

[From Rick Marken (2007.09.25.1110)]

Bill Powers (2007.09.25.1108 MDT)

I didn't see this coming at all, Rick. How elegant. It allows you to explain
not only the findings that fit the hypothesis, but the findings that don't fit.
More than anything, I appreciate your use of relative levels, Psi1 and Psi2,
rather than trying slavishly to adhere to my 11 defined levels. This is how
we will eventually find the right definitions of levels.

Thanks. Yes, I am very comfortable with using your proposed levels as
heuristics. I think they are very helpful -- and probably very close
to being right -- but I don't take them as absolute truth, like the
Bible and Koran, for example;-)

Context effects would quality as relationship effects, wouldn't they?

Maybe, maybe not. I think one idea about the reason for the Mueller
Lyer effect is that the Arrowhead vs Feather figures are seen as 2 D
representations of 3 D wire frame figures, the Arrowhead version being
the figure with the edge coming toward the viewer and the Feather
version being the figure with the edge going away from the viewer. The
idea is that the illusion occurs because you are perceiving a 3 D
configuration in imagined space; the illusion occurs because the same
sensory line length (edge) is "corrected" to be longer when it is seen
as father away (Feathers) than when it is seen as close (Arrowheads).
So the context effect could be a configuration rather than a
relationship effect.

Best

Rick

···

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

[Bill_Powers1]

I think one idea about the
reason for the Mueller

Lyer effect is that the Arrowhead vs Feather figures are seen as 2 D

representations of 3 D wire frame figures, the Arrowhead version
being

the figure with the edge coming toward the viewer and the Feather

version being the figure with the edge going away from the
viewer.
[From Bill Powers (2007.09.25.1208 MDT)]

Rick Marken (2007.09.25.1110) –

Then it should be enhanced if the lines are drawn as 3-D parallelopipes
in a 3D space with perspective.

Best,.

Bill P.

[Martin_Taylor2]

[Martin Taylor 2007.09.25.14.12]

[From Bill Powers (2007.09.24.2306 MDT)]

Martin Taylor 2007.09.24.23.09 --

[Martin Taylor 2007.09.24.17.06 --
Your spinning disc experiment preceded my waterfall illusion by about 30 years.

Were the data really good enough to distinguish two exponentials? I was happy just to get a reasonable fit to a single exponential.

Here's a scan from the publication of parts of two traces from the same subject. Note that the "speed" scale is logarithmic.

The illusory speed seems to have decreased to about 2.5 degrees per second after about a minute and a half and then stopped decreasing . I wouldn't believe any fluctuations beyond that point.

I guess what you believe is up to you. However, the trends were pretty consistent. If you want to imagine what rotary speed 2.5 degrees/sec means, think of the second-hand of a watch, moving at 6 deg/sec. It's about half that, which is far from threshold on a

Of course there's nothing to prevent fitting another exponential to the remainder of the data, but why not 1/t or even just a straight line? Just about any line would produce an equally good fit. after the 1.5 minute mark.

As the figure caption says, the fit shown is just a snip from a much longer track. The text says: "A trial usually continued until the speed of the test disk was less than 1 deg/sec, or until tracking had continued for 15 minutes." By eye, I'd think the track shown was fitted from the full 13 minutes ater the break at about 1 1/2 minutes. The decay time constant for the first phase for a 320 sec "inducing" period averaged over subjects was about 2 min, for the second phase nearer 20 min.

What was the accuracy with which your apparatus could maintain a specific speed below 2.5 degrees per second?

I can't tell you that at this late date, but I'd be really surprised if it was worse than 0.1 deg/sec. Judging from the published pair of tracks, it can't have been worse than that, because that subject was controlling to within 0.1 deg/sec most of the time. We had a pretty good workshop in those days, and this was intended as precision gear

After a minute and a half there isn't much waterfall illusion left, either, and imagination is all too easy to inject into the experience.

Yes, but there's no imagination in a compensatory tracking task. All the subject is doing is keeping teh disk stationary, not asking him/herself whether they can still see an illusory movement.

