Talking Ruler

[From Bruce Abbott (970305.0855 EST)]

I've been thinking about Bill's (970228.1826 MST) hypothetical "talking
ruler" control system. I had offered the following version:

I can
think of two or three ways to model this as a product of control action;
for example, the input line may establish a kind of "feeling" for what the
judgment should be, which is compared to the judgement one begins to
announce; if these differ the person begins to vary the judgement output
until it matches the "feeling" for what the judgement should be.

But then you have to ask, "where does this 'feeling' come from?" My
answer is that it comes from the learned function that relates the input
line length to the judgment one "feels" is correct. If the control system
just described is doing its job, then the (final) announced judgement will
correspond to the output of the function, or perhaps vary closely around
it depending on what disturbances are acting on the system.

This brought the following response from Bill:

These ideas represent a progression toward a purely PCT view, but I can
think of ways to get still closer. . . .

So what is happening when a person is acting as a talking ruler? I would
guess that the person sorts through imagined verbal size-judgements until
one is found which, if someone else uttered it, would evoke a picture of
something of about the right size. . . . The
object, apparently, was to perceive two senses of length and control for
their being the same. One of them came from the visual image; the other one
came from (imagined) words referring to lengths.

But how do these two proposals differ? In both proposals the presented line
evokes a sense of length, which is then compared to another, imaginary line
associated with a number. In both proposals the sense of length of the
imaginary line is varied until it matches that of the perceived line. Both
thus function as control systems, bringing the sense of length evoked by the
imaginary line into match with the sense of length evoked by the perceived line.

So what is the difference between these two versions that brings the second
one "still closer toward a purely PCT view"? Apparently it is this: In my
proposal the sense of length of the perceived line is compared to remembered
lines; these then evoke remembered perceptions of verbal size-judgements.
In Bill's proposal the verbalized numbers come out of nowhere (i.e., it
provides no mechanism whereby imagined verbal size-judgements are selected
for evaluation); these then evoke senses of length.

Now, what I want to know is, if imagined verbal size-judgements can evoke a
sense of length, why can't imagined line-lengths evoke a remembered
perception of verbal size judgements? And what makes the former "closer to
a purely PCT view" than the latter?

Still slithering in the evolutionary muck,

Bruce

[From Bill Powers (970405.0916 MST)]

Bruce Abbott (970305.0855 EST)--

But how do these two proposals differ? In both proposals the presented
line evokes a sense of length, which is then compared to another,
imaginary line associated with a number.

Not quite. You can't compare a sense of length with a line. You can only
compare it with another sense of length. The basic proposal was that there
are two senses of length, one derived from a spoken number and the other
derived from a visual image of a line. By varying the (imagined) number, you
vary the associated sense of length, which you then compare with the sense
of length being derived from the visual image. When you judge that the two
senses of length are in the right relationship, you speak the imagined
number (that is, you create in your own perceptions, by speaking, the sound
that the imagined number evokes when someone else speaks it, or when you see
the number written).

In both proposals the sense of length of the
imaginary line is varied until it matches that of the perceived line.

Again, not quite, from the PCT perspective. The sense of length you get from
the line you're actually perceiving is not compared against the sense of
length from a variable imagined (visual) line, but against the sense of
length you get from imagining a variable verbal number (with units) like
"six inches." You're not going to convert the imagined line into an actual
line (although, in a different application, you could: "draw a line the same
length as this line").

This is not to say that you can't compare a line with an imagined line. You
can. But that you can do nonverbally. You can also look at an object across
the room, then down at your hands, and adjust the distance between your
hands to be the same as the perceived size of the object (or twice as big,
or whatever). But whatever the relationship, it must be between perceptions
of the same kind. You can't perceive the distance between your hand and
Middle C.

In Bill's proposal the verbalized numbers come out of nowhere (i.e., it
provides no mechanism whereby imagined verbal size-judgements are selected
for evaluation); these then evoke senses of length.

I can't, of course, draw you a control system that can generate words and
convert them into evoked senses of length (if I could, I'd be too rich to
truck with the likes of you). But that's the basic process I'm describing.
It's the same process we use when a name is perceived as the name _of an
attribute_ of perception: when we hear the word "green" and perceive an
associated color, or hear "big" and perceive largeness.

I can accept that between the spoken words and the sense of length there
might be a memory-associated object that is evoked by the verbal term:
"one-foot ruler" calls to mind a lot of images of rulers. Then I can compare
such an imagined object with the presently-perceived object. But however
it's done, the judgement of sameness has to come from perceptions of the
same kind.

Now, what I want to know is, if imagined verbal size-judgements can evoke
a sense of length, why can't imagined line-lengths evoke a remembered
perception of verbal size judgements?

