# 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:** 19\
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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 11, 2009, 3:09pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/41 "2009-03-11T15:09:21Z")

</div>

[From Bill Powers (2009.03.11.0745)]

I’m supposed to go to a conference at Pam Fox’s “Hotel Villa  
Nirvana” with some others from IAACT on Monday. At the moment I’m on  
antibiotics for a nasty bronchitis thing and don’t know if I’m up to the  
trip. This sounds like a blog, but stay tuned.

Martin Taylor 2009.03.08.14.39 –

> I’m interested in more than just  
> the search for the controlled variable. I want to know something about  
> the properties of the control loops, and in particular the properties of  
> their component pathways. That’s one reason for continuing to concentrate  
> on the Schouten experiment. I’ll use conventional research when it seems  
> to have something useful to say, which I think is the case more often  
> than you think is the case.

I think that’s a reasonable objective (in case anyone asks what I think  
is reasonable). Just to stick with the basic PCT methodology, however, I  
think that the first step in any such investigation is to establish  
beyond a resonable doubt what it is that you’re investigating. Exactly  
what are the control loops involved in the Schouten experiment? The  
evidence on that score is pretty sparse, since no attempt was (or could  
have been) made to identify the controlled variable, the means of sensing  
it, and the means of affecting it. Before you can measure the properties  
of a control loop, or convince anyone that that’s what you’re measuring,  
you must identify the control loop with whatever tests are appropriate. I  
don’t care whether you call the approach the Test for the Controlled  
Variable, but to preserve the chain of evidence, so to speak, you have to  
provide some formal reason to suppose that the control system has been  
identified as far as possible. It’s easy to investigate the properties of  
phlogiston if you don’t have to demonstrate that there’s such a thing as  
phlogiston. I don’t want other scientists to think of PCT as  
phlogiston.

> In the opposite direction, PCT  
> ought to be able to say something useful about most observations of the  
> behaviour of a person, no matter how the data were collected – by casual  
> observation, conventional experiment, or experiment based on PCT  
> analysis.

I really don’t agree with that. There are certain things you need to know  
before you’re justified in saying anything about human control systems.  
At least you need to know what the behavior is controlling, and to find  
that out you have to do things that aren’t ordinarily done in an  
experiment designed under a different theory. For example, I suspect that  
in an operant-conditioning experiment, what is being controlled by the  
subject organism is some aspect of the reinforcer delivered by pressing a  
lever, or some effect of doing that. The simplest way to rule out that  
possibility is to apply a disturbance directly to the variable being  
controlled, as you define it. If the effect is exactly what you would  
predict from knowing the disturbance, and if nothing the subject does  
tends to reduce that effect rather strongly, you can give up that  
hypothesis without any strain. If that test is passed, you can go on to  
identify the particular inputs and outputs that go in and out of the  
hypothesized control system, or if you have a publication deadline you  
can assume with at least some confidence that there’s a control system  
involved somehow, somewhere. But who would think of adding and  
subtracting food from the cup that is normally filled by the rat’s  
pressings of a lever? (fortunately, some people studying obesity did that  
with animals who fed themselves entirely by pressing the bar, with the  
results we would expect);

In fact, Bruce Abbott found that our initial assumptions about a rat’s  
control systems were wrong: by subtracting out the feeding time from the  
total experimental time, Bruce showed that the rats did NOT vary their  
rate of bar-pressing as the rate of reinforcement changed. They  
apparently just pressed as fast as they could or else didn’t press at  
all. We would have looked pretty silly if we had reported our results  
before realizing that. Later we realized that the standard method of  
maintaining body weight at 80% of the free-feeding level was an  
experimenter-driven control process that competed with the rats’ own  
control systems, if any, so we were preventing any normal control process  
in the rats based on body weight from working.

The main thing I don’t recommend is actually a very bad habit  
psychologists often get into: making a fundamental assumption, and then  
simply proceeding as if it’s right without pausing for any kind of test.  
One particularly bad example was something I read in Carver &  
Scheier. They were looking for some effect of self-awareness on something  
or other. What they did to manipulate self-awareness was to place a  
mirror in the same room with the subject. This is the same principle used  
in designing the Three Mile Island reactor controls: measure the command  
that was supposed to open or close a cooling-water valve, instead of  
verifying the effect on water flow. Does placing a mirror in a room  
increase the self-awareness of a subject in the same room? Maybe. Maybe  
not. Since we have no way to detect self-awareness itself, there is no  
way to test this assumption. Of course that renders the rest of the  
experiment as useless as the critical light on the panel of indicators at  
Three Mile Island, which showed only that a switch was in the  
“on” position. So there was a mirror in the room when the  
person did something. So what?

If S-R psychologists had been required to demonstrate that everything  
called a “response” was a response to a specific stimulus  
as predicted by S-R theory, S-R psychology wouldn’t have lasted  
long.

> The question really is  
> whether any particular researcher wants to consider particular aspects  
> either of data or of mechanism. And that’s a question of the particular  
> researcher’s reference values for controlled perceptions, something that  
> can be influenced by, but not easily controlled by other  
> people.

I think that in any scientific culture, we place requirements on each  
other to build our ideas on firm foundations, not just on assumptions.  
People can differ on what they call a firm foundation, but I don’t think  
that any scientific journal worthy of that name would accept a paper in  
which the primary facts needed to support the conclusions were simply  
made up by the author. It’s not just a matter of personal preferences and  
academic freedom. Think of the 150 years science wasted on phlogiston,  
just because nobody asked how we could find out if it really  
existed.

I have no objection to measuring the properties of control systems to any  
depth one finds interesting. But I’m not going to believe a word of it if  
you don’t first show that you’re actually studying a control process. We  
have to prove that we studying something every time we study it, or the  
results are simply worthless. It really doesn’t take that long to check  
out a few assumptions. A chemist doesn’t simply assume that his measuring  
scales are calibrated right, or that the liquid in a bottle is really  
sulphuric acid. We learn mainly from the times when the assumptions  
prove, to our surprise and edification, to be wrong – but that will  
never happen if we don’t test them.

Best,

Bill P.

---

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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 11, 2009, 5:27pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/42 "2009-03-11T17:27:32Z")

</div>

[From Rick Marken (2009.03.11.1030)]

> Bill Powers (2009.03.11.0745)]
> 
> I’m supposed to go to a conference at Pam Fox’s “Hotel Villa  
> Nirvana” with some others from IAACT on Monday. At the moment I’m on  
> antibiotics for a nasty bronchitis thing and don’t know if I’m up to the  
> trip. This sounds like a blog, but stay tuned.

Please take care of yourself. Mexico is having a drug war anyway so it’s probably not a good idea to go down there until the US ends Prohibition II, which will probably be never.

> Martin Taylor 2009.03.08.14.39 –
> 
> > I’m interested in more than just  
> > the search for the controlled variable. I want to know something about  
> > the properties of the control loops, and in particular the properties of  
> > their component pathways.

> 

> I think that’s a reasonable objective (in case anyone asks what I think  
> is reasonable). Just to stick with the basic PCT methodology, however, I  
> think that the first step in any such investigation is to establish  
> beyond a resonable doubt what it is that you’re investigating. Exactly  
> what are the control loops involved in the Schouten experiment? The  
> evidence on that score is pretty sparse, since no attempt was (or could  
> have been) made to identify the controlled variable, the means of sensing  
> it, and the means of affecting it.

Precisely my point, though, as usual, made more cogently and respectfully.

> Before you can measure the properties  
> of a control loop, or convince anyone that that’s what you’re measuring,  
> you must identify the control loop with whatever tests are appropriate.

Yea!!

