# Levels of perception (Re: PCT researcher who doesn't talk)

**URL:** <http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362>\
**Category:** CSG2009\
**Created:** [February 22, 2009, 10:01pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362 "2009-02-22T22:01:43Z")\
**Posts on this page:** 20\
**Page:** 2

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [February 28, 2009, 6:09pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/21 "2009-02-28T18:09:57Z")

</div>

[From Bill Powers (2009.02.28.0943 MST)]

Martin Taylor 2009.02.28.10.46 --

> [to Rick Marken] You question two of these control systems because they are "open". In past discussions, such systems have been called "fire and forget". There's nothing a gunner can do to make a shell more or less likely to hit its target after it has been launched. But the gunner can observe the fall of shot and correct the aim for the next shot. You could call this a kind of "learning".

You could also call it a control loop that uses discrete sampled variables rather than continuous ones. A slowing factor is needed for stability, which is why the aiming point is changed only in small increments on each trial. The size of the increments has to be such that the absolute error is not greater on each successive trial. Ideally it should be just large enough to correct the error, but normal variations and disturbances make it necessary to use smaller steps than the maximum ones possible for stable operation.

> A different control loop that controls the perception of fall of shot affects the parameters of the "shooting" control loop, not the signal values during the execution of a single shot.

You're just describing different levels of control.

At the higher level, perceptual signals do not represent the signal values during execution of a single shot. They represent some sort of running average of the perceived fall of the shot. The gunner's mate says "We're getting closer," showing that even though the last splash has disappeared, he's still perceiving the distance to the target, in fact a series of distances ("getting closer").

I think you're overlooking a simple analog solution to this control problem. Let the perception of the fall of the shot be the running average of, say, the last three shots, computed once per shot. At the same time this average is taken, the position of the target is also perceived, and the perception represents the average distance between the average splash and the target. The error signal or (possibly two error signals, azimuth and range) causes the next aiming point to shift to reduce the distance to the target, and the next shell is fired. A simple fixed algorithm will thus gradually reduce the average distance of the splash from the target until the pattern of splashes is centered on the target or a hit is registered. This is a control system, not an open-loop system. I think this kind of control system works at the logic level -- it's a program as I've described it.

Best,

Bill P.

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**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [February 28, 2009, 7:14pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/22 "2009-02-28T19:14:44Z")

</div>

[Martin Taylor 2009.02.28.14.08]

> [From Bill Powers (2009.02.28.0943 MST)]
> 
> Martin Taylor 2009.02.28.10.46 --
> 
> > [to Rick Marken] You question two of these control systems because they are "open". In past discussions, such systems have been called "fire and forget". There's nothing a gunner can do to make a shell more or less likely to hit its target after it has been launched. But the gunner can observe the fall of shot and correct the aim for the next shot. You could call this a kind of "learning".
> 
> You could also call it a control loop that uses discrete sampled variables rather than continuous ones. A slowing factor is needed for stability, which is why the aiming point is changed only in small increments on each trial. The size of the increments has to be such that the absolute error is not greater on each successive trial. Ideally it should be just large enough to correct the error, but normal variations and disturbances make it necessary to use smaller steps than the maximum ones possible for stable operation.
> 
> > A different control loop that controls the perception of fall of shot affects the parameters of the "shooting" control loop, not the signal values during the execution of a single shot.
> 
> You're just describing different levels of control.
> 
> At the higher level, perceptual signals do not represent the signal values during execution of a single shot. They represent some sort of running average of the perceived fall of the shot. The gunner's mate says "We're getting closer," showing that even though the last splash has disappeared, he's still perceiving the distance to the target, in fact a series of distances ("getting closer").
> 
> I think you're overlooking a simple analog solution to this control problem. Let the perception of the fall of the shot be the running average of, say, the last three shots, computed once per shot. At the same time this average is taken, the position of the target is also perceived, and the perception represents the average distance between the average splash and the target. The error signal or (possibly two error signals, azimuth and range) causes the next aiming point to shift to reduce the distance to the target, and the next shell is fired. A simple fixed algorithm will thus gradually reduce the average distance of the splash from the target until the pattern of splashes is centered on the target or a hit is registered. This is a control system, not an open-loop system. I think this kind of control system works at the logic level -- it's a program as I've described it.

I have no real comment on this, other than to say that I think you offer possible explicit mechanisms to do what I said must be done in a higher-level control system whose output changes the parameters of the "shooting" system, as opposed to being done within the "fire and forget" shooting control loop itself. I don't think I overlooked either an analogue or a program-level mechanism. I ignored mechanism entirely, just noting that changing the gunner's aiming point is done by a control system other than the one that releases the shot.

Martin

---

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**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 1, 2009, 6:22pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/23 "2009-03-01T18:22:42Z")

</div>

[From Rick Marken (2009.03.01.1020)]

Sorry, had to take time off to celebrate the birthdays of two  
remarkable economists who were, coincidentally, born on the same day,  
February 28: Paul Krugman and myself.

> Martin Taylor (2009.02.28.10.46) --

> I should have said "a  
> single scalar variable for which the control has some influence on the  
> probability that the subject's button push corresponds to the light that  
> turns on."

Before we go on I wonder if you could clarify, again, what the data in  
the Schouten study show. I am under the (perhaps incorrect) impression  
that the graph you posted shows a measure of response accuracy (d') as  
a function of the delay between the onset of a light and the third of  
a sequence of beeps with which subjects are supposed to synchronize  
their responses. Most importantly , I am under the impression that the  
measure of response accuracy (d') measures accuracy only in terms of  
how often the subject presses the right (and wrong) lighted button.

The d' measure with which I am familiar is a function of the  
proportion of hits and false alarms in the experiment. In the Schouten  
experiment I would imagine that a hit occurs when pressing the right  
button (Pr) occurs after the right button is illuminated (Lr) or when  
when pressing the left button (Pl) occurs after left button is  
illuminated (Ll). So the proportion of hits, p(H), is  
p(Pr|Lr)+p(Pl|Ll). False alarms occur when the opposite button to the  
one illuminated is pressed. So p(FA) = p(Pr|Ll)+p(Pl|Lr). d' = f(p(H),  
p(FA)), the function, as I recall, being the difference standard  
normal deviates corresponding to p(H) and p(FA).

So I understand the graph of the Schouten data to show nothing about  
the relative timing of the third beep and the press, unless the d'  
measure is somehow scaled in terms of that relative timing. If it is,  
please explain how. Otherwise, I am assuming that the only trials  
included in the d' measure shown in your graph are those on which the  
subject's button presses were synchronous with the third beep, at  
least to the experimenter's satisfaction.

Is this right?

Best

Rick

> **···**
>
> --  
> Richard S. Marken PhD  
> rsmarken@gmail.com

---

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**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [March 2, 2009, 4:34am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/24 "2009-03-02T04:34:33Z")

</div>

[Martin Taylor 2009.03.01.22.59]

> ```auto
> 
> [From Rick Marken (2009.03.01.1020)]
> Sorry, had to take time off to celebrate the birthdays of two
> remarkable economists who were, coincidentally, born on the same day,
> February 28: Paul Krugman and myself.
> 
> ```

Well, belated happy birthday, and may your joint endeavours speed the  
economic recovery 🙂

> ```auto
> 
> ```
> 
> > ```auto
> > Martin Taylor (2009.02.28.10.46) --
> > 
> > ```
> 
> ```auto
> 
> ```
> 
> > ```auto
> > I should have said "a
> > single scalar variable for which the control has some influence on the
> > probability that the subject's button push corresponds to the light that
> > turns on."
> > 
> > ```
> 
> ```auto
> Before we go on I wonder if you could clarify, again, what the data in
> the Schouten study show. I am under the (perhaps incorrect) impression
> that the graph you posted shows a measure of response accuracy (d') as
> a function of the delay between the onset of a light and the third of
> a sequence of beeps with which subjects are supposed to synchronize
> their responses.
> 
> ```

Yes, but I don’t usually think of d’ as a measure of response accuracy,  
since response accuracy is the raw data and d’ the derived measure.

> ```auto
> Most importantly , I am under the impression that the
> measure of response accuracy (d') measures accuracy only in terms of
> how often the subject presses the right (and wrong) lighted button.
> 
> ```

What is the thought behind that word “only”? The choice of button press  
is indeed the only output the subject makes that is related to which  
light the subject perceives to have been lit, but your use of “only”  
suggests that you think the d’ measure should include some other data,  
and I can’t guess where that other data might come from.

