Uncertainty (was second-order and third-order beliefs)

[MartinT]

[Martin Taylor 2008.03.27.09.31]

[Rick Marken (2008.03.23.1650)]

This thread should have been renamed a long time ago. The original thread under the "second and third order beliefs" subject has been unfortunately diverted into an enquiry into uncertainty.

Looking back on the "uncertainty" branch of the thread, it's interesting to observe the classic conflict dynamic, in which positions draw apart. Initially, we had a near agreement:

->[From Rick Marken (2008.03.18.1200)]
->
->> Martin Taylor (2008.03.18.01.31)_-
->
->> We can control for achieving a reference value
->> of that perception of uncertainty, too, by acting to get more
->> information.
->
->Yes, I agree. But now you are controlling for another perception: certainty.
->
->> Are you suggesting the we never are uncertain?
->
->No. I'm suggesting that certainly is a perceptual variable itself,
->separate from other perceptions, like my perception of the letters in
->this sentence.

Somehow this has diverged to a point where Rick seems to be arguing that we don't perceive uncertainty about a perception, but only perceive the existence of a conflict among possible responses when we are asked what category a perception belongs to, and I have been aqsking how this would work. I'd like to get back to working from the original understanding, and get on with seeking a mechanism within a PCT structure for generating the perceptio0n of uncertainty and maintaining its linkage with the perception that is undertain.

I've been awaiting a response to the four points I raised [Martin Taylor 2008.03.23.17.40] to explain why I question the unsupported assertion that the perception of uncertainty must be a perception of conflict. No such response seems to be forthcoming, other than another unsupported assertion of the same thing, in a message that also includes a misrepresentation of the dynamic example of deblurring pseudo-handwriting I offered [Martin Taylor 2008.03.22.23.03] to illustrate uncertainty decreasing and then increasing as the presentation becase sharper.

So, while continuing to await consideration (by anybody) of my four points, I will give a short response to [Rick Marken (2008.03.23.1650)].

> > Let me ask

  >you this: is there any difference in uncertainty for an unfocused
  >image of clear handwriting versus a perfectly focused image of blurry
  >handwriting that look exactly the same?

  No difference in the uncertainty about what is written. What
  uncertainty did you have in mind when you asked the question?

Uncertainty about what is actually written.

What else do you think I had in mind? You seem to disagree with me while repeating what I wrote.

In your example, what is
actually written is some words in a nice, clean script.

No it isn't. What is written is not words at all, if by "written words" you mean a string of letters in an order corresponding to some real or implicit dictionary. There are NO letters in the example other than the first letters of the pseudo-words. All that follows the initial letter is a hand-drawn sine wave and some more or less vertical lines projecting above or below the wiggle.

I know I am
seeing a blurred image of this text because that is what I am told and
that is what I see as the animation focuses the text.

Who told you that? And does it matter, if you believe there are words there? I'm happy the animation did allow you to read the pseudo-text, but apparently the example was not clear enough to show you the end point, which was intended to show that you were perceiving words in something that did not contain the letters you had previously perceived to be there.

So my perfectly focused image of blurred, illegible script looks just
like your unfocused image of clean, legible script. In other words the
perceptions are the same in both cases.

The low-level perceptions are the same, for sure. But we aren't talking about them.

The uncertainty, then, is
clearly not a feature of the perception itself. The uncertainty in
your example exists only when you tell me that the perception is a
blurred image of legible text.

The uncertainty is in your perception of what is written, no matter how you came to believe that the blur represents something written.

I think you are trying to say that our
uncertainty about a perception is in the perception itself; that the
blurred image that you posted is an example of an uncertain
perception.

The blurred image is not a perception at all. It is input from which you create perceptions at many levels. In it, you may perceive writing. Your perception of the content of that writing is uncertain. If you don't perceive writing in the blur, then of course you have no perception of writing about which you could be uncertain.

I am trying to demonstrate that that is an incorrect view
of the uncertainty of perception.

I have several times said that I am trying to look for a correct view of the uncertainty of perception. I'm quite willing to accept that the view you ascribe to me (about which I am uncertain) could be incorrect. My only fixed point is that I do often perceive that particular perceptions are uncertain.

My questions all are about what kind of structure within the perceptual input side of a PCT complex control system (such as HPCT) would accommodate a perception that another perception is uncertain to a reportable degree. You have acknowledged that this does occur in your own case, and appears to occur in subjects in experiments in which they are asked to report their level of uncertainty.

[Rick Marken (2008.03.23.2130)] to Bill Powers

Of course I don't think the conflict is independent of the perception;
I think I mentioned the relevance of perception in an earlier post.
What you get on each trial is a perception, P, and a conflict exists
if the value of P is such that one system corrects it's error by
saying that P represents "tone present" and the other corrects it's
error by saying that P represents "tone not present".

Could you draw a diagram of these two control systems, showing their connections to the input data, where the conflict arises, what, precisely, is the perception each controls, and what are the input and output linkages to whatever control system controls the level of uncertainty about P?

A careful diagram of that nature would make the discussion a lot easier to continue meaningfully. I cannot get from your text to an understanding of the control of uncertainty about P -- a control system like the one in me that is producing output that is this part of my message. The output of this particular uncertainty control system is acting to influence, and with luck to reduce, my perception of uncertainty about your meaning, for which I have a reference level of "low".

At the moment, although I perceive high uncertainty about your meaning, I do not perceive any conflict among your possible meanings, since although I have a belief (defined by [Bill Powers (2008.03.187.1509 MDT)] to be a perception with a possibility of doubt) that you intend your statement to have some relevant meaning, yet I have no possibilities for meanings that could be in conflict.

Meanwhile, I await comment on my four points.

Martin

[rsmarken]

[From Rick Marken (2008.03.27.1010)]

Martin Taylor (2008.03.27.09.31)--

Somehow this has diverged to a point where Rick seems to be arguing
that we don't perceive uncertainty about a perception

No. I'm saying that we can perceive uncertainty about a perception;
it's uncertainty about whether a perception indicates something about
another perception; for example, whether the perception of a sound
indicates the addition of a tone or not. What I'm objecting to is the
idea that uncertainty is part of the perception of sound itself.

I've been awaiting a response to the four points I raised [Martin
Taylor 2008.03.23.17.40]

They just seemed a bit contentious and I was kind of busy at the time.
But if you keep asking I might find time to answer.

Me:

>So my perfectly focused image of blurred, illegible script looks just
>like your unfocused image of clean, legible script. In other words the
>perceptions are the same in both cases.

The low-level perceptions are the same, for sure. But we aren't
talking about them.

Really. Then we agree.

The uncertainty is in your perception of what is written, no matter
how you came to believe that the blur represents something written.

Now I'm confused again. What is the perception of "what is written".
And how does uncertainty get into it. Is it carried along in the
perceptual signal. Is your model of perception different than the PCT
model? Let's use your blurred text as an example. I view this text as
being perceived at many levels -- many types of perceptions of the
same physical situation -- simultaneously. It's perceived as
intensities , sensations (gray scale levels), configurations (shapes
and blurs) and so on up to categories (letters, words). Uncertainty
is, from my point of, a perception _about_ some perceptual level at
which we experience your text. Uncertainty is another perception (a
high level one) that, in your example, is about, say, what words are
written. If you are asked "what is written" and you take this to mean
"what words are written" then you will experience uncertainty because
you don't get a strong perception of any particular words at the
category level. I see it as like the pandemonium model at the word
perception level where many word demons are screaming at the same
time; so it's difficult to answer the question "what does the text
say; what are the words" with any confidence.

The blurred image is not a perception at all.

Gee, then how did you know it was there;-)

It is input from which
you create perceptions at many levels.

Ah, you mean the physical variable when you talk about "blurred image". OK.

In it, you may perceive
writing. Your perception of the content of that writing is uncertain.

This is where we get off. Maybe it's just a verbal thing. I would
would not say that my perception of the writing is uncertain. The
perception of the writing is what it is. I would say I am uncertain
_about_ what the perception should be called. This is actually the
same way perceptual uncertainty is viewed in conventional psychology
as well. In signal detection theory, for example, the perception
itself is not "uncertain"; it is the basis for a decision about
whether it should be called "signal" or "noise". The uncertainty is
_about_ the perception; what it should be called. The perception
itself is not uncertain.

Me:

> I am trying to demonstrate that that is an incorrect view
>of the uncertainty of perception.

I have several times said that I am trying to look for a correct view
of the uncertainty of perception. I'm quite willing to accept that
the view you ascribe to me (about which I am uncertain) could be
incorrect. My only fixed point is that I do often perceive that
particular perceptions are uncertain.

You, I believe, are simply making the mistake of ascribing the
perception of uncertainty to the perceptions themselves, the ones
about which you are uncertain. So you see the blurred text as having
"uncertainty". I think this is a mistake -- an understandable one, by
the way -- very much like attributing "negative valence" to our
perception of objects in the world that we find unattractive. It's not
the perception of the objects themselves that has the negative
valence, of course; it's the difference between our perception our
reference for what we want the perception to be that makes the
perception seem negative. So, hard as it is to believe, it's not
neo-conservatives themselves that are so unpleasant; it's how far they
are from our references for decency, kindness and wisdom. Some people
actually think of neo-conservatism as a good thing, just as some
people (like me) experience no uncertainty when presented with blurred
writing. There is no uncertainty when I don't have a reference for
perceiving what is written (what the words are).