A remembered LENGTH is not of the same type as a remember LINE. And a
remembered VERBAL PHRASE is not of the same type as a remembered LENGTH.

A perceptual judgement is not the same thing as a spoken phrase. To the
external observer, it is the phrase that is "the judgement," as in
"pronouncing judgement." But to the judge, the perceptual judgement has to
come first; then it is translated into a spoken phrase that identifies the
judgement that has already been made. You're conflating judgement, the
perception, with judgement, the (spoken) action.

If Mary weren't bustling around collection stuff to do our taxes (I run the
computer), I'd figure out a diagram to show what I mean. But maybe now you
can do that, keeping in mind that only likes can be compared with likes.

Best,

Bill P.

[From Bruce Abbott (970305.2140 EST) --

Bill Powers (970405.0916 MST)]

Bruce Abbott (970305.0855 EST)

I'm not particularly enamoured by my proposed line-length judgement
mechanism, but I'm still trying to determine where it conflicts with PCT
rules. So let's go over this again.

But how do these two proposals differ? In both proposals the presented
line evokes a sense of length, which is then compared to another,
imaginary line associated with a number.

Not quite. You can't compare a sense of length with a line. You can only
compare it with another sense of length. The basic proposal was that there
are two senses of length, one derived from a spoken number and the other
derived from a visual image of a line.

You draw a distinction I do not intend. I intend that a sense of length
(derived from the perceived line) be compared to a sense of length (derived
from the imagined line).

By varying the (imagined) number, you
vary the associated sense of length, which you then compare with the sense
of length being derived from the visual image. When you judge that the two
senses of length are in the right relationship, you speak the imagined
number (that is, you create in your own perceptions, by speaking, the sound
that the imagined number evokes when someone else speaks it, or when you see
the number written.

Yes, and by varying the (imagined) line, you vary the associated sense of
length, which you then compare with the sense of length being derived from
the visual image. So far I don't see much difference between these proposals.

This is not to say that you can't compare a line with an imagined line. You
can. But that you can do nonverbally. You can also look at an object across
the room, then down at your hands, and adjust the distance between your
hands to be the same as the perceived size of the object (or twice as big,
or whatever). But whatever the relationship, it must be between perceptions
of the same kind. You can't perceive the distance between your hand and
Middle C.

A sense of length of the perceived line is being compared to a sense of
length of the imagined line. Those _are_ perceptions of the same kind.

In Bill's proposal the verbalized numbers come out of nowhere (i.e., it
provides no mechanism whereby imagined verbal size-judgements are selected
for evaluation); these then evoke senses of length.

I can't, of course, draw you a control system that can generate words and
convert them into evoked senses of length (if I could, I'd be too rich to
truck with the likes of you). But that's the basic process I'm describing.
It's the same process we use when a name is perceived as the name _of an
attribute_ of perception: when we hear the word "green" and perceive an
associated color, or hear "big" and perceive largeness.

It's worse than that: you can't explain how your system manages to choose
verbal tags that are initially reasonably close to the actual line length.
Mary's initial thought was "six inches," not "sixty inches."

I can accept that between the spoken words and the sense of length there
might be a memory-associated object that is evoked by the verbal term:
"one-foot ruler" calls to mind a lot of images of rulers. Then I can compare
such an imagined object with the presently-perceived object. But however
it's done, the judgement of sameness has to come from perceptions of the
same kind.

But you can't accept that between the sense of length and memory for verbal
tags associated with given lengths? Or am I misreading you here?

Now, what I want to know is, if imagined verbal size-judgements can evoke
a sense of length, why can't imagined line-lengths evoke a remembered
perception of verbal size judgements?

A remembered LENGTH is not of the same type as a remember LINE.

So what? A remembered line can evoke a sense of length in the same way that
a perceived line does. So let's assume that we're comparing apples to apples.

And a
remembered VERBAL PHRASE is not of the same type as a remembered LENGTH.

True but irrelevant. The verbal phrase is not compared to anything, two
feelings of length are compared.

A perceptual judgement is not the same thing as a spoken phrase. To the
external observer, it is the phrase that is "the judgement," as in
"pronouncing judgement." But to the judge, the perceptual judgement has to
come first; then it is translated into a spoken phrase that identifies the
judgement that has already been made. You're conflating judgement, the
perception, with judgement, the (spoken) action.

The mechanism I described has resulted in the selection of a remembered line
(or sense of length, if you prefer) of the right length; this evokes the
remembered verbal judgement (a perception) associated with that particular
remembered line (or sense of length). The only remaining question, then, is
how one controls for verbally echoing that verbal perception. Neither of us
have the answer to how that's done but, like you, I assume that it's
accomplished via control.

If Mary weren't bustling around collection stuff to do our taxes (I run the
computer), I'd figure out a diagram to show what I mean. But maybe now you
can do that, keeping in mind that only likes can be compared with likes.