I don't recall the illusion lasting that long, but maybe it did. It's a fairly easy illusion to create on a computer screen, as would be your rotating disk. What sort of background surround was there, against which to judge the rotation?

Plain white cardboard.

The eye can rotate about +/- 5 degrees around a vertical axis, so there are possible 'rotary nystagmus' effects from that.

That couldn't affect the data, or at least I don't see how it could. I can see how it might induce abrupt steps in the track around a steady trend, though. In fact, one might guess that to be a possible reason for the step-like appearance of the second phase of the two published tracks.

It's so easy to do the experiment again, there's no reason to dredge up the old data. The experimental details would be useful.

I'm not interested. I only brought it up because you mentioned you had done essentially the same experiment, and I wanted to corroborate your result (the exponential decay) with the added stuff about the second phase (and a lot more if you are really interested. If you want to do the experiment again, I'kk send you a paper copy of all the relevant papers -- I haven't mentioned all of them.

As to the other subject,

That's an interesting variant of the experiment. It doesn't address the same issue, but it's interesting in its own right. My results don't suggest that there would be any distortion at a given inter-dot spacing, but it doesn't suggest there is no distortion, either. It's agnostic on the issue.

The question is whether you were seeing a local dot-to-dot interaction of perceptions, or an interaction of the dot spacings with the images of the arrows at the left and right of the space where the dots were. It's hard to judge from the data, which are very noisy even when presented as averages across subjects. The data you showed isn't even symmetrical around the midpoint of the bounding arrowheads, is it?

Nothing in the data relates to where a particular interdot interval was along the path between the points. I don't know what it would mean to be "symmetrical around the midpoint of the arrowheads".

It's hard to speak of an illusion when not everyone has it, or has it in the same direction. I definitely think the experiment needs to be done again.

Here's a variant that should be workable with one degree of freedom: have the usual empty Mueller-Lyer figure (empty meaning with no line connecting the points). Somewhere between the points place four dots, and give the subject control of one of them, say the left one. Ask that the subject keep the left-to-second-left distance the same as the right-to-second-right distance while you, as a disturbance, vary the right-to-second-right distance and at the same time move the dot pairs to different places in the area of the points. (As I was writing this paragraph, I realized that there's no need for the dots and points to be colinear. One could map out the distortions, if there are any, all around the figure this way, and there needn't even be two opposed arrowheads or feathers, one right angle should show some effect.)

Wouldn't you expect left-right symmetry in the effect? Oh, I see, you would move the dots in each pair by the same amounts along the horizontal axis, symmetrically around the center between the two arrowheads, or even to different points. Yes, that might be a good way to do it.

The question is whether we're seeing an effect that varies with distance from the arrow or feather end, or an effect that spreads equally across the space between the bounding arrows/feathers. In your tests, did you select points so that you could see if the effect was symmetrical left and right?

I'm not sure how to interpret your question. There is no effect within either the Feathers or the Arrowheads, at least not an effect measured in my study. All I did was to compare every possible perceived inter-dot interval in the A figure with the corresponding interdot interval in the B figure. There are no "within figure" comparisons. You are suggesting looking within the figures to see where the unexpected result comes from. That's an interesting follow-up, but you won't find any relevant data in my study, even if the raw data did miraculously show up.

If the arrows/feathers have anything to do with it, the effect should be the same for dot-pairs whose centers are equally far left and right from the point of symmetry.

My study suggests that short distances along the line connecting the points are seen differently _relative to longer distances_ in the two figures. To put it crudely, if with no arrowheads or feathers, 1 + 1 + 1 = 3, then in one case 0.9 + 0.9 + 0.9 = 3.1 while in the other 1.1 + 1.1 + 1.1 = 2.9. If I imagine your layout properly, what you would find would be that 0.9 = 0.9, 1.1 = 1.1, and 3.1 = 3.1 and 2.9 = 2.9. But I'm probably not seeing in my mind what you are seeing in yours.