Best

Rick

···

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

[MartinT]

[Martin Taylor 2008.03.27.14.39]

[From Rick Marken (2008.03.27.1010)]

Martin Taylor (2008.03.27.09.31)--

  Somehow this has diverged to a point where Rick seems to be arguing
  that we don't perceive uncertainty about a perception

No. I'm saying that we can perceive uncertainty about a perception;
it's uncertainty about whether a perception indicates something about
another perception; for example, whether the perception of a sound
indicates the addition of a tone or not. What I'm objecting to is the
idea that uncertainty is part of the perception of sound itself.

  I've been awaiting a response to the four points I raised [Martin
  Taylor 2008.03.23.17.40]

They just seemed a bit contentious and I was kind of busy at the time.
But if you keep asking I might find time to answer.

OK. Here's the quotation:

···

--------------------------------------
Firstly, I have not given a model, because I've only been talking about a phenomenon, as you asked me to do when I suggested that it would be prefereable to develop a model to test before designing experiments to test it.

Secondly, I have given reasons why, although I might accept your proposal for the perception of uncertainty in some conditions, it clearly is not acceptable under other conditions that offer a similar subjective experience. That leads me to be skeptical about it for those circumstances in which it would otherwise be plausible.

Thirdly (and this is halfway new), to argue that you are perceiving conflict is not to answer the question about how the perception of uncertainty is linked to a perception of something concrete; it merely moves it to a question of how the perception is linked to a relationship between two perceptions of something more concrete.

Fourthly (also, new). the kind of conflict you (actually Bill, I think) propose is of a kind not hitherto discussed in the context of HPCT. Normally, conflict in HPCT is taken to mean a problem in controlling one perception to two different reference values (or N perceptions to M > N values). Here, we have no such control problem. It's a problem purely with what IS, not about what you can control.
-------------------------------------

Me:

  >So my perfectly focused image of blurred, illegible script looks just
  >like your unfocused image of clean, legible script. In other words the
  >perceptions are the same in both cases.

  The low-level perceptions are the same, for sure. But we aren't
  talking about them.

Really. Then we agree.

  The uncertainty is in your perception of what is written, no matter
  how you came to believe that the blur represents something written.

Now I'm confused again. What is the perception of "what is written".

PCT has many levels of perception. To perceive the content of writing on a page is something we do quite normally. I think you are being deliberately obtuse.

And how does uncertainty get into it. Is it carried along in the
perceptual signal.

That is indeed the question at issue. Or one of several questions. It's a question to which I am trying to work out an answer.

Is your model of perception different than the PCT
model?

"The" PCT model? Which one of the myriads of possibilities? Your proposal that the perception of uncertainty is actually the perception of conflict at the category level seems different from standard HPCT, if that's what you are asking. Can we find a model that isn't? That would be a nice result, but it's not a nevessary one.

  A model in which perceptions are complex-valued is not different from PCT. It's just different from "classical" HPCT in which perceptual values are real-valued scalars. I'm not putting that forward as "THE" model. It's just a suggestion I made in response to Bill P at the beginning of this subthread [Martin Taylor 2008.03.17.18:00], based on the success of one company when they used complex-valued signals in their multilevel neural nets. But they were only trying to develop category perceptions, not control them. Their categories were more accurate using fewer nodes in the networks when the signals were complex-valued. I'm by no means wedded to that idea. I just think it might be worth looking into.

Let's use your blurred text as an example. I view this text as
being perceived at many levels -- many types of perceptions of the
same physical situation -- simultaneously. It's perceived as
intensities , sensations (gray scale levels), configurations (shapes
and blurs) and so on up to categories (letters, words). Uncertainty
is, from my point of, a perception _about_ some perceptual level at
which we experience your text. Uncertainty is another perception (a
high level one) that, in your example, is about, say, what words are
written. If you are asked "what is written" and you take this to mean
"what words are written" then you will experience uncertainty because
you don't get a strong perception of any particular words at the
category level.

Yes, so far I think we agree.

I see it as like the pandemonium model at the word
perception level where many word demons are screaming at the same
time; so it's difficult to answer the question "what does the text
say; what are the words" with any confidence.

Yes. In fact that, in slightly different words, is the description I gave in [Martin Taylor 2008.03.18.09.58] and [Martin Taylor 2008.03.22.14.22].

> The blurred image is not a perception at all.
> It is input from which
> you create perceptions at many levels.
> In it, you may perceive

  writing. Your perception of the content of that writing is uncertain.

This is where we get off. Maybe it's just a verbal thing. I would
would not say that my perception of the writing is uncertain. The
perception of the writing is what it is.

Do you mean by that your perception of the _content_ of the writing -- the sense of what is written? That's the perception I was talking about.

I would say I am uncertain
_about_ what the perception should be called.

Which seems one level below a perception of the content, if by "should be called" you mean "how it shold be sounded out" or something like that.

This is actually the
same way perceptual uncertainty is viewed in conventional psychology
as well. In signal detection theory, for example, the perception
itself is not "uncertain"; it is the basis for a decision about
whether it should be called "signal" or "noise". The uncertainty is
_about_ the perception; what it should be called. The perception
itself is not uncertain.

Maybe it is a verbal problem. If I have a perception that I am uncertain about your meaning, is my perception of your meaning uncertain? I would say it is. Perhaps you would say it isn't.

>>Me:

  > I am trying to demonstrate that that is an incorrect view
  >of the uncertainty of perception.

  I have several times said that I am trying to look for a correct view
  of the uncertainty of perception. I'm quite willing to accept that
  the view you ascribe to me (about which I am uncertain) could be
  incorrect. My only fixed point is that I do often perceive that
  particular perceptions are uncertain.

You, I believe, are simply making the mistake of ascribing the
perception of uncertainty to the perceptions themselves, the ones
about which you are uncertain.

What I am trying to do is to see how the perception of uncertainty about a paerception is and remains linked to the perception in question. I neither ascribe the uncertainty to the perception (in the sense of being a component variable in the perception) nor assert that it isn't. You, on the other hand, start with the position that it is "a mistake" to consider the possibility that a measure of uncertainty is carried along with the value of the perception.

So you see the blurred text as having
"uncertainty". I think this is a mistake -- an understandable one, by
the way -- very much like attributing "negative valence" to our
perception of objects in the world that we find unattractive. It's not
the perception of the objects themselves that has the negative
valence, of course; it's the difference between our perception our
reference for what we want the perception to be that makes the
perception seem negative.

I don't accept the analogy. I do agree about "negative valence" but my agreement is because that does fall out from the basic structure of PCT. The perception of uncertainty does not exist within any single control system other than one designed to perceive uncertainty. Such a system myst also have a second variable that identifies what it is that is uncertain, or else that identification is hard-wired into the perceptual side of the system that controls the perception that is uncertain.

You propose that the hard-wiring is not into the perceptual side of the system that controls the perception, but into the output sides of whatever higher-level signal use the "uncertain" perception, and that come into conflict because ot the possibility that the perception might represent any of several environmental possibilities. To me that sounds very complicated and hard to instantiate.

Either way, the uncertainty perception is somehow linked to the perception that is uncertain, and the question remains as to how the value of the uncertainty is created in the input function of the uncertainty perception control system.

There is no uncertainty when I don't have a reference for
perceiving what is written (what the words are).

Does that mean you can be uncertain about your perception of something only when you have a reference value for what it should be?

Martin

[rsmarken]

[From Rick Marken (2008.03.27.1400)]

Martin Taylor (2008.03.27.14.39) --

OK. Here's the quotation:
--------------------------------------
Firstly, I have not given a model, because I've only been talking
about a phenomenon,

OK.

Secondly, I have given reasons why, although I might accept your
proposal for the perception of uncertainty in some conditions, it
clearly is not acceptable under other conditions that offer a similar
subjective experience. T

OK.

Thirdly (and this is halfway new), to argue that you are perceiving
conflict is not to answer the question about how the perception of
uncertainty is linked to a perception of something concrete; it
merely moves it to a question of how the perception is linked to a
relationship between two perceptions of something more concrete.

OK.

Fourthly (also, new). the kind of conflict you (actually Bill, I
think) propose is of a kind not hitherto discussed in the context of
HPCT.

Well, it is. But it's no big deal. I think there are other,simpler way
to deal with this "uncertainty" thing anyway.

Now I have answered the questions. Let's go on.

>And how does uncertainty get into it. Is it carried along in the
>perceptual signal.

That is indeed the question at issue. Or one of several questions.
It's a question to which I am trying to work out an answer.

Well, work away. I already have an answer that satisfies me.
Uncertainty is not in perceptual signals at all; it is a judgment
about perceptions. You don't like that answer so there we jolly well
are. You go ahead and work out the answer to your satisfaction. I've
given you all the help I can.

  A model in which perceptions are complex-valued is not different
from PCT. It's just different from "classical" HPCT in which
perceptual values are real-valued scalars.

PCT isn't Coca-Cola. The idea that perceptions are scalar variables is
central to PCT. If you've got some other idea about how perceptions
should be represented in the model, then you've got a new model and
you would have to show me (anyway) why such a change is needed; what
data it accounts for that can't be accounted for by PCT.