> ```auto
> The d' measure with which I am familiar is a function of the
> proportion of hits and false alarms in the experiment.
> 
> ```

That’s an inferior type of experiment, and not the kind of experiment  
Schouten did. It’s inferior because the calculation of d’ depends quite  
nastily on the prior knowledge the subject has on exactly what form the  
signal will have if it is present, and on the subject’s criterion for  
saying “yes I saw it”. It’s only in the case of what Tanner and  
Birdsall called SKE (Signal Known Exactly) that the assumptions of  
equal variance for noise alone (N) and signal plus noise (SN) apply,  
and when they don’t apply, the ROC curve changes shape. It becomes  
asymmetric and approaches a threshold-like form. This isn’t just a  
theoretical problem, but a real-life one, as we demonstrated in a  
series of auditory detection studies (we provided waveform shape  
information in the ear opposite to the one that might contain the  
signal to create the SKE situation; by doing that, the SKE case could  
give detection levels as much as 10-15db better than the normal “did  
you hear it” situation).

This kind of problem is largely avoided in the two alternative forced  
choice (2AFC) experiment, because the asymmetries in the two  
alternatives balance one another. It is all discussed in the second of  
the two handwritten Bayesian seminar papers I put on my web site a few  
weeks ago (linked from ).  
Schouten’s experiment is 2AFC, so the d’ values are more likely to be  
reliable than they would be for a hit-and-false-alarm kind of  
experiment.  
I assume that Schouten did one of three things: (1) binned the results  
according to when the button was actually pressed, or (2) trained the  
subjects so that they were pretty accurate with their synchrony to the  
third button, or (3) recorded the results according to when the third  
bip actually happened, and assumed the subjects were accurate enough  
for his purposes. The time markers are separated by only about 20 msec,  
so I don’t know which of these was the case. It probably says in  
Schouten’s paper in “Attention and Perfoemance 1”, which I have  
somewhere – probably in one of about 20 cardboard boxes into which my  
stuff was packed in a series of office downsizings over the last  
decade. So the graph does show the relative timing of the third beep  
and the press in one way or another, but I don’t know precisely in  
which of the possible ways.  
I very much doubt that Schouten would have dropped any data, which is  
the implication I get from your “the only trials”. But I don’t know at  
first hand.  
For the purposes of continuing to correct our misunderstandings about  
control systems and the analysis of component pathways, the important  
thing is still that the button presses are assumed to result from the  
subject’s best effort to control the match between the light perceived  
and the answer that the experimenter has told the subject is  
appropriate for each light. The timing results really have no bearing  
on that aspect. Where the timing results matter is that they provide a  
measure of the channel capacity of the pathway marked in red on most of  
my diagrams – from sensing the light to the output of the perceptual  
function that creates the interpreted category for the location  
perception.  
Martin

> **···**
>
> [http://www.mmtaylor.net/Academic.html](http://www.mmtaylor.net/Academic.html)
> 
> > ```auto
> > So I understand the graph of the Schouten data to show nothing about
> > the relative timing of the third beep and the press,
> > 
> > ```
> 
> > ```auto
> > 
> > I am assuming that the only trials
> > included in the d' measure shown in your graph are those on which the
> > subject's button presses were synchronous with the third beep, at
> > least to the experimenter's satisfaction.
> > Is this right?
> > 
> > ```

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [March 2, 2009, 9:35am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/25 "2009-03-02T09:35:14Z")

</div>

Hi, Denny --

I'm trying these two papers out on you first. One is about economics,  
the other is about astronomy. The one on astronomy grabs me -- I  
think it could be done using my little star-tracking mount and a  
computer-controllable camera with a fast telephoto lens. Got a  
dark-sky location somewhere nearby?

Love,

Dad

[StarPhotometry.doc](http://discourse.iapct.org/uploads/short-url/qoPHVbLWnFBVQtH9VKgaUAGtFRk.doc) (15 KB)

[Adversarial.doc](http://discourse.iapct.org/uploads/short-url/flbojTivQizX1nonWyiPKVWqaEv.doc) (30.5 KB)

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [March 2, 2009, 9:38am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/26 "2009-03-02T09:38:29Z")

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[From Bill Powers (2009.03.02.0237 MST)]

Sorry about that last post with the two attachments. I don't know how  
I managed to send it to CSGnet. Of course any comments are welcome.

Bill P.

[StarPhotometry.doc](http://discourse.iapct.org/uploads/short-url/qoPHVbLWnFBVQtH9VKgaUAGtFRk.doc) (15 KB)

[Adversarial.doc](http://discourse.iapct.org/uploads/short-url/flbojTivQizX1nonWyiPKVWqaEv.doc) (30.5 KB)

---

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**Author:** ![Dick\_Robertson](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/d/2acd7d/32.png) [@Dick\_Robertson](http://discourse.iapct.org/u/Dick_Robertson)\
**Post date:** [March 3, 2009, 1:48am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/27 "2009-03-03T01:48:56Z")

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[From Dick Robertson, 2009.03.02.1950CDT]

Happy belated birthday Rick

Best,

Dick R

---

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**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 3, 2009, 6:29am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/28 "2009-03-03T06:29:43Z")

</div>

[From Rick Marken (2009.03.02.2230)]

> Martin Taylor (2009.03.01.22.59)--
> 
> > Rick Marken (2009.03.01.1020)--

> > Before we go on I wonder if you could clarify, again, what the data in  
> > the Schouten study show. I am under the (perhaps incorrect) impression  
> > that the graph you posted shows a measure of response accuracy (d') as  
> > a function of the delay between the onset of a light and the third of  
> > a sequence of beeps with which subjects are supposed to synchronize  
> > their responses.
> 
> Yes

Good, that's what I thought.

> > Most importantly , I am under the impression that the  
> > measure of response accuracy (d') measures accuracy only in terms of  
> > how often the subject presses the right (and wrong) lighted button.
> 
> What is the thought behind that word "only"?

I realized that there were two variables that the subject was asked to  
control in this experiment: 1) synchrony of a button press with the  
3rd bip and 2) match of button press to button light. And then I also  
realized that only the ability to control variable 2, the match, is  
measured by d'. Assuming that Schouten would only include trials in  
the d' measure when the press was synchronous with the 3rd bip, then  
at all delays between light and 3rd bip for which d' was measured, the  
subject was pressing the button (right or wrong) in synchrony with the  
light. This suggests to me that the difference in ability to control  
variable 2 (as measured by d') as a function of light/3rd bip delay is  
a result of perceptual processing rather than comparison or response  
production time, just as in my perceptual hierarchy demo. So the fact  
that a delay of about 350 msec is needed for nearly perfect control of  
variable 2 (the light/press match) suggests that the variable  
controlled in this experiment is, indeed, at an intermediate level  
between transition (which in my study tool a frame rate of 250  
msec/frame) and sequence (which in my demo takes about 500 msec/frame.

> For the purposes of continuing to correct our misunderstandings about  
> control systems and the analysis of component pathways, the important thing  
> is still that the button presses are assumed to result from the subject's  
> best effort to control the match between the light perceived and the answer  
> that the experimenter has told the subject is appropriate for each light.

Yes, I agree. And control of this variable is nearly perfect (for most  
subjects) when the delay between the elements of this perception  
(light and press) is about 350msec, just as control of a transition  
(apparent movement clockwise or counterclockwise) is nearly perfect  
when the delay between the appearance of one element of movement and  
another is 250 msec or just as control of a sequence is nearly  
perfect when the delay between the appearance of each element of the  
sequence is 500 msec

> The timing results really have no bearing on that aspect.

But in the graph you presented the timing results do seem to have a  
lot to do with how well the subject controls the match between light  
and press. At a small delay between light and 3rd bip (which coincides  
with the press) there is almost no control; d' is nearly 0. At a delay  
of 350 msec between light and press (3rd bip) control is nearly  
perfect; the subject is always pressing only the button that was lit.

> Where the timing  
> results matter is that they provide a measure of the channel capacity of the  
> pathway marked in red on most of my diagrams -- from sensing the light to  
> the output of the perceptual function that creates the interpreted category  
> for the location perception.

What you call "channel capacity" is what I would call "time required  
to compute a perception of that type" (whatever the type is). So,  
again, I think we are in complete agreement, we're just using  
different words.

Best

Rick

> **···**
>
> --  
> Richard S. Marken PhD  
> rsmarken@gmail.com

---

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**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 3, 2009, 6:31am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/29 "2009-03-03T06:31:03Z")

</div>

[From Rick Marken (2009.03.02.2232)]

> Dick Robertson, 2009.03.02.1950CDT]
> 
> Happy belated birthday Rick

Thanks, Dick!

Best

Rick

> **···**
>
> –  
> Richard S. Marken PhD  
> [rsmarken@gmail.com](mailto:rsmarken@gmail.com)

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [March 4, 2009, 10:17am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/30 "2009-03-04T10:17:09Z")

</div>

[From Bill Powers (2009.03.04.0237 MST)]

Rick Marken (2009.03.02.2230) –

> So the fact
> 
> that a delay of about 350 msec is needed for nearly perfect control  
> of
> 
> variable 2 (the light/press match) suggests that the variable
> 
> controlled in this experiment is, indeed, at an intermediate level
> 
> between transition (which in my study tool a frame rate of 250
> 
> msec/frame) and sequence (which in my demo takes about 500  
> msec/frame.