I've visualizing points arranged like this,ranging smoothly from (1) to (5):

(1) * * * * * * * <--- squeezed at ends

(2) * * * * * * *
   (3) * * * * * * * <--- equal spacing

(4) * * * * * * *

(5) * * * * * * * <--- squeezed at center

If there is an effect that varies with distance from the ends, we would not expect to see the spacing of line (3), but one of the others, and to see an effect from arrows opposite to the effect from feathers.

What would your proposed distortions predict for the outcome above?

No prediction at all. I don't assert (or assume) that there's any distortion of that kind. Nor do I assume there isn't. If any of those distortions actually occur, it would be interesting in respect of the illusion itself, but I doubt it would shed any light on the results of my study.

If the interpretation holds that I thought Rick and I agreed on (but which he seems now to disavow), it's simply a contrast effect. The subject perceives the inter-point distance as longer in the F figure, and the short inter-dot intervals seem shorter by contrast. That interpretation says nothing about where the short interval sits within the longer interval, and I don't know of any other studies that would help in makign a guess. My first intuitive guess would be that the position wouldn't matter much at all. All the interdot distances would be a little "squeezed" in the F figure (where the total distance is long) and "stretched" in the A figure (where the total distance is short). That wouldn't show up in your proposed experimental arrangement.

What would be interesting is if you did get the kind of distortion you depict, but it went in opposite directions in the two figures. I'm not sure what it would mean in the context of the original study, but maybe it would mean something.

Martin

[Martin_Taylor2]

[Martin Taylor 2007.09.25.14.14]

[From Rick Marken (2007.09.25.0915)]

... My model of perception is that there are hierarchical layers of perceptual function (gee, what a coincidence; isn't there is esoteric theory of mind that says the same thing;-).

In my model of perception the lowest level perceptual functions produce a perception that is related to the magnitude of physical stimuli. This is what is called the psychophysical function in psychology and can be represented as Psi = f(s). In the chart I sent I assumed that f() is logarithmic when s is the length of a line so that Psi = k log s.

In my model of perception, the effect of context is included in perceptions at a higher level; perceptions created by perceptual functions that take the outputs of lower level perceptual functions as inputs. So the perception of line length in the context of other lines is created by a perceptual function that takes Psi values (call them Psi1 to indicate that they are level 1 perceptions) as inputs. I assume that the output of these higher level functions, which we can call Psi2, are the basis for judgments of line length when we see context affecting these judgments. So a higher level perception that is used in judging line length in the context of other line lengths (as in your Mueller Lyer study) might be Psi2 = g(Psi11, Psi12,...Psi1n). What I plotted in my graph as the Psi values for the Arrowhead and Feather contexts were actually Psi2 values; I just picked g() functions that would transform the log s (Psi1) values to give the right results. The log function that produces the Psi1 values is the same for both the Arrowhead and Feather context.

My model of perception assumes that the low and high level perceptions (Psi1s and Psi2s) are present simultaneously. Subjects who show a pronounced context effect are mainly paying attention to the higher level perception, Psi2; those who do not show pronounced context effects (or who learn not to show them) are able to focus on the lower level perception, Psi1. In most psychophysical experiments, context is held constant so it it shouldn't matter whether judgments are based on Psi1 or Psi2 level perception.

I've quoted this extensively, because I think it's a very interesting total revision of the "standard" hierarchy. In the standard hierarchy, a perception at one level is of a qualitatively different kind than a perception at another level. An intensity is an intensity, and a configuration is a configuration. You can't (in the normally understood version of HPCT) parse an intensity out of a configuration -- or else I've been misinterpreting HPCT for many years.

You are allowing for a novel possibility -- that two well separated levels can create perceptual fucntions that are qualitatively the same. "Qualitatively" means that consciously we perceive them as being the same or different kinds of thing. I like it, because it accounts for one's ability to take different views that can reduce or enhance some illusions.

But it still produces the same issue.

Whether this model is correct or not, I hope it shows what I mean when I say that your results doesn't rule out the possibility of a single psychophysical function. I see the psychophysical function as the level 1 perceptual functions, which seem to be either logarithmic or, certainly, loggish;-) Context effects, like those seen in your study, don't necessarily change the nature of the psychophysical (level 1) functions; indeed, they don't have to change these functions at all. They just change the outputs of higher level -- I would say configuration level -- perceptual functions.