I'm not putting that
forward as "THE" model. It's just a suggestion I made in response to
Bill P at the beginning of this subthread [Martin Taylor
2008.03.17.18:00], based on the success of one company when they used
complex-valued signals in their multilevel neural nets.

Was it a control model?Was there data they were explaining?There are
all kinds of complicated and sophisticated mathematical models going
around -- witness Modern Control Theory -- that do all kinds of
amazing things. That's nice but I'm only interested in models as a way
of understanding purposeful behavior, not models sui generis.

In it, you may perceive

>> writing. Your perception of the content of that writing is uncertain.
>
>This is where we get off. Maybe it's just a verbal thing. I would
>would not say that my perception of the writing is uncertain. The
>perception of the writing is what it is.

Do you mean by that your perception of the _content_ of the writing
-- the sense of what is written? That's the perception I was talking
about.

Yes. I don't think _any_ perception is uncertain. There is no extra
uncertainty that goes along with _any_ perception; perceptions are
just what they are. Uncertainty is a perception _about_ another
perception;uncertainty is a higher level perception that takes a
perception, such as that of the content of the writing (I presume you
mean the words, such as they can are) as input.

Maybe it is a verbal problem. If I have a perception that I am
uncertain about your meaning, is my perception of your meaning
uncertain? I would say it is. Perhaps you would say it isn't.

Let me do it in diagram form:

                --> [P1] -->p1 ("horse")

E(h*r**e)

               --> [P2]--> p2("hoarse")

E is the physical situation, such as your blurred image. In this case
I represent that physical situation as (h*r**e). P1 and P2 are
category level perceptual functions, one for the perception of the
word "horse" and the other for the perception of the word "hoarse". I
assume that these two perceptual functions put out approximately
equally strong signals so that p1 is about the same magnitude as p2.
So at the category level, E is perceived (weakly) as both "horse" and
"hoarse". There is nothing uncertain about p1 and p2; both of these
perceptions exist, albeit weakly. The uncertainty exists when, for
whatever higher level reason, I have to decide whether what I am
seeing is "really" "horse" or "hoarse". So imagine another control
system (or systems) with a perceptual function to the right that takes
both p1 and p2 as inputs; that is the system or systems that is
experiencing uncertainty; it's an experience (perception) that is
_about_ (is a function of) the ambiguous perceptions.

> There is no uncertainty when I don't have a reference for
>perceiving what is written (what the words are).

Does that mean you can be uncertain about your perception of
something only when you have a reference value for what it should be?

Not quite. I think we experience uncertainty only when we take a
perception to be evidence of some other state of affairs. In that
case, we are in the position we are in when we do experiments; we get
the data (perception) and then we have to decide whether the data
warrant rejection of the null hypothesis. In fact, we are very often
in the position of treating perceptions as evidence of some other
state of affairs, and whenever we do this we experience uncertainty.
Is the faint sound I just heard evidence that someone is at the door?
Does the drop in pressure mean that rain is on the way? Is the odd
shaped rock a fossil femur? Is the blurred text an English sentence?
But when we don't treat these same perceptions as evidence of some
other state of affairs there is no uncertainty; we just hear the
sound, see the drop in pressure, the odd shaped rock, the blurry text.
So, yes, I think "uncertainty" only exists when perceptions are
treated as evidence of something else; uncertainty is not in any way
intrinsic to the perceptions themselves.

Best

Rick

···

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

[MartinT]

[Martin Taylor 2008.03.27.23.07]

I asked Rick to address some issues with his proposal that the perception of uncertainty of a perception is actuall a perception of the existence of a conflict among the outputs of control systems that include that perception among their various inputs.

[From Rick Marken (2008.03.27.1400)]

Martin Taylor (2008.03.27.14.39) --

  OK. Here's the quotation:
  --------------------------------------
  Firstly, I have not given a model, because I've only been talking
  about a phenomenon,

OK.

Well, at least you agree there is a phenomenon. That's good.

  Secondly, I have given reasons why, although I might accept your
  proposal for the perception of uncertainty in some conditions, it
  clearly is not acceptable under other conditions that offer a similar
  subjective experience. T

OK.

Are you planning to address those reasons?

  Thirdly (and this is halfway new), to argue that you are perceiving
  conflict is not to answer the question about how the perception of
  uncertainty is linked to a perception of something concrete; it
  merely moves it to a question of how the perception is linked to a
  relationship between two perceptions of something more concrete.

OK.

Will you address this question?

  Fourthly (also, new). the kind of conflict you (actually Bill, I
  think) propose is of a kind not hitherto discussed in the context of
  HPCT.

Well, it is.

That bald assertion needs explanation. Your diagram below does not constitute such an explanation.

But it's no big deal. I think there are other,simpler way
to deal with this "uncertainty" thing anyway.

By which, I suppose you mean you have a new explanation, not the one involving this novel kind of conflict, which is rather complicated, not "simpler". You don't describe the simpler way in the message to which I am responding, but I suppose you will in a separate message.

Now I have answered the questions. Let's go on.

Huh?? "Now that I have answered the questions"? Where? When?

  >And how does uncertainty get into it. Is it carried along in the
  >perceptual signal.

  That is indeed the question at issue. Or one of several questions.
  It's a question to which I am trying to work out an answer.

Well, work away. I already have an answer that satisfies me.
Uncertainty is not in perceptual signals at all; it is a judgment
about perceptions.

We know that each uncertainty perception is about another perception. Each perception potentially has an uncertainty that might possibly be perceived. What I am looking for is some answer beyond that simple statement, an answer that addresses two issues: (1) how is the magnitude of the uncertainty computed in a perceptual input function of an uncertainty control system, and (2) how is the uncertainty linked to the perception that is perceived to be uncertain.

As to (2), your "conflict" diagram shows conflict between two systems, each of which has among its inputs the perception being judged uncertain. Among other questions raised by this baroque construction, I may ask how the perception of uncertainty is associated with the particular input that is shared between the to conflicted control systems, rather than with any of their other inputs, given that the system that peceives the uncertainty has no way of knowing what the inputs to those systems might be.

You don't like that answer so there we jolly well
are.

I can't think why you insist I don't like the statement that an uncertainty is about a perceptual signal. Is it because I have suggested the possibility that the uncertainty signal is transmitted along with the value signal?

You go ahead and work out the answer to your satisfaction. I've
given you all the help I can.

Help that consists of reiterating one mantra and refusing to consider the questions that arise from that mantra.

   A model in which perceptions are complex-valued is not different

> from PCT. It's just different from "classical" HPCT in which

  perceptual values are real-valued scalars.

PCT isn't Coca-Cola. The idea that perceptions are scalar variables is
central to PCT.

No, you are mistaken. What is central to PCT is that behaviour is the control of perception. What form a "perception" takes is central to a particular flavour of PCT. Even HPCT could be constructed with complex-valued signals, though "classic" HPCT is not.

If you've got some other idea about how perceptions
should be represented in the model, then you've got a new model and
you would have to show me (anyway) why such a change is needed; what
data it accounts for that can't be accounted for by PCT.

You are correct in this, provided that for "accounted for by PCT" you substitute "accounted for by classical HPCT".

I'm not putting that
  forward as "THE" model. It's just a suggestion I made in response to
  Bill P at the beginning of this subthread [Martin Taylor
  2008.03.17.18:00], based on the success of one company when they used
  complex-valued signals in their multilevel neural nets.

Was it a control model?Was there data they were explaining?

They were not explaining anything. They were using neural nets in a practical (indeed potentially life-threatening) situation to categorize or to evaluate rather noisy data that were proving intractable for conventional neural nets, or that needed many more nodes in the conventional nets to categorize the same data. Since the perceptual side of a classical HPCT hierarchy is exactly a perceptron, it seemed (and seems) to me not unreasonable that we might have evolved similar ways to improve our abilities to extract the sense of the environment into the perceptions that we control.

> >This is where we get off. Maybe it's just a verbal thing. I would

>would not say that my perception of the writing is uncertain. The
>perception of the writing is what it is.

  Do you mean by that your perception of the _content_ of the writing
  -- the sense of what is written? That's the perception I was talking
  about.

Yes. I don't think _any_ perception is uncertain. There is no extra
uncertainty that goes along with _any_ perception; perceptions are
just what they are. Uncertainty is a perception _about_ another
perception;

So far, OK.

uncertainty is a higher level perception that takes a
perception, such as that of the content of the writing (I presume you
mean the words, such as they can are) as input.

Here's where we part company, at "higher level". In classical HPCT, each level has its own characteristic type -- intensities, sequences, categories, events, principles, systems, etc. I have not yet heard of a level called "uncertainties". And yet we can perceive our own uncertainty about a perception at any of those levels. For me, it is usually the case that the higher the level, the grater the uncertainty associated with my perceptions. In classical HPCT, level-jumping is not exactly forbidden on the perceptual side of the hierarchy, but I know of no case up to now in which every level (including systems and principles) is expected to have its perceptual signal jump to the input functions at one specified "higher level".

> Maybe it is a verbal problem. If I have a perception that I am

  uncertain about your meaning, is my perception of your meaning
  uncertain? I would say it is. Perhaps you would say it isn't.