I see your reasoning. This suggests that relationships are the main level  
involved in the timing, which makes sense. Other levels, however, are  
also involved because of having to recognize the presentation, and there  
is uncertainty in how long it takes for the output to be generated and to  
bring the force on the button to the level needed to close the  
contact.

> The timing results really have no bearing on that aspect.

> But in the graph you presented  
> the timing results do seem to have a
> 
> lot to do with how well the subject controls the match between light
> 
> and press. At a small delay between light and 3rd bip (which  
> coincides
> 
> with the press) there is almost no control; d’ is nearly 0. At a  
> delay
> 
> of 350 msec between light and press (3rd bip) control is nearly
> 
> perfect; the subject is always pressing only the button that was  
> lit.

> > Where the timing
> 
> > results matter is that they provide a measure of the channel  
> > capacity of
> 
> > the pathway marked in red on most of my diagrams – from sensing the  
> > light \> to the output of the perceptual function that creates the  
> > interpreted
> 
> > category for the location perception.
> 
> What you call “channel capacity” is what I would call  
> "time required
> 
> to compute a perception of that type" (whatever the type is).  
> So,
> 
> again, I think we are in complete agreement, we’re just using
> 
> different words.

I agree. Channel capacity is a theoretical concept somewhat removed from  
the actual situation (the channel capacity is being measured only in  
short bursts of information so there is no way to know what the  
steady-state capacity would be). And the forced-choice format is somewhat  
artificial, too: I would probably be a bad subject who resists making a  
choice when I am too uncertain to believe I know which light went on. My  
effective channel capacity, in normal circumstances, would be  
considerably lower than what this experiment would suggest.  
Of course that might be of interest to a geriatric psychologist, and I  
leave the ambiguity of that one unresolved.  
As a circuit-oriented theoretician I view this experiment as a clever way  
of estimating the rise-time of a perceptual signal. The 1/e time would  
seem to be about 50 milliseconds.  
One point: in judging level in the hierarchy on the basis of reaction  
times, it’s essential to look only for the _shortest_ reaction  
times. A task at any level can involve longer reaction times depending on  
the complexity of the task and the properties of the comparator, output  
function, and environmental feedback function: just suppose that the  
button is on a lever with a damper connected to it (like a screen door  
closer). Any level from transitions upward can involve very long times,  
like the length of the event called Beethoven’s 5th Symphony, or getting  
a college degree. Only the simplest tasks can reveal the actual minimum  
reaction time. The Schouten experiment is not the simplest possible  
task.  
When I measured reaction times as the delay between a mechanical  
disturbance and the first appearance of electromygraph responses in  
_pronator teres,_ I came up with about 50 milliseconds (back in the  
1950s). Of course that was much shorter than what would be measured by  
looking for movement of the hand or a contact closure of a switch. It  
showed that some rather large portion of reported reaction times was  
determined mainly by Newton’s laws of motion rather than delays in the  
nervous system.

On that basis, I would measure the first reaction time in the Schouten  
experiment at about 210 milliseconds, the intercept of the one-subject  
plot with the time axis. That is when the perceptual input function  
begins to respond to inputs from below, which implies that this is how  
long it takes for the lower levels to start providing those inputs after  
the light goes on.

Then there is another reaction time, less well-defined, which involves  
the rise time of the higher perceptual signal measured in the Schouten  
experiment. At what time should we say that the perceptual signal exists?  
When half the responses are correct? 95% of them (2-sigma)? The latter  
would occur 50 milliseconds after the shortest reaction time deduced from  
the data. But that is smaller than our uncertainty about how long it  
takes after getting a correct identification for the contact under the  
button to be closed. I think we’re exceeding the discriminative power of  
this experiment (and also of the concept of reaction time).

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [March 4, 2009, 10:42pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/31 "2009-03-04T22:42:04Z")

</div>

[Martin Taylor 2009.03.04.16.05]

> ```auto
> [From Rick Marken (2009.03.02.2230)]
> 
> ```
> 
> > ```auto
> > Martin Taylor (2009.03.01.22.59)--
> > 
> > ```
> > 
> > > ```auto
> > > Rick Marken (2009.03.01.1020)--
> > > 
> > > ```
> > > 
> > > ```auto
> > > Most importantly , I am under the impression that the
> > > measure of response accuracy (d') measures accuracy only in terms of
> > > how often the subject presses the right (and wrong) lighted button.
> > > 
> > > ```
> > 
> > ```auto
> > What is the thought behind that word "only"?
> > 
> > ```
> 
> ```auto
> I realized that there were two variables that the subject was asked to
> control in this experiment: 1) synchrony of a button press with the
> 3rd bip and 2) match of button press to button light. And then I also
> realized that only the ability to control variable 2, the match, is
> measured by d'. Assuming that Schouten would only include trials in
> the d' measure when the press was synchronous with the 3rd bip, then
> at all delays between light and 3rd bip for which d' was measured, the
> subject was pressing the button (right or wrong) in synchrony with the
> light. This suggests to me that the difference in ability to control
> variable 2 (as measured by d') as a function of light/3rd bip delay is
> a result of perceptual processing rather than comparison or response
> production time, just as in my perceptual hierarchy demo.
> 
> ```

I agree. At delays for which the straight line increase of d’^2 is  
valid, the differences in d’^2 are a result of perceptual processing.  
Delays less than about 230 msec (for Subject B – it’s different for  
others, according to the graph) can be thought of as transport lag,  
which could include several different things: the “button-press”  
control system processing, physical dynamics of finger motion, neural  
signal time … and not least, possibly a fixed lag in addition to the  
differential processing in the “red” path from lights to the  
match-control loop input.

> ```auto
> So the fact
> that a delay of about 350 msec is needed for nearly perfect control of
> variable 2 (the light/press match) suggests that the variable
> controlled in this experiment is, indeed, at an intermediate level
> between transition (which in my study tool a frame rate of 250
> msec/frame) and sequence (which in my demo takes about 500 msec/frame.
> 
> ```

You may well be right, but I think I need a more detailed analysis of  
the control systems and pathways that model your data before I accept  
that you must be. To me, this equivalence is suggestive, no more. One  
issue is that Schouten’s experiment was done only with one brightness  
level of the lights. I’d be willing to bet that if the experiment were  
redone with lights brighter or dimmer than used by Schouten, or with  
patches that had a clear demarcation or no demarcation, or with a  
single patch that lit with different colours, one would still get  
straight lines, but with quite varying slopes for the different  
conditions. The level of the perception would be the same in a diagram  
(possibly not for the colours), but the time to a sufficiently high  
value of d’ (say 2.5) would be very different.

> > ```auto
> > Where the timing
> > results matter is that they provide a measure of the channel capacity of the
> > pathway marked in red on most of my diagrams -- from sensing the light to
> > the output of the perceptual function that creates the interpreted category
> > for the location perception.
> > 
> > ```
> 
> ```auto
> What you call "channel capacity" is what I would call "time required
> to compute a perception of that type" (whatever the type is). So,
> again, I think we are in complete agreement, we're just using
> different words.
> 
> ```

Maybe, but I’m not sure yet. “Time required to compute a perception of  
that type” could be translated as “time required to reach d^ = (say)  
2.5”. That is equivalent to “Time required to acquire X bits of  
information about the perception”. If the transport lag did not come  
into it, then dividing X by the time in question (about 330 msec for  
subject B) would indeed be the channel capacity. The channel capacity  
would be X/0.33 or 3_X. But transport lag does come into it, and the  
time that enters the channel capacity calculation has to be measured  
from the start of the rising straight line, or around 230 msec. That  
being the case, the channel capacity would be 10_X. The question is  
“what is X?”

The argument in my “BayesianSeminar\_2” gives d’^2 = 8ln(2) \* U, where U  
is the information that could be carried by this channel regarding the  
differences between the two most discriminable members of an ensemble  
that contained entities all equally discriminable from some signal half  
the size of the entity in question. In this case, the two most  
discriminable members are “left on - right off”, and “left off - right  
on”. For such an ensemble the information about the differences between  
any one ensemble member and the null state is U = d’^2/2ln(2) =  
1.39\*d’^2. For d’ = 2.5, U = 8.8, and the channel capacity would be 88  
bits/second. (In the paper, we said that these same data, using the  
same analysis gave 140 bits/sec. I don’t know where the difference  
comes from; either I must have miscalculated or we miscalculated in  
1967. Perhaps my by-eye reading off the graph is inaccurate).

Does this tell you we are in agreement, or that we are not? I can’t say.

Martin

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 5, 2009, 6:11am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/32 "2009-03-05T06:11:26Z")

</div>

[From Rick Marken (2009.03.04.2210)]

> Bill Powers (2009.03.04.0237 MST)–

> I see your reasoning. This suggests that relationships are the main level  
> involved in the timing, which makes sense. Other levels, however, are  
> also involved

Of course. But the main controlled variable is the light/press relationship because that’s one that was measured.