I suppose it depends what you mean by "the psychophysical function". Usually, that refers to the relation between the perceived magnitude and the physical magnitude of something. You are proposing a multi-level mechanism, but there's still only one perceived value at a time. You don't perceive two inter-dot distances, or even a diffuse distance. You perceive a distance, and that distance has a relationship with the physical distance. That relationship (the psychophysical function) depends on the configurational context. What mechanisms operate below that level is interesting, but not relevant.

Now, with this new reconstruction of HPCT to allow intensity-quality perceptions to be produced at the configuration level as well as at the intensity level, and for the two to interact to produce a "final" intensity perception, maybe there are a lot more ways that the interactions of qualitatively identical perceptions from different levels could account for puzzling phenomena.

It does, though, put front and centre the distinction between "perceptual signal" and "conscious perception".

It's all very intriguing.

Martin

PS: I see Bill endorses your proposed revision of HPCT. That's good!

[rsmarken]

[From Rick Marken (2007.09.25.1150)]

Martin Taylor (2007.09.25.14.12)

If the interpretation holds that I thought Rick and I agreed on (but
which he seems now to disavow), it's simply a contrast effect.

Nope, I don't disavow it at all. It's the one shown in the figure I sent.

Best

Rick

···

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

[Martin_Taylor2]

[Martin Taylor 2007.09.25.14.33]

[From Bill Powers (2007.09.25.1108 MDT)]

I think there's still a lot we don't know about internal adjustments of perceptual properties. I was talking with David Goldstein just now about getting used to bifocals, and the learning that takes place so you don't get dizzy when you look down (either when putting the bifocals on or when switching to single-focus computer glasses).

That was a core theme of Jim Taylor's "The Behavioural basis if Perception". He took it to be a question of behavioural feedback having unwanted effects on the perception. In PCT terms, he would have been saying that errors were not being reduced by behaviour that normally would have reduced it.

As we discussed many years ago, "reorganization" can have several guises, one of which is a resetting of perceptual functions. What Jim (no relation) found was that the sensation of the glasses on one's face could become factored into the perception of the world. Initially, when putting on the glasses (he used displacement or inverting prisms), the world looked wrong and one indeed stumbled and failed to pick up things correctly, and so forth. After a while of behaving ineffectively in the distored world, the world began to look normal and one's actions became effective. But then taking the specs off produced the inverse after-effect -- wrong appearance, ineffective behaviour. However, with practice, putting on and taking off the spectacles can be done with no problem. The world switches more or less instantly so that it looks right with the specs on or off.

The kicker came when Jim replaced the prisms by plain glass (or maybe he just removed them). Then when one put on the specs, the world went wrong again. The sensations of the specs apparently flipped a switch or modulated the perception so that the inversion or displacement was elimination, but if there was no inversion or displacement, that "correction" wasn't very helpful!

There's a marvellous movie of this effect, showing Seymour Papert riding a bicycle. He rides, and then puts on the specs (left-right inverting, I think). he crashes instantly. The movie shows this happening several times until Papert manages to keep riding, if wobbly, and after more trials he rides noramlly, but when he takes the specs off he crashes. After more training, he can put the specs on and off while riding, with no problem. But at the end of the film, Jim gives him the specs that don't invert, and Papert crashes instantly he puts them on. Of course, from this description, you can't tell much, but Papert (with whom Jim worked on his book) said that the overt results reflected what he perceived.

Doesn't help much with explaining the mechanism for the effects, but I guess its a datum that ties in with the other thread and with Rick's multi-level interpretation of how configuration changes intensity perception.

Martin

[rsmarken]

[From Rick Marken (2007.09.25.1200)]

Martin Taylor (2007.09.25.14.14) --

> Rick Marken (2007.09.25.0915)

>In my model of perception, the effect of context is included in
>perceptions at a higher level; perceptions created by perceptual
>functions that take the outputs of lower level perceptual functions
>as inputs.

I've quoted this extensively, because I think it's a very interesting
total revision of the "standard" hierarchy.