Let me do it in diagram form:

                --> [P1] -->p1 ("horse")

E(h*r**e)

               --> [P2]--> p2("hoarse")

E is the physical situation, such as your blurred image. In this case
I represent that physical situation as (h*r**e). P1 and P2 are
category level perceptual functions, one for the perception of the
word "horse" and the other for the perception of the word "hoarse".

Fine.

I
assume that these two perceptual functions put out approximately
equally strong signals so that p1 is about the same magnitude as p2.

Unnecessary limitation, since one could be much stronger than the other. But let that pass.

So at the category level, E is perceived (weakly) as both "horse" and
"hoarse". There is nothing uncertain about p1 and p2; both of these
perceptions exist, albeit weakly.

What does a "weak" perception mean, at the category level? Is "weakness" at the category level the same as uncertainty about whether the input data are consistent with membership in the category? If so, then there's no need for the conflict construction, but if not, what is signified by a "weak" category perception?

The uncertainty exists when, for
whatever higher level reason, I have to decide whether what I am
seeing is "really" "horse" or "hoarse". So imagine another control
system (or systems) with a perceptual function to the right that takes
both p1 and p2 as inputs; that is the system or systems that is
experiencing uncertainty; it's an experience (perception) that is
_about_ (is a function of) the ambiguous perceptions.

OK. I accept this as quite plausible, but it leaves two problems, numbered 2 and 3 in my list of four. I don't believe it satisfies number 4, either, but we can let that pass.

> There is no uncertainty when I don't have a reference for
  >perceiving what is written (what the words are).

  Does that mean you can be uncertain about your perception of
  something only when you have a reference value for what it should be?

Not quite. I think we experience uncertainty only when we take a
perception to be evidence of some other state of affairs.

I am uncertain what you mean by "some other state of affairs". Aren't all perceptions evidence of some state of affairs outside the control system in question?

In that
case, we are in the position we are in when we do experiments; we get
the data (perception) and then we have to decide whether the data
warrant rejection of the null hypothesis.

[Aside: This is a statement about psychological statistics against which I have argued since my days in graduate school. But that's a different thread, and one not for this mailing list.]

In fact, we are very often
in the position of treating perceptions as evidence of some other
state of affairs, and whenever we do this we experience uncertainty.
Is the faint sound I just heard evidence that someone is at the door?

Otherwise stated: "I have an uncertain perception that someone is at the door." The faint sound is a clear perception. It provides one of the many possible inputs to the perception of someone at the door.

Does the drop in pressure mean that rain is on the way? Is the odd
shaped rock a fossil femur? Is the blurred text an English sentence?
But when we don't treat these same perceptions as evidence of some
other state of affairs there is no uncertainty; we just hear the
sound, see the drop in pressure, the odd shaped rock, the blurry text.

Exactly. Clear perceptions at one level can contribute to the input functins that create uncertain perceptions at another level.

So, yes, I think "uncertainty" only exists when perceptions are
treated as evidence of something else; uncertainty is not in any way
intrinsic to the perceptions themselves.

I'm intrigued by your notion that some of the things we consciously perceive are not "perceptions" (in your examples, the person at the door, the impending rain, the femur, the text).

If they aren't perceptions, what are they, within the construct of HPCT?

Martin

[rsmarken]

[From Rick Marken (2008.03.27.2240)]

Martin Taylor (2008.03.27.23.07) --

We know that each uncertainty perception is about another perception.
Each perception potentially has an uncertainty that might possibly be
perceived.

In the sense that each perception could be taken as evidence of some
state of affairs, yes.

What I am looking for is some answer beyond that simple
statement, an answer that addresses two issues: (1) how is the
magnitude of the uncertainty computed in a perceptual input function
of an uncertainty control system

It's probably different in different situations. In the tone detection
experiment, my guess is that the "magnitude of uncertainty" is
inversely related to the perception of loudness and tone-ness in a
frequency/time band surrounding the frequency/time location of the
tone (when it is added). At least, so says the results of my doctoral
dissertation.

and (2) how is the uncertainty
linked to the perception that is perceived to be uncertain.

I don't understand the problem there. I presume the perception of
uncertainty is linked to the perception that is perceived to be
uncertain via the "uncertainty" perceptual function that takes the
perception that is perceived to be uncertain as one of its inputs.

As to (2), your "conflict" diagram shows conflict between two
systems, each of which has among its inputs the perception being
judged uncertain. Among other questions raised by this baroque
construction, I may ask how the perception of uncertainty is
associated with the particular input that is shared between the to
conflicted control systems, rather than with any of their other
inputs, given that the system that peceives the uncertainty has no
way of knowing what the inputs to those systems might be.

I don't understand the problem; since when does a system having a
perception, like uncertainty, need to know the inputs to the
perceptual function that creates that perception? I can have (and
control) the perception of line position without knowing the lower
level perceptions that contribute to that perception.

I can't think why you insist I don't like the statement that an
uncertainty is about a perceptual signal. Is it because I have
suggested the possibility that the uncertainty signal is transmitted
along with the value signal?

Yes.

>Yes. I don't think _any_ perception is uncertain. There is no extra
>uncertainty that goes along with _any_ perception; perceptions are
>just what they are. Uncertainty is a perception _about_ another
>perception;

So far, OK.

>uncertainty is a higher level perception that takes a
>perception, such as that of the content of the writing (I presume you
>mean the words, such as they can are) as input.

Here's where we part company, at "higher level". In classical HPCT,
each level has its own characteristic type -- intensities, sequences,
categories, events, principles, systems, etc. I have not yet heard of
a level called "uncertainties".

I think uncertainty is a logic or program type of perception. It's a
perception like:

if (p>c) then p1 is probably true.

And yet we can perceive our own
uncertainty about a perception at any of those levels.

This is an interesting empirical question. If uncertainly is, as I
hypothesize, a program type perception and if the hierarchical
perceptual control model is correct then it should be impossible to
perceive the uncertainty of perceptual types above that level; so we
should be unable to be uncertain about principles and system concepts.

For me, it is
usually the case that the higher the level, the grater the
uncertainty associated with my perceptions.

Could you describe an example of that kind of uncertainty?

>Not quite. I think we experience uncertainty only when we take a
>perception to be evidence of some other state of affairs.

I am uncertain what you mean by "some other state of affairs". Aren't
all perceptions evidence of some state of affairs outside the control
system in question?

No, I think perceptions are our experience of the current "state of
affairs"; they are not usually treated as evidence of some state of
affairs outside the control system (only philosophers treat them that
way, and only when they are on duty;-)) nor are they often treated as
evidence of some other possible perception (I don't treat every sound
I hear as evidence that someone is at the door or that the house is
settling; it's just sounds).

>Does the drop in pressure mean that rain is on the way? Is the odd
>shaped rock a fossil femur? Is the blurred text an English sentence?
>But when we don't treat these same perceptions as evidence of some
>other state of affairs there is no uncertainty; we just hear the
>sound, see the drop in pressure, the odd shaped rock, the blurry text.

Exactly. Clear perceptions at one level can contribute to the input
functins that create uncertain perceptions at another level.

Right on!

>So, yes, I think "uncertainty" only exists when perceptions are
>treated as evidence of something else; uncertainty is not in any way
>intrinsic to the perceptions themselves.

I'm intrigued by your notion that some of the things we consciously
perceive are not "perceptions" (in your examples, the person at the
door, the impending rain, the femur, the text).

If they aren't perceptions, what are they, within the construct of HPCT?

Sorry, I stated it poorly. I should have said:

So, yes, I think "uncertainty" only exists when perceptions are
treated as evidence of other possible perceptions, like the perception
of a sound being evidence that I could go to the door and perceive
someone there;uncertainty is not in any way
intrinsic to the perceptions themselves.

How's that? Now we are all agreement, yes?

Best regards

Rick

···

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

[MartinT]

[Martin Taylor 2008.03.30.10.01]

[From Rick Marken (2008.03.27.2240)]

How's that? Now we are all agreement, yes?

Unfortunately, no. Not yet, though we may be getting closer.

One of the things I like about arguing with you is that it makes me clarify my own thoughts. I believe we both believe this material is important, and we are not playing word games or one-upmanship. That belief means that even when I simply don't understand why you put things the way you do, or initially think something is silly, I find it worthwhile to try to go into the issue deeply enough that we can be assured we are on common ground apart from three possibilities:

1. You know something I don't.
2. I know something you don't.
3. We know the same things but use them to make different intepretations.

To find out which of these applies to any particular disagreement is often a problem. It gets obscured in verbal battles on details that usually prove irrelevant to the issue. That's hard to avoid. For example, even now, I'm not clear that the word "uncertainty" means the same to you as to me. If that is so, it may be why it is so hard to come to a common understanding.

And now, back to the matter at hand.

> Martin Taylor (2008.03.27.23.07) --

  We know that each uncertainty perception is about another perception.
  Each perception potentially has an uncertainty that might possibly be
  perceived.

In the sense that each perception could be taken as evidence of some
state of affairs, yes.

Here's a place where I don't understand your meaning. Let me try to clarify what I mean by "uncertainty perception is about another perception".

We presume the existence of an exterior reality. A perception is an internal value that is a function of some properties of that external reality and of some internal states. I see the words "function of some properties of that external reality" as equivalent to "evidence of some state of affairs".

If you accept that, we are on common ground, and I will assume that to be the case. If you mean something else, you must clarify.