Now that I've made it clear (I hope) that I _am_ comparing likes to likes,
what remaining problems do you see with my proposal with respect to its
being kosher PCT? Does it simply lack the Rabbi's blessing or does it still
have pork in it? (:->

Still swimming in the molecular soup (and
possibly evolving in the wrong direction),

Bruce

[From Bill Powers (970206.0527 MST)]

Actually the comet was worth getting up this early for. The tail is a good
one degree long to my weak eyes, and in the binoculars it extends the full
diameter of the field. It must be getting close to 0 magnitude, and there's
still a month or more to go. It's starting to show low in the northwest in
the evening, too, setting before the end of twilight but still looking good.
No moon in the morning for the next two weeks.

Bruce Abbott (970305.2140 EST) --

Dear Primaeval Slime:

I'm not particularly enamoured by my proposed line-length judgement
mechanism, but I'm still trying to determine where it conflicts with PCT
rules. So let's go over this again.

OK. The problem with your original Talking Ruler proposal was that you
described it as "visual length in, vocal judgment out." This was offered, if
I remember right, as an open-loop phenomenon that could be used to study
perception, without requiring PCT.

But that's how the _user_ of the Talking Ruler would see it. What I've been
trying to do is show how this appearance could be brought about without that
conversion ever taking place. That is, without using this:

physical line --> perception ---> generation of vocal output

What I offered instead was this:

                  ref = 0 ("same")
                      >
  p = pL1 - pL2 |
        ----------->[Comp]->--error ---
       > >
    [Inp Funct] [Output Func]
       / \ |
   pL1/ \pL2 |
     / \ |
[conversion to length perc] |
    > > >
    > > v
    > --<-[imagination]--<---word
    > > >
    ^ ^ v
    > > >
vis line heard word (perc) spoken word (ref sig)
               \ /
                ..........<...........
                   ext feedback loop \
                                       --> to experimenter

The imagination connection has to be switched so you perceive either the
imagined word or the word you actually speak. If the output line is also
switched, the process of matching is done silently until the error is zero,
with the spoken word being uttered only at the end. If the output goes both
ways (or the person doesn't use imagination at all), you hear the person
saying "32, no, 52, no, 51 millimeters."

I can't fill in the conversion from an error to a new word. Length-words are
clearly ordered in memory, or somewhere, so one can scan from small to
large. So perhaps the error signal runs a "scan pointer" which the output
function converts to a reference signal for hearing a size-word: a large
error signal points to words at the "large" end of the scale, and so on.
Note that when no word has been heard yet, the visible-line input leads to a
large (or at least increasing) error signal. The longer the line, the faster
the error moves toward the "big" end.

However, as soon as the first word is imagined there is an immediate
adjustment of the scan pointer in the direction appropriate to the remaining
error. Hmm, there appears to be an integrator in the "error" path.

This fanciful picture shows how the appearance of an
visual-input-to-vocal-output link could be created without any such link
existing inside the organism. The only direct association is from either a
visual line or a spoken word to a perception of length, on the perceptual
side of the system. On the output side, the choice of word is _varied_ until
a match is achieved. There is no fixed output association.

If you look over some of your proposals, I think you will see that they
match the above diagram. But your original proposal does not. Also, I hope
you can see that uttering words that purport to indicate perceptions doesn't
actually reveal what the perceptions are. All you end up knowing is that the
uttered word leads to the same perception of length that the visual line
leads to. What that perception of length is, we still don't know.

Note the strong family resemblance to Hans Blom's MCT model.

Note also that if the task were to _draw_ a line of the same length as the
visual line, the output would be a drawing motion and the corresponding
input another visual perception of line length.

Best,

Bill P.

[From Bruce Abbott (970306.1125 EST)]

Bill Powers (970206.0527 MST)

Actually the comet was worth getting up this early for. The tail is a good
one degree long to my weak eyes, and in the binoculars it extends the full
diameter of the field. It must be getting close to 0 magnitude, and there's
still a month or more to go. It's starting to show low in the northwest in
the evening, too, setting before the end of twilight but still looking good.
No moon in the morning for the next two weeks.

Sounds great. Now if we can only get another clear morning in Fort Wayne . . .

Bruce Abbott (970305.2140 EST)

Dear Primaeval Slime:

Actually I'm more like diluvian sludge, but don't tell anyone.

OK. The problem with your original Talking Ruler proposal was that you
described it as "visual length in, vocal judgment out." This was offered, if
I remember right, as an open-loop phenomenon that could be used to study
perception, without requiring PCT.

This is something of a misunderstanding. What I had in mind was the notion
that this system would be open loop _with respect to the judgement_. That
is, the person would no longer be receiving verbal information about the
actual length of the line as had been the case during training. Thus,
whatever judgements were announced would have to be given without the judge
receiving another length-judgement from the experimenter that could be used
for error correction.