> I  
> don’t care whether you call the approach the Test for the Controlled  
> Variable

Me neither, though it’s hard to think of what else to call it. Maybe we could call it “Bill”😉

> but to preserve the chain of evidence, so to speak, you have to  
> provide some formal reason to suppose that the control system has been  
> identified as far as possible. It’s easy to investigate the properties of  
> phlogiston if you don’t have to demonstrate that there’s such a thing as  
> phlogiston. I don’t want other scientists to think of PCT as  
> phlogiston.

Right on!

Take care of yourself. I hope you feel better soon. The warm weather in Mexico might actually be good for you.

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 14, 2009, 11:56pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/43 "2009-03-14T23:56:09Z")

</div>

[From Bill Powers (2009.03.14.1703 MST)]

Martin Taylor 2009.03.14.17.04

> > 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 could see no connection between what you discussed an the rate of information transfer.

I know you can't, but I see one. We're still not talking about the same thing.

> > 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,
> 
> The rate of information transfer depends not only on bandwidth but also on SNR.

Yes, and the SNR I am talking about is essentially infinite during most the the time interval I am talking about. The SNR is apparently zero until about 200 milliseconds after one light has turned on, because there is no signal. The guesses are random until then. Starting the time clock at the (approx) 200 millisecond mark where the proportion of correct guesses is starting to rise above 50%, we see that the probability of a correct guess rises quickly by about 3 standard deviations in 50 milliseconds, or 17 milliseconds per standard deviation, at which delay the probability of guessing wrong has dropped (from my tables for a Gaussian distribution) to 0.0027, for an SNR of around 370:1. By this time the rate of information transfer must be almost zero, since there is essentially no uncertainty left (if you wait for the signal to rise by one more standard deviation, the probability of error goes to 0.000063).

But there is no reason to think that the relationship signal has reached its maximum, or even half or a quarter of its maximum, 50 or 60 milliseconds after the signal begins to rise. If you were to ask the person to react to the light by adjusting its brightness to match some standard, that adjustment would be going on for many times the initial 50-millisecond mark.

If control depended on information flow, it would not be possible to do the task I describe, because that flow would drop rapidly to zero long before the match within some criterion is achieved (as I understand you to be measuring information flow).

What the Schouten experiment does is to examine the probablity of perceiving the correct light at a time when the perceived difference in brightess of the two lights is comparable to the noise level in perceiving the brightness relationship. That noise level can be very small, however, in comparison with the final perceived brightness difference. If we look at relationship signals a hundred or more milliseconds further delayed, there is essentially no noise in them. No further information is being transmitted, yet I would be surprised if control were not even better than it was earlier.

> > Ninety-five percent of the uncertainty is removed in the first 50 milliseconds after the initial rise,
> 
> You have no measure of that. From the data, there is nothing from which you could estimate what percentage of the uncertainty is removed in 50 msec.

I just showed you that measure. You get it by looking at the measured fraction of correct guesses for a given delay in making the guess. That can be taken as the probability of making a correct guess, and given that probability you can use the statistical tables to find out how many standard devations above the noise level the relationship signal is at that delay. You don't know the actual signal level or noise level, but you know their ratio. This assumes a  
Gaussian distribution, but if you assume a different distribution you can do a similar calculation using it, or you can simply measure the distribution and use that.

This is why I asked earlier if the basic data taken during this experiment is the fraction of correct guesses at each delay. If it is, then you have the probability of a correct guess right away as a function of delay. Given that probability and a Gaussian distribution, you can determine the relative standard deviation of the noise and the signal-to-noise ratio. The linear relationship between delay and d'^2 (which you said was the standard deviation) is simply what you would expect if the distribution were Gaussian. I suspect that d'^2 is calculated from the fraction of correct guesses in a way that uses the probability tables the way I am doing.

I think that's enough to get into for now.

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:** [March 5, 2009, 4:12am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/44 "2009-03-05T04:12:29Z")

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[Martin Taylor 09.03.0.4.17.42]

> [From Bill Powers (2009.03.04.0237 MST)]
> 
> Rick Marken (2009.03.02.2230) –
> 
> > > 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).

Technically, you are correct. However, since the data fall very  
precisely on a straight line, they are consistent both with the  
hypothesis that the measured capacity is the same as the steady state  
channel capacity and with the hypothesis that what is measured is only  
a burst capacity.

Other experiments, though, may argue for this being a burst rate. Even  
if this were true for those experiments, all of them use static signal  
presentations, and the answer might be different for a varying  
presentation. There’s really no point in continuing to gather data when  
you have enough and the situation isn’t changing. Since we are asking  
about the channel capacity for perception, we can’t use control  
bandwidth as a useful measure of the steady state channel capacity,  
control bandwidth being possibly limited by other parts of the control  
circuit, not least by the transport lag that would cause oscillation  
for too high a gain at too high a frequency.

> 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.

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).

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!

> 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. 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.

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. Above, you talk about “the rise time of  
a perceptual signal” as though you subscribe to this view. Here, you  
seem to deny it.

As I see it, you can ask “At what time should we say the perceptual  
signal exists” only when you are up to at least the category level,  
since only at and above that level is it possible to say categorically  
“yes” or “no” to “does the perceptual signal exist?” That’s the level  
at which an appropriate answer can be given by a button push rather  
than by a continuously variable handle.

> 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).

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?  
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._"

As an aside, an interesting result from that set of experiments was  
uniformly that when a person had to attend to two or more  
discriminations (even though answering about only one) the total  
information capacity for the discriminations was 85% of that available  
for one of them, whether the multiple discriminations were in the same  
modality or across modalities, which suggests that the controlled  
perception involved is at some level where the actual modality has been  
transformed into a more abstract representation.

Martin

---

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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 7, 2009, 5:27am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/45 "2009-03-07T05:27:49Z")

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[Martin Taylor 2009.03.07.00.19]

> [From Bill Powers (2009.03.06.1035 MST)]

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.

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.

However, I am glad that the discussion to this point has at least made it clear that not all data acquired by psychologists unaware of PCT is invalid.

Martin

---

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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 7, 2009, 5:29am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/46 "2009-03-07T05:29:51Z")

</div>

[Martin Taylor 2009.03.07.00.28]

> [From Rick Marken (2009.03.04.2230)]
> 
> > Martin Taylor  
> > (2009.03.04.16.05) –

> > “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.

> 

Nor does “green” exist in a colour-blind person’s view of things.

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 9, 2009, 1:11am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/47 "2009-03-09T01:11:10Z")

</div>

[From Rick Marken (2009.03.08.1810)]

> Martin Taylor (2009.03.07.00.19) –

> However, I am glad that the discussion to this point has at least made it clear  
> that not all data acquired by psychologists unaware of PCT is invalid.

My argument (the one made in my “revolution” paper) is not that the data from psychological experiments is invalid. Data is just data. What is invalid (I argue) is the interpretation of this data. What the discussion so far has made clear (to me, anyway) is that it is possible to look carefully at what was actually done in a conventional experiment and understand it in terms of controlled variables and the effects of disturbances on these variables. So the results of such experiments can be useful, to the extent that they suggest further research using methods that are appropriate to the study of closed loop systems, such as the test for the controlled variable.

I never doubted that the results of conventional research might be useful or suggestive; indeed, I said just that in the last section of my paper (on “How to Have a Revolution”). In that section I said:

> The move to closed-loop psychology, when it happens, will be like starting psychology all over again, based on a new foundation: the closed-loop control model of behavioral organization. If, while pursuing the new psychology, we find useful or suggestive results obtained from the old one, so much the better.

My focus, however, is on trying to encourage researchers to drop what they are doing and to start doing research on closed loop systems the right way. My concern is that this move will be inhibited if researchers see _too much_ value in what has already been done using conventional methods. That was actually the whole point of my paper. I know that researchers want to stick with what they know and see value in it. But the control theory revolution won’t happen (I believe) until researchers are willing to start off in a completely new direction, looking only at the data collected using the old methods as, at best, suggestive of what to look at using the new ones.