Not at all; same old hierarchy.

In the standard
hierarchy, a perception at one level is of a qualitatively different
kind than a perception at another level. An intensity is an
intensity, and a configuration is a configuration.

Yep, that's the way mine works.

You can't (in the
normally understood version of HPCT) parse an intensity out of a
configuration -- or else I've been misinterpreting HPCT for many
years.

I don't think one is parsing an intensity out of a configuration when
they judge a components of a configuration; if they are judging the
line as part of a configuration then I think they are judging the line
as a configuration perception.

You are allowing for a novel possibility -- that two well separated
levels can create perceptual fucntions that are qualitatively the
same.

No. I think of the intensity perception of the line, s, as Psi1 = k
log s and the configuration perception of s as Psi2 = Psi1/m +Psi1 or
something like that.

PS: I see Bill endorses your proposed revision of HPCT. That's good!

Because it's not a revision.

Best

Rick

···

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

[Martin_Taylor2]

[Martin Taylor 2007.09.25.15.18]

[From Rick Marken (2007.09.25.1200)]

Martin Taylor (2007.09.25.14.14) --

> Rick Marken (2007.09.25.0915)

>In my model of perception, the effect of context is included in
>perceptions at a higher level; perceptions created by perceptual
>functions that take the outputs of lower level perceptual functions

> >as inputs.

You can't (in the
normally understood version of HPCT) parse an intensity out of a
configuration -- or else I've been misinterpreting HPCT for many
years.

I don't think one is parsing an intensity out of a configuration when
they judge a components of a configuration; if they are judging the
line as part of a configuration then I think they are judging the line
as a configuration perception.

I'm afraid I don't understand this within the conventional HPCT hierarchic arrangement. Are you saying that the single value of the perceptual signal in a configuration control unit IS an intensity perception? It sure sounds like that.

You are allowing for a novel possibility -- that two well separated
levels can create perceptual fucntions that are qualitatively the
same.

No. I think of the intensity perception of the line, s, as Psi1 = k
log s and the configuration perception of s as Psi2 = Psi1/m +Psi1 or
something like that.

Just what IS "the configuration perception of s"?

As I understand the "same old hierarchy", s is a physical value that is transformed into ps1 by the perceptual input function at the intensity level. Many other physical stimuli are also transformed into perceptual signal values at the same (intensity) level. We can lump them together as a vector X. X along with ps1 form the input into the the perceptual input function of one control unit at the next level, to form ps2. ps2 has a single value, say 3.2. There are lots of values of s and of the components of X that could lead to the same 3.2 value of ps2. This process of combining many inputs to produce a single value goes on through the levels, if you are using "the same old hierarchy". How do you extract a "judgment" of s out of this single value at ANY level above the intensity level?

I'm really mystified as to how you can, with a straight face (not being able to see your face, I just assume it to be straight), say you are dealing with "the same old hierarchy".

> PS: I see Bill endorses your proposed revision of HPCT. That's good!

Because it's not a revision.

Well, it's certainly a revision to my understanding of the elements and functions in an HPCT hierarchy. I guess I need to go back to PCT 101 and relearn all I thought I knew about HPCT (not PCT, because I think your idea is a very good one in PCT). The first thing I have to unlearn is that a perceptual signal at any level is a scalar variable constructed from a set of source inputs. What's the next?

Martin

[Bill_Powers1]

[To Rick Marken] PS: I see Bill
endorses your proposed revision of HPCT. That’s good!
[From Bill Powerss (2007.09.25.1618 MDT)]

Martin Taylor 2007.09.25.14.1]–

No, I approved of using relative levels instead of the absolute ones I
defined. I think Rick mis-spoke when he used the word
:"intensity."If I were going to try to guess at levels, I would
suppose that a pair of dots might constitute a minimal configuration with
a size attribute, and that in comparing one configuration to another you
would be making a relationship judgement. But the details very much
remain to be worked out.

Since your data extend for 20 minutes, I don’t think it unreasonable to
fit an exponential to that long tail. But the signal is getting pretty
well buried in the noise by the end of the run.

Best.

Bill P.