A perception is a value, but for various reasons including the influences of other internal states and influences, external and internal, that we can collectively call "noise", the perceptual value is not always the same even for a given set of values of the external properties. Conversely, the same perceptual value can arise for different values of the external properties.

I'm not talking here about the kind of "different values" that arise in, say, x = a + b, where a = 4, b = 1 gives x the same value as a = 2, b = 3. I'm talking about x = (a + b) + n, where n is the influence of the other factors, so that x = 5 can mean a+b = 6, n = -1 or a+b = 4, n = 1. Here, "x" is the perceived value of a+b.

You may ask "why is not x a perception of a + b + n rather than of a + b"?" There are two answers, one fairly trivial, the other deeper. The trivial answer is that "n" includes a changing variety of influences including internal ones such as hormone levels, randomness in neural firing rates, and the like. The control actions affect (a+b), not the contributors to "n". The deeper one deserves a thread on its own, since it touches on why PCT allows us to assert the existence of an external reality -- through control that can change x by influencing the perceived values of a or b.

What I am coming to is my understanding of "uncertainty", which is based on the fact if the perception "x" has a given value, the value of "a+b" is not always the same. The "uncertainty" of the perception "x" is derived from the range of values of "a+b" consistent with that value of "x".

I can read that as being consistent with your "each perception could be taken as evidence of some state of affairs", if "x" is the perception and "a+b" is the state of affairs. If you don't think it is consistent, then please take up the argument there. Meanwhile, I will continue on the assumption of consistency.

> What I am looking for is some answer beyond that simple

  statement, an answer that addresses two issues: (1) how is the
  magnitude of the uncertainty computed in a perceptual input function
  of an uncertainty control system

It's probably different in different situations. In the tone detection
experiment, my guess is that the "magnitude of uncertainty" is
inversely related to the perception of loudness and tone-ness in a
frequency/time band surrounding the frequency/time location of the
tone (when it is added). At least, so says the results of my doctoral
dissertation.

Those do indeed seem to be the physical factors that affect the uncertainty as to whether the tone was explicitly presented (and of the perception of its pitch, too). The surrounding frequency-time band takes the place of "n" in "x = (a+b) + n" above. The uncertainty about whether the tone was presented takes the form of a perceived probability that it was, and the uncertainty about its pitch takes the form of a probability density distribution about the most likely frequency (as you know, but others may not, "frequency" is physical, and is an important influence, but not the only influence, on the subjective property "pitch"). In both cases (existence and pitch) the value of the perception "x" is clear, and the uncertainty is about the value of "a+b", to which "x" corresponds.

> and (2) how is the uncertainty

  linked to the perception that is perceived to be uncertain.

I don't understand the problem there. I presume the perception of
uncertainty is linked to the perception that is perceived to be
uncertain via the "uncertainty" perceptual function that takes the
perception that is perceived to be uncertain as one of its inputs.

I would presume that, too. But your "conflict" diagram does not show such a connection. The perception presumed to be uncertain doesn't appear among the inputs to whatever computes its uncertainty, at least not directly. It appears only because it happens to be among the contributors to two category perceptual units that cannot co-occur -- i.e. cannot both say "it's my category" simultaneously.

[Aside: In itself, "cannot co-occur" suggests a cross-linkage among control units at the same level. Such cross-linkages do not occur in "classical" HPCT, which isn't an argument against the concept, though it does require a modification to HPCT.]

The more difficult issue is with the example of pitch uncertainty, where the uncertainty is about the frequency of the tone that gives rise to the perception of pitch. No conflict arises in this case, since the plausible frequencies occupy a continuum of possibilities.

My question in both cases relates to your insistence that the data that give rise to the perception of uncertainty about a perception cannot be carried along with the perception. If you are right, the data that permit the perception of uncertainty are either derived from the perception itself or are carried by some independent pathway. If the former, the question is "how?". It cannot be from the statistics of long observation, because brief flashes usually yield more uncertain perceptions than do continued observation -- the perception of pitch is very much a case in point. If the uncertainty data are carried on a separate pathway, the question again arises as to how the perception of uncertainty is linked to every perception that might possibly be uncertain in the sense described above.

> I can't think why you insist I don't like the statement that an

  uncertainty is about a perceptual signal. Is it because I have
  suggested the possibility that the uncertainty signal is transmitted
  along with the value signal?

Yes.

Why should that be inconsistent with the uncertainty being about the value that it accompanies? It seems to me that if the uncertainty signal propagates alongside the value signal, it is a strong indicator that the uncertainty is about that value. I suspect a misunderstanding here of a kind I can't identify.

> >uncertainty is a higher level perception that takes a

  >perception, such as that of the content of the writing (I presume you

> >mean the words, such as they can are) as input.

  Here's where we part company, at "higher level". In classical HPCT,
  each level has its own characteristic type -- intensities, sequences,
  categories, events, principles, systems, etc. I have not yet heard of
  a level called "uncertainties".

I think uncertainty is a logic or program type of perception. It's a
perception like:

if (p>c) then p1 is probably true.

or, in the example of pitch perception, assuming p' (frequency, the 'state of affairs, to use your words) is the outer-world variable corresponding to p (pitch), "if p = x, then p' has a probability P of being within e of x'", where P and e have some functional relationship.

  And yet we can perceive our own
  uncertainty about a perception at any of those levels.

This is an interesting empirical question. If uncertainly is, as I
hypothesize, a program type perception and if the hierarchical
perceptual control model is correct then it should be impossible to
perceive the uncertainty of perceptual types above that level; so we
should be unable to be uncertain about principles and system concepts.

About our perceptions of their current states, yes. However, I find myself usually quite uncertain about systems concepts. Isn't much of science an attempt to develop systems that conform to normal experience? Isn't much og maturation the ability to be more able to perceive accurately at higher and higher perceptual levels? It seems to me that it is precisely these higher levels about which we are most uncertain -- not, perhaps, about our refeence values for them, but about their perceptual values.

So, yes, I think "uncertainty" only exists when perceptions are
treated as evidence of other possible perceptions, like the perception
of a sound being evidence that I could go to the door and perceive
someone there;uncertainty is not in any way
intrinsic to the perceptions themselves.

How's that? Now we are all agreement, yes?

Apparently not, but there seem to be some signs of convergence. It is a problem that is worth clarifying.

Martin

PS. I may not be able to devote much more time to this in the near future. In two weeks I wil be away for three weeks, and there's a lot of preparation to do for the meeting that begins that sojourn. Apart from rounding up all the data to do my taxes

[rsmarken]

[From Rick Marken (2008.03.30.1010)]

Martin Taylor (2008.03.30.10.01) --

Here's a place where I don't understand your meaning. Let me try to clarify
what I mean by "uncertainty perception is about another perception".

We presume the existence of an exterior reality. A perception is an
internal value that is a function of some properties of that external
reality and of some internal states. I see the words "function of some
properties of that external reality" as equivalent to "evidence of some
state of affairs".

If you accept that, we are on common ground, and I will assume that to be
the case. If you mean something else, you must clarify.

I think you've put your finger on the basic difference between our
points of view on perception and, at the same time, the basic
difference between the PCT and conventional psychological view of
perception. In conventional psychology (and in the minds of many lay
people) perception is "evidence of some external state of affairs". I
don't see perception that way at all. I do think of perceptions as
functions of aspects of an external reality. But I don't think that is
equivalent to their being evidence of some state of affairs in that
external reality. I don't treat my own perceptions that way and I
don't believe they are treated that way in PCT. For example, I don't
treat my perception of the letters I'm typing as evidence about some
external state of affairs; they are simply letters what I control by
pressing the appropriate keys on the keyboard. I don't treat the
letters as evidence of the physical situations (the pixels, light
waves or packets, etc) that causes them, via my perceptual functions.

from a phenomenological point of view perceptions _are_ reality; they
are external reality rom my perspective. When going about my ordinary
business of controlling my perceptual experience, I have never treated
my perceptions as evidence of the state of some external reality; I
treat my perceptions _as_ external reality. Sometimes I take these
perceptions as evidence of other possible _perceptions_, such as when
I take the perception of the faint knock at the door as evidence that
a person is at the door. But, except when I'm in a physics lab, I
don't treat the perceptions themselves -- like the faint knock -- as
evidence of their cause in external reality -- the acoustical pressure
waves that presumably cause oscillations in my middle ear bones, etc.

A perception is a value, but for various reasons including the influences
of other internal states and influences, external and internal, that we can
collectively call "noise", the perceptual value is not always the same even
for a given set of values of the external properties. Conversely, the same
perceptual value can arise for different values of the external properties.

This is a theory of perception. My own perceptions are rarely "noisy",
except for my perceptions of noise itself. And whether the physical
cause of those perceptions is exactly the same on different occasions
is rarely of concern to me. I know that it's true, but it's never a
concern. For example. the fact that the configuration "t" is always
made by slightly different combinations of pixels is irrelevant to me
as I control my perceptions of the words I type.

What I am coming to is my understanding of "uncertainty", which is based on
the fact if the perception "x" has a given value, the value of "a+b" is not
always the same. The "uncertainty" of the perception "x" is derived from the
range of values of "a+b" consistent with that value of "x".