Best

Rick

> **···**
>
> * * *
> 
> Richard S. Marken PhD  
> [rsmarken@gmail.com](mailto: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 9, 2009, 12:38am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/48 "2009-03-09T00:38:50Z")

</div>

[Martin Taylor 2009.03.08.17.53]

referring back to [From Bill Powers (2009.03.06.1035 MST)]

> [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?

I haven’t been ignoring you. I simply don’t know how to sort out the  
misunderstanding. When I said “We clearly don’t speak the same  
language”, I meant a higher-level “language” than just English. Up  
until your message, I had thought we were talking much the same  
language and just had different understandings of the techical aspects.  
But now I see that I was wrong, and I’m completely at a loss to figure  
out how to generate a translation mechanism. You use English words in a  
way that seems as though they should mean something, but to me they  
don’t. Reading your words is like making sense of a surrealist  
painting; it makes the head spin. I don’t know if you are making a  
mistake or not, in your own language.  
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”. It  
just doesn’t make any sense, but since it appears to make sense to you,  
it must be that some of the words mean something different to you than  
they mean to me. For another example: “_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_.”" Who, in natural language or in scientific theory,  
ever considered “information” to mean “important implications”? I’ve  
certainly never heard “information” used to mean “implications of  
action” before. But this seems to be part of your meaning of  
“information”, even when you are critiquing my mathematical analyses.  
There are many other examples in which the sequences of words you use  
just make no sense to me, and so I really don’t know whether you are  
self-consistent or not (I think self-consistency is a necessary but not  
sufficient condition for avoiding error). I do know that very little in  
your message says things I would say about information and its  
measurement. But then it seems apparent that by “information” you mean  
something utterly different from what I would mean if I used the term  
either in casual conversation or technically. Technically, for example,  
assuming the Shannon way of using the term (as reduction of  
uncertainty), you would be quite wrong to say: “_“John hit Mary” has  
the same  
number of bits of information as “Mary hit John”_”, since the  
listener’s prior probabilities of the two messages would very likely be  
different for the two sentences. Shannon makes it quite clear that the  
distribution of probabilities over what you expect is a major component  
of the information in a message. If someone had already told you that  
John hit Mary, then “John hit Mary” has nearly zero bits of information  
about John and Mary (although it may inform you that the speaker did  
not know you already knew), whereas “Mary hit John” may have quite a  
few, depending on what you believe about Mary’s propensity to hit back.  
At least that would be so according to Shannon. To put it in everyday  
language, the less surprising the message, the less information it  
carries about the matter concerned.  
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.

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. 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. 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.

Martin

---

<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 9, 2009, 3:28pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/49 "2009-03-09T15:28:22Z")

</div>

[Martin Taylor 2009.03.08.11.23]

> [From Rick Marken (2009.03.08.1810)]
> 
> > Martin Taylor (2009.03.07.00.19) –
> 
> > However, I am glad that the discussion to this point has at least  
> > made it clear
> 
> > that not all data acquired by psychologists unaware of PCT is  
> > invalid.
> 
> My argument (the one made in my “revolution” paper) is not that the  
> data from psychological experiments is invalid. Data is just data. What  
> is invalid (I argue) is the interpretation of this data. What the  
> discussion so far has made clear (to me, anyway) is that it is possible  
> to look carefully at what was actually done in a conventional  
> experiment and understand it in terms of controlled variables and the  
> effects of disturbances on these variables. So the results of such  
> experiments can be useful, to the extent that they suggest further  
> research using methods that are appropriate to the study of closed loop  
> systems, such as the test for the controlled variable.
> 
> I never doubted that the results of conventional research might be  
> useful or suggestive; indeed, I said just that in the last section of  
> my paper (on “How to Have a Revolution”). In that section I said:
> 
> > The move to closed-loop psychology, when it  
> > happens, will be like starting psychology all over again, based on a  
> > new foundation: the closed-loop control model of behavioral  
> > organization. If, while pursuing the new psychology, we find useful or  
> > suggestive results obtained from the old one, so much the better.
> 
> My focus, however, is on trying to encourage researchers to drop what  
> they are doing and to start doing research on closed loop systems the  
> right way. My concern is that this move will be inhibited if  
> researchers see _too much_ value in what has already been done using  
> conventional methods. That was actually the whole point of my paper. I  
> know that researchers want to stick with what they know and see value  
> in it. But the control theory revolution won’t happen (I believe) until  
> researchers are willing to start off in a completely new direction,  
> looking only at the data collected using the old methods as, at best,  
> suggestive of what to look at using the new ones.

I think I am in complete agreement with what you say here, and I have  
said that I thought you had written a good paper.

If I have any problem in this area it is based on our historical  
interactions, in which you have often suggested I am too open to  
accepting results obtained in conventional manners, and I have said you  
dismiss them too readily. I don’t expect that difference of opinion to  
change much simply because we agree on what you say above.

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 9, 2009, 5:43pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/50 "2009-03-09T17:43:10Z")

</div>

[From Rick Marken (2009.03.08.1040)]

> Martin Taylor (2009.03.08.11.23)–
> 
> > Rick Marken (2009.03.08.1810)–
> > 
> > I never doubted that the results of conventional research might be  
> > useful or suggestive…
> > 
> > My focus, however, is on trying to encourage researchers to drop what  
> > they are doing and to start doing research on closed loop systems the  
> > right way…

> I think I am in complete agreement with what you say here, and I have  
> said that I thought you had written a good paper.

Great. So let’s start talking about how to create some research jewels based on the closed loop model of behavior and set aside (for now) the attempts to see what kinds of silk purses can be made out of the sow’s ear of conventional research based on the open loop model. I’m just worried that if we keep focusing on what can be salvaged from causal research we’ll never get started on control research.

Best

Rick

> **···**
>
> –  
> Richard S. Marken PhD  
> [rsmarken@gmail.com](mailto: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 9, 2009, 6:45pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/51 "2009-03-09T18:45:58Z")

</div>

[Martin Taylor 2009.03.08.14.39]

> [From Rick Marken (2009.03.08.1040)]
> 
> > Martin Taylor  
> > (2009.03.08.11.23)–
> > 
> > > Rick Marken (2009.03.08.1810)–
> > > 
> > > I never doubted that the results of conventional research might be  
> > > useful or suggestive…
> > > 
> > > My focus, however, is on trying to encourage researchers to drop what  
> > > they are doing and to start doing research on closed loop systems the  
> > > right way…

> > I think I am in complete agreement with what you say here, and I have  
> > said that I thought you had written a good paper.

> Great. So let’s start talking about how to create some research jewels  
> based on the closed loop model of behavior and set aside (for now) the  
> attempts to see what kinds of silk purses can be made out of the sow’s  
> ear of conventional research based on the open loop model. I’m just  
> worried that if we keep focusing on what can be salvaged from causal  
> research we’ll never get started on control research.

I’m interested in more than just the search for the controlled  
variable. I want to know something about the properties of the control  
loops, and in particular the properties of their component pathways.  
That’s one reason for continuing to concentrate on the Schouten  
experiment. I’ll use conventional research when it seems to have  
something useful to say, which I think is the case more often than you  
think is the case.

In the opposite direction, PCT ought to be able to say something useful  
about most observations of the behaviour of a person, no matter how the  
data were collected – by casual observation, conventional experiment,  
or experiment based on PCT analysis. The question really is whether any  
particular researcher wants to consider particular aspects either of  
data or of mechanism. And that’s a question of the particular  
researcher’s reference values for controlled perceptions, something  
that can be influenced by, but not easily controlled by other people.

Martin

---

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**Post date:** [March 10, 2009, 5:23am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/52 "2009-03-10T05:23:12Z")

</div>

[From Rick Marken (2009.03.08.2225)]

> Martin Taylor (2009.03.08.14.39)–

> 

> I’m interested in more than just the search for the controlled  
> variable. I want to know something about the properties of the control  
> loops, and in particular the properties of their component pathways.  
> That’s one reason for continuing to concentrate on the Schouten  
> experiment. I’ll use conventional research when it seems to have  
> something useful to say, which I think is the case more often than you  
> think is the case.