> I agree. Channel capacity is a theoretical concept somewhat removed from  
> the actual situation

That’s the polite way to put it;-)

> As a circuit-oriented theoretician I view this experiment as a clever way  
> of estimating the rise-time of a perceptual signal. The 1/e time would  
> seem to be about 50 milliseconds.

I’m not sure that I would call it “clever” myself. I think an experiment is clever if the cleverness was intentional. I don’t think Schouten conceived of the experiment as a way of estimating the rise time of a perceptual signal corresponding to the state of the relationship between light and press. The cleverness is in the minds of those who were able to piece through the experiment and figure out that it could be seen that way.

> One point: in judging level in the hierarchy on the basis of reaction  
> times, it’s essential to look only for the _shortest_ reaction  
> times. A task at any level can involve longer reaction times depending on  
> the complexity of the task and the properties of the comparator, output  
> function, and environmental feedback function

Yes, that’s why I use the same output (mouse click) to control the configuration, transition and sequence in my hierarchy demo. But the fact is that reaction time can be taken out of play completely by just measuring the frame rate at which each perception becomes controllable. The demo is currently set up so that the frame rates are above the threshold for perceiving each type of perception. But I would like to re-write the demo so that frame rate can be adjusted until a particular perception can just be controlled at some level.

> just suppose that the  
> button is on a lever with a damper connected to it (like a screen door  
> closer). Any level from transitions upward can involve very long time

Right. That’s why frame rate (the equivalent of the light-press delay in the Schouten study) is a nice way to measure the time constant for different levels of perception; reaction times are not involved. In my demo I shouldn’t have even measured reaction times; it’s the frame rate that gives the best measure of the time constant for a pereptual type, I think.

Best

Rick

> **···**
>
> –  
> Richard S. Marken PhD  
> [rsmarken@gmail.com](mailto:rsmarken@gmail.com)

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 5, 2009, 6:28am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/33 "2009-03-05T06:28:58Z")

</div>

[From Rick Marken (2009.03.04.2230)]

> Martin Taylor (2009.03.04.16.05) –

> I agree.

Great.

> > ```auto
> > So the fact
> > that a delay of about 350 msec is needed for nearly perfect control of
> > variable 2 (the light/press match) suggests that the variable
> > controlled in this experiment is, indeed, at an intermediate level
> > between transition (which in my study tool a frame rate of 250
> > msec/frame) and sequence (which in my demo takes about 500 msec/frame.
> > 
> > ```

> You may well be right, but I think I need a more detailed analysis of  
> the control systems and pathways that model your data before I accept  
> that you must be.

Me too.

> One  
> issue is that Schouten’s experiment was done only with one brightness  
> level of the lights. I’d be willing to bet that if the experiment were  
> redone with lights brighter or dimmer than used by Schouten, or with  
> patches that had a clear demarcation or no demarcation, or with a  
> single patch that lit with different colours, one would still get  
> straight lines, but with quite varying slopes for the different  
> conditions.

I don’t think the slopes are what matters; it’s the delay (frame rate) where control becomes possible – ~350 msec in this case – that’s important (to me, anyway). And if the variable controlled is the light-press relationship then I think neither light intensity (as long as the light were visible), nor hue nor patchiness will affect the frame rate necessary for control of the relationship. But that’s just a prediction.

> > ```auto
> > What you call "channel capacity" is what I would call "time required
> > to compute a perception of that type" (whatever the type is). So,
> > again, I think we are in complete agreement, we're just using
> > different words.
> > 
> > ```

> Maybe, but I’m not sure yet.

I’m not sure either; I was just trying to be agreeable;-)

> “Time required to compute a perception of  
> that type” could be translated as “time required to reach d^ = (say)  
> 2.5”. That is equivalent to “Time required to acquire X bits of  
> information about the perception”…
> 
> Does this tell you we are in agreement, or that we are not? I can’t say.

Well, then, I’m going to have to guess that we’re not in agreement about channel capacity because, if channel capacity has something to do with acquiring bits of information about a perception, then it doesn’t exist in my PCT view of things.

Best

Rick

> **···**
>
> –  
> Richard S. Marken PhD  
> [rsmarken@gmail.com](mailto:rsmarken@gmail.com)

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [March 5, 2009, 7:51pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/34 "2009-03-05T19:51:57Z")

</div>

[From Bill Powers (2009.03.05.1005 MST)]

Martin Taylor 09.03.0.4.17.42 –

> Your effective channel capacity  
> would not be affected by your reluctance to answer until you acquired  
> sufficient data. What would be affected would be the apparent transport  
> lag, or the d’^2 you require before making a free-timed decision (the  
> usual form of a reaction time experiment).

But there would still be a rising d^2 after the minimum time lag, in a  
forced-choice experiment. It might have a steeper slope, but there would  
still be a range from “just barely willing to make a choice” to  
“no problem, absolutely sure.” Well, maybe. Of course the  
choices, when made, would give d’^2 some distance above the origin of the  
Schouten data, so you’re probably right.

> As for the forced-choice with  
> deadline being an artificial situation, I just ask whether you have never  
> found yourself having to choose between two alternative courses of action  
> when you would prefer to wait to get more information about the  
> situation. If you have never had to make a choice before getting all the  
> information you might have wanted, you haven’t lived!

I usually wait until I’m pretty sure, and devote my efforts before then  
to making the decision unneccessary just yet. The main thing is that I  
know what the outcome is quite likely to be if I decide prematurely:  
wrong. If you have only a 60% chance of choosing right, you might as well  
not choose, because your estimate of the chances is probably off by a  
large amount, too. Of course if I get to make the same choice over and  
over, the picture would be different, more like the Schouten data, I  
imagine. Knowing I had a lot of chances would definitely change my  
tolerance for being wrong. I’m not a gambler; knowing that the dice have  
been weighted a little in my favor does not tempt me to bet my bankroll  
on a few throws. Twenty-five cents, maybe.

> > As a circuit-oriented  
> > theoretician I view this experiment as a clever way of estimating the  
> > rise-time of a perceptual signal. The 1/e time would seem to be about 50  
> > milliseconds.
> 
> I have seen no evidence of an exponential curve in the data presented, so  
> I would certainly not try to venture a guess such as  
> that.

You’re right, and I didn’t state the case correctly. What I should have  
said was that the signal rises fast enough to be clear of the noise by 2  
or 3 standard devations in about 50 milliseconds. We don’t know how large  
the signal would eventually get or what its 1/e rise time would be,  
because (a) that depends on the light intensity, and (b) the measurements  
plotted extend only to about 2.2 standard deviations (square root of 5),  
and anyway the probability of a correct guess is so close to 1 by then  
that it can’t really be measured in any reasonable number of trials.

Use Courier (monospaced) font for this plot:

> **···**
>
> - 
> 
> - 
> 
> ```
> SIGNAL     
> 
> ```
> 
> - 
> 
> - \< ----- approx 1/e rise time at this signal  
> magnitude
> 
> –\*------------------1 SD noise------------------------------
> 
> \*------------------------------------------------------------
> 
> ^  
> ^  
> TIME AXIS -------\>
> 
> > >
> 
> > 50 msec, 95% probability correct
> 
> > 
> 
> ------- Threshold time of perceptual signal rise
> 
> > I might, however, guess  
> > that by 50 msec the subject had acquired half the information needed in  
> > an ordinary “as soon as possible” reaction time experiment. In  
> > our other experiments (about which I include a quote below), it seemed  
> > that the rise of d’^2 fits two straight lines better than an  
> > exponential.
> 
> Whatever the case, you can see that my hypothesis might give a different  
> answer for the channel capacity. If the magnitude of the perceptual  
> signal is as shown in the above diagram, the 1/e rise time, which is  
> related to bandwidth, can be much longer than the time it takes to arrive  
> at 95% correct choices. Bandwidth is usually stated as 0.35/T where T is  
> the rise-time (10% to 90%).
> 
> From a Wiki page we have this, for C = channel capacity in bits/sec, B =  
> single-pole bandwidth in Hertz, S/N = signal to (Gaussian) noise ratio  
> (in standard deviations?):  
> ![C = B \log \left( 1+\frac{S}{N} \right)\](http://discourse.iapct.org/uploads/default/original/2X/9/99d012520cfea39ed97b5b908f7e17c419840bf6.png)Anyhow, it’s clear that the linear rise seen in the Schouten data  
> could represent just a small part of a 1 - e^-n rise in perceptual signal  
> after the initial detection of a light, with the actual bandwidth of the  
> perceptual signal being unknown. The same data would be observed for all  
> combinations of rise time and asymptotic magnitude of the perceptual  
> signal that give the same slope of the data near the origin relative to  
> the noise level. This means that you can’t calculate the channel capacity  
> of the perceptual input function, if my model is correct, without knowing  
> the magnitude of the perceptual signal at asymptote and its 1/e rise  
> time.
> 
> > As a circuit-oriented  
> > theoretician, you are probably interested in the bandwidths of different  
> > connections in the control loop, because they affect the stability of  
> > feedback circuits. “Channel Capacity” is a generalization of  
> > the linear concept “Bandwidth”, applicable in linear and  
> > non-linear situations.
> 
> > > Then there is another reaction  
> > > time, less well-defined, which involves the rise time of the higher  
> > > perceptual signal measured in the Schouten experiment. At what time  
> > > should we say that the perceptual signal exists?
> > 
> > I thought perceptual signals always existed, but just had different  
> > magnitudes at different times.
> 
> I meant, at what time would the observer start to react as if it exists?  
> I would not say it exists until it reached somewhere between the 1- and  
> 2-sigma level, though of course an oscilloscope connected in the right  
> place would show a signal before then.
> 
> > Above, you talk about  
> > “the rise time of a perceptual signal” as though you subscribe  
> > to this view. Here, you seem to deny it.
> 
> Just more verbal miscommunication.
> 
> > I take it that you are  
> > expressing an opinion based on faith, in opposition to the precise  
> > straight-line data that Schouten obtained, but that you seem to be saying  
> > is impossible?
> 
> Well, thanks. I hope you can see now what I was talking about.
> 
> > Back to channel capacity. Here’s  
> > a quote from a different section of the same paper from which I took the  
> > Schouten diagram, about my own experiments (“Quantification of  
> > Shared Capacity Processing”. Taylor, Lindsay and Forbes, Acta  
> > Psychologica 27, (1967) 223-229). The data were reported elsewhere. If  
> > it’s of interest I might be able to find the paper with the  
> > data:  
> > _"Among our experiments on audio-visual capacity sharing have been  
> > some in which presentation time was an experimental variable. … For the  
> > immediate purposes it suffices to remark that the subjects had to make  
> > one or more of four discriminations: left-right discrimination of a dot  
> > on a TV screen, up-down position of the same dot, pitch of a tone burst  
> > presented simultaneously with the dot, and intensity of the same tone  
> > burst. The stimulus duration in various experiments has been varied from  
> > as low as 33 msec to as high as 4 sec. For all four aspects of the  
> > stimulus (we consider the dot and the tone to constitute a single  
> > stimulus) we have consistently found that d’^2 rises linearly with  
> > presentation time up to 130 msec or so, and that for longer intervals the  
> > rise, while possibly linear, is very much slower. These results are  
> > consistent with the proposition that d’^2 is an additive measure of  
> > discrimination performance, while suggesting that the processor can work  
> > effectively on only the first 130 msec of the  
> > signal._"
> 
> I think that the interpretation you put on this kind of data will depend  
> very critically on the model you’re assuming in the background. To  
> “make a discrimination” suggests some sort of threshold effect,  
> where you get a signal when the input is above the threshold and no  
> signal when it’s not. Just what sort of “processor” were you  
> envisioning? When you say “the subject had acquired half the  
> information needed in an ordinary “as soon as possible”  
> reaction time”, I wonder what sort of process could use half of the  
> information needed and make any sense of it at all: “Four and years  
> our” doesn’t help me at all toward “Four score and seven years  
> ago our forefathers…”
> 
> While the concept of channel capacity is relevant to analog systems as  
> well as digital ones, its meaning is rather different when amplitude  
> measures matter as much as durations and times of occurrance. In the  
> Schouten case above, the amplitude of the perceptual response to the  
> light matters because the part of the curve that is near the noise level  
> does not distinguish between members of a family of curves having the  
> same measured initial slope, and the channel capacity that actually  
> exists can’t be calculated without knowing which member of that family is  
> present. It is certainly not the case that an analogue circuit could  
> “work effectively only on the first 130 milliseconds of the  
> signal”, especially when that part of the signal gives no  
> information about what the signal does after reaching that level. To the  
> contrary, most of what happens depends on the behavior of the signal  
> through its whole course – unless you arrange the task so that there is  
> no measured consequence of the signal after the response has been  
> made.
> 
> Best,
> 
> Bill P.

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [March 6, 2009, 6:01am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/35 "2009-03-06T06:01:24Z")

</div>

[Martin Taylor 2009.03.06.00.04]

> [From Bill Powers (2009.03.05.1005 MST)]
> 
> Martin Taylor 09.03.0.4.17.42 –
> 
> > As for the forced-choice  
> > with  
> > deadline being an artificial situation, I just ask whether you have  
> > never  
> > found yourself having to choose between two alternative courses of  
> > action  
> > when you would prefer to wait to get more information about the  
> > situation. If you have never had to make a choice before getting all  
> > the  
> > information you might have wanted, you haven’t lived!
> 
> I usually wait until I’m pretty sure, and devote my efforts before then  
> to making the decision unneccessary just yet. The main thing is that I  
> know what the outcome is quite likely to be if I decide prematurely:  
> wrong. If you have only a 60% chance of choosing right, you might as  
> well  
> not choose, because your estimate of the chances is probably off by a  
> large amount, too.

That’s your privilege, of course, but if it happened to be a tiger  
rather than your friend who made that leaf rustle, you’d be dead by  
then. Think about your everyday life. Do you never have to make choices  
by deadlines, whether you have got enough data to be quite sure of the  
best choice? Do you never vote (I assume you never have much really  
solid information about most of the candidates for office). One of the  
few things I remember from my short days as a student of Industrial  
Engineering was the professor pointing out that “Inaction can be  
extreme action”.

> > > As a circuit-oriented  
> > > theoretician I view this experiment as a clever way of estimating the  
> > > rise-time of a perceptual signal. The 1/e time would seem to be about  
> > > 50  
> > > milliseconds.
> > 
> > I have seen no evidence of an exponential curve in the data presented,  
> > so  
> > I would certainly not try to venture a guess such as  
> > that.
> 
> You’re right, and I didn’t state the case correctly. What I should have  
> said was that the signal rises fast enough to be clear of the noise by  
> 2  
> or 3 standard devations in about 50 milliseconds. We don’t know how  
> large  
> the signal would eventually get or what its 1/e rise time would be,  
> because (a) that depends on the light intensity, and (b) the  
> measurements  
> plotted extend only to about 2.2 standard deviations (square root of  
> 5),  
> and anyway the probability of a correct guess is so close to 1 by then  
> that it can’t really be measured in any reasonable number of trials.

That was precisely what made me interested in the Schouten study in the  
first place. It is indeed extremely difficult to determine the  
detectability or discriminability of obvious things like bright lights  
or the locations of well separated things. I saw the Schouten technique  
as a possible way to get at these very detectable or very discriminable  
signals, which orthodox techniques cannot touch for the reason you  
mention.

> > Back to channel  
> > capacity. Here’s  
> > a quote from a different section of the same paper from which I took  
> > the  
> > Schouten diagram, about my own experiments (“Quantification of  
> > Shared Capacity Processing”. Taylor, Lindsay and Forbes, Acta  
> > Psychologica 27, (1967) 223-229). The data were reported elsewhere. If  
> > it’s of interest I might be able to find the paper with the  
> > data:
> > 
> > ```
> > *"Among our experiments on audio-visual capacity sharing have
> > 
> > ```
> > 
> > been  
> > some in which presentation time was an experimental variable. … For  
> > the  
> > immediate purposes it suffices to remark that the subjects had to make  
> > one or more of four discriminations: left-right discrimination of a dot  
> > on a TV screen, up-down position of the same dot, pitch of a tone burst  
> > presented simultaneously with the dot, and intensity of the same tone  
> > burst. The stimulus duration in various experiments has been varied  
> > from  
> > as low as 33 msec to as high as 4 sec. For all four aspects of the  
> > stimulus (we consider the dot and the tone to constitute a single  
> > stimulus) we have consistently found that d’^2 rises linearly with  
> > presentation time up to 130 msec or so, and that for longer intervals  
> > the  
> > rise, while possibly linear, is very much slower. These results are  
> > consistent with the proposition that d’^2 is an additive measure of  
> > discrimination performance, while suggesting that the processor can  
> > work  
> > effectively on only the first 130 msec of the  
> > signal.\*"
> 
> I think that the interpretation you put on this kind of data will  
> depend  
> very critically on the model you’re assuming in the background. To  
> “make a discrimination” suggests some sort of threshold effect,  
> where you get a signal when the input is above the threshold and no  
> signal when it’s not.

Obviously I knew nothing of PCT at the time. Now I would work with the  
same model we have been discussing, with the exception that there would  
be four “match” control loops for the main presentation, and another  
control system (possibly multi-level – I haven’t thought about it) for  
which the output selects which of the four “match” systems is allowed  
to send its output as a reference value to the button-push.

> Just what sort of “processor” were you  
> envisioning? When you say “the subject had acquired half the  
> information needed in an ordinary “as soon as possible”  
> reaction time”, I wonder what sort of process could use half of the  
> information needed and make any sense of it at all:

Well, you see what such a process can do in the Schouten data, when you  
look at the graph for about 270 msec delay. By that time, the  
"processor’ has half the information it has by 320 msec. It is able to  
get (from memory) about 85% correct button presses.