I can read that as being consistent with your "each perception could be
taken as evidence of some state of affairs", if "x" is the perception and
"a+b" is the state of affairs.

This is not at all what I meant. You are talking about the perception
as being ambiguous evidence of the physical state of affairs that is
the basis of perception. I don't think anyone but a physicist or
philosopher ever experiences that kind of uncertainty about a
perception. The uncertainty I'm talking about is quite different; it's
more like uncertainty about what _might be perceived_ given what _is
perceived_. It is an uncertainty that exiist only when we treat
perceptions as _evidence_ about the state of the world (which is
really evidence of other perceptions because we can only know the
world as perception). The faint knock a the door is a perception; no
uncertainty about that. It is a controllable perception. If I want it
to be louder I can move toward the source; if I want it to be softer I
can move away or put my fingers in my ears. The sound is a perfectly
certain, controllable perception. If, for some higher level reason
(because I am expecting a guest, say) I treat the sound as evidence of
someone being at the door then the faintness of the sound may lead me
to be uncertain that the sound was produced by someone at the door.

So, all in all, I think the problem we have with "uncertainly" comes
from our having very different ideas about the nature of perception.
You think that because perception is a function of physical variables
that it is (uncertain) evidence of the physical situation that caused
the perception. I think perception is a function of physical
variables, period.

Good luck on the taxes. I already finished mine.

Best regards

Rick

···

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

[MartinT]

Re: Uncertainty (was second-order and third-order
beliefs)
[Martin Taylor 2008.03.30.15.35]

[From Rick Marken (2008.03.30.1010)]

Martin Taylor (2008.03.30.10.01) –

Here’s a place where I don’t understand your meaning. Let
me try to clarify

what I mean by “uncertainty perception is about another
perception”.

We presume the existence of an exterior reality. A
perception is an

internal value that is a function of some properties of that
external

reality and of some internal states. I see the words
"function of some

properties of that external reality" as equivalent to
"evidence of some

state of affairs".

If you accept that, we are on common ground, and I will
assume that to be

the case. If you mean something else, you must clarify.

I think you’ve put your finger on the basic difference between our

points of view on perception and, at the same time, the basic

difference between the PCT and conventional psychological view of

perception. In conventional psychology (and in the minds of many
lay

people) perception is “evidence of some external state of
affairs”. I

don’t see perception that way at all. I do think of perceptions as

functions of aspects of an external reality.

OK. You have me more confused than ever. If a perception is a function
of aspects of an external reality, how can it not be evidence of some
external state of affairs? Here’s the canonical control loop (I prefer
to put the sign inversion in the PIF, to make clear the symmetry
between the two external inputs. It makes no difference to the
maths).

In the canonical control diagram, how do you conceive the
relation between the perception p and the external state of affairs at
the conjunction of o and d? Isn’t the value of p at least some
evidence as to the state of affairs at that conjunction? Doesn’t the
fact that varying o consistently tends to vary p argue that p is
evidence for the state at the conjunction?

But I don’t think that is

equivalent to their being evidence of some state of affairs in
that

external reality. I don’t treat my own perceptions that way and I

don’t believe they are treated that way in PCT. For example, I
don’t

treat my perception of the letters I’m typing as evidence about
some

external state of affairs; they are simply letters what I control
by

pressing the appropriate keys on the keyboard.

Don’t you act as though the letters actually exist in the
external world on the screen or paper? If you perceived that nothing
changed on the screen or paper when you typed, or that an “r”
appeared when you had intended a “t”, wouldn’t you consider
that as evidence that something had gone wrong with your control?
Wouldn’t you think your perception was some kind of evidence about
whether there was a letter, and about what letter it was?

I don’t treat the

letters as evidence of the physical situations (the pixels, light

waves or packets, etc) that causes them, via my perceptual
functions.

What do these lower-level perceptions or theoretical constructs
have to do with the relation between your perception of the letters
and the external state of affairs regarding the letters – the
presumed existence of the letters on the screen or on the paper in the
external world?

From a phenomenological point of view
perceptions are reality; they

are external reality rom my perspective.

Indeed they are. How do you square that with a statement that they are
NOT evidence of the external reality?

When going about my ordinary

business of controlling my perceptual experience, I have never
treated

my perceptions as evidence of the state of some external reality;
I

treat my perceptions as external reality.

As do we all, except when we suspect that the perception might be
illusory or based on too little evidence.

Sometimes I take these

perceptions as evidence of other possible perceptions, such as
when

I take the perception of the faint knock at the door as evidence
that

a person is at the door. But, except when I’m in a physics lab,
I
don’t treat the perceptions themselves –
like the faint knock – as

evidence of their cause in external reality – the acoustical
pressure

waves that presumably cause oscillations in my middle ear bones,
etc.

Who would? I’m puzzled as to what you think you understand about
what I have been saying. You keep bringing in things like wave packets
and acoustical pressure waves, which, though they may be the physical
means of affecting our sensors, have very little to do with the
uncertainties of our perceptions beyond that role. I can imagine you
as a gentleman of the 18th century, being brought a message saying
that your father was ill, complaining that the severity of the disease
couldn’t be perceived because you hadn’t been informed whether the
courier had a white horse. You would, however, be certain of your
perception of the severity of the disease.

The situation you describe certainly can give rise to one kind of
uncertainty, the recognition of missing inputs to a perceptual input
function. Which leads to a question of how you perceive the
“missingness” of the information that would allow you to be
more sure of whether there is a person at the door. The perception of
uncertainty, though, is about the perception of the presence of the
person. Another possible uncertainty at a different level is about
whether the knock you faintly heard actually came from something
hitting the door, because if it didn’t, it is no evidence for (or
against) a person being there. You could imagine a host of reasons for
that sound to have occurred

A perception is a value, but
for various reasons including the influences

of other internal states and influences, external and internal,
that we can

collectively call “noise”, the perceptual value is not
always the same even

for a given set of values of the external properties. Conversely,
the same

perceptual value can arise for different values of the external
properties.

This is a theory of perception. My own perceptions are rarely
“noisy”,

except for my perceptions of noise itself. And whether the
physical

cause of those perceptions is exactly the same on different
occasions

is rarely of concern to me. I know that it’s true, but it’s never
a

concern. For example. the fact that the configuration “t” is
always

made by slightly different combinations of pixels is irrelevant to
me

as I control my perceptions of the words I type.

It’s also irrelevant to the uncertainty I was talking about,
which could be exemplified by “is it a 1 (one) or an l (ell) (or
a t or an f or an i or an r)?”

What I am coming to is my
understanding of “uncertainty”, which is based on

the fact if the perception “x” has a given value, the
value of “a+b” is not

always the same. The “uncertainty” of the perception
“x” is derived from the

range of values of “a+b” consistent with that value of
“x”.

I can read that as being consistent with your "each
perception could be

taken as evidence of some state of affairs", if “x”
is the perception and

“a+b” is the state of affairs.
This is not at all what I meant. … The
uncertainty I’m talking about is quite different; it’s
more like uncertainty about what might
be perceived given what _is

perceived_.

Yes. Your is a different source of uncertainty, and it’s
uncertainty about a different thing – imagination.

It is an uncertainty that exiist
only when we treat

perceptions as evidence about the state of the world (which is

really evidence of other perceptions because we can only know the

world as perception). The faint knock a the door is a perception;
no

uncertainty about that. It is a controllable perception. If I want
it

to be louder I can move toward the source; if I want it to be softer
I

can move away or put my fingers in my ears.

You can’t. It only happened once.

The sound is a perfectly

certain, controllable perception. If, for some higher level reason

(because I am expecting a guest, say) I treat the sound as evidence
of

someone being at the door then the faintness of the sound may lead
me

to be uncertain that the sound was produced by someone at the
door.

And what do you do then? Do you act to gather more information
relevant to the “person at the door” perception? If so, then
you are treating it in just the same way as when you deblur the
blurred pseudo-writing (assuming you have control over the degree of
blur), or when you change the font to see whether a letter is 1 or l,
or 8 or 0. You perceive that there is uncertainty about the
perception, and you act to control that uncertainty perception to a
fairly low reference level.

So, all in all, I think the problem we
have with “uncertainly” comes

from our having very different ideas about the nature of
perception.

Possibly, but I am uncertain about that. If you accept the basic
nature of the control loop, as in the diagram, I don’t see how we can
have very different ideas about the nature of perception.

You think that because perception is a
function of physical variables

that it is (uncertain) evidence of the physical situation that
caused

the perception. I think perception is a function of physical

variables, period.

Those statement are not inconsistent with each other. I believe
both that perception is a function of physical variables inside and
outside the brain, and that it is uncertain evidence of a state of the
world (not necessarily a physical state – I can be uncertain about
the commitment of our current Prime Minister or your President to the
fundamental principles of democracy, an uncertainty that has very
little to do with the pixels involved in reading the paper or watching
the news on TV.

Good luck on the taxes. I already
finished mine.

Thanks. I believe your deadline is before ours, but also I
imagine you are more careful in keeping you records straight than I am

Martin

[MartinT]

Re: Uncertainty (was second-order and third-order
beliefs)
[Martin Taylor 2008.03.30.16.27]

Postscript.

[From Rick Marken (2008.03.30.1010)]

Martin Taylor (2008.03.30.10.01) –

Here’s a place where I don’t understand your meaning. Let
me try to clarify

what I mean by “uncertainty perception is about another
perception”.