Because of this, the judge would have to rely on internal criteria for
determining what length to announce when presented with a given line. If we
can assume that the judge is controlling for being truthful, then, through
whatever mechanism is employed to arrive at the judgement, the judgement
will tend to follow the internal criteria and the reported length will vary
according to the internal criteria established during training. The
information obtained by the experimenter will be the same and just as
reflective of the judge's conversion of sense-perception to number whether
the experimenter views the system involved as an open or closed loop.

What I was arguing was that the procedures used in this and other
psychophysical research are capable of yielding correct information about
the relationship between sense-perception and a person's judgements, even
though the experimenter may be treating the system during testing as if it
were an open-loop system. Viewed externally, the only important difference
between a true open-loop system that links sense-perception to judgement via
direct association and one that does so via a closed-loop system such as the
one you proposed is that the latter will tend to be more stable, assuming
(as seems reasonable) that the system will be subject to disturbances. A
rough analogy would be the comparison of two systems for varying voltage
output, one of which varies the setting of a potentiometer and the other the
reference setting of a voltage regulator. (I say rough because it would not
actually be the reference that is varied in the latter case, but the
essential difference in behavior is what I'm after here.) Both systems
would vary their output in proportion to input but only the latter would
tend to ignore changes in source voltage (within limits).

I like your imagined system for "converting" the perception of line-length
to a verbal judgement, although it seems to me that I am doing something
somewhat different when making such judgements. It seems to me that I have
some knowledge of what number "goes" with certain lengths, having often
measured such distances. For example, I seem to "know" what a distance of 6
inches looks, and I can picture marking off several such lengths on end as I
would if using a 6-inch rule. It may be an illusion, but I seem to derive a
number by measuring the object in the mind's eye rather than by picking a
number out of a hat and then determining whether the resulting sense of
length matches the length of the object I am measuring.

Of course, both process could be operating. Having arrived at a judgement,
I might then try to picture a line of that length and do the comparison as
you suggest. But I think that more is going on than just thinking up
numbers that evoke different senses of length, with regard to the way I seem
to perform the task. In any event, this is an empirical question that would
make a nice research project for someone. Is there anyone out there who has
a different apparent method for arriving at such judgements? I'd like to
hear your account.

Regards,

Bruce

[From Bill Powers (970307.0858 MST)]

Bruce Abbott (970306.1125 EST)]

This is something of a misunderstanding. What I had in mind was the
notion that this system would be open loop _with respect to the >judgement_.

Ah. There is the ambiguity that separates us. When you say "judgment" you
are referring to the spoken words. I am referring to the perception of size
or similarity of sizes, which has to exist before it can be described in
words. I am referring to an input process; you are referring to a physical
output.

That
is, the person would no longer be receiving verbal information about the
actual length of the line as had been the case during training. Thus,
whatever judgements were announced would have to be given without the
judge receiving another length-judgement from the experimenter that could
be used for error correction.

That's the _external_ error you're talking about, the error as the
experimenter perceives it. I was speaking of the speaker's own perception of
the meaning of his words, in relation to the size-meaning that the person
wanted to communicate.

Because of this, the judge would have to rely on internal criteria for
determining what length to announce when presented with a given line.

Yes, that is what happens in the diagram I posted.

If we
can assume that the judge is controlling for being truthful, then, through
whatever mechanism is employed to arrive at the judgement, the judgement
will tend to follow the internal criteria and the reported length will
vary according to the internal criteria established during training.

Yes, exactly: the _output_ will vary so as to satisfy the internal criteria.

The information obtained by the experimenter will be the same and just as
reflective of the judge's conversion of sense-perception to number whether
the experimenter views the system involved as an open or closed loop.

If you still think this, you have missed my point. The "report" is the
verbal output. The speaker converts a perception of his own verbal output
into a sense of length, just as he would if someone else spoke the same
words. That perception is judged in relation to another perception, another
sense of length, that arises from seeing the line. If we knew how both the
words and the visual line were converted into perceptions of length, then we
could say that the words are a measure of the perception. But we don't know
that. Just to put it simply, suppose that the line-length were converted to
a sense of length according to the 1.9 power of the actual line length, and
a spoken number were converted to a sense of length according to the 1.4
power of the number. Then we would observe that the spoken word corresponds
to the actual line length according to the 0.5 power of the line length. If
we concluded that the perception of line length went as the 0.5 power of
actual length, we would be wrong. That would be the _apparent_ law, but it
would not be the actual law for either perception. That would be the law
relating the _report_ to the line length, but not the law relating the
_perception_ to the line length.

This, by the way, is what's wrong with Stevens' Power Law of perception.

Best,

Bill P.