More generally, now knowing something of PCT, I would equate  
“processor” with the complex of control loops that interact to enable  
the subject to perform in teh experiment as the experimenter asks.

> “Four and years  
> our” doesn’t help me at all toward “Four score and seven years  
> ago our forefathers…”

However, it might help you perceive that neither “To be or not to be”  
nor “We shall fight on the beaches” was the quote from which some words  
had been obscured by noise bursts. Possibly if someone mentioned  
“forefathers”, that might even be enough to cue you into recognizing  
which words you missed. Shannon did determine that the redundancy of  
English is about 50%, meaning that in a long passage with a random 50%  
of the words substituted by gaps or backouts (so you know where they  
were), you will be able to correctly replace most of the missing words.  
But that really has nothing to do with the case at hand, which is the  
rate of gain of information over time. Your example might have been a  
slightly better analogy if you had said “Four score and seven” rather  
than “Four an years our”.

> While the concept of channel capacity is relevant to analog systems as  
> well as digital ones, its meaning is rather different when amplitude  
> measures matter as much as durations and times of occurrance. In the  
> Schouten case above, the amplitude of the perceptual response to the  
> light matters because the part of the curve that is near the noise  
> level  
> does not distinguish between members of a family of curves having the  
> same measured initial slope, and the channel capacity that actually  
> exists can’t be calculated without knowing which member of that family  
> is  
> present.

I would prefer to continue this kind of discussion if I was assured  
that you understood the analysis that allows us to equate d’^2 with  
information. It’s on page 13-14 of my Bayesian\_Seminar\_2.pdf. Shannon’s  
expression ![c9381f69e65d9c81edae2056095f2f74.png](http://discourse.iapct.org/uploads/default/original/2X/7/7af4aa68093f204a5e8cfe925db81d51364c773e.png), which you mention from the wiki page, is central to the  
argument. Given that, the equation of d’^2 and information follows from  
the fact that d’^2 = 2E/No under the same “ideal observer” conditions  
that apply to Shannon’s formula, where E is the signal energy and No  
the noise power per unit bandwidth.

> It is certainly not the case that an analogue circuit  
> could  
> “work effectively only on the first 130 milliseconds of the  
> signal”, especially when that part of the signal gives no  
> information about what the signal does after reaching that level.

No, but it seems to be the case that at least some of the human sensory  
systems have that limitation, at least with static signal bursts such  
as our tones and light flashes. Garner found the same thing in the  
1950s, when measuring channel capacities was all the rage. He was  
looking at information integration in hearing. He found the same as we  
did a decade later, that there is a break at around 130 msec between  
complete information integration and a following slower rise.

If there were a similar break at other perceptual levels, the break  
time would presumably be longer the higher the level. That might be yet  
another way of teasing out the levels of perception.

One question of real interest is whether the 130 msec interval has any  
relevance when the signal is changing. A very crude notion might be  
that it might suggest a rough limit on the rapidity with which we could  
see (and control?) independent values of a variable at the level of  
sensation, at about 7 per second. I don’t remember whether that was one  
of Rick’s levels, and if it was, whether his rate was in that ballpark.  
It’s a very much slower rate than visual flicker fusion rate (around 60  
Hz) or the ability to detect auditory modulation, but it could be a  
rate at which we can perceive the individual changes of level. Just a  
speculation…

Martin

---

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**Post date:** [March 6, 2009, 7:12pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/36 "2009-03-06T19:12:41Z")

</div>

[From Bill Powers (2009.03.06.1035 MST)]

[Martin Taylor 2009.03.06.00.04]

> > [WTP] I usually wait until I’m  
> > pretty sure, and devote my efforts before then to making the decision  
> > unneccessary just yet. The main thing is that I know what the outcome is  
> > quite likely to be if I decide prematurely: wrong. If you have only a 60%  
> > chance of choosing right, you might as well not choose, because your  
> > estimate of the chances is probably off by a large amount, too.

> [MMT] That’s your privilege, of  
> course, but if it happened to be a tiger rather than your friend who made  
> that leaf rustle, you’d be dead by then.

Made-up positive examples don’t prove your case. For every one of those,  
there are many negative examples. The conditions, remember, are that it  
is almost equally likely that your response will be wrong: if there’s  
only one possible place the tiger could be when you hear a leaf rustle,  
then by all means run for your life in a direction away from the tiger,  
assuming you’re pretty sure what direction that is. But if running could  
equally well take you toward the tiger, it doesn’t matter whether you act  
or not: you have a fifty-fifty (or 60-40 or 40-60) chance of being dead  
if you act even sooner than if you did nothing. You may take some comfort  
from knowing that you at least did _something,_ but we’re talking  
about cases in which you will do the right thing only about half of the  
time, and in which doing the wrong thing is very bad.

> Think about your everyday  
> life. Do you never have to make choices by deadlines, whether you have  
> got enough data to be quite sure of the best choice?

I think of a way to put off the deadline, because I know that just acting  
in order to be acting is futile, and uses up resources I might need. I  
have much more faith in my ability to handle whatever comes up than I do  
in my ability to correctly forecast the future and have the appropriate  
action all ready. For one thing, having the appropriate action all ready  
can be a terrible handicap if what happens is different from what you  
expected. That can be much worse than doing nothing but remaining  
alert.

> Do you never vote (I assume you  
> never have much really solid information about most of the candidates for  
> office).

Yes, of course, and it’s been a long time since I had a hard time  
deciding. When I know nothing about candidates on a ballot, I just skip  
that item. Why bother, when half of the time I will make a choice that  
turns out exactly wrong?

> One of the few things I  
> remember from my short days as a student of Industrial Engineering was  
> the professor pointing out that “Inaction can be extreme  
> action”.

Sure, it can be. But is it usually? You can always make up a scenario  
under which any proposal would be correct. But that doesn’t tell us what  
sort of policy to follow in general. In general, I would say that  
inaction has many advantages over action when you’re not reasonably sure  
of what the right action would be.

> > and anyway the probability  
> > of a correct guess is so close to 1 by then that it can’t really be  
> > measured in any reasonable number of trials.
> 
> That was precisely what made me interested in the Schouten study in the  
> first place. It is indeed extremely difficult to determine the  
> detectability or discriminability of obvious things like bright lights or  
> the locations of well separated things. I saw the Schouten technique as a  
> possible way to get at these very detectable or very discriminable  
> signals, which orthodox techniques cannot touch for the reason you  
> mention.

I need to ask again what the actual observed variable was in these  
experiments. Wasn’t it a count of correct and incorrect responses at each  
delay time? Isn’t that why you need so many trials when the probability  
of a wrong response gets down to 0.003? That’s the probability at 3  
sigma. As I’ve been understanding this, the measure of d’ is derived from  
the measured probabilities of getting a correct answer, which is Nc/N,  
where Nc is the number of correct choices and N is the total number of  
choices at a given delay. Since you have to measure those probabilities,  
you’re not gaining any advantage by the Schouten approach.

It seems that d’ is derived from those probability measurements, not the  
other way around. Given the probability of a correct choice, we can use  
the tables to find out how many standard deviations over the noise level  
correspond to that probability, assuming a Gaussian distribution of the  
noise. From this we can deduced what the underlying noise level is. This  
seems to fit the data, since the probabilities you mention that go with  
different values of d’ approach certainty very rapidly with each added  
increment in d’. The straight lines in Schouten show that the  
distribution is Gaussian.

> Well, you see what such a  
> process can do in the Schouten data, when you look at the graph for about  
> 270 msec delay. By that time, the "processor’ has half the  
> information it has by 320 msec. It is able to get (from memory) about 85%  
> correct button presses.

This estimate of how much information exists at each delay depends very  
strongly on how you think this detection works. What you describe can  
also be imitated by a series resistor terminated by a capacitor connected  
to ground, followed by a threshold detector. To characterize the voltage  
on the capacitor at a given time as “information” is simply a  
matter of what computation you choose to use. What you call  
“processing” is simply a flow of current into the capacitor.  
This is why I ask what model you’re assuming. If we’re just talking about  
an R-C circuit, the concept of information is overcomplicating something  
very simple. You can think of a computer accumulating digital information  
over time and reasoning out what it means on the basis of the information  
so far received, or you can just think of a capacitor charging up. The  
latter could be much closer to what is actually happening; all that  
“processing” would then be a figment of the imagination that  
adds complexity without increasing our understanding.

> More generally, now knowing  
> something of PCT, I would equate “processor” with the complex  
> of control loops that interact to enable the subject to perform in the  
> experiment as the experimenter asks.

I would equate it with something much simpler, since this experiment is  
focused on just one perceptual input function. The other complexities are  
there in the background, but the experiment is not measuring  
them.