We presume the existence of an exterior reality. A
perception is an

internal value that is a function of some properties of that
external

reality and of some internal states. I see the words
"function of some

properties of that external reality" as equivalent to
"evidence of some

state of affairs".

If you accept that, we are on common ground, and I will
assume that to be

the case. If you mean something else, you must clarify.

I think you’ve put your finger on the basic difference between our

points of view on perception and, at the same time, the basic

difference between the PCT and conventional psychological view of

perception. In conventional psychology (and in the minds of many
lay

people) perception is “evidence of some external state of
affairs”. I
don’t see perception that way at
all.

…

What I am coming to is my understanding of
“uncertainty”, which is based on

the fact if the perception “x” has a given value, the
value of “a+b” is not

always the same. The “uncertainty” of the perception
“x” is derived from the

range of values of “a+b” consistent with that value of
“x”.

I can read that as being consistent with your "each
perception could be

taken as evidence of some state of affairs", if “x”
is the perception and

“a+b” is the state of affairs.

This is not at all what I meant. You are talking about the
perception

as being ambiguous evidence of the physical state of affairs that
is

the basis of perception. I don’t think anyone but a physicist
or

philosopher ever experiences that kind of uncertainty about a

perception.

Here’s a diagram of what I mean. Maybe it will make it a little
clearer. The “state of affairs” is at the conjunction of o
and d.

I hope this helps.

Martin

[Bill_Powers1]

[From Bill Powers (2008.03.30.1045 MDT)]
Martin Taylor 2008.03.30.16.27 –
… and Rick Marken.
It’s been useful to watch this interchange without getting involved for a
few days. I think the basic problem here is that there isn’t any
agreement on what “uncertainty” means. Martin thinks there can
be an “uncertainty signal” accompanying every perceptual
signal; Rick thinks uncertainty is in the perceptual input functions of
the beholder and is just an attitude toward other perceptions. I think
it’s a queasy feeling in the pit of the stomach that comes from having to
do something but not knowing what to do. But what is uncertainty, really?
One way to define it is in terms of variability. But that would mean that
in any single sample of a perceptual signal, there is never any
uncertainty, because variability exists only in multiple samples.
So suppose we have a perception p which varies over a set of samples as
sin(n) + R, where R is a random variable. This gives us the following
series of readings: p = (0.7,2.2.,-0.4. 0.01, 1.06). and on and on. Is
there anything uncertain about this series of readings? Rick says no;
Martin sort of agrees, and I agree too. That is exactly the set of
readings (perceptions) that was obtained. So where is any uncertainty? We
might say it is in the hypothesis that this series of numbers come a sine
function plus a random variable. We might feel quite uncertain about that
hypothesis, since any series of numbers at all would fit it, unless we
were a lot more specific about the random variable’s distribution and
mean. Any uncertainty would arise only at higher levels of analysis. And
it could be mistaken: maybe the series of numbers is an exact
representation of exactly how some real mechanism behaved.
In the case of the smoothed random disturbances I use in tracking
experiments, that is exactly the case. The disturbance is a
computer-generated pattern that varies through time in a way that seems
unpredictable (and hence uncertain) more than a few tenths of a second
into the future – yet if the “randomize” function isn’t used,
running the program a second time will generate exactly the same
pattern of disturbances. It is completely determinate and not uncertain
at all. In fact even with the “randomize” function in use to
reset the random seed from the system clock, the waveform remains totally
determinate – although nobody human who doesn’t know the exact system
time could predict it, and every such human would be almost totally
uncertain about its future values. So this tells us we can be uncertain
about a perception of a completely determinate variable. The uncertainty
arises not from the presumed thing being perceived, but strictly from the
observer’s inability to find any way to predict it.

How, then, would we be able to generate a complex number with one number
representing the perceived value of the external variable, and the second
number representing the uncertainty in that external variable? We
couldn’t, because there is no uncertainty in the external variable to
detect.

The only uncertainty that is available to be detected is in some
higher-level perceptual signal, say one that represents an expected value
of a perception derived by a specific algorithm from completely certain
lower-level perceptions. Another still higher-level input function might
then compare the expected value with the observed value when it happens,
and from that derive a signal indicating the average amount of error in
the prediction, which would represent the uncertainty. Of course these
are just levels inside the program level, levels of of organization of a
program rather than fundamental levels of perception. I have thus offered
a definition of uncertainty.

Even in the case of h**r*e, which can (with the help of imagination) be
perceived both as “hoarse” and “hearse” by different
perceptual input functions at the configuration level, there is no
uncertainty until it is necessary to make a decision based on a guess as
to what the original word was. This is Rick’s “conflict”
version of uncertainty about categorization. Does the string of letters
indicate a class of animals, or a class of mortuary equipment? It can be
perceived both ways, but logic tells us that objects nust be in one or
another class if they’re mutually-exclusive, so we must decide, and a
decision is a conflict that must be resolved. Since there are missing
letters, there is no way to decide what the letters “really”
were before the snow on the screen obliterated them. All we can do is
consider the surrounding context, if it’s relevant, or resort to
crank-turning statistics and ask how often the letters present go with
various combinations of the missing ones. The error bars in the
statistics then measure the uncertainty of the guess on which we base the
decision. And note that it’s impossible to perceive the uncertainty in a
single instance.

The biggest problem is that only the experimenter can know how many times
the word was really “hearse” and how many times it was
“hoarse,” so only the experimenter can perceive the actual
uncertainty in the situation presented to the subject.

Any other definitions of uncertainty?

Best,

Bill P.

···

[rsmarken]

[From Rick Marken (2008.03.31.0920)]

Bill Powers (2008.03.30.1045 MDT)

It's been useful to watch this interchange without getting involved for a
few days. I think the basic problem here is that there isn't any agreement
on what "uncertainty" means.

I think that's kind of true. Though I have been working under the
assumption that we had agreed that a tone detection experiment is the
prototype of what we are calling "uncertainty". In that experiment,
the subject listens to noise bursts, some of which have a tone added
and some of which don't, and says whether each noise burst contained a
tone or not. In this case the uncertainty is of the type you describe:
"a queasy feeling in the pit of the stomach that comes from having to
do something but not knowing what to do", which is the same as my idea
of uncertainty. In the tone detection experiment, you often don't know
(are in conflict about) whether to say "tone" or "no tone" about a
noise burst.

I would be happy for you to continue this conversation with Martin; I
can't make heads or tails of it anymore. For example, I have no idea
how to deal the the diagram in Martin's "Postscript" post (Martin
Taylor 2008.03.30.16.27). Perhaps Martin could explain how this would
apply to a compensatory tracking task, for example. Where in the
actual tracking task is the distortion and noise that is shown to
enter the PIF after the cursor position (o+d) is displayed?

Best

Rick

···

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

[Bill_Powers1]

[From Bill Powers (2008.03.30.1140 MDT)]

Rick Marken (2008.03.31.0920) --

"a queasy feeling in the pit of the stomach that comes from having to
do something but not knowing what to do", which is the same as my idea
of uncertainty. In the tone detection experiment, you often don't know
(are in conflict about) whether to say "tone" or "no tone" about a
noise burst.

I still don't see "not knowing what to say" as the uncertainty which leads to not knowing what to say. It's the uncertainty that comes first, then not knowing what to say, as I see it. If you didn't have to say something, you would still be uncertain, wouldn't you? "Everyone please Xp#c$%u&^! their books immediately" -- what is it you're supposed to do with your books? You don't even know what the sentence means, and the not-knowing leads to that feeling of uncertainty.

Anyhow, that just supports the idea that we don't have a common definition of uncertainty, so there's no way to talk about it yet. If you have to say "Don't quibble, everyone knows what uncertainty is," you have basically abandoned rational discourse.

Perhaps Martin could explain how this would apply to a compensatory tracking task, for example. Where in the actual tracking task is the distortion and noise that is shown to enter the PIF after the cursor position (o+d) is displayed?

I think the issue is just how much uncertainty there is in normal perceptions. And actually, in the tracking task, I think a conventional analysis would say there is a lot of uncertainty in the cursor position, because it's being disturbed by an invisible influence derived from a table of random numbers. To the control system, however, there's very little difference between controlling the disturbed and the undisturbed cursor when tracking a moving target: the organization of the control system remains exactly the same in either case. If you change the disturbance from random to sinusoidal, you improve the control only by a tiny amount -- it certainly doesn't become perfect just because the disturbance is regular. Whatever the effect on control of uncertainty in this task, it's really very small unless you go to an extreme amount of masking of the perception -- an amount that hardly ever occurs in nature, or that occurs only twice a day in deep twilight.

Read my "essay on the obvious". I think psychology has ignored the huge regularities in perception simply because it hasn't had much luck in predicting behavior.

Best,

Bill P.

[rsmarken]

[From Rick Marken (2008.03.31.1835)]

Bill Powers (2008.03.30.1140 MDT)

I still don't see "not knowing what to say" as the uncertainty which leads
to not knowing what to say. It's the uncertainty that comes first, then not
knowing what to say, as I see it.