OK, but have you ever used control theory based research? Ever done research using control methods like the test for the controlled variable? Might you be finding conventional research (like Schouten’s) to be useful because it’s more confortable to stick with what is familiar rather than try something new?

> In the opposite direction, PCT ought to be able to say something useful  
> about most observations of the behaviour of a person, no matter how the  
> data were collected – by casual observation, conventional experiment,  
> or experiment based on PCT analysis.

Sure And I think that was shown, for example, with the Schouten experiment where it became clear (to me, anyway) that the behavior in that experiment could be explained as the control of a relationship perception (light/press) and that the quality of control was determined by the timing of the elements of the perception, which affects the ability to perceive the variable under control. But just “saying things” like this about this kind of data is not the same as actually doing the kind of research that could tell you what is really going on – what variables are under control and how they are being controlled.

> The question really is whether any  
> particular researcher wants to consider particular aspects either of  
> data or of mechanism.

It seems to me that the question is whether any particular researcher wants to take seriously the possibility that organisms – the subjects of their research – are organized as closed loop control systems. A researcher who does take it seriously will (I believe) then have the courage to try something new and concentrate on doing research using control theory based methods.

Best

Rick

> **···**
>
> –  
> Richard S. Marken PhD  
> [rsmarken@gmail.com](mailto: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 14, 2009, 9:03pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/53 "2009-03-14T21:03:22Z")

</div>

[Martin Taylor 2009.03.14.16.33]

> [From Rick Marken (2009.03.08.2225)]
> 
> > Martin Taylor  
> > (2009.03.08.14.39)–

> > I’m interested in more than just the search for the controlled  
> > variable. I want to know something about the properties of the control  
> > loops, and in particular the properties of their component pathways.  
> > That’s one reason for continuing to concentrate on the Schouten  
> > experiment. I’ll use conventional research when it seems to have  
> > something useful to say, which I think is the case more often than you  
> > think is the case.

> OK, but have you ever used control theory based research? Ever done  
> research using control methods like the test for the controlled  
> variable? Might you be finding conventional research (like Schouten’s)  
> to be useful because it’s more confortable to stick with what is  
> familiar rather than try something new?

I thought about your questions and wondered whether you might be right.  
So I went back through my research history, and what I found made me  
think you probably are not right.

Item: My thesis predicted a well-defined pattern of errors when  
locating a dot on an index card or in reproducing a simple drawn  
figure. It was based on the notion that one’s perception of a distance  
differed when one was controlling one end of the distance as compared  
to when one is presented with both ends, and following this up I did a  
fair amount of magnitude matching based on the idea that control made a  
difference. In fact, my first presentation to a scientific conference  
was based on this, with S.S.Stevens in the audience. Since I was  
essentially arguing that his methods of magnitude estimation were  
misguided because he didn’t take into account the effects of control,  
he asked a lot of questions, and in fact I had tea with him and his  
wife afterwards to try to get some of the concepts reconciled. I don’t  
think we did, but he was a nice person to talk with.

Item: When I was studying aftereffects, one technique I used was to  
allow the subject to control to oppose the after effect – making the  
perception be “normal” (i.e. keep a display perceptually stationary  
after observing a moving one).

Item: Most of my research was on discrimination under different  
conditions, studying the limits on people’s capability, using  
methodology that our recent discussion has shown to be valid in a PCT  
framework.

Item: My Layered Protocol Theory of dialogue was used in analyzing both  
natural dialogues and the design of computer interfaces, and was found  
to be a special case of PCT.

In addition to these, you know I have done specifically PCT research to  
look at what aspects of control are affected by sleep loss.

So, though your questions may be quite reasonable to ask, I think their  
implications are misguided, even though I cannot, for obvious reasons,  
evaluate them by introspection. I have never had any interest in “the  
test for the controlled variable” because that was never the question  
at issue for me (and still has not been). One always assumed that the  
subject was trying to control what the experimenter asked her to  
control. In everyday life, at any one moment we are usually controlling  
many low-level variables, and are changing whatever high-level  
variables are of momentary interest. Testing for the controlled  
variable is of interest when one wants to figure out, as you have,  
whether a perception of “size” refers to area, perimeter, or some other  
function of the shape, or what it is that a fielder controls when  
trying to catch a ball, and it is very important when one is interested  
in clinical psychology. I’m more interested in “how” than in “what”. I  
hope that’s permissible?

I do, however, continue to believe that a lot of “conventional”  
research has provided data that is and continues to be useful in a PCT  
framework. In [Martin Taylor 2009.02.17.11.23] I presented one  
situation where it can be valid (on which nobody has commented), and  
that is a situation that I think covers quite a lot of “conventional”  
research, including most of my own.

Martin

---

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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 14, 2009, 10:08pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/54 "2009-03-14T22:08:14Z")

</div>

[Martin Taylor 2009.03.14.17.04]

> [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 could see no connection between what you discussed an the rate of  
information transfer.

> 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,

The rate of information transfer depends not only on bandwidth but also  
on SNR.

> 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,

You have no measure of that. From the data, there is nothing from which  
you could estimate what percentage of the uncertainty is removed in 50  
msec.

> 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.

You have no idea how full it is going to get, when you are measuring  
just the flow from the tap. The channel capacity is that flow rate –  
or rather, the flow rate provides a lower bound on the channel  
capacity, and is a measure of the effective channel capacity.

> 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,

I’ve tried to point out that this tacit assumption should be dropped,  
have I not?

> 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.

Why not? The channel capacity is the maximum that could be transmitted  
over the channel. If the recipient knew beforehand what would be sent,  
no information would be transmitted over the channel, but that would  
not affect the channel capacity. If, in the Schouten experiment, the  
subject was warned beforehand which light would go on, then he could  
press the correct button no matter what the delay. As the experiment  
was actually run, the subject had only a 50-50 chance of hitting the  
right button if the delay was less than about 200 msec, so clearly that  
information was not available, and all the information relevant to the  
choice of button was passed through the channel in question.

> 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.

OK. You are getting the idea!

> 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.

Oh, it’s carrying something, all right, but what it is carrying depends  
on the recipient as much as on the sender.

> 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.

Yes, you do seem to be getting it. That’s the essence of LPT. No third  
party can possibly tell for sure what messages are passing between two  
parties on a dialogue.

> > 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.

Think of the bathtub again, but have it filled by a hose rather than a  
faucet. I can measure the rate of flow out of the hose nozzle, but that  
only limits how much of the water gets into the bathtub. If the hose is  
pointed in the other direction, the bathtub stays empty; of if the  
bathtub is already overflowing, the level doesn’t change even when all  
the water from the hose is aimed at the tub. The hose flow is channel  
capacity; the change in bathtub level is information received.

> > 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.

That’s why LPT is based on feedback loops in both parties. The sender  
controls for seeing aspects of the recipient that would suggest that te  
recipient has “got the message” (done the sender’s bidding, understood  
what the sender said,…), while the recipient controls for perceiving  
that the sender believes the recipient to have “go the message”. Both  
act to influence the other’s perceptions until both arrive at  
sufficiently low values of the error signal. Unlike a lecture or a  
written book, a dialogue is the interplay of control systems.

> 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.

When you are talking with someone, do you never ask the equivalent of  
“how’s that again?” I have observed, of course, that in our own  
interactions you are much more liable to assume I have meant something  
quite other than what I did mean than you are to ask, so I can well  
believe that you do as you say. But different people have different  
biases in this respect.