> > “Four and years our”  
> > doesn’t help me at all toward “Four score and seven years ago our  
> > forefathers…”
> 
> However, it might help you perceive that neither “To be or not to  
> be” nor “We shall fight on the beaches” was the quote from  
> which some words had been obscured by noise bursts.

But there is nothing in that stream of words that tells me how much, if  
anything, is missing from it. The original sentence could be “four  
and twenty blackbirds, a verse from the years of our childhood.”  
Information is not interchangeable, so we get can get half of the way to  
understanding given ANY half of the bits. When we actually have half of  
the information, we don’t know that, since we have no idea how much we  
have missed or how much is yet to come. “On the nose” does not  
give us half of the information in “Mary kissed John on the  
nose” or “Mary socked John on the nose” or “That is  
right on the nose.”

> Possibly if someone  
> mentioned “forefathers”, that might even be enough to cue you  
> into recognizing which words you missed.

Or that could completely mislead you if the original sentence was another  
one I mentioned. Information theory has nothing to do with meaning; it’s  
just a way of characterizing channel capacity, no matter what message is  
being carried by the channel. “John hit Mary” has the same  
number of bits of information as “Mary hit John” but the two  
clearly do not mean the same thing.

> Shannon did determine that  
> the redundancy of English is about 50%, meaning that in a long passage  
> with a random 50% of the words substituted by gaps or backouts (so you  
> know where they were), you will be able to correctly replace most of the  
> missing words. But that really has nothing to do with the case at hand,  
> which is the rate of gain of information over time. Your example might  
> have been a slightly better analogy if you had said “Four score and  
> seven” rather than “Four an years our”.

How would that help us arrive at the rest of the sentence, which is  
“… is a quotation from Lincoln”? “Half of the  
information,” as you use the term, implies that any half of the bits  
will do, in or out of sequence, with large gaps or small.

> > While the concept of channel  
> > capacity is relevant to analog systems as well as digital ones, its  
> > meaning is rather different when amplitude measures matter as much as  
> > durations and times of occurrance. In the Schouten case above, the  
> > amplitude of the perceptual response to the light matters because the  
> > part of the curve that is near the noise level does not distinguish  
> > between members of a family of curves having the same measured initial  
> > slope, and the channel capacity that actually exists can’t be calculated  
> > without knowing which member of that family is present.
> 
> I would prefer to continue this kind of discussion if I was assured that  
> you understood the analysis that allows us to equate d’^2 with  
> information. It’s on page 13-14 of my Bayesian\_Seminar\_2.pdf. Shannon’s  
> expression  
> ![C = B \log \left( 1+\frac{S}{N} \right)\]()  
> , which you mention from the wiki page, is central to the argument. Given  
> that, the equation of d’^2 and information follows from the fact  
> that d’^2 = 2E/No under the same “ideal observer”  
> conditions that apply to Shannon’s formula, where E is the signal energy  
> and No the noise power per unit bandwidth.

I don’t think you understand the point I am making. The actual channel  
capacity can be calculated from the measured bandwidth. I showed that the  
same model will yield the same information content as you measure it even  
when the actual channel capacity varies enormously. That is because the  
1/e rise time of the perceptual signal can generate initial rise rates of  
the signal that are indistinguishable from one another even if the 1 -  
e^-kt waveforms have greatly different values of k – which determines  
the bandwidth. If you’re only looking at the first 5% or less of the  
total rise, the exponential differs from a straight line by at most 1  
part in 400, which would never be detected in this experiment.  
I was hoping you would look at my argument and realize for yourself that  
this is a large loophole in the Schouten experiment. The conclusions you  
draw about the first 130 milliseconds apply only to that first 130  
milliseconds. They say nothing about the actual channel capacity of the  
perceptual input function you’re trying to characterize. The actual  
channel capacity depends on how the perceptual signal behaves even after  
the contribution of noise has become only a small part of the total  
signal. If you were to apply a sine-wave disturbance to the light  
intensity, you would find that the perceptual signal would have a much  
smaller amplitude and a much larger phase lag than you would expect from  
the channel capacity you measure over 130 milliseconds after a step-rise  
in intensity. That is because most of the perceptual signal variation  
would occur when the signal is far above the noise level and represents  
the light intensity very accurately (save for nonlinearities). Your  
approach does not consider that the signal contains any information after  
the second or third sigma of excess over the noise level. Relative to the  
assigned task, which is merely to report “detected”, that may  
be true. But it has nothing to do with the channel capacity of that input  
function, which is a physical property that doesn’t depend on what the  
signal is or what use it made of it.  
I would be much more interested in an argument that _forces_ you to  
equate d^2 with information, and that pins down a definition of  
information that is not simply the equation by which you calculate it. I  
just don’t think that “Your girlfriend is 18 years old”  
contains as much information as “Your girlfriend is 17 years  
old,” if by “information” you mean “important  
implications.” If you’re just counting bits, that’s fine: sometimes  
we might want to know how many bits per second a given channel can  
transmit, even not knowing which bits they will be. But that kind of  
knowledge is a far cry from what we normally mean by information, which  
is what the string of bits conveys by way of meaning. Shannon hijacked  
the term, but I don’t admit that he got away with it. If he had just  
called the units “Shannons” we would be much better off. The  
connection with the term “information” is entirely  
gratuitous.

> > It is certainly not the case  
> > that an analogue circuit could “work effectively only on the first  
> > 130 milliseconds of the signal”, especially when that part of the  
> > signal gives no information about what the signal does after reaching  
> > that level.
> 
> No, but it seems to be the case that at least some of the human sensory  
> systems have that limitation, at least with static signal bursts such as  
> our tones and light flashes.

But you’re finding out only that the signal-to-noise ratio is lowest in  
the first 130 milliseconds, not what the control system using that signal  
does on the basis of its changing (and accurately-perceived) amplitude  
after the uncertainty has dropped essentially to zero. You’re thinking  
that the only thing such a signal could be used for is to trigger a  
simple act, a “response.” But if, instead of a button, we had  
provided the subject with two potentiometers to turn, and told the  
subject to keep both lights below some particular brightness (perhaps  
compared with another light), the first 130 milliseconds wouldn’t matter  
much because most of the control action would be taking place after that.  
Yet the perceptual input function could be the same physical one measured  
in the Schouten experiment.

> Garner found the same  
> thing in the 1950s, when measuring channel capacities was all the rage.  
> He was looking at information integration in hearing. He found the same  
> as we did a decade later, that there is a break at around 130 msec  
> between complete information integration and a following slower  
> rise.

My objection is simply that if you use the data to calculate  
“shannons,” that is all you will get: an arbitrary measure of a  
physical process, or part of it. It’s like deciding to measure something  
in units of quarts per log(parsec). Sure, you can probably come up with a  
formula for converting a physical measurement into those units, but  
what’s the justification? That’s what I see as missing from these  
applications of information theory that go far beyond channel capacity.  
Is the fact that you CAN compute information capacity any indication that  
you should? Or that what you’re computing has anything to do with any  
independent definition of “information?”

Best,

Bill P.

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [March 6, 2009, 9:52pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/37 "2009-03-06T21:52:50Z")

</div>

[From Rick Marken (2009.03.06.1350)]

> Bill Powers (2009.03.06.1035 MST)

> Made-up positive examples don’t prove your case…

> My objection is simply that if you use the data to calculate  
> “shannons,” that is all you will get: an arbitrary measure of a  
> physical process, or part of it. It’s like deciding to measure something  
> in units of quarts per log(parsec).

This post was brilliant; just beautiful. Sure better than my little screeds. On that last note, I actually had a dream about you last night; you were nodding approvingly about my having adopted a more “up a level” approach to argument and I was saying that I was afraid I was falling back into my “down a level” bad groove. But you just ignored me; very MOL;-)

Thanks for the very _informative_ (non-Shannon version) read and for being so nice to me in my dreams. I didn’t deserve it.

Best

Rick

> **···**
>
> –  
> Richard S. Marken PhD  
> [rsmarken@gmail.com](mailto:rsmarken@gmail.com)

---

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**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [March 7, 2009, 6:55pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/38 "2009-03-07T18:55:38Z")

</div>

[From Bill Powers (2009.03.-7.1144 MST)]

Martin Taylor 2009.03.07.00.19 --

> I find myself completely flabbergasted at your comments on information and channel capacity, to the extent that I have no idea where to begin to continue the discussion. "Flabbergasted" at the truly fundamental misunderstandings expressed is perhaps rather too weak for the astonishment I experienced on reading your message! We clearly don't speak the same  
> language, and for me to comment further would be obviously pointless.

Perhaps instead of thinking about everything that needs to be said, you could think about the first misunderstanding on my part that needs to be corrected before anything else can be fixed. If just one fundamental point could be settled, perhaps the next one would yield more easily. Obviously, what I said about information theory and channel capacity makes sense to me, but not to you. If there is a "truly fundamental misunderstanding," wouldn't it be important to clear it up? If it's so obvious to you that the error lies completely on my side, you should be able to see where I went off the tracks and set me straight. I, obviously, can't see where the mistake is. Don't I usually change my tune if I see I've said something wrong?