I think the "not knowing what to say" is the feeling that we describe
as uncertainty. What leads to not knowing what to say is having a
perception that about which several things could be said with nearly
equal validity (lack of error). At least, that's the way it seems to
me in the tone detection task. If all I had to do was listen to the
noise bursts I would have no uncertainty about what I am hearing on
each occasion: a schuch sound. If I am told that a tone has been added
to some of the sounds and that I am to decide whether or not each
includes the tone, the the same tones lead to a feeling of uncertainty
about whether there is a tone or not.

If you didn't have to say something, you
would still be uncertain, wouldn't you?

Not necessarily. I would not be uncertain if I didn't have to come to
some conclusion based on the perception. For example, in your example:

"Everyone please Xp#c$%u&^! their books immediately"

I experience no uncertainty until I take it as a sentence from which I
am supposed to derive some meaning; in this case, come to some
conclusion about what the sentence is instructing me to do. Otherwise,
there is no uncertainty about the fact that the sentence in front of
me is: "Everyone please Xp#c$%u&^! their books immediately". When I
first read the sentence it was a nice clear sentence with those funny
characters in it. I didn't feel uncertainty until I put myself in the
position of hearing that in class from the teacher. Then I would be
uncertain about what to conclude about what I should do based on that
sentence. So it's only when I treated the sentence perception as an
instruction (a perception from which I was to draw a conclusion about
what I was being asked to do) rather than just a string of words (and
a non-word) that I felt uncertainty.

Best

Rick

···

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

[Bill_Powers1]

[From Bill Powers (2008.03.31.2013 MDT)]

Rick Marken (2008.03.31.1835) --

If I am told that a tone has been added
to some of the sounds and that I am to decide whether or not each
includes the tone, the the same tones lead to a feeling of uncertainty
about whether there is a tone or not.

I conclude that we mean different things by "uncertainty." I certainly don't mean JUST an emotion. The same sensations can arise in many other ways, and I can be uncertain without having those particular sensations. Even when it's unimportant to me, I can perceive that a perception is unpredictable to some degree. Like knowing that p < 0.5, implying more uncertainty in the measurement than p < 0.05.

I see several candidates for definitions of uncertainty about a perception:

1. The perception itself seems to vary randomly so there is no way to predict its next value.

2. The perception is itself relatively constant, but is masked by random noise which makes it hard to perceive at all, or to perceive in a consistent way.

3. The perception is ambiguous, in that parts of its lower-level components are missing so they could be filled in by imagination in different ways, each leading to a different familiar perception.

These are quite different mechanisms, and using the same word for all of them implies that we are talking about something happening at the destination of the information, not the source.

Any other candidates?

Best,

Bill P.

[rsmarken]

[From Rick Marken (2008.04.01.1345)]

Bill Powers (2008.03.31.2013 MDT)--

I conclude that we mean different things by "uncertainty.".

Maybe. Could someone remind me why this "uncertainty" thing came up in
the first place.

I see several candidates for definitions of uncertainty about a perception:

1. The perception itself seems to vary randomly so there is no way to
predict its next value.

2. The perception is itself relatively constant, but is masked by random
noise which makes it hard to perceive at all, or to perceive in a consistent
way.

3. The perception is ambiguous, in that parts of its lower-level components
are missing so they could be filled in by imagination in different ways,
each leading to a different familiar perception.

I see all of these as being consistent with what I mean by
uncertainty, which is a state that can exist only when a person has
the purpose of making an inference, prediction or decision about a
possible state of affairs based on a perception that is assumed to be
evidence regarding that state of affairs. In your example 1 there is
uncertainty if a person has the purpose of predicting the next value
of the perception based on the present value, where the present value
is taken to be evidence of what might happen next. In your example 2
there is uncertainty if a person has the purpose of perceiving the
perception that is masked based on a perception of the masked
perception, where the masked perception is taken to be evidence of
what perception is masked. Same for example 3, where there is
uncertainty if the person has the purpose of perceiving the complete
perception that about which the ambiguous perception is assumed to be
evidence.

I guess I'm saying that I don't think it makes sense to talk about
perceptions themselves as being uncertain. Perceptions are just
perceptions. They become "unpredictable", "masked" or "ambiguous" only
when there is the purpose to use those perceptions as evidence of
something else (the thing to be predicted, detected or identified).

Best

Rick

···

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

[Bill_Powers1]

[From Bill Powers (2008.03.31.1932 MDT)]

Rick Marken (2008.04.01.1345) --

I guess I'm saying that I don't think it makes sense to talk about
perceptions themselves as being uncertain. Perceptions are just
perceptions. They become "unpredictable", "masked" or "ambiguous" only
when there is the purpose to use those perceptions as evidence of
something else (the thing to be predicted, detected or identified).

I basically agree with you, but I'm trying to make the whole discussion depend less on "how we think of it" and more on stateable principles. You can define uncertainty as an objective state of affairs if that's what you want to do, like Heisenberg saying that position and momentum themselves are uncertain, independently of the observer. That's a proposition, and it can be discussed and argued about, but not by saying we don't like it or believe it. You propose another definition of uncertainty. Is it a better one? Of course you think it is, but why should anyone else think it is?

I think we're trying to define a term, not really look at a phenomenon. Either we'll agree on a definition or we won't. At the moment it doesn't matter to me, because I don't use the idea of uncertainty in my work very much, except when talking about things like prediction errors, which fits in with your proposed definition. I don't think Martin will accept it, but we'll see. I'm not inclined to shut Martin off by dismissing his interests, but if they're too far from mine, I'm willing for us to go our separate ways on this subject. It would be nice to get some kind of convergence, though.

Best,

Bill P.

[MartinT]

[Martin Taylor 2008.04.02]

[From Bill Powers (2008.03.31.1932 MDT)]

Rick Marken (2008.04.01.1345) --

I guess I'm saying that I don't think it makes sense to talk about
perceptions themselves as being uncertain. Perceptions are just
perceptions. They become "unpredictable", "masked" or "ambiguous" only
when there is the purpose to use those perceptions as evidence of
something else (the thing to be predicted, detected or identified).

I basically agree with you, but I'm trying to make the whole discussion depend less on "how we think of it" and more on stateable principles.

I sent out a long message on this on Monday, but it hasn't shown up. I'm going to send it again, despite the likelihood that you will see it twice.

Martin

[MartinT]

Re: Uncertainty (was second-order and third-order
beliefs)
[Martin Taylor 2008.04.02.10.38]

[From Rick Marken
(2008.04.01.1345)]

Could someone remind me why this
“uncertainty” thing came up in
the first place.

Check out [Bill Powers (2008.03.187.1509 MDT)]:

···

---

Suppose I say, “I am seeing a blue ball.” Focus on
the “blue” term. That is a description of an experience that
is happening now. I am simply saying the word I use to refer to
experiencing that color.

Now suppose I say “I believe I am seeing a blue ball.”
That is not a description of an experience, but a comment about the
experience. In fact, I think that using the term “believe”
in that context introduces some uncertainty into the statement that is
not in the previous statement.

---

and my response

---

At any rate, it seems to me that
saying I believe something introduces the possibility of doubt.
“He’s an honest person,” versus “I believe he’s an
honest person”.

Yes, I agree. That’s the distinction I would make between the
kind of perception in “I see a chair in this room” and
“I believe there is a chair in the next room” and “I
believe that what I see through the fog is a chair”. They are all
perceptions, but the latter two have less supporting information –
the perceptual input function has ambiguous inputs along with the well
defined ones.

This suggests that all perceptions actually have two
attributes: the value and the uncertainty.

---

I have an ulterior reason, as well, which is that one of the
important issues in developing interactive displays (i.e. ones that
involve overt control by the user) is how to represent on the display
the user’s uncertainty about the validity or importance of something
represented, or the uncertainty inherent in the acquisition of the
data or the procedures for creating a representation from the
data.

The question of representing the user’s uncertainty about some
represented (or potentially to be represented) datum is the
computer-based equivalent of the issue that started this thread –
second and third order beliefs.

I don’t really want to start a thread on this aspect ofthe issue
now, but I thought it might help in understanding one of the reasons I
am pursuing the question (whenever my ISP allows my messages to reach
CSGnet).

Martin

I see several candidates for definitions of uncertainty
about a perception:

1. The perception itself seems to vary randomly so there is
   no way to

predict its next value.

2. The perception is itself relatively constant, but is
   masked by random

noise which makes it hard to perceive at all, or to perceive in a
consistent

way.

3. The perception is ambiguous, in that parts of its
   lower-level components

are missing so they could be filled in by imagination in
different ways,

each leading to a different familiar perception.

These are not “definitions” of uncertainty. They are
among the many possible reasons for it.

Martin

[MartinT]

[Martin Taylor 2008.04.02.10.59]

Ooops. The following was inadvertently appended to my reply to Rick without attribution. It was in response to [Bill Powers (2008.03.31.2013 MDT)]

···

[Martin Taylor 2008.04.02.10.38]

  I see several candidates for definitions of uncertainty about a perception:

  1. The perception itself seems to vary randomly so there is no way to
predict its next value.

  2. The perception is itself relatively constant, but is masked by random
noise which makes it hard to perceive at all, or to perceive in a consistent
way.

  3. The perception is ambiguous, in that parts of its lower-level components
are missing so they could be filled in by imagination in different ways,
each leading to a different familiar perception.

These are not "definitions" of uncertainty. They are among the many possible reasons for it.

Martin