I went so far as to find Schouten’s paper in the Library (after which I  
found it on my own shelf – go figure), and I note that he did some  
preliminary “free reaction” (as fast as you can) runs. He found great  
differences among the subjects in the error rate (between 0.4% and 4.0%  
on average between his subjects A and B) and the speed of the responses  
(average 335 and 290 msec respectively), but when he plotted the error  
rate against actual reaction time, they seemed to fall near a single  
curve (it’s hard to see precisely because he plotted on a linear  
scale). Some people are happy making a reasonable guess, while others  
want to be more certain before they commit.

> > 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.

I thought about this, and I agree that in some cases one will  
mistakenly believe one has a correct understanding, but I don’t think  
that is the usual situation. More commonly, I think, one either has a  
correct understanding or one remains uncertain and asks for  
clarification.

When one (as recipient) believes wrongly that one understands, the  
result is likely to be error in some related controlled perception. The  
partner (the sender) is most likely to be the one whose controlled  
perception experiences increased error, as when you close the door  
after I ask you to close the window and you signal that you have  
understood.

The result of this is likely to be more actions on the part of the  
sender to reduce the error in the controlled variable (door open,  
window closed). Or else actions to close off the conversation, such as  
by getting up to open the door and close the window.

![Schouten_accuracy-8.jpg](http://discourse.iapct.org/uploads/default/original/2X/b/b38a05ff03612f3cf4b96b34e6d5abcad2f59c25.jpeg)

> **···**
>
> * * *
> 
> On the Schouten experiment, I now have more details to answer some past  
> questions: The bips were 20 msec long, separated by 75 msec. Schouten  
> measured the actual response time and used that in plotting the data,  
> not the requested response time. He noted that for the shorter  
> requested response times the subjects tended to delay their actual  
> responses.
> 
> In [From Bill Powers (2009.03.09.0215 MST)] you say:
> 
> ------------quote---------
> 
> 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.
> 
> ----------end quote-----------
> 
> This is exactly how Schouten saw it, and I have and had no reason to  
> disagree. It’s where I started. Here’s one of his diagrams to  
> illustrate the point:
> 
> ![]()
> 
> It was my knowledge that d’^2 was a measure of the information  
> available from a discrimination of such accuracy that allowed me to  
> plot the information gain over time by subject B and by the “average  
> subject” for the figure I showed in several earlier messages. There’s  
> no conflict between his model (which is also yours) and my calculation  
> of information gain rate. I don’t remember whether Schouten gave me his  
> data to make my calculations – I suspect he did, because the meeting  
> was close to his laboratory – or whether I read off his graphs (which  
> would have been rather hard to do accurately). Bandwidth doesn’t come  
> into it explicitly; as I said in an earlier message, channel capacity  
> is a generalized version of bandwidth, which includes sampling accuracy  
> in addition to bandwidth.
> 
> The reason I did the recomputation in terms of d’^2 was that it is  
> impossible to measure differences in discriminability when d’ gets much  
> above 2.5 or 3. At the time I was working on a theory that perceived  
> magnitude (S.S.Stevens, if you like) was proportional to the  
> discriminability of the difference between the ends of an interval. In  
> my thesis work it would have been the difference between the  
> discriminability of a one inch distance between two dots when the  
> subject was or was not controlling the position of one of the dots.
> 
> In my first published paper I predicted the existence and parametric  
> form of an illusion that I had never seen mentioned, simply on the  
> basis that a path perceived to be straight would be a geodesic in a  
> space in which the discriminability of different possible paths was  
> affected by the proximity of a nearby disk. Given that, the properties  
> of partial differential equations allowed for the computation of the  
> parametric form of the illusion (a straight line as a function of disk  
> diameter, which was fitted very closely by the data). I also made a  
> correct counter-intuitive prediction that subjects who were more  
> precise would show more illusion. So I was interested in measuring the  
> differences in discriminabilities at levels far, far, higher than can  
> be measured by conventional means. The rate of information gain from  
> the discrimination seemed to be a reasonable way of differentiating  
> such big differences.
> 
> To Rick: As for what the subjects were controlling, I asked them to say  
> whether a straight line between the dots would go through the disk or  
> bypass it. I assume they were controlling for telling me what they saw,  
> but beyond that, I can’t guess. But I don’t think that makes the data  
> any the less reliable.
> 
> Martin

---

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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 15, 2009, 4:36am UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/55 "2009-03-15T04:36:01Z")

</div>

[Martin Taylor 2009.03.14.23.17]

> [From Bill Powers (2009.03.14.1703 MST)]
> 
> Martin Taylor 2009.03.14.17.04
> 
> > > 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 could see no connection between what you discussed an the rate of information transfer.
> 
> I know you can't, but I see one. We're still not talking about the same thing.

From the rest of your message, we most decidedly are not. I'm trying to discuss Shannon's information and uncertainty measures, and you seem determined that this should not be discussed, by substituting your own definitions for Shannon's, and then making inferences based on your definitions rather than his, which makes discussion rather difficult. You have a habit of talking about very small things as though they are zero, which makes discussion rather difficult. You talk about signal to noise ratio as though it changes during the presentation of an ongoing signal, and that also makes discussion difficult. You use your own definition of "uncertainty" to dispute the calculations based on the technical definition, and that makes discussion difficult. And from all that you the derive the preposterous statement

> If control depended on information flow, it would not be possible to do the task I describe, because that flow would drop rapidly to zero long before the match within some criterion is achieved (as I understand you to be measuring information flow).

As you misunderstand me to be measuring information flow.

> What the Schouten experiment does is to examine the probablity of perceiving the correct light at a time when the perceived difference in brightess of the two lights is comparable to the noise level in perceiving the brightness relationship. That noise level can be very small, however, in comparison with the final perceived brightness difference. If we look at relationship signals a hundred or more milliseconds further delayed, there is essentially no noise in them.

That the integrated noise level becomes very small in comparison with the final perceived brightness difference is the very reason that I wanted to calculate the information rate rather than the uncomputable residual uncertainty at long delay, so I agree with the second sentence. I explained that in the message to which you are responding, and gave examples in which the discrimination was of location separation between dots over separations of inches seen at normal reading distance. To equate "essentially no noise" with "no noise" is a real sticking point. You assert "essentially no" is equal to zero, and then say:

> No further information is being transmitted,

which does follow from your equation of "very small" with "zero", but does not follow from the facts of the situation.

> > > Ninety-five percent of the uncertainty is removed in the first 50 milliseconds after the initial rise,
> > 
> > You have no measure of that. From the data, there is nothing from which you could estimate what percentage of the uncertainty is removed in 50 msec.
> 
> I just showed you that measure.

You did no such thing. So far as I can see, you seem to take "proportion of uncertainty" to be the proportion of the range between 50% and 100% correct, so that by the time the subject is getting 75%, half the uncertainty has been removed. Except that can't be it, because you say 95% is removed in 50 msec, when by eye it looks to me as though the percentage correct is around 80-85%, so I am quite uncertain as to what you must mean. Either way, it's Humpty-Dumpty language in a discussion based around Shannon uncertainty measures. If I "define" a step to be roughly a quarter million miles, I can get to the moon in one step. But that doesn't much help NASA.

> You get it by looking at the measured fraction of correct guesses for a given delay in making the guess. That can be taken as the probability of making a correct guess, and given that probability you can use the statistical tables to find out how many standard devations above the noise level the relationship signal is at that delay. You don't know the actual signal level or noise level, but you know their ratio. This assumes a  
> Gaussian distribution, but if you assume a different distribution you can do a similar calculation using it, or you can simply measure the distribution and use that.
> 
> This is why I asked earlier if the basic data taken during this experiment is the fraction of correct guesses at each delay. If it is, then you have the probability of a correct guess right away as a function of delay. Given that probability and a Gaussian distribution, you can determine the relative standard deviation of the noise and the signal-to-noise ratio. The linear relationship between delay and d'^2 (which you said was the standard deviation) is simply what you would expect if the distribution were Gaussian.

You can't derive the linear relation over time from an assumption that the noise distribution is Gaussian. The linearity of the relation comes about from the very particular way that the standard deviation of the distribution (if it is Gaussian) changes over time -- the inverse of its square varies linearly with time. That "particular way" can be derived from an assumption that the noise contributions on successive samples are of equal variance, the sample values are independent of each other, and all samples contribute equally to the reduction in the overall variance (where the separation of samples is 1/2W, and W is the bandwidth), whether the distribution is Gaussian or not. That "sampling" notion is an intellectual convenience, not a proposal that the sensory systems actually do sample. Shannon shows how this intellectual convenience applies to continuous signals.

> I suspect that d'^2 is calculated from the fraction of correct guesses in a way that uses the probability tables the way I am doing.

Of course it is. I told you it was. And it keeps growing as the proportion correct goes from 90% to 99% to 99.9% to 99.9999% .... You have in these data absolutely zero indication of what proportion of the uncertainty is removed in 50 msec, or in 100 msec, because you have absolutely nothing in the data to tell you what the eventual limiting uncertainty might be. The only thing these data show is that the rate of information gain is constant over the range of delays measured, after the initial transport lag (and gives a measure of what that rate is).

Of course, we presume that there would be a time after which there would be no point in continuing to gain information, because for control one usually doesn't need micrometric precision, but we have no indication of it in these data. I suggested in an earlier message that this point might come after about 130 msec, based on a fallible memory of long ago experiments. In the case of a binary choice experiment, for all practical purposes there wouldn't be much point in waiting until you were sure of making less than one error in a billion trials -- indeed, Schouten mentions that a good part of the training with the bips was needed in order to get subjects to withhold their responses for long delays (he went up to 800 msec, but the results for the long delays aren't reported because there were too few errors to allow a reliable (or any) calculation of d'). People just don't want to wait that long to make their decision.

Martin

---

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**Post date:** [March 15, 2009, 3:02pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/56 "2009-03-15T15:02:54Z")

</div>

[Martin Taylor 2009.03.15.10.02]

> [Martin  
> Taylor 2009.03.14.23.17]
> 
> > ```
> > [From Bill Powers (2009.03.14.1703 MST)]
> > 
> > ```
> > 
> > Martin Taylor 2009.03.14.17.04
> > 
> > > > ```
> > > > 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 could see no connection between what you discussed an the rate of  
> > > information transfer.
> > 
> > I know you can’t, but I see one. We’re still not talking about the same  
> > thing.
> 
> from the rest of your message, we most decidedly are not.

I think I have to apologise to you. I’ve been blind to what should have  
been apparent to me about where you have been coming from. This morning  
I awoke with a possible insight as to why we seem to be talking past  
one another. It has to do with information always being about  
something. We have been thinking about different “somethings”.

I’ve been working on the assumption that you had read the relevant  
portion of my Bayesian notes, and without thinking further about it,  
I’ve been assuming that you understood that the information being  
transmitted was about the lights. That was always my background  
assumption throughout the discussion, since I have been assuming that  
you had read the relevant part of my Bayesian Seminar 2, as I asked  
some time ago. But now, this morning, I think maybe you have been  
thinking of the information transmitted only about the location of the  
lit light, a one-bit discrimination. That would fit your talk about  
“half the information”, a concept that baffled me in the context of the  
information being about the lights rather than only about the location  
of the lit light.

Here’s a graph of the uncertainty of a one-bit choice as a function of  
the prior probability of one of the choices being correct  
(Sum(-plog2(p) - (1-p)log2(1-p))). To make this concrete, let’s say  
that if the subject already had a probability x of choosing the lit  
light, her remaining uncertainty would be y bits. Flip the chart upside  
down to get the information already received. The right panel is just a  
magnification of the high-probability part above 95% correct.

 ![bit_rate.jpg](http://discourse.iapct.org/uploads/default/original/2X/2/2f0b5a36b64d6ad12342b9305e2aeffc7332e006.jpeg)

When the subject gets 89% correct, the remaining uncertainty is 0.5  
bits, and the subject has gained half the information that could be  
eventually available about the location of the lit light. When the  
subject has obtained 95% of the available information about the  
location of the light, she can get about 99.45% correct.

I think this may be what you have been thinking of, while I have been  
thinking of the steady availability of information about the lights,  
which is about much more than just the choice of which of the two is  
lit.

Does this seem right? Are our views reconciled, or at least nearer to  
being so?

Martin

---

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**Post date:** [March 15, 2009, 5:06pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/57 "2009-03-15T17:06:11Z")

</div>

[From Bill Powers (2009.03.15.0720 MDT)] –

Martin Taylor 2009.03.14.23.17 –

> I’m trying to discuss Shannon’s  
> information and uncertainty measures, and you seem determined that this  
> should not be discussed, by substituting your own definitions for  
> Shannon’s, and then making inferences based on your definitions rather  
> than his, which makes discussion rather difficult.

I’m not intentionally changing Shannon’s definitions. We are simply  
imagining the physical situation differently – using different models of  
what may be going on, prior to any application of information  
theory.  
I am seeing a perceptual input function that receives inputs, via  
intervening lower-level input functions, from two light sources that turn  
on and off. It reports, as a signal, the unbalance between the lower  
signals. This higher PIF contains a constant Gaussian noise source of  
unspecified _but unchanging_ magnitude that is always present. The  
noise does not vary with magnitudes of the input signals. It’s the  
background hiss in the receiver.

As I imagine this system, the presence of a constant noise signal means  
that with no light on, sampling the relationship signal at any fixed time  
will generate a signal equally likely to indicate “left” or  
“right”. With continued repetitions, the proportion of correct  
guesses to total guesses will approach 50%. As the samples are delayed  
more and more after a light turns on, this long-term average will remain  
50% until the sample delay equals the transport lag.

When the delay exceeds the transport lag, the noise-free component of the  
left-right signal begins to rise in the correct direction (separate left  
and right signals would be needed in a nervous system). For small added  
sample delays the noise component still dominates. As the sample delay  
increases more, the systematic component increases, and we observe (over  
many repetitions at the same sample delay) a bias in the guesses toward  
the correct direction that increases with sample delay. The probability  
of a correct guess begins to increase. At a sampling delay such that the  
systematic signal is twice the standard deviation of the (constant)  
noise signal, the long-term fraction of correct guesses has become  
95%.

In the Schouten data, we can see that the transport lag for subject B is  
about 230 milliseconds. That is where the fraction of correct guesses  
begins to rise above 50%. Had the data been plotted as percent correct  
guesses versus sampling delay, we would have seen a negative-accelerated  
curve that approaches asymptote very soon after the initial rise above  
50% – it would be 99% in less than 50 milliseconds after the transport  
lag. Actually, the original data would have been the fraction of correct  
guesses at each delay, with the value of d’ or d’^2 being calculated from  
that.

A different assumption would be that the noise level rather than being  
constant is Poisson-distributed, proportional to the square root of  
signal level. In that case the signal-to-noise ratio would increase as  
the square root of the signal rather than linearly as in the above, and  
the approach to asymptote would be slower. So there is some possibility  
of deducing the distribution from knowledge of the probability of a  
correct guess.

As you can see, this is a purely physical analysis based on a model, and  
says nothing about information. You can use the Shannon formulation if  
you like, but it’s not necessary for characterizing the performance of  
this model.

> You have a habit of  
> talking about very small things as though they are zero, which makes  
> discussion rather difficult.

Funny, I was noticing a similar tendency in you, though in the opposite  
direction. It seems that when differences get smaller, you crank up the  
gain so they look just as large as before, forgetting that their  
importance is getting smaller each time you increase the magnification.  
It’s true that 99.99% correct is not the same as 100% correct, but the  
difference is not the kind that makes a difference to any normal  
person.

> You talk about signal to  
> noise ratio as though it changes during the presentation of an ongoing  
> signal, and that also makes discussion difficult.

What makes it difficult is that I don’t think you have understood my  
model yet. I assume a constant amount of background noise, with the  
signal changing magnitude relative to the noise. I see the signal as  
increasing with time after the initial transport lag, while the noise  
level remains the same. This means that there is less relative random  
error in a large signal than in a small one, and I treat errors of less  
than a few tenths of a percent as negligible, as any good engineer  
would.

> You use your own  
> definition of “uncertainty” to dispute the calculations based  
> on the technical definition, and that makes discussion difficult. And  
> from all that you the derive the preposterous statement
> 
> > If control depended on information flow, it would not be possible to do  
> > the task I describe, because that flow would drop rapidly to zero long  
> > before the match within some criterion is achieved (as I understand you  
> > to be measuring information flow).

What you haven’t seen here is that I am assuming some small constant RMS  
noise which matters only when the systematic component of signal is of  
comparable size, a few milliseconds after the transport lag is finished.  
As the systematic part of the signal increases after that point,  
snapshots of the total signal at the same time delay will record more  
signal but the same noise, so signal-to-noise ratio will increase as we  
look at points farther to the right. It also increases during each trial,  
because the noise is constant but the signal is increasing as time  
progresses.

> > I just showed you that measure.

> You did no such thing.

Well I did so, and nyaa nyaa to you.

> So far as I can see, you seem to  
> take “proportion of uncertainty” to be the proportion of the  
> range between 50% and 100% correct, so that by the time the subject is  
> getting 75%, half the uncertainty has been removed.

No. I take the uncertainty to be 10% when 90% of the guesses are right,  
1% when 99% of the guesses are right, and so on.

> Except that can’t be it,  
> because you say 95% is removed in 50 msec, when by eye it looks to me as  
> though the percentage correct is around 80-85%,

You’re not reading the figure right, or I have it scaled wrong. The  
ordinate is not percentage correct, it’s that measure d’^2, which you say  
is the standard deviation of the noise. In 50 milliseconds, d’^2  
increases by about 3 standard deviations, showing that the signal  
increases to 3 SD above the chance level, which, my statistical tables  
says, means that the fraction correct must be around 99.73%. By my count  
that leaves an uncertainty of only about 0.27%. Maybe I misunderstood  
what you said about the scaling of the ordinate. In that case, you can  
substitute the correct numbers. They won’t be drastically different from  
mine, since the probability of an error drops so fast with each added  
standard deviation.

> You can’t derive the linear  
> relation over time from an assumption that the noise distribution is  
> Gaussian.

I’m assuming a perceptual signal that rises linearly after the initial  
transport lag, not deriving it. That signal will lead to a straight line  
on the Schouten diagram if the distribution is Gaussian.

> The linearity of the relation  
> comes about from the very particular way that the standard deviation of  
> the distribution (if it is Gaussian) changes over time – the inverse of  
> its square varies linearly with time. That “particular way” can  
> be derived from an assumption that the noise contributions on successive  
> samples are of equal variance, the sample values are independent of each  
> other, and all samples contribute equally to the reduction in the overall  
> variance (where the separation of samples is 1/2W, and W is the  
> bandwidth), whether the distribution is Gaussian or not. That  
> “sampling” notion is an intellectual convenience, not a  
> proposal that the sensory systems actually do sample.

I think you’re just describing the same relationships in my statistical  
tables that I use, which show the probable occurrance of a deviation as a  
function of the ratio of that deviation to a standard deviation. In the  
Schouten experiment, the probable occurrance is measured, and from that  
you deduce how many standard deviations above noise that is, assuming a  
Gaussian distribution. I am taking the ordinate in the diagram as the  
computed standard deviation, and using the tables the other way to  
compute what the percent correct over a large number of trials must have  
been.

My hypothetical perceptual signal has a certain magnitude as a function  
of time: constant at zero, then rising linearly at least at first. If you  
measure its amplitude in units of standard deviation of the noise, which  
is just a scalar number, it would lie on top of the Schouten data (or it  
would show up as a fuzzy cloud of curves with an average value  
corresponding to the Schouten data).

> > I suspect that d’^2 is  
> > calculated from the fraction of correct guesses in a way that uses the  
> > probability tables the way I am doing.
> 
> Of course it is. I told you it was. And it keeps growing as the  
> proportion correct goes from 90% to 99% to 99.9% to 99.9999% … You  
> have in these data absolutely zero indication of what proportion of the  
> uncertainty is removed in 50 msec, or in 100 msec, because you have  
> absolutely nothing in the data to tell you what the eventual limiting  
> uncertainty might be.

Well, that one really escapes me. In your series, it looks to me as if  
the uncertainty is decreasing from 10% to 1% to 0.1% to 0.00001% …, and  
it looks as if the eventual limiting uncertainty is going to be, well,  
just roughly speaking, zero.

> The only thing these data show  
> is that the rate of information gain is constant over the range of delays  
> measured, after the initial transport lag (and gives a measure of what  
> that rate is).

I think that makes no sense at all. At a constant rate of information  
gain, you’re saying, the rate at which we approach the final answer gets  
slower and slower without limit. I just can’t see that in going from 90%  
right to 99% right, we are gaining the same amount of information that we  
gain in going from 99% right to 99.9% right. If that is what information  
theory says, then the word “information” in that context means  
something different from what it means to me.

> Of course, we presume that there  
> would be a time after which there would be no point in continuing to gain  
> information, because for control one usually doesn’t need micrometric  
> precision, but we have no indication of it in these  
> data.

What you’re saying is that as we gain in precision, information becomes  
rapidly less useful in moving us toward the exact answer. I suspect that  
you’re mentally viewing this situation on a logarithmic scale, which  
makes the shrinking uncertainty into a constant ratio. In that sort of  
presentation you can never get to zero error, and it always looks as if  
you still have as much uncertainty as you had before. Well, come to think  
of it, information is defined as a log function, isn’t it? That may  
explain your inability ever to admit that some differences are too small  
to matter.

> I suggested in an earlier  
> message that this point might come after about 130 msec, based on a  
> fallible memory of long ago experiments. In the case of a binary  
> choice experiment, for all practical purposes there wouldn’t be much  
> point in waiting until you were sure of making less than one error in a  
> billion trials – indeed, Schouten mentions that a good part of the  
> training with the bips was needed in order to get subjects to withhold  
> their responses for long delays (he went up to 800 msec, but the results  
> for the long delays aren’t reported because there were too few errors to  
> allow a reliable (or any) calculation of d’). People just don’t want to  
> wait that long to make their decision.

OK, so my understanding is confirmed: the experimental data are in units  
of

fraction of correct responses (or fraction of errors). If you showed  
plots with that as the ordinate, you would get a curve approaching an  
asymptote (100%), not a straight line. The “discriminability”  
measure introduces the Gaussian distribution which has a form such that  
one unit of discriminabilty is proportional to one unit of signal  
amplitude relative to noise level. My model says that there is a  
perceptual signal that increases linearly with time after the transport  
delay, and that with a constant noise level this means that the signal  
increases a certain number of standard deviations above the noise, at the  
rate of about 1 standard deviation in 17 milliseconds. By requiring  
subjects to report the unbalance of light intensities at specific delays,  
the experiment effectively records the signal magnitude at specific  
delays after onset of the light. The signal magnitude is deduced from the  
percent correct guesses, plus the assumed distribution.

The linearity of the response as plotted in Fig. 1 depends entirely on  
the assumed form of the noise distribution. If the noise is  
Poisson-distributed, signal-to-noise ratio will be the square root of  
signal magnitude, whereas with constant Gaussian noise it will be  
proportional to signal magnitude. Maybe that’s the difference between  
using d’ and using d’^2. Of course it may be that in computing the  
measure each way, you get a straight line but of different  
slope.

I’m sure our onlookers are getting terribly bored with this, but they  
don’t have to read it, do they?

Best,

Bill P.

---

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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 15, 2009, 5:31pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/58 "2009-03-15T17:31:15Z")

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[From Bill Powers (2009.03.15.1112 MDT)]

Martin Taylor 2009.03.15.10.02 --

> I've been working on the assumption that you had read the relevant portion of my Bayesian notes, and without thinking further about it, I've been assuming that you understood that the information being transmitted was about the lights. That was always my background assumption throughout the discussion, since I have been assuming that you had read the relevant part of my Bayesian Seminar 2, as I asked some time ago. But now, this morning, I think maybe you have been thinking of the information transmitted only about the location of the lit light, a one-bit discrimination. That would fit your talk about "half the information", a concept that baffled me in the context of the information being about the lights rather than only about the location of the lit light.

Sorry, Martin, that gets us nowhere. I don't understand what "information about the lights" you mean, if it's not which one is lit. The manufacturer, the price, the difference in brightness, the distance between them, the part number ...?

As to the idea of a prior probability of choosing the lit light, I don't see how that can be anything other than 0.5, since either light can come on and there is no way to predict which one. If there is a subjective probability other than 0.5, it's a delusion, and makes no difference in the chances of picking the next light correctly. You'll lose at roulette playing rouge e noir at the same rate no matter what you think your chances are.

I'm afraid that there is something about the whole Bayesian approach that I simply don't get -- or with which I disagree so thoroughly that I can't believe it's what is actually proposed.

I have to spend most of today that remains getting ready for my trip starting tomorrow. I'll have my laptop but have no idea whether there will be time or facilities for pursuing this.

re my just previous post:  
Measuring uncertainty in bits does make it a log measure, so if the same percentage error remains after every improvement, there is no decrease in uncertainty no matter how close to zero the error in ordinary units is. Didn't someone named Xeno come up with this one a long time ago?

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:** [March 15, 2009, 6:12pm UTC](http://discourse.iapct.org/t/levels-of-perception-re-pct-researcher-who-doesnt-talk/6362/59 "2009-03-15T18:12:01Z")

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[Martin Taylor 2009.03.15.13.38]

> [From Bill Powers (2009.03.15.1112 MDT)]
> 
> Martin Taylor 2009.03.15.10.02 –
> 
> > ```
> > I've been working on the assumption that you
> > 
> > ```
> > 
> > had read the relevant portion of my Bayesian notes, and without  
> > thinking further about it, I’ve been assuming that you understood that  
> > the information being transmitted was about the lights. That was always  
> > my background assumption throughout the discussion, since I have been  
> > assuming that you had read the relevant part of my Bayesian Seminar 2,  
> > as I asked some time ago. But now, this morning, I think maybe you have  
> > been thinking of the information transmitted only about the location of  
> > the lit light, a one-bit discrimination. That would fit your talk about  
> > “half the information”, a concept that baffled me in the context of the  
> > information being about the lights rather than only about the location  
> > of the lit light.
> 
> Sorry, Martin, that gets us nowhere.

Oh well, I tried, and I still think this is where we have a  
miscommunication.

> I don’t understand what “information about the lights” you  
> mean, if it’s not which one is lit. The manufacturer, the price, the  
> difference in brightness, the distance between them, the part number  
> …?

It means anything that could be perceived about the lights as a  
consequence of one of them being lit that could not be perceived about  
them when neither was lit. The choice of which was lit is only one  
possibility. It’s impossible to enumerate the potentially infinite  
variety of others, but some possibilities might include the sparkle  
pattern due to the cover glass, the distance between them (which you  
mentioned), the colour, the shape of the cover glass, …

> As to the idea of a prior probability of choosing the lit light, I  
> don’t see how that can be anything other than 0.5, since either light  
> can come on and there is no way to predict which one.

I must have been unclear. The prior probability at delay zero is indeed  
50%, but at delay 250 msec it has risen a bit, and by 300 msec there  
isn’t much uncertainty left. The prior at any particular moment depends  
on all the data gathered up to that moment.

> I’m afraid that there is something about the whole Bayesian approach  
> that I simply don’t get – or with which I disagree so thoroughly that  
> I can’t believe it’s what is actually proposed.

I get the feeling you are looking for complication when what exists is  
clean and simple. There just isn’t any complexity in the Bayesian  
approach beyond the everyday observation that if you have some notion  
why a particular event should occur and it does, you feel confirmed in  
your reasoning, whereas if it doesn’t, you feel your reasoning must  
have some flaw. Example: you see a big black cloud that seems to be  
moving your way, and you reason that it should start raining soon. If  
it doesn’t, you might consider another possibility, such as perhaps  
that it was a cloud of smoke rather than a raincloud. If you then  
observe that the cloud continues to be big and black in the direction  
it was at first, but seems lighter and wispier in the opposite  
direction, you feel more assured that it was smoke and not a raincloud.

If you are considering two lines of reasoning and you might be prepared  
to accept either (such as raincloud or smoke), you look for some  
prediction made by one and not the other, and see which more nearly  
agrees with your observations. If both are reasonably close, but one is  
better, you look for more observations that might distinguish them, but  
this time you are a bit biased toward accepting the one that better fit  
your first observation.

That’s really all there is to it, set in quantitative form.

> Measuring uncertainty in bits does make it a log measure, so if the  
> same percentage error remains after every improvement, there is no  
> decrease in uncertainty no matter how close to zero the error in  
> ordinary units is.

What do you mean? I can’t relate this to anything I have said, or that  
you have said previously. Did the curves I showed look like logarithms  
of y against x to you? They don’t to me. Uncertainty is quantified as  
Sigma(-plog2(p)) where p is summed over all the non-overlapping  
possibilities.  
from your earlier message today [From Bill Powers (2009.03.15.0720  
MDT)], we are indeed imagining exactly the same physical situation, and  
presumably have been all along:  
----------quote--------  
We are simply  
imagining the physical situation differently – using different models  
of  
what may be going on, prior to any application of information  
theory.  
I am seeing a perceptual input function that receives inputs, via  
intervening lower-level input functions, from two light sources that  
turn  
on and off. It reports, as a signal, the unbalance between the lower  
signals. This higher PIF contains a constant Gaussian noise source of  
unspecified _but unchanging_ magnitude that is always present.  
The  
noise does not vary with magnitudes of the input signals. It’s the  
background hiss in the receiver.

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

Good. I had been imagining you to be thinking that the background noise  
magnitude was indeed diminishing with time. Your language certainly  
suggested so. So that misunderstanding, at least, can be cleared up.

But this is not:

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

A different assumption would be that the noise level rather than being  
constant is Poisson-distributed, proportional to the square root of  
signal level. In that case the signal-to-noise ratio would increase as  
the square root of the signal rather than linearly as in the above, and  
the approach to asymptote would be slower. So there is some possibility  
of deducing the distribution from knowledge of the probability of a  
correct guess.

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

You don’t have to say Poisson-distributed. You just have to say “with a  
variance dependent on the signal level”. You can have  
Poisson-distributed noise that is independent of the signal level, just  
as you can have Gaussian noise that depends on the signal level.

Going back to a discussion earlier this year or late last year (I’m not  
going to search for it) on the fine structure of the neural impulses,  
the most likely distribution seems to me to be Poisson, but dependent  
on the intensity of the light source, not on the amount of information  
so far transmitted about the decision. However, since there are many  
affected nerve fibres, the additive property would make the overall  
distribution indistinguishable from Gaussian, so the distinction seems  
unimportant. It would, however, suggest that the rate of information  
gain (rise in d^2) implicit in Schouten’s data would be lower if the  
lights were appreciably dimmer.

It is, of course, possible that later processing stages might have  
noise variances that depended on the levels of their own perceptual  
signals, but Schouten’s data suggest that if they do, the effect is  
negligible under the conditions of the experiment.

Martin

Martin

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