Best,

Bill P.

---

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**Post date:** [March 9, 2009, 8:54am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/39 "2009-03-09T08:54:58Z")

</div>

[From Bill Powers (2009.03.09.0215 MST)]

[Martin Taylor 2009.03.07.00.19]

> We clearly don't speak the same language, and for me to comment further would be obviously pointless.

> So I won't. I'll just continue to use information theory and channel capacity correctly, and hope that something of its value will come across on occasion.

Perhaps if I boil my proposition down to its minimum form something useful may yet emerge from it.

Let's say that in this channel there is a signal that begins to rise about 200 milliseconds after a light turns on, with an amplitude A described by

A = Ao(1 - e^-k(t - To)) for t \>= To and To = 200 msec.

This signal represents the difference in perceived intensity between two lights.

Let the net difference signal s be the sum of A and a zero-average random variable R with a Gaussian distribution:

s = A + R.

Now we can ask, what is the probability that s will be \>= zero, indicating (arbitrarily) that the right-hand light is lit when it is actually lit? It is simply the probability that A will be greater than -R. I am skipping over scaling factors and the necessary summing of effects in two directions.

The Schouten experiment arranges for the perceived brightness difference between the two lights to be sampled at various times t after To, which means sampling it at various values of A[t]. The fraction of correct guesses to total guesses for a given time delay t will depend on the probability that A[t] \> -R, which can be calculated from formulae or tables. If A[t] is plotted in units of standard deviations of R, and the distribution of R is Gaussian, the result will be a straight line during the linear rise portion of the perceptual signal.

Obviously a number of details need to be cleaned up, but that is the structure of the model I proposed for the subject in the Schouten experiment. It should be possible to adjust the parameters of the cleaned-up model to match its performance to the results for real subjects.

This may show that I have no conception of how to use the concepts of channel capacity and information theory correctly, but I think it also shows that the results of the Schouten experiment can be understood without bringing in those concepts, however applicable they may be.

Best,

Bill P.

---

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**Post date:** [March 9, 2009, 3:46pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/40 "2009-03-09T15:46:16Z")

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[From Bill Powers (2009.03.09.0759 MST)]

Martin Taylor 2009.03.08.17.53 –

> For just one example, take  
> “_I showed that the same model will yield the same information  
> content as you measure it even when the actual channel capacity varies  
> enormously_.” This, to me, is like saying “I showed that you  
> get the same amount of water in the bathtub per minute, whether the tap  
> is wide open or nearly shut”.

What I thought I had shown was that the measurement of perceptual  
information in the first fraction of a second after the light goes on  
does not treat the perceptual signal as a continuing analog measure. I  
mentioned that if this same light perception were used during continuous  
control of light intensity, its bandwidth, and hence its formal maximum  
rate of information transfer, would depend on the long-term rise time  
which could be many times slower than the initial increase in  
signal-to-noise ratio. Ninety-five percent of the uncertainty is removed  
in the first 50 milliseconds after the initial rise, yet the input  
signal’s time constant could be five or ten times that long. The capacity  
of the channel to represent changes in the controlled variable would  
customarily be measured by using that time-constant, not the  
signal-to-noise ratio during the first few milliseconds of signal after a  
step-change of the input. What you’re saying, it seems to me, is that all  
you have to do is observe the water level in the tub for the first 10  
seconds, and from that you can infer how full it is going to  
get.

This is actually taking us back to the discussions of “subjective  
probability.” If probability is something that has existence outside  
a person, which is what we tacitly assume when we calculate it from  
observations of external events, then it can’t also be subjective and  
different for each person. The same holds for information – if the  
maximum information capacity of a channel can be calculated by a formula  
involving bandwidth and signal-to-noise ratio, it can’t also vary from  
person to person depending on what surprises that person. We must be  
talking about two different things. If the same  
maximum-information-capacity message can convey knowledge to one person  
and nothing to another person, then clearly we have to look inside the  
person to see what is really happening – the message is only part of the  
story. The idea that the message is carrying something from one person to  
another, other than photons or sound waves, is simply a misunderstanding,  
like the “looking rays” that came out of people’s eyes in  
midaeval drawings.

I think that’s really the most basic of my problems with the idea of  
information transfer. I don’t think there is any information  
“in” a message. All the information that seems to be  
transmitted is really coming from inside the person receiving the  
message. The person has learned to use certain perceptions as pointers to  
other perceptions of his own, and assumes that when those same pointers  
are provided to others, the other person will be reminded of the same  
perceptions. Of course as the present interchange is illustrating quite  
well, that simply isn’t how it works. Each of us supplies his own  
meanings when presented with the lower-level inputs we call messages.  
Nothing is carried from outside the person to inside except the message  
itself, and even that is perceived at the destination in ways the  
originator couldn’t have anticipated. It is rather miraculous that we can  
get any feeling of communicating with each other in a consistent way.  
When this process breaks down, as it has done here, we can see how  
precarious communication really is, particularly at higher  
levels.

> One thing you say does coincide  
> with what most writers on information claim: “_Information theory  
> has nothing to do with meaning_;”. I’ve always disagreed with  
> that claim, even though it is generally accepted. Because the information  
> gained from a particular physical message depends entirely on what you  
> knew about the subject beforehand, it seems to me that information theory  
> has everything to do with meaning. But channel capacity does not. It  
> represents the maximum rate at which information could be transmitted  
> through that medium, independent of the circumstances and the prior  
> knowledge of the receiver.

But the same channel capacity would be computed even though what is  
transmitted means something to one person and nothing to another. How can  
you say that channel capacity has something to do with information? To  
me, that is a self-contradiction.

To say the information “gained from a message” depends entirely  
on what you knew about the subject beforehand comes within hailing  
distance of my view. The main difference is that I don’t think the  
message does anything but be a set of perceptions. We don’t actually  
“gain” something “from” the message. We use the  
message as a pointer to experiences of our own, as when I say  
“red” and you are reminded of experiencing that color as a  
color rather than a word. The color you’re reminded of is probably not  
the exact shade of red as the color I’m reminded of, but at this low  
level of perception the differences in meaning don’t usually cause  
problems (except to interior decorators). However, as we proceed to  
higher levels, the experiences we are reminded of by hearing or reading  
words like “information” can diverge sharply. Then the  
contradictions and inconsistencies multiply and become obvious.

> The central concept of the  
> Layered Protocol Theory of dialogue is the hierarchy of one’s perceptions  
> of the dialogue partner at many levels of abstraction, and their  
> relations to the corresponding reference perceptions of the partner.  
> Misunderstandings occur when there is uncertainty about the perception of  
> the partner, or more particularly when the perception of the partner is a  
> bad representation of the facts.

While I agree in general with LPT, I have reservations about some aspects  
of it. It seems to me that you have too much faith in the ability of one  
person to grasp, simply through informal interactions, what another  
person is perceiving. I don’t think it’s that easy or that we do it that  
well. It’s not that we’re “uncertain” about the perception of  
the partner – we’re quite certain, but about the wrong thing. We don’t,  
or I should say I don’t since I may be a freak, look over the field of  
all the things the partner might mean and try to fill in the blanks. We  
do a certain amount of that, but mostly we just assume that the meaning  
that springs instantly to mind when the partner speaks is the meaning the  
partner intended. The problem is not too much uncertainty; it’s too  
little.

> If your perception of the  
> partner doesn’t conform to the facts, attempts to correct the error are  
> likely to work in an ineffective direction, and won’t reduce it. If you  
> speak Chinese and I speak Albanian, our communication won’t improve until  
> either I learn Chinese or you learn Albanian.

But even then, the word “family” will probably not be given the  
same meanings by the two parties. My point is that they _will_ give  
meanings to the word they perceive, but the meanings will come from their  
own memories, not from the word or the other person’s memories. I repeat,  
this is not a matter of decreasing uncertainty; it is being certain and  
at the same time mistaken.

> Likewise, if we are to have a  
> meaningful discussion about information, it can’t happen if it is true  
> both that I have no concept of what you mean by the word, and that you  
> have no concept of what I mean by it. Judging by your previous message,  
> both of these are in fact true.

Yes, and by my way of seeing it, it can’t be otherwise. I can’t  
experience your meanings. You are surprised, even flabbergasted, when I  
use words in ways that you can’t fit meanings to in an  
internally-consistent way. I’m not surprised when this happens the other  
way around; I expect it. I know that I don’t know what you mean by  
“information.” I can only try to pick up hints from the way you  
use the word in sentences. When I can’t put those meanings together into  
a consistent framework in my own mind, all I can do is sputter “But  
… but… but…” and say what I am getting from the words. Of  
course I have to convey that to you with more words, and who knows  
whether we are converging to a stable picture, or working our way farther  
and farther away from one?

Best,

Bill